AIJRSTEM issue 13 vol1

ISSN (PRINT): 2328-3491 ISSN (ONLINE): 2328-3580 ISSN (CD-ROM): 2328-3629

Issue 13, Volume 1 & 2 December, 2015-February, 2016

American International Journal of Research in Science, Technology, Engineering & Mathematics

International Association of Scientific Innovation and Research (IASIR) (An Association Unifying the Sciences, Engineering, and Applied Research)

STEM International Scientific Online Media and Publishing House Head Office: 148, Summit Drive, Byron, Georgia-31008, United States.

Offices Overseas: Germany, Australia, India, Netherlands, Canada.

Website: www.iasir.net, E-mail (s): iasir.journals@iasir.net, iasir.journals@gmail.com, aijrstem@gmail.com

PREFACE We are delighted to welcome you to the thirteenth issue of the American International Journal of Research in Science, Technology, Engineering & Mathematics (AIJRSTEM). In recent years, advances in science, technology, engineering, and mathematics have radically expanded the data available to researchers and professionals in a wide variety of domains.

This unique combination of theory with data has the potential to have broad impact on educational research and practice. AIJRSTEM is publishing high-quality, peer-reviewed papers covering topics such as Computer and computational sciences, Physics, Chemistry, Mathematics, Applied mathematics, Biochemistry, Robotics, Statistics, Electrical & Electronics engineering, Mechanical & Industrial engineering, Civil Engineering, Aerospace engineering, Chemical engineering, Astrophysics, Nanotechnology, Acoustical engineering, Atmospheric

sciences,

Biological

sciences,

Education

and

Human

Resources,

Environmental research and education, Geosciences, Social, Behavioral and Economic sciences, Geospatial technology, Cyber security, Transportation, Energy and Power, Healthcare, Hospitality, Medical and dental sciences, Marine sciences, Renewable sources of energy, Green technologies, Theory and models and other closely related fields in the discipline of Science, Technology, Engineering & Mathematics. The editorial board of AIJRSTEM is composed of members of the Teachers & Researchers community who have expertise in the fields of Science, Technology, Engineering & Mathematics in order to develop and implement widespread expansion of high�quality common standards and assessments. These fields are the pillars of growth in our modern society and have a wider impact on our daily lives with infinite opportunities in a global marketplace. In order to best serve our community, this Journal is available online as well as in hard-copy form. Because of the rapid advances in underlying technologies and the interdisciplinary nature of the field, we believe it is important to provide quality research articles promptly and to the widest possible audience.

We are happy that this Journal has continued to grow and develop. We have made every effort to evaluate and process submissions for reviews, and address queries from authors and the general public promptly. The Journal has strived to reflect the most recent and finest researchers in the field of emerging technologies especially related to science, technology, engineering & mathematics. This Journal is completely refereed and indexed with major databases like: IndexCopernicus, Computer Science Directory, GetCITED, DOAJ, SSRN, TGDScholar, WorldWideScience, CiteSeerX, CRCnetBASE, Google Scholar, Microsoft Academic

Search,

INSPEC,

ProQuest,

ArnetMiner,

Base,

ChemXSeer,

citebase,

OpenJ-Gate, eLibrary, SafetyLit, SSRN, VADLO, OpenGrey, EBSCO, ProQuest, UlrichWeb, ISSUU, SPIE Digital Library, arXiv, ERIC, EasyBib, Infotopia, WorldCat, .docstoc JURN, Mendeley,

ResearchGate,

cogprints,

OCLC,

iSEEK,

Scribd,

LOCKSS,

CASSI,

E-PrintNetwork, intute, and some other databases.

We are grateful to all of the individuals and agencies whose work and support made the Journal's success possible. We want to thank the executive board and core committee members of the AIJRSTEM for entrusting us with the important job. We are thankful to the members of the AIJRSTEM editorial board who have contributed energy and time to the Journal with their steadfast support, constructive advice, as well as reviews of submissions.

We are deeply indebted to the numerous anonymous reviewers who have contributed expertly evaluations of the submissions to help maintain the quality of the Journal. For this thirteenth issue, we received 86 research papers and out of which only 26 research papers are published in two volumes as per the reviewers’ recommendations. We have highest respect to all the authors who have submitted articles to the Journal for their intellectual energy and creativity, and for their dedication to the field of science, technology, engineering & mathematics.

This issue of the AIJRSTEM has attracted a large number of authors and researchers across worldwide and would provide an effective platform to all the intellectuals of different streams to put forth their suggestions and ideas which might prove beneficial for the accelerated pace of development of emerging technologies in science, technology, engineering & mathematics and may open new area for research and development. We hope you will enjoy this thirteenth issue of the American International Journal of Research in Science, Technology, Engineering & Mathematics and are looking forward to hearing your feedback and receiving your contributions.

(Administrative Chief)

(Managing Director)

(Editorial Head)

--------------------------------------------------------------------------------------------------------------------------The American International Journal of Research in Science, Technology, Engineering & Mathematics (AIJRSTEM), ISSN (Print): 2328-3491, ISSN (Online): 2328-3580, ISSN (CD-ROM): 2328-3629 (December, 2015-February, 2016, Issue 13, Volume 1 & 2).

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BOARD MEMBERS

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EDITOR IN CHIEF Prof. (Dr.) Waressara Weerawat, Director of Logistics Innovation Center, Department of Industrial Engineering, Faculty of Engineering, Mahidol University, Thailand.

Prof. (Dr.) Yen-Chun Lin, Professor and Chair, Dept. of Computer Science and Information Engineering, Chang Jung Christian University, Kway Jen, Tainan, Taiwan.

Divya Sethi, GM Conferencing & VSAT Solutions, Enterprise Services, Bharti Airtel, Gurgaon, India.

CHIEF EDITOR (TECHNICAL) Prof. (Dr.) Atul K. Raturi, Head School of Engineering and Physics, Faculty of Science, Technology and Environment, The University of the South Pacific, Laucala campus, Suva, Fiji Islands.

Prof. (Dr.) Hadi Suwastio, College of Applied Science, Department of Information Technology, The Sultanate of Oman and Director of IETI-Research Institute-Bandung, Indonesia.

Dr. Nitin Jindal, Vice President, Max Coreth, North America Gas & Power Trading, New York, United States.

CHIEF EDITOR (GENERAL) Prof. (Dr.) Thanakorn Naenna, Department of Industrial Engineering, Faculty of Engineering, Mahidol University, Thailand.

Prof. (Dr.) Jose Francisco Vicent Frances, Department of Science of the Computation and Artificial Intelligence, Universidad de Alicante, Alicante, Spain.

Prof. (Dr.) Huiyun Liu, Department of Electronic & Electrical Engineering, University College London, Torrington Place, London.

ADVISORY BOARD Prof. (Dr.) Kimberly A. Freeman, Professor & Director of Undergraduate Programs, Stetson School of Business and Economics, Mercer University, Macon, Georgia, United States.

Prof. (Dr.) Klaus G. Troitzsch, Professor, Institute for IS Research, University of Koblenz-Landau, Germany.

Prof. (Dr.) T. Anthony Choi, Professor, Department of Electrical & Computer Engineering, Mercer University, Macon, Georgia, United States.

Prof. (Dr.) Fabrizio Gerli, Department of Management, Ca' Foscari University of Venice, Italy.

Prof. (Dr.) Jen-Wei Hsieh, Department of Computer Science and Information Engineering, National Taiwan University of Science and Technology, Taiwan.

Prof. (Dr.) Jose C. Martinez, Dept. Physical Chemistry, Faculty of Sciences, University of Granada, Spain.

Prof. (Dr.) Panayiotis Vafeas, Department of Engineering Sciences, University of Patras, Greece.

Prof. (Dr.) Soib Taib, School of Electrical & Electronics Engineering, University Science Malaysia, Malaysia.

Prof. (Dr.) Vit Vozenilek, Department of Geoinformatics, Palacky University, Olomouc, Czech Republic.

Prof. (Dr.) Sim Kwan Hua, School of Engineering, Computing and Science, Swinburne University of Technology, Sarawak, Malaysia.

Prof. (Dr.) Jose Francisco Vicent Frances, Department of Science of the Computation and Artificial Intelligence, Universidad de Alicante, Alicante, Spain.

Prof. (Dr.) Rafael Ignacio Alvarez Sanchez, Department of Science of the Computation and Artificial Intelligence, Universidad de Alicante, Alicante, Spain.

Prof. (Dr.) Praneel Chand, Ph.D., M.IEEEC/O School of Engineering & Physics Faculty of Science & Technology The University of the South Pacific (USP) Laucala Campus, Private Mail Bag, Suva, Fiji.

Prof. (Dr.) Francisco Miguel Martinez, Department of Science of the Computation and Artificial Intelligence, Universidad de Alicante, Alicante, Spain.

Prof. (Dr.) Antonio Zamora Gomez, Department of Science of the Computation and Artificial Intelligence, Universidad de Alicante, Alicante, Spain.

Prof. (Dr.) Leandro Tortosa, Department of Science of the Computation and Artificial Intelligence, Universidad de Alicante, Alicante, Spain.

Prof. (Dr.) Samir Ananou, Department of Microbiology, Universidad de Granada, Granada, Spain.

Dr. Miguel Angel Bautista, Department de Matematica Aplicada y Analisis, Facultad de Matematicas, Universidad de Barcelona, Spain.

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Prof. (Dr.) Prof. Adam Baharum, School of Mathematical Sciences, University of Universiti Sains, Malaysia, Malaysia.

Dr. Cathryn J. Peoples, Faculty of Computing and Engineering, School of Computing and Information Engineering, University of Ulster, Coleraine, Northern Ireland, United Kingdom.

Prof. (Dr.) Pavel Lafata, Department of Telecommunication Engineering, Faculty of Electrical Engineering, Czech Technical University in Prague, Prague, 166 27, Czech Republic.

Prof. (Dr.) P. Bhanu Prasad, Vision Specialist, Matrix vision GmbH, Germany, Consultant, TIFACCORE for Machine Vision, Advisor, Kelenn Technology, France Advisor, Shubham Automation & Services, Ahmedabad, and Professor of C.S.E, Rajalakshmi Engineering College, India.

Prof. (Dr.) Anis Zarrad, Department of Computer Science and Information System, Prince Sultan University, Riyadh, Saudi Arabia.

Prof. (Dr.) Mohammed Ali Hussain, Professor, Dept. of Electronics and Computer Engineering, KL University, Green Fields, Vaddeswaram, Andhra Pradesh, India.

Dr. Cristiano De Magalhaes Barros, Governo do Estado de Minas Gerais, Brazil.

Prof. (Dr.) Md. Rizwan Beg, Professor & Head, Dean, Faculty of Computer Applications, Deptt. of Computer Sc. & Engg. & Information Technology, Integral University Kursi Road, Dasauli, Lucknow, India.

Prof. (Dr.) Vishnu Narayan Mishra, Assistant Professor of Mathematics, Sardar Vallabhbhai National Institute of Technology, Ichchhanath Mahadev Road, Surat, Surat-395007, Gujarat, India.

Dr. Jia Hu, Member Research Staff, Philips Research North America, New York Area, NY. Prof. Shashikant Shantilal Patil SVKM, MPSTME Shirpur Campus, NMIMS University Vile Parle Mumbai, India.

Prof. (Dr.) Bindhya Chal Yadav, Assistant Professor in Botany, Govt. Post Graduate College, Fatehabad, Agra, Uttar Pradesh, India.

REVIEW BOARD Prof. (Dr.) Kimberly A. Freeman, Professor & Director of Undergraduate Programs, Stetson School of Business and Economics, Mercer University, Macon, Georgia, United States.

Prof. (Dr.) Klaus G. Troitzsch, Professor, Institute for IS Research, University of Koblenz-Landau, Germany.

Prof. (Dr.) T. Anthony Choi, Professor, Department of Electrical & Computer Engineering, Mercer University, Macon, Georgia, United States.

Prof. (Dr.) Yen-Chun Lin, Professor and Chair, Dept. of Computer Science and Information Engineering, Chang Jung Christian University, Kway Jen, Tainan, Taiwan.

Prof. (Dr.) Jen-Wei Hsieh, Department of Computer Science and Information Engineering, National Taiwan University of Science and Technology, Taiwan.

Prof. (Dr.) Jose C. Martinez, Dept. Physical Chemistry, Faculty of Sciences, University of Granada, Spain.

Prof. (Dr.) Joel Saltz, Emory University, Atlanta, Georgia, United States.

Prof. (Dr.) Panayiotis Vafeas, Department of Engineering Sciences, University of Patras, Greece.

Prof. (Dr.) Soib Taib, School of Electrical & Electronics Engineering, University Science Malaysia, Malaysia.

Prof. (Dr.) Sim Kwan Hua, School of Engineering, Computing and Science, Swinburne University of Technology, Sarawak, Malaysia.

Prof. (Dr.) Jose Francisco Vicent Frances, Department of Science of the Computation and Artificial Intelligence, Universidad de Alicante, Alicante, Spain.

Prof. (Dr.) Rafael Ignacio Alvarez Sanchez, Department of Science of the Computation and Artificial Intelligence, Universidad de Alicante, Alicante, Spain.

Prof. (Dr.) Francisco Miguel Martinez, Department of Science of the Computation and Artificial Intelligence, Universidad de Alicante, Alicante, Spain.

Prof. (Dr.) Antonio Zamora Gomez, Department of Science of the Computation and Artificial Intelligence, Universidad de Alicante, Alicante, Spain.

Prof. (Dr.) Leandro Tortosa, Department of Science of the Computation and Artificial Intelligence, Universidad de Alicante, Alicante, Spain.

Prof. (Dr.) Samir Ananou, Department of Microbiology, Universidad de Granada, Granada, Spain.

Dr. Miguel Angel Bautista, Department de Matematica Aplicada y Analisis, Facultad de Matematicas, Universidad de Barcelona, Spain.

Prof. (Dr.) Prof. Adam Baharum, School of Mathematical Sciences, University of Universiti Sains, Malaysia, Malaysia.

Prof. (Dr.) Huiyun Liu, Department of Electronic & Electrical Engineering, University College London, Torrington Place, London.

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Dr. Cristiano De Magalhaes Barros, Governo do Estado de Minas Gerais, Brazil.

Prof. (Dr.) Pravin G. Ingole, Senior Researcher, Greenhouse Gas Research Center, Korea Institute of Energy Research (KIER), 152 Gajeong-ro, Yuseong-gu, Daejeon 305-343, KOREA Prof. (Dr.) Dilum Bandara, Dept. Computer Science & Engineering, University of Moratuwa, Sri Lanka.

Prof. (Dr.) Faudziah Ahmad, School of Computing, UUM College of Arts and Sciences, University Utara Malaysia, 06010 UUM Sintok, Kedah Darulaman Prof. (Dr.) G. Manoj Someswar, Principal, Dept. of CSE at Anwar-ul-uloom College of Engineering & Technology, Yennepally, Vikarabad, RR District., A.P., India.

Prof. (Dr.) Abdelghni Lakehal, Applied Mathematics, Rue 10 no 6 cite des fonctionnaires dokkarat 30010 Fes Marocco.

Dr. Kamal Kulshreshtha, Associate Professor & Head, Deptt. of Computer Sc. & Applications, Modi Institute of Management & Technology, Kota-324 009, Rajasthan, India.

Prof. (Dr.) Anukrati Sharma, Associate Professor, Faculty of Commerce and Management, University of Kota, Kota, Rajasthan, India.

Prof. (Dr.) S. Natarajan, Department of Electronics and Communication Engineering, SSM College of Engineering, NH 47, Salem Main Road, Komarapalayam, Namakkal District, Tamilnadu 638183, India.

Prof. (Dr.) J. Sadhik Basha, Department of Mechanical Engineering, King Khalid University, Abha, Kingdom of Saudi Arabia Prof. (Dr.) G. SAVITHRI, Department of Sericulture, S.P. Mahila Visvavidyalayam, Tirupati517502, Andhra Pradesh, India.

Prof. (Dr.) Shweta jain, Tolani College of Commerce, Andheri, Mumbai. 400001, India Prof. (Dr.) Abdullah M. Abdul-Jabbar, Department of Mathematics, College of Science, University of Salahaddin-Erbil, Kurdistan Region, Iraq.

Prof. (Dr.) P.Sujathamma, Department of Sericulture, S.P.Mahila Visvavidyalayam, Tirupati517502, India.

Prof. (Dr.) Bimla Dhanda, Professor & Head, Department of Human Development and Family Studies, College of Home Science, CCS, Haryana Agricultural University, Hisar- 125001 (Haryana) India.

Prof. (Dr.) Manjulatha, Dept of Biochemistry,School of Life Sciences,University of Hyderabad,Gachibowli, Hyderabad, India.

Prof. (Dr.) Upasani Dhananjay Eknath Advisor & Chief Coordinator, ALUMNI Association, Sinhgad Institute of Technology & Science, Narhe, Pune- 411 041, India.

Prof. (Dr.) Sudhindra Bhat, Professor & Finance Area Chair, School of Business, Alliance University Bangalore-562106.

Prof. Prasenjit Chatterjee , Dept. of Mechanical Engineering, MCKV Institute of Engineering West Bengal, India.

Prof. Rajesh Murukesan, Deptt. of Automobile Engineering, Rajalakshmi Engineering college, Chennai, India.

Prof. (Dr.) Parmil Kumar, Department of Statistics, University of Jammu, Jammu, India Prof. (Dr.) M.N. Shesha Prakash, Vice Principal, Professor & Head of Civil Engineering, Vidya Vikas Institute of Engineering and Technology, Alanahally, Mysore-570 028 Prof. (Dr.) Piyush Singhal, Mechanical Engineering Deptt., GLA University, India.

Prof. M. Mahbubur Rahman, School of Engineering & Information Technology, Murdoch University, Perth Western Australia 6150, Australia.

Prof. Nawaraj Chaulagain, Department of Religion, Illinois Wesleyan University, Bloomington, IL. Prof. Hassan Jafari, Faculty of Maritime Economics & Management, Khoramshahr University of Marine Science and Technology, khoramshahr, Khuzestan province, Iran Prof. (Dr.) Kantipudi MVV Prasad , Dept of EC, School of Engg, R.K.University,Kast urbhadham, Tramba, Rajkot-360020, India.

Prof. (Mrs.) P.Sujathamma, Department of Sericulture, S.P.Mahila Visvavidyalayam, ( Women's University), Tirupati-517502, India.

Prof. (Dr.) M A Rizvi, Dept. of Computer Engineering and Applications, National Institute of Technical Teachers' Training and Research, Bhopal M.P. India Prof. (Dr.) Mohsen Shafiei Nikabadi, Faculty of Economics and Management, Industrial Management Department, Semnan University, Semnan, Iran.

Prof. P.R.SivaSankar, Head, Dept. of Commerce, Vikrama Simhapuri University Post Graduate Centre, KAVALI - 524201, A.P. India.

Prof. (Dr.) Bhawna Dubey, Institute of Environmental Science( AIES), Amity University, Noida, India.

Prof. Manoj Chouhan, Deptt. of Information Technology, SVITS Indore, India.

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Prof. Yupal S Shukla, V M Patel College of Management Studies, Ganpat University, KhervaMehsana, India.

Prof. (Dr.) Amit Kohli, Head of the Department, Department of Mechanical Engineering, D.A.V.Institute of Engg. and Technology, Kabir Nagar, Jalandhar, Punjab(India) Prof. (Dr.) Kumar Irayya Maddani, and Head of the Department of Physics in SDM College of Engineering and Technology, Dhavalagiri, Dharwad, State: Karnataka (INDIA).

Prof. (Dr.) Shafi Phaniband, SDM College of Engineering and Technology, Dharwad, INDIA. Prof. M H Annaiah, Head, Department of Automobile Engineering, Acharya Institute of Technology, Soladevana Halli, Bangalore -560107, India.

Prof. (Dr.) Shriram K V, Faculty Computer Science and Engineering, Amrita Vishwa Vidhyapeetham University, Coimbatore, India.

Prof. (Dr.) Sohail Ayub, Department of Civil Engineering, Z.H College of Engineering & Technology, Aligarh Muslim University, Aligarh. 202002 UP-India Prof. (Dr.) Santosh Kumar Behera, Department of Education, Sidho-Kanho-Birsha University, Purulia, West Bengal, India.

Prof. (Dr.) Urmila Shrawankar, Department of Computer Science & Engineering, G H Raisoni College of Engineering, Nagpur (MS), India.

Prof. Anbu Kumar. S, Deptt. of Civil Engg., Delhi Technological University (Formerly Delhi College of Engineering) Delhi, India.

Prof. (Dr.) Meenakshi Sood, Vegetable Science, College of Horticulture, Mysore, University of Horticultural Sciences, Bagalkot, Karnataka (India) Prof. (Dr.) Prof. R. R. Patil, Director School Of Earth Science, Solapur University, Solapur, India.

Prof. (Dr.) Manoj Khandelwal, Dept. of Mining Engg, College of Technology & Engineering, Maharana Pratap University of Agriculture & Technology, Udaipur-313 001 (Rajasthan), India Prof. (Dr.) Kishor Chandra Satpathy, Librarian, National Institute of Technology, Silchar-788010, Assam, India.

Prof. (Dr.) Juhana Jaafar, Gas Engineering Department, Faculty of Petroleum and Renewable Energy Engineering (FPREE), Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor.

Prof. (Dr.) Rita Khare, Assistant Professor in chemistry, Govt. Women,s College, Gardanibagh, Patna, Bihar, India.

Prof. (Dr.) Raviraj Kusanur, Dept of Chemistry, R V College of Engineering, Bangalore-59, India.

Prof. (Dr.) Hameem Shanavas .I, M.V.J College of Engineering, Bangalore, India.

Prof. (Dr.) Sandhya Mehrotra, Department of Biological Sciences, Birla Institute of Technology and Sciences, Pilani, Rajasthan, India.

Prof. (Dr.) Dr. Ravindra Jilte, Head of the Department, Department of Mechanical Engineering,VCET, Thane-401202, India.

Prof. (Dr.) Sanjay Kumar, JKL University, Ajmer Road, Jaipur Prof. (Dr.) Pushp Lata Faculty of English and Communication, Department of Humanities and Languages, Nucleus Member, Publications and Media Relations Unit Editor, BITScan, BITS, PilaniIndia Prof. Arun Agarwal, Faculty of ECE Dept., ITER College, Siksha 'O' Anusandhan University Bhubaneswar, Odisha, India Prof. (Dr.) Pratima Tripathi, Department of Biosciences, SSSIHL, Anantapur Campus Anantapur515001 (A.P.) India.

Prof. (Dr.) Sudip Das, Department of Biotechnology, Haldia Institute of Technology, I.C.A.R.E. Complex, H.I.T. Campus, P.O. Hit, Haldia; Dist: Puba Medinipur, West Bengal, India.

Prof. (Dr.) ABHIJIT MITRA , Associate Professor and former Head, Department of Marine Science, University of Calcutta , India.

Prof. (Dr.) N.Ramu , Associate Professor , Department of Commerce, Annamalai University, AnnamalaiNadar-608 002, Chidambaram, Tamil Nadu , India.

Prof. (Dr.) Saber Mohamed Abd-Allah, Assistant Professor of Theriogenology , Faculty of Veterinary Medicine , Beni-Suef University , Egypt.

Prof. (Dr.) Ramel D. Tomaquin, Dean, College of Arts and Sciences Surigao Del Sur State University (SDSSU), Tandag City Surigao Del Sur, Philippines.

Prof. (Dr.) Bimla Dhanda, Professor & Head, Department of Human Development and Family Studies College of Home Science, CCS, Haryana Agricultural University, Hisar- 125001 (Haryana) India.

Prof. (Dr.) R.K.Tiwari, Professor, S.O.S. in Physics, Jiwaji University, Gwalior, M.P.-474011, India.

Prof. (Dr.) Sandeep Gupta, Department of Computer Science & Engineering, Noida Institute of Engineering and Technology, Gr.Noida, India.

Prof. (Dr.) Mohammad Akram, Jazan University, Kingdom of Saudi Arabia.

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Prof. (Dr.) Sanjay Sharma, Dept. of Mathematics, BIT, Durg(C.G.), India.

Prof. (Dr.) Manas R. Panigrahi, Department of Physics, School of Applied Sciences, KIIT University, Bhubaneswar, India.

Prof. (Dr.) P.Kiran Sree, Dept of CSE, Jawaharlal Nehru Technological University, India Prof. (Dr.) Suvroma Gupta, Department of Biotechnology in Haldia Institute of Technology, Haldia, West Bengal, India.

Prof. (Dr.) SREEKANTH. K. J., Department of Mechanical Engineering at Mar Baselios College of Engineering & Technology, University of Kerala, Trivandrum, Kerala, India Prof. Bhubneshwar Sharma, Department of Electronics and Communication Engineering, Eternal University (H.P), India.

Prof. Love Kumar, Electronics and Communication Engineering, DAV Institute of Engineering and Technology, Jalandhar (Punjab), India.

Prof. S.KANNAN, Department of History, Annamalai University, Annamalainagar- 608002, Tamil Nadu, India.

Prof. (Dr.) Hasrinah Hasbullah, Faculty of Petroleum & Renewable Energy Engineering, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia.

Prof. Rajesh Duvvuru, Dept. of Computer Sc. & Engg., N.I.T. Jamshedpur, Jharkhand, India.

Prof. (Dr.) Bhargavi H. Goswami, Department of MCA, Sunshine Group of Institutes, Nr. Rangoli Park, Kalawad Road, Rajkot, Gujarat, India.

Prof. (Dr.) Essam H. Houssein, Computer Science Department, Faculty of Computers & Informatics, Benha University, Benha 13518, Qalyubia Governorate, Egypt.

Arash Shaghaghi, University College London, University of London, Great Britain.

Prof. Rajesh Duvvuru, Dept. of Computer Sc. & Engg., N.I.T. Jamshedpur, Jharkhand, India.

Prof. (Dr.) Anand Kumar, Head, Department of MCA, M.S. Engineering College, Navarathna Agrahara, Sadahalli Post, Bangalore, PIN 562110, Karnataka, INDIA. Prof. (Dr.) Venkata Raghavendra Miriampally, Electrical and Computer Engineering Dept, Adama Science & Technology University, Adama, Ethiopia.

Prof. (Dr.) Jatinderkumar R. Saini, Director (I.T.), GTU's Ankleshwar-Bharuch Innovation Sankul &Director I/C & Associate Professor, Narmada College of Computer Application, Zadeshwar, Bharuch, Gujarat, India.

Prof. Jaswinder Singh, Mechanical Engineering Department, University Institute Of Engineering & Technology, Panjab University SSG Regional Centre, Hoshiarpur, Punjab, India- 146001.

Prof. (Dr.) S.Kadhiravan, Head i/c, Department of Psychology, Periyar University, Salem- 636 011,Tamil Nadu, India.

Prof. (Dr.) Mohammad Israr, Principal, Balaji Engineering College,Junagadh, Gujarat-362014, India.

Prof. (Dr.) VENKATESWARLU B., Director of MCA in Sreenivasa Institute of Technology and Management Studies (SITAMS), Chittoor.

Prof. (Dr.) Deepak Paliwal, Faculty of Sociology, Uttarakhand Open University, Haldwani-Nainital Prof. (Dr.) Dr. Anil K Dwivedi, Faculty of Pollution & Environmental Assay Research Laboratory (PEARL), Department of Botany,DDU Gorakhpur University,Gorakhpur-273009, India.

Prof. R. Ravikumar, Department of Agricultural and Rural Management, TamilNadu Agricultural University, Coimbatore-641003,Tamil Nadu, India.

Prof. (Dr.) R.Raman, Professor of Agronomy, Faculty of Agriculture, Annamalai university, Annamalai Nagar 608 002Tamil Nadu, India.

Prof. (Dr.) Ahmed Khalafallah, Coordinator of the CM Degree Program, Department of Architectural and Manufacturing Sciences, Ogden College of Sciences and Engineering Western Kentucky University 1906 College Heights Blvd Bowling Green, KY 42103-1066 Prof. (Dr.) Asmita Das , Delhi Technological University (Formerly Delhi College of Engineering), Shahbad, Daulatpur, Delhi 110042, India.

Prof. (Dr.)Aniruddha Bhattacharjya, Assistant Professor (Senior Grade), CSE Department, Amrita School of Engineering , Amrita Vishwa VidyaPeetham (University), Kasavanahalli, Carmelaram P.O., Bangalore 560035, Karnataka, India Prof. (Dr.) S. Rama Krishna Pisipaty, Prof & Geoarchaeologist, Head of the Department of Sanskrit & Indian Culture, SCSVMV University, Enathur, Kanchipuram 631561, India Prof. (Dr.) Shubhasheesh Bhattacharya, Professor & HOD(HR), Symbiosis Institute of International Business (SIIB), Hinjewadi, Phase-I, Pune- 411 057 Prof. (Dr.) Vijay Kothari, Institute of Science, Nirma University, S-G Highway, Ahmedabad 382481, India.

Prof. (Dr.) Raja Sekhar Mamillapalli, Department of Civil Engineering at Sir Padampat Singhania University, Udaipur, India.

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Prof. (Dr.)B. M. Kunar, Department of Mining Engineering, Indian School of Mines, Dhanbad 826004, Jharkhand, India.

Prof. (Dr.) Prabir Sarkar, Assistant Professor, School of Mechanical, Materials and Energy Engineering, Room 307, Academic Block, Indian Institute of Technology, Ropar, Nangal Road, Rupnagar 140001, Punjab, India.

Prof. (Dr.) K.Srinivasmoorthy, Associate Professor, Department of Earth Sciences, School of Physical,Chemical and Applied Sciences, Pondicherry university, R.Venkataraman Nagar, Kalapet, Puducherry 605014, India.

Prof. (Dr.) Bhawna Dubey, Institute of Environmental Science (AIES), Amity University, Noida, India.

Prof. (Dr.) P. Bhanu Prasad, Vision Specialist, Matrix vision GmbH, Germany, Consultant, TIFACCORE for Machine Vision, Advisor, Kelenn Technology, France Advisor, Shubham Automation & Services, Ahmedabad, and Professor of C.S.E, Rajalakshmi Engineering College, India.

Prof. (Dr.)P.Raviraj, Professor & Head, Dept. of CSE, Kalaignar Karunanidhi, Institute of Technology, Coimbatore 641402,Tamilnadu,India.

Prof. (Dr.) Damodar Reddy Edla, Department of Computer Science & Engineering, Indian School of Mines, Dhanbad, Jharkhand 826004, India.

Prof. (Dr.) T.C. Manjunath, Principal in HKBK College of Engg., Bangalore, Karnataka, India.

Prof. (Dr.) Pankaj Bhambri, I.T. Deptt., Guru Nanak Dev Engineering College, Ludhiana 141006, Punjab, India .

Prof. Shashikant Shantilal Patil SVKM, MPSTME Shirpur Campus, NMIMS University Vile Parle Mumbai, India.

Prof. (Dr.) Shambhu Nath Choudhary, Department of Physics, T.M. Bhagalpur University, Bhagalpur 81200, Bihar, India.

Prof. (Dr.) Venkateshwarlu Sonnati, Professor & Head of EEED, Department of EEE, Sreenidhi Institute of Science & Technology, Ghatkesar, Hyderabad, Andhra Pradesh, India.

Prof. (Dr.) Saurabh Dalela, Department of Pure & Applied Physics, University of Kota, KOTA 324010, Rajasthan, India.

Prof. S. Arman Hashemi Monfared, Department of Civil Eng, University of Sistan & Baluchestan, Daneshgah St.,Zahedan, IRAN, P.C. 98155-987 Prof. (Dr.) R.S.Chanda, Dept. of Jute & Fibre Tech., University of Calcutta, Kolkata 700019, West Bengal, India.

Prof. V.S.VAKULA, Department of Electrical and Electronics Engineering, JNTUK, University College of Engg., Vizianagaram5 35003, Andhra Pradesh, India.

Prof. (Dr.) Nehal Gitesh Chitaliya, Sardar Vallabhbhai Patel Institute of Technology, Vasad 388 306, Gujarat, India.

Prof. (Dr.) D.R. Prajapati, Department of Mechanical Engineering, PEC University of Technology,Chandigarh 160012, India.

Dr. A. SENTHIL KUMAR, Postdoctoral Researcher, Centre for Energy and Electrical Power, Electrical Engineering Department, Faculty of Engineering and the Built Environment, Tshwane University of Technology, Pretoria 0001, South Africa.

Prof. (Dr.)Vijay Harishchandra Mankar, Department of Electronics & Telecommunication Engineering, Govt. Polytechnic, Mangalwari Bazar, Besa Road, Nagpur- 440027, India.

Prof. Varun.G.Menon, Department Of C.S.E, S.C.M.S School of Engineering, Karukutty, Ernakulam, Kerala 683544, India.

Prof. (Dr.) U C Srivastava, Department of Physics, Amity Institute of Applied Sciences, Amity University, Noida, U.P-203301.India.

Prof. (Dr.) Surendra Yadav, Professor and Head (Computer Science & Engineering Department), Maharashi Arvind College of Engineering and Research Centre (MACERC), Jaipur, Rajasthan, India.

Prof. (Dr.) Sunil Kumar, H.O.D. Applied Sciences & Humanities Dehradun Institute of Technology, (D.I.T. School of Engineering), 48 A K.P-3 Gr. Noida (U.P.) 201308 Prof. Naveen Jain, Dept. of Electrical Engineering, College of Technology and Engineering, Udaipur-313 001, India.

Prof. Veera Jyothi.B, CBIT ,Hyderabad, Andhra Pradesh, India.

Prof. Aritra Ghosh, Global Institute of Management and Technology, Krishnagar, Nadia, W.B. India Prof. Anuj K. Gupta, Head, Dept. of Computer Science & Engineering, RIMT Group of Institutions, Sirhind Mandi Gobindgarh, Punajb, India.

Prof. (Dr.) Varala Ravi, Head, Department of Chemistry, IIIT Basar Campus, Rajiv Gandhi University of Knowledge Technologies, Mudhole, Adilabad, Andhra Pradesh- 504 107, India Prof. (Dr.) Ravikumar C Baratakke, faculty of Biology,Govt. College, Saundatti - 591 126, India.

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Prof. (Dr.) NALIN BHARTI, School of Humanities and Social Science, Indian Institute of Technology Patna, India.

Prof. (Dr.) Shivanand S.Gornale, Head, Department of Studies in Computer Science, Government College (Autonomous), Mandya, Mandya-571 401-Karanataka Prof. (Dr.) Naveen.P.Badiger, Dept.Of Chemistry, S.D.M.College of Engg. & Technology, Dharwad-580002, Karnataka State, India.

Prof. (Dr.) Bimla Dhanda, Professor & Head, Department of Human Development and Family Studies, College of Home Science, CCS, Haryana Agricultural University, Hisar- 125001 (Haryana) India.

Prof. (Dr.) Tauqeer Ahmad Usmani, Faculty of IT, Salalah College of Technology, Salalah, Sultanate of Oman, Prof. (Dr.) Naresh Kr. Vats, Chairman, Department of Law, BGC Trust University Bangladesh Prof. (Dr.) Papita Das (Saha), Department of Environmental Science, University of Calcutta, Kolkata, India Prof. (Dr.) Rekha Govindan , Dept of Biotechnology, Aarupadai Veedu Institute of technology , Vinayaka Missions University , Paiyanoor , Kanchipuram Dt, Tamilnadu , India Prof. (Dr.) Lawrence Abraham Gojeh, Department of Information Science, Jimma University, P.o.Box 378, Jimma, Ethiopia Prof. (Dr.) M.N. Kalasad, Department of Physics, SDM College of Engineering & Technology, Dharwad, Karnataka, India Prof. Rab Nawaz Lodhi, Department of Management Sciences, COMSATS Institute of Information Technology Sahiwal Prof. (Dr.) Masoud Hajarian, Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, General Campus, Evin, Tehran 19839,Iran Prof. (Dr.) Chandra Kala Singh, Associate professor, Department of Human Development and Family Studies, College of Home Science, CCS, Haryana Agricultural University, Hisar- 125001 (Haryana) India Prof. (Dr.) J.Babu, Professor & Dean of research, St.Joseph's College of Engineering & Technology, Choondacherry, Palai,Kerala.

Prof. (Dr.) Pradip Kumar Roy, Department of Applied Mechanics, Birla Institute of Technology (BIT) Mesra, Ranchi-835215, Jharkhand, India.

Prof. (Dr.) P. Sanjeevi kumar, School of Electrical Engineering (SELECT), Vandalur Kelambakkam Road, VIT University, Chennai, India.

Prof. (Dr.) Debasis Patnaik, BITS-Pilani, Goa Campus, India.

Prof. (Dr.) SANDEEP BANSAL, Associate Professor, Department of Commerce, I.G.N. College, Haryana, India.

Dr. Radhakrishnan S V S, Department of Pharmacognosy, Faser Hall, The University of Mississippi Oxford, MS-38655, USA Prof. (Dr.) Megha Mittal, Faculty of Chemistry, Manav Rachna College of Engineering, Faridabad (HR), 121001, India.

Prof. (Dr.) Mihaela Simionescu (BRATU), BUCHAREST, District no. 6, Romania, member of the Romanian Society of Econometrics, Romanian Regional Science Association and General Association of Economists from Romania Prof. (Dr.) Atmani Hassan, Director Regional of Organization Entraide Nationale Prof. (Dr.) Deepshikha Gupta, Dept. of Chemistry, Amity Institute of Applied Sciences,Amity University, Sec.125, Noida, India Prof. (Dr.) Muhammad Kamruzzaman, Deaprtment of Infectious Diseases, The University of Sydney, Westmead Hospital, Westmead, NSW-2145.

Prof. (Dr.) Meghshyam K. Patil , Assistant Professor & Head, Department of Chemistry,Dr. Babasaheb Ambedkar Marathwada University,Sub-Campus, Osmanabad- 413 501, Maharashtra, INDIA Prof. (Dr.) Ashok Kr. Dargar, Department of Mechanical Engineering, School of Engineering, Sir Padampat Singhania University, Udaipur (Raj.) Prof. (Dr.) Sudarson Jena, Dept. of Information Technology, GITAM University, Hyderabad, India Prof. (Dr.) Jai Prakash Jaiswal, Department of Mathematics, Maulana Azad National Institute of Technology Bhopal-India Prof. (Dr.) S.Amutha, Dept. of Educational Technology, Bharathidasan University, Tiruchirappalli620 023, Tamil Nadu-India Prof. (Dr.) R. HEMA KRISHNA, Environmental chemistry, University of Toronto, Canada.

Prof. (Dr.) B.Swaminathan, Dept. of Agrl.Economics, Tamil Nadu Agricultural University, India.

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Prof. (Dr.) Meghshyam K. Patil, Assistant Professor & Head, Department of Chemistry, Dr. Babasaheb Ambedkar Marathwada University, Sub-Campus, Osmanabad- 413 501, Maharashtra, INDIA Prof. (Dr.) K. Ramesh, Department of Chemistry, C .B . I. T, Gandipet, Hyderabad-500075 Prof. (Dr.) Sunil Kumar, H.O.D. Applied Sciences &Humanities, JIMS Technical campus,(I.P. University,New Delhi), 48/4 ,K.P.-3,Gr.Noida (U.P.) Prof. (Dr.) G.V.S.R.Anjaneyulu, CHAIRMAN - P.G. BOS in Statistics & Deputy Coordinator UGC DRS-I Project, Executive Member ISPS-2013, Department of Statistics, Acharya Nagarjuna University, Nagarjuna Nagar-522510, Guntur, Andhra Pradesh, India Prof. (Dr.) Sribas Goswami, Department of Sociology, Serampore College, Serampore 712201, West Bengal, India.

Prof. (Dr.) Sunanda Sharma, Department of Veterinary Obstetrics Y Gynecology, College of Veterinary & Animal Science,Rajasthan University of Veterinary & Animal Sciences,Bikaner334001, India.

Prof. (Dr.) S.K. Tiwari, Department of Zoology, D.D.U. Gorakhpur University, Gorakhpur-273009 U.P., India.

Prof. (Dr.) Praveena Kuruva, Materials Research Centre, Indian Institute of Science, Bangalore560012, INDIA Prof. (Dr.) Rajesh Kumar, Department Of Applied Physics , Bhilai Institute Of Technology, Durg (C.G.) 491001 Prof. (Dr.) Y.P.Singh, (Director), Somany (PG) Institute of Technology and Management, Garhi Bolni Road, Delhi-Jaipur Highway No. 8, Beside 3 km from City Rewari, Rewari-123401, India.

Prof. (Dr.) MIR IQBAL FAHEEM, VICE PRINCIPAL &HEAD- Department of Civil Engineering & Professor of Civil Engineering, Deccan College of Engineering & Technology, Dar-us-Salam, Aghapura, Hyderabad (AP) 500 036.

Prof. (Dr.) Jitendra Gupta, Regional Head, Co-ordinator(U.P. State Representative)& Asstt. Prof., (Pharmaceutics), Institute of Pharmaceutical Research, GLA University, Mathura.

Prof. (Dr.) N. Sakthivel, Scientist - C,Research Extension Center,Central Silk Board, Government of India, Inam Karisal Kulam (Post), Srivilliputtur - 626 125,Tamil Nadu, India.

Prof. (Dr.) Omprakash Srivastav, Centre of Advanced Study, Department of History, Aligarh Muslim University, Aligarh-202 001, INDIA. Prof. (Dr.) K.V.L.N.Acharyulu, Associate Professor, Department of Mathematics, Bapatla Engineering college, Bapatla-522101, INDIA. Prof. (Dr.) Fateh Mebarek-Oudina, Assoc. Prof., Sciences Faculty,20 aout 1955-Skikda University, B.P 26 Route El-Hadaiek, 21000,Skikda, Algeria.

NagaLaxmi M. Raman, Project Support Officer, Amity International Centre for Postharvest, Technology & Cold Chain Management, Amity University Campus, Sector-125, Expressway, Noida Prof. (Dr.) V.SIVASANKAR, Associate Professor, Department Of Chemistry, Thiagarajar College Of Engineering (Autonomous), Madurai 625015, Tamil Nadu, India (Dr.) Ramkrishna Singh Solanki, School of Studies in Statistics, Vikram University, Ujjain, India Prof. (Dr.) M.A.Rabbani, Professor/Computer Applications, School of Computer, Information and Mathematical Sciences, B.S.Abdur Rahman University, Chennai, India Prof. (Dr.) P.P.Satya Paul Kumar, Associate Professor, Physical Education & Sports Sciences, University College of Physical Education & Sports, Sciences, Acharya Nagarjuna University, Guntur.

Prof. (Dr.) Fazal Shirazi, PostDoctoral Fellow, Infectious Disease, MD Anderson Cancer Center, Houston, Texas, USA Prof. (Dr.) Omprakash Srivastav, Department of Museology, Aligarh Muslim University, Aligarh202 001, INDIA. Prof. (Dr.) Mandeep Singh walia, A.P. E.C.E., Panjab University SSG Regional Centre Hoshiarpur, Una Road, V.P.O. Allahabad, Bajwara, Hoshiarpur Prof. (Dr.) Ho Soon Min, Senior Lecturer, Faculty of Applied Sciences, INTI International University, Persiaran Perdana BBN, Putra Nilai, 71800 Nilai, Negeri Sembilan, Malaysia Prof. (Dr.) L.Ganesamoorthy, Assistant Professor in Commerce, Annamalai University, Annamalai Nagar-608002, Chidambaram, Tamilnadu, India.

Prof. (Dr.) Vuda Sreenivasarao, Professor, School of Computing and Electrical Engineering, Bahir Dar University, Bahirdar,Ethiopia Prof. (Dr.) Umesh Sharma, Professor & HOD Applied Sciences & Humanities, Eshan college of Engineering, Mathura, India.

Prof. (Dr.) K. John Singh, School of Information Technology and Engineering, VIT University, Vellore, Tamil Nadu, India.

Prof. (Dr.) Sita Ram Pal (Asst.Prof.), Dept. of Special Education, Dr.BAOU, Ahmedabad, India.

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Prof. Vishal S.Rana, H.O.D, Department of Business Administration, S.S.B.T'S College of Engineering & Technology, Bambhori,Jalgaon (M.S), India.

Prof. (Dr.) Chandrakant Badgaiyan, Department of Mechatronics and Engineering, Chhattisgarh.

Dr. (Mrs.) Shubhrata Gupta, Prof. (Electrical), NIT Raipur, India.

Prof. (Dr.) Usha Rani. Nelakuditi, Assoc. Prof., ECE Deptt., Vignan’s Engineering College, Vignan University, India.

Prof. (Dr.) S. Swathi, Asst. Professor, Department of Information Technology, Vardhaman college of Engineering(Autonomous) , Shamshabad, R.R District, India.

Prof. (Dr.) Raja Chakraverty, M Pharm (Pharmacology), BCPSR, Durgapur, West Bengal, India Prof. (Dr.) P. Sanjeevi Kumar, Electrical & Electronics Engineering, National Institute of Technology (NIT-Puducherry), An Institute of National Importance under MHRD (Govt. of India), Karaikal- 609 605, India.

Prof. (Dr.) Amitava Ghosh, Professor & Principal, Bengal College of Pharmaceutical Sciences and Research, B.R.B. Sarani, Bidhannagar, Durgapur, West Bengal- 713212.

Prof. (Dr.) Om Kumar Harsh, Group Director, Amritsar College of Engineering and Technology, Amritsar 143001 (Punjab), India.

Prof. (Dr.) Mansoor Maitah, Department of International Relations, Faculty of Economics and Management, Czech University of Life Sciences Prague, 165 21 Praha 6 Suchdol, Czech Republic.

Prof. (Dr.) Zahid Mahmood, Department of Management Sciences (Graduate Studies), Bahria University, Naval Complex, Sector, E-9, Islamabad, Pakistan.

Prof. (Dr.) N. Sandeep, Faculty Division of Fluid Dynamics, VIT University, Vellore-632 014.

Mr. Jiban Shrestha, Scientist (Plant Breeding and Genetics), Nepal Agricultural Research Council, National Maize Research Program, Rampur, Chitwan, Nepal.

Prof. (Dr.) Rakhi Garg, Banaras Hindu University, Varanasi, Uttar Pradesh, India.

Prof. (Dr.) Ramakant Pandey. Dept. of Biochemistry. Patna University Patna (Bihar)-India.

Prof. (Dr.) Nalah Augustine Bala, Behavioural Health Unit, Psychology Department, Nasarawa State University, Keffi, P.M.B. 1022 Keffi, Nasarawa State, Nigeria.

Prof. (Dr.) Mehdi Babaei, Department of Engineering, Faculty of Civil Engineering, University of Zanjan, Iran.

Prof. (Dr.) A. SENTHIL KUMAR., Professor/EEE, VELAMMAL ENGINEERING COLLEGE, CHENNAI Prof. (Dr.) Gudikandhula Narasimha Rao, Dept. of Computer Sc. & Engg., KKR & KSR Inst Of Tech & Sciences, Guntur, Andhra Pradesh, India.

Prof. (Dr.) Dhanesh singh, Department of Chemistry, K.G. Arts & Science College, Raigarh (C.G.) India.

Prof. (Dr.) Syed Umar , Dept. of Electronics and Computer Engineering, KL University, Guntur, A.P., India.

Prof. (Dr.) Rachna Goswami, Faculty in Bio-Science Department, IIIT Nuzvid (RGUKT), DistrictKrishna , Andhra Pradesh - 521201 Prof. (Dr.) Ahsas Goyal, FSRHCP, Founder & Vice president of Society of Researchers and Health Care Professionals Prof. (Dr.) Gagan Singh, School of Management Studies and Commerce, Department of Commerce, Uttarakhand Open University, Haldwani-Nainital, Uttarakhand (UK)-263139 (India) Prof. (Dr.) Solomon A. O. Iyekekpolor, Mathematics and Statistics, Federal University, WukariNigeria.

Prof. (Dr.) S. Saiganesh, Faculty of Marketing, Dayananda Sagar Business School, Bangalore, India.

Dr. K.C.Sivabalan, Field Enumerator and Data Analyst, Asian Vegetable Research Centre, The World Vegetable Centre, Taiwan Prof. (Dr.) Amit Kumar Mishra, Department of Environmntal Science and Energy Research, Weizmann Institute of Science, Rehovot, Israel Prof. (Dr.) Manisha N. Paliwal, Sinhgad Institute of Management, Vadgaon (Bk), Pune, India Prof. (Dr.) M. S. HIREMATH, Principal, K.L.ESOCIETY’S SCHOOL, ATHANI, India Prof. Manoj Dhawan, Department of Information Technology, Shri Vaishnav Institute of Technology & Science, Indore, (M. P.), India Prof. (Dr.) V.R.Naik, Professor & Head of Department, Mechancal Engineering , Textile & Engineering Institute, Ichalkaranji (Dist. Kolhapur), Maharashatra, India Prof. (Dr.) Jyotindra C. Prajapati,Head, Department of Mathematical Sciences, Faculty of Applied Sciences, Charotar University of Science and Technology, Changa Anand -388421, Gujarat, India Prof. (Dr.) Sarbjit Singh, Head, Department of Industrial & Production Engineering, Dr BR Ambedkar National Institute of Technology, Jalandhar, Punjab,India

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Prof. (Dr.) Professor Braja Gopal Bag, Department of Chemistry and Chemical Technology, Vidyasagar University, West Midnapore Prof. (Dr.) Ashok Kumar Chandra, Department of Management, Bhilai Institute of Technology, Bhilai House, Durg (C.G.) Prof. (Dr.) Amit Kumar, Assistant Professor, School of Chemistry, Shoolini University, Solan, Himachal Pradesh, India Prof. (Dr.) L. Suresh Kumar, Mechanical Department, Chaitanya Bharathi Institute of Technology, Hyderabad, India.

Scientist Sheeraz Saleem Bhat, Lac Production Division, Indian Institute of Natural Resins and Gums, Namkum, Ranchi, Jharkhand Prof. C.Divya , Centre for Information Technology and Engineering, Manonmaniam Sundaranar University, Tirunelveli - 627012, Tamilnadu , India Prof. T.D.Subash, Infant Jesus College Of Engineering and Technology, Thoothukudi Tamilnadu, India Prof. (Dr.) Vinay Nassa, Prof. E.C.E Deptt., Dronacharya.Engg. College, Gurgaon India.

Prof. Sunny Narayan, university of Roma Tre, Italy.

Prof. (Dr.) Sanjoy Deb, Dept. of ECE, BIT Sathy, Sathyamangalam, Tamilnadu-638401, India.

Prof. (Dr.) Reena Gupta, Institute of Pharmaceutical Research, GLA University, Mathura-India Prof. (Dr.) P.R.SivaSankar, Head Dept. of Commerce, Vikrama Simhapuri University Post Graduate Centre, KAVALI - 524201, A.P., India Prof. (Dr.) Mohsen Shafiei Nikabadi, Faculty of Economics and Management, Industrial Management Department, Semnan University, Semnan, Iran.

Prof. (Dr.) Praveen Kumar Rai, Department of Geography, Faculty of Science, Banaras Hindu University, Varanasi-221005, U.P. India Prof. (Dr.) Christine Jeyaseelan, Dept of Chemistry, Amity Institute of Applied Sciences, Amity University, Noida, India Prof. (Dr.) M A Rizvi, Dept. of Computer Engineering and Applications , National Institute of Technical Teachers' Training and Research, Bhopal M.P. India Prof. (Dr.) K.V.N.R.Sai Krishna, H O D in Computer Science, S.V.R.M.College,(Autonomous), Nagaram, Guntur(DT), Andhra Pradesh, India.

Prof. (Dr.) Ashok Kr. Dargar, Department of Mechanical Engineering, School of Engineering, Sir Padampat Singhania University, Udaipur (Raj.) Prof. (Dr.) Asim Kumar Sen, Principal , ST.Francis Institute of Technology (Engineering College) under University of Mumbai , MT. Poinsur, S.V.P Road, Borivali (W), Mumbai, 400103, India, Prof. (Dr.) Rahmathulla Noufal.E, Civil Engineering Department, Govt.Engg.College-Kozhikode Prof. (Dr.) N.Rajesh, Department of Agronomy, TamilNadu Agricultural University -Coimbatore, TamilNadu, India Prof. (Dr.) Har Mohan Rai, Professor, Electronics and Communication Engineering, N.I.T. Kurukshetra 136131,India Prof. (Dr.) Eng. Sutasn Thipprakmas from King Mongkut, University of Technology Thonburi, Thailand Prof. (Dr.) Kantipudi MVV Prasad, EC Department, RK University, Rajkot.

Prof. (Dr.) Jitendra Gupta,Faculty of Pharmaceutics, Institute of Pharmaceutical Research, GLA University, Mathura.

Prof. (Dr.) Swapnali Borah, HOD, Dept of Family Resource Management, College of Home Science, Central Agricultural University, Tura, Meghalaya, India Prof. (Dr.) N.Nazar Khan, Professor in Chemistry, BTK Institute of Technology, Dwarahat-263653 (Almora), Uttarakhand-India Prof. (Dr.) Rajiv Sharma, Department of Ocean Engineering, Indian Institute of Technology Madras, Chennai (TN) - 600 036, India.

Prof. (Dr.) Aparna Sarkar, PH.D. Physiology, AIPT, Amity University , F 1 Block, LGF, Sector125,Noida-201303, UP, India.

Prof. (Dr.) Manpreet Singh, Professor and Head, Department of Computer Engineering, Maharishi Markandeshwar University, Mullana, Haryana, India.

Prof. (Dr.) Sukumar Senthilkumar, Senior Researcher, Advanced Education Center of Jeonbuk for Electronics and Information Technology, Chon Buk National University, Chon Buk, 561-756, SOUTH KOREA. .

Prof. (Dr.) Hari Singh Dhillon, Assistant Professor, Department of Electronics and Communication Engineering, DAV Institute of Engineering and Technology, Jalandhar (Punjab), INDIA. .

Prof. (Dr.) Poonkuzhali, G., Department of Computer Science and Engineering, Rajalakshmi Engineering College, Chennai, INDIA. .

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Prof. (Dr.) Bharath K N, Assistant Professor, Dept. of Mechanical Engineering, GM Institute of Technology, PB Road, Davangere 577006, Karnataka, India.

Prof. (Dr.) F.Alipanahi, Assistant Professor, Islamic Azad University, Zanjan Branch, Atemadeyeh, Moalem Street, Zanjan IRAN. Prof. Yogesh Rathore, Assistant Professor, Dept. of Computer Science & Engineering, RITEE, Raipur, India Prof. (Dr.) Ratneshwer, Department of Computer Science (MMV),Banaras Hindu University Varanasi-221005, India.

Prof. Pramod Kumar Pandey, Assistant Professor, Department Electronics & Instrumentation Engineering, ITM University, Gwalior, M.P., India.

Prof. (Dr.)Sudarson Jena, Associate Professor, Dept.of IT, GITAM University, Hyderabad, India Prof. (Dr.) Binod Kumar, PhD(CS), M.Phil(CS), MIEEE,MIAENG, Dean & Professor( MCA), Jayawant Technical Campus(JSPM's), Pune, India.

Prof. (Dr.) Mohan Singh Mehata, (JSPS fellow), Assistant Professor, Department of Applied Physics, Delhi Technological University, Delhi Prof. Ajay Kumar Agarwal, Asstt. Prof., Deptt. of Mech. Engg., Royal Institute of Management & Technology, Sonipat (Haryana), India.

Prof. (Dr.) Siddharth Sharma, University School of Management, Kurukshetra University, Kurukshetra, India.

Prof. (Dr.) Satish Chandra Dixit, Department of Chemistry, D.B.S.College, Govind Nagar,Kanpur208006, India.

Prof. (Dr.) Ajay Solkhe, Department of Management, Kurukshetra University, Kurukshetra, India.

Prof. (Dr.) Neeraj Sharma, Asst. Prof. Dept. of Chemistry, GLA University, Mathura, India.

Prof. (Dr.) Basant Lal, Department of Chemistry, G.L.A. University, Mathura, India.

Prof. (Dr.) T Venkat Narayana Rao, C.S.E, Guru Nanak Engineering College, Hyderabad, Andhra Pradesh, India.

Prof. (Dr.) Rajanarender Reddy Pingili, S.R. International Institute of Technology, Hyderabad, Andhra Pradesh, India.

Prof. (Dr.) V.S.Vairale, Department of Computer Engineering, All India Shri Shivaji Memorial Society College of Engineering, Kennedy Road, Pune-411 001, Maharashtra, India.

Prof. (Dr.) Vasavi Bande, Department of Computer Science & Engineering, Netaji Institute of Engineering and Technology, Hyderabad, Andhra Pradesh, India Prof. (Dr.) Hardeep Anand, Department of Chemistry, Kurukshetra University Kurukshetra, Haryana, India.

Prof. Aasheesh shukla, Asst Professor, Dept. of EC, GLA University, Mathura, India.

Prof. S.P.Anandaraj., CSE Dept, SREC, Warangal, India.

Prof. (Dr.) Chitranjan Agrawal, Department of Mechanical Engineering, College of Technology & Engineering, Maharana Pratap University of Agriculture & Technology, Udaipur- 313001, Rajasthan, India.

Prof. (Dr.) Rangnath Aher, Principal, New Arts, Commerce and Science College, Parner, DistAhmednagar, M.S. India.

Prof. (Dr.) Chandan Kumar Panda, Department of Agricultural Extension, College of Agriculture, Tripura, Lembucherra-799210 Prof. (Dr.) Latika Kharb, IP Faculty (MCA Deptt), Jagan Institute of Management Studies (JIMS), Sector-5, Rohini, Delhi, India.

Raj Mohan Raja Muthiah, Harvard Medical School, Massachusetts General Hospital, Boston, Massachusetts.

Prof. (Dr.) Chhanda Chatterjee, Dept of Philosophy, Balurghat College, West Bengal, India.

Prof. (Dr.) Mihir Kumar Shome , H.O.D of Mathematics, Management and Humanities, National Institute of Technology, Arunachal Pradesh, India Prof. (Dr.) Muthukumar .Subramanyam, Registrar (I/C), Faculty, Computer Science and Engineering, National Institute of Technology, Puducherry, India.

Prof. (Dr.) Vinay Saxena, Department of Mathematics, Kisan Postgraduate College, Bahraich – 271801 UP, India.

Satya Rishi Takyar, Senior ISO Consultant, New Delhi, India.

Prof. Anuj K. Gupta, Head, Dept. of Computer Science & Engineering, RIMT Group of Institutions, Mandi Gobindgarh (PB) Prof. (Dr.) Harish Kumar, Department of Sports Science, Punjabi University, Patiala, Punjab, India.

Prof. (Dr.) Mohammed Ali Hussain, Professor, Dept. of Electronics and Computer Engineering, KL University, Green Fields, Vaddeswaram, Andhra Pradesh, India.

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Prof. (Dr.) Manish Gupta, Department of Mechanical Engineering, GJU, Haryana, India.

Prof. Mridul Chawla, Department of Elect. and Comm. Engineering, Deenbandhu Chhotu Ram University of Science & Technology, Murthal, Haryana, India.

Prof. Seema Chawla, Department of Bio-medical Engineering, Deenbandhu Chhotu Ram University of Science & Technology, Murthal, Haryana, India.

Prof. (Dr.) Atul M. Gosai, Department of Computer Science, Saurashtra University, Rajkot, Gujarat, India.

Prof. (Dr.) Ajit Kr. Bansal, Department of Management, Shoolini University, H.P., India.

Prof. (Dr.) Sunil Vasistha, Mody Institute of Tecnology and Science, Sikar, Rajasthan, India.

Prof. Vivekta Singh, GNIT Girls Institute of Technology, Greater Noida, India.

Prof. Ajay Loura, Assistant Professor at Thapar University, Patiala, India.

Prof. Sushil Sharma, Department of Computer Science and Applications, Govt. P. G. College, Ambala Cantt., Haryana, India.

Prof. Sube Singh, Assistant Professor, Department of Computer Engineering, Govt. Polytechnic, Narnaul, Haryana, India.

Prof. Himanshu Arora, Delhi Institute of Technology and Management, New Delhi, India.

Dr. Sabina Amporful, Bibb Family Practice Association, Macon, Georgia, USA. Dr. Pawan K. Monga, Jindal Institute of Medical Sciences, Hisar, Haryana, India.

Dr. Sam Ampoful, Bibb Family Practice Association, Macon, Georgia, USA. Dr. Nagender Sangra, Director of Sangra Technologies, Chandigarh, India.

Vipin Gujral, CPA, New Jersey, USA. Sarfo Baffour, University of Ghana, Ghana.

Monique Vincon, Hype Softwaretechnik GmbH, Bonn, Germany.

Natasha Sigmund, Atlanta, USA. Marta Trochimowicz, Rhein-Zeitung, Koblenz, Germany.

Kamalesh Desai, Atlanta, USA. Vijay Attri, Software Developer Google, San Jose, California, USA. Neeraj Khillan, Wipro Technologies, Boston, USA. Ruchir Sachdeva, Software Engineer at Infosys, Pune, Maharashtra, India.

Anadi Charan, Senior Software Consultant at Capgemini, Mumbai, Maharashtra.

Pawan Monga, Senior Product Manager, LG Electronics India Pvt. Ltd., New Delhi, India.

Sunil Kumar, Senior Information Developer, Honeywell Technology Solutions, Inc., Bangalore, India.

Bharat Gambhir, Technical Architect, Tata Consultancy Services (TCS), Noida, India.

Vinay Chopra, Team Leader, Access Infotech Pvt Ltd. Chandigarh, India.

Sumit Sharma, Team Lead, American Express, New Delhi, India.

Vivek Gautam, Senior Software Engineer, Wipro, Noida, India.

Anirudh Trehan, Nagarro Software Gurgaon, Haryana, India.

Manjot Singh, Senior Software Engineer, HCL Technologies Delhi, India.

Rajat Adlakha, Senior Software Engineer, Tech Mahindra Ltd, Mumbai, Maharashtra, India.

Mohit Bhayana, Senior Software Engineer, Nagarro Software Pvt. Gurgaon, Haryana, India.

Dheeraj Sardana, Tech. Head, Nagarro Software, Gurgaon, Haryana, India.

Naresh Setia, Senior Software Engineer, Infogain, Noida, India.

Raj Agarwal Megh, Idhasoft Limited, Pune, Maharashtra, India.

Shrikant Bhardwaj, Senior Software Engineer, Mphasis an HP Company, Pune, Maharashtra, India.

Vikas Chawla, Technical Lead, Xavient Software Solutions, Noida, India.

Kapoor Singh, Sr. Executive at IBM, Gurgaon, Haryana, India.

Ashwani Rohilla, Senior SAP Consultant at TCS, Mumbai, India.

Anuj Chhabra, Sr. Software Engineer, McKinsey & Company, Faridabad, Haryana, India.

Jaspreet Singh, Business Analyst at HCL Technologies, Gurgaon, Haryana, India.

TOPICS OF INTEREST Topics of interest include, but are not limited to, the following:  Computer and computational sciences  Physics  Chemistry  Mathematics  Actuarial sciences  Applied mathematics  Biochemistry, Bioinformatics  Robotics  Computer engineering  Statistics  Electrical engineering & Electronics  Mechanical engineering  Industrial engineering  Information sciences  Civil Engineering  Aerospace engineering  Chemical engineering  Sports sciences  Military sciences  Astrophysics & Astronomy  Optics  Nanotechnology  Nuclear physics  Operations research  Neurobiology & Biomechanics  Acoustical engineering  Geographic information systems  Atmospheric sciences  Educational/Instructional technology  Biological sciences  Education and Human resource  Extreme engineering applications  Environmental research and education  Geosciences  Social, Behavioral and Economic sciences  Advanced manufacturing technology  Automotive & Construction  Geospatial technology  Cyber security  Transportation  Energy and Power  Healthcare & Hospitality  Medical and dental sciences  Pesticides  Marine and thermal sciences  Pollution  Renewable sources of energy  Industrial pollution control  Hazardous and e-waste management  Green technologies  Artificial/computational intelligence  Theory and models

TABLE OF CONTENTS American International Journal of Research in Science, Technology, Engineering & Mathematics ISSN (Print): 2328-3491, ISSN (Online): 2328-3580, ISSN (CD-ROM): 2328-3629 (December, 2015-February, 2016, Issue 13, Volume 1 & 2) Issue 13, Volume 1 Paper Code

Paper Title

Page No.

AIJRSTEM 15-806

Review on Steam Coal –Sampling & Preparation D. Mahapatra

01-09

AIJRSTEM 15-808

Lagrange Formalism for Electron Field in Terms of Strengths (E,H) and (E',H') Dr. Bulikunzira Sylvestre

10-13

AIJRSTEM 15-809

Experimental Investigation on the strength characteristics of Polymer Based GGBFS Concrete Vinaykumar S. Jatti

14-17

AIJRSTEM 15-813

HF Propagation Variation on a Path Aligned Along the Mid-latitude Trough During Winter Mfon O. Charles, Mike Warrington

18-27

AIJRSTEM 15-814

Synthesis and Characterization of Bismuth Doped Barium Titanate S. Islam, A. Siddika, N. A Ahmed, N. Khatun, S. N. Rahman

28-32

AIJRSTEM 15-817

Two Way Signal Coordination by Using Simple Progressive System for Three-Signalized Intersections Morugu Srujan Kumar, Bhasker Valkati, Dr.R. Srinivasa Kumar

33-38

AIJRSTEM 15-818

Fingerprint Image De-noising by Various Filters for Different Noise using Wavelet Transform Liton Devnath, Prof. Dr. Rafiqul Islam

39-44

AIJRSTEM 15-821

Channel Capacity Analysis of MIMO OFDM System Using Water Filling Algorithm under AWGN and Rayleigh Fading Channel Vipin Kumar, Dr. Praveen Dhyani, Anupma

45-49

AIJRSTEM 15-822

ENERGY ANALYSIS OF DISTILLERY SYSTEMS OF AN ALCOHOL FACTORY BY ENERGY AUDIT Samuel Gebremariam Haile, Mukesh Didwania

50-58

AIJRSTEM 15-825

Genetic Algorithm Approach to Multi-Objective Linear Fractional Programming Problems Savita Mishra

59-65

AIJRSTEM 15-836

Event-Triggered Localization Algorithm Based On Rf with IR Fingerprint and RSSI with PSO Techniques Ahmed Ali Saihood

66-72

AIJRSTEM 15-841

Observations of HF Propagation on a Path Aligned Along the Mid-latitude Trough during Summer Mfon O. Charles, Mike Warrington

73-82

AIJRSTEM 15-847

Invariant Lagrangian for Electron Field in Terms of Complex Isotropic Vectors Dr. Bulikunzira Sylvestre

83-86

AIJRSTEM 15-852

Effect of Electrification in Presence of Non- Uniform Heat Source/Sink on Unsteady Boundary Layer Flow and Heat Transfer in a Fluid With Suspended Particulate Matter (SPM) Over An Inclined Stretching Sheet Runu Sahu, S.K.Mishra

87-98

Issue 13, Volume 2 Paper Code

Paper Title

Page No.

AIJRSTEM 15-854

Multiple Sclerosis Modulating the Epigenome Dr. Syed Mohamed Ibrahim Sulthan

104-110

AIJRSTEM 15-855

Video Watermarking Techniques for Digital Right Management: A Review tour Shaloo Kikan, Ved Ram Singh

111-117

AIJRSTEM 15-862

Special Pairs of Pythagorean Triangles and Jarasandha Numbers G.Janaki, C.Saranya

118-120

AIJRSTEM 15-865

Influence of pretension in Identification of Cracks in Beams Using Mode Shape Techniques K.Gopi Sankar, Dr.G.V.Rama Rao, Dr. L. Venkat

121-126

AIJRSTEM 15-867

Bioenergy and Its Environmental Impacts Dr.Vanita Kumari Sapra

127-131

AIJRSTEM 15-868

Electrical and Optical Properties of Copper Indium GalliumTelluride Films C. Vinothini

132-133

AIJRSTEM 15-869

An Introduction to Differentiation and Integration of Rhotrices Muhammad Aminu

134-138

AIJRSTEM 15-871

Experimental Investigation on Mechanical Properties of Indigenous Rubber Products Mohammad Ikthair Hossain Soiket, Md. Ruhul Amin Rana, Jawad Al Ratun

139-142

AIJRSTEM 15-873

A Review on Steam Coal Analysis -Moisture D. Mahapatra.

143-152

AIJRSTEM 15-875

An analysis on the implementation of soft computing techniques to solve multi-level mathematical programming problems Savita Mishra

153-159

AIJRSTEM 15-880

INFLUENCE THE LOCATION AND CRACK ANGLE ON THE STRESS INTENSITY FACTOR Najah Rustum Mohsin

160-168

AIJRSTEM 15-881

Cheiloscopy; Since instigation to vital role in an investigation Amit Chauhan, Varsha Chauhan, Dr. S. K. Shukla

169-172

American International Journal of Research in Science, Technology, Engineering & Mathematics

Available online at http://www.iasir.net

ISSN (Print): 2328-3491, ISSN (Online): 2328-3580, ISSN (CD-ROM): 2328-3629 AIJRSTEM is a refereed, indexed, peer-reviewed, multidisciplinary and open access journal published by International Association of Scientific Innovation and Research (IASIR), USA (An Association Unifying the Sciences, Engineering, and Applied Research)

A Review on Steam Coal –Sampling & Preparation D. Mahapatra.

Trimex Industries Pvt. Ltd., Chennai, INDIA Abstract: Coal have been classified into many types, grades, ranks etc. mostly on the basis of physicochemical parameters, utility and commercial aspects. It is interesting to note that all the classification cited do not refer to Steam Coal. The entire range of all chemical properties are covered under the term steam coal, from lignite to anthracite. Coal is a biochemical sedimentary rock with very high heterogeneity in chemistry both organic as well inorganic components, different maceral constituents, diverse physical properties. Steam coal if blended to meet the commercial criteria, adds more complexity. The sampling of such heterogeneous mass is very critical. A review of the available methods of sampling and its possibility of true application by the end user has been reviewed.

Key Words: Coal, Classification, Sampling, preparation and test methods, Indian Standards (IS), ISO, ASTM I. Introduction Coal is a combustible black or dark brown sedimentary rock, fossil fuel and is formed from the decomposition of organic materials originally accumulated in swamps and peat bogs that have been subjected to geologic heat and pressure over millions of years, composed mostly of carbon and hydrocarbons. The degree of change undergone by a coal as it matures from peat to anthracite is known as coalification. The transformation of vegetable matter into peat and coal is commonly regarded as proceeding as two steps, called as biochemical and physicochemical stage of coalification [1] respectively. The results of this process, i.e. the type of peat and coal formed, depend on the phytogenic input and the environmental conditions under which it is transformed into peat. Different biological, chemical and physical constraints result in different peat types which during the subsequent physicochemical coalification are transformed into different coal types without losing their paleoenvironmental signature. Coalification is a dehydrogenation process with a reaction rate slower by many orders of magnitude than that of carbonization. Coalification has an important bearing on coal's physical and chemical properties and is referred to as the 'rank' of the coal. Ranking is determined by the degree of transformation of the original plant material to carbon. The ranks of coals, from those with the least carbon to those with the most carbon, are lignite, sub-bituminous, bituminous and anthracite.

Many classifications of coal are available in literature. Any classification of coal should be scientific and systematic and should take into account the fundamental characters of coal. For example, (a) Classification by visual characters and classification based on their source of genesis was the initial way, which was changed by ultimate analysis: Regnault-Grüner-Brosquet System [2]. (b)Syler’s classification [3] the complete system was published in 1899. His classification divided coal into 7 carbon planes and 2 hydrogen planes, (c) Grout and Ralston classification: In 1907 Grout [4] plotted C (carbon), H(hydrogen), and O(oxygen) contents of American coal on a tri-axial diagram. The plot separated cannel coal (high H) from ordinary coal. Classification was based on dry-ash free analysis including fixed carbon and total carbon. (d) In1915 Ralston [5] extended the study and found coal of equal volatile matter (isovols) and equal calorific value (isocals) can be represented by straight lines in the triangle. (e) Frazer’s classification: in 1877, [6] he used fuel ratio to classify coal as given: Coals of lower rank than bituminous were not considered. Study was on only Pennsylvania coal. He divided four coal type depending on fuel ratio (FR) as anthracite 100-12 2, semi anthracite 8-12 3, semi bituminous 5-8 4.

Bituminous 0-5. (f) Campbell classification: [7] also based on fuel ratio but all coals below 5 FR were taken as bituminous coal. In 1926, he combined fuel ratio to different characteristics for distinguishing lower rank coal.

He divided four coal type depending on fuel ratio as anthracite 10-50 2. semi anthracite 5-10 3. semi bituminous 2.5-5 4. bituminous <2.5. Classification involving both proximate analysis and calorific value: (g) Parr’s classification [8]: considered volatile carbon, total carbon, inert volatile matter and gross coal index (C+ available H+ Sulphur). The basis was volatile carbon*100/total carbon and gave a new classification in 1928 as below - anthracite 0-8 15000-16500, semi anthracite 8-12 15000-16500, bituminous A 12-24 15000-16500, bituminous B 25-50 15000-16500, bituminous C 30-55 14000-15000, bituminous D 35-60 12500-14000, lignite 35-60 11000-12500 and peat 55-80 9000-110000. (h) A.S.T.M. Classification [9]: it classifies coal to 4 broad classes based on fixed carbon and calorific value (BTU) on dry mineral matter free basis. Applicable only to

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vitrinite rich coal and excludes southern Gondwanaland coal. Gross heating value found on a moist and mineral matter free basis. Moist refers to the natural inherent water contained (MJ/kg X 430.11=Btu/lb.). Coals containing 69 wt. % or more fixed carbon on a dry mmf basis are ranked according to their fixed carbon content regardless of their gross heating value. (i) Classification by National Coal Board [10]: specifically designed for commercial use which is rank based. Uses 3-digit code to identify main class, class and subclass to which a coal belongs. Applicable to vitrinite rich coal, volatile matter in dmmf basis and Gray-King coke type values are considered. (j) International Classification of hard coal [11]: mainly for anthracites and bituminous coal but covers fairly all kinds. Uses 14-digit code that defines 8 parameters namely: 1- vitrinite reflectance, 2- inertinite content, 3- exinite/liptinite content, 4- caking property-free swelling index (FSI), 5-VM (volatile matter), 6-ash, 7- S (Sulphur) and 8- gross calorific value. (k) Classification of Indian Coal [12]: scientific coding of Indian coal has 3 basic parameters and 1 supplementary parameter: 1st digit (1-9) corresponds to calorific value (dmmf), 2nd (0-9) one volatile matter (dmmf), 3rd (0-5) one coke type, and 4th (1-6) one: maximum thickness of plastic layer for caking coal and M (moisture) % for non-caking. (l) Grading of Indian Coal [13]: For grading of non-coking coal useful heat value is used, which is calculated by HU= 8900-138(ash + moisture) kcal/kg, which excludes coal from North East India. (m) ISO Standard 11760, Classification of coals [14], was published in 2005. This classification system divides coals into three primary categories, low rank, medium rank, and high rank. The parameters used to classify the coals into the primary ranks and subcategories are vitrinite reflectance, vitrinite content, moisture, and ash yield.

Coal have been classified into many types, grades, ranks etc. mostly on the basis of physico-chemical parameters, utility and commercial aspects. It is interesting to note that all the classification quoted do not refer to Steam Coal. Steam coal, intermediate in rank between subbituminous coal and anthracite according to the coal classification used in the United States and Canada for boilers. In Britain bituminous coal is commonly called “steam coal,” and in Germany the term Steinkohle (“rock coal”) is used. While coking (metallurgical) coal and steam (thermal) coal have similar geologic origins, their commercial markets and industrial uses are vastly different. However, the fundamental difference between two types of coal is in their caking property.

Non-coking coal (usually referred to as thermal coal) cannot form cake when heated in absence of air; whereas, when coking coal is heated in absence of air above 900 degrees (ash fusion temperature) the constituents start fusing and form a large chucky mass, knows as coke. A coking coal if not suitable for metallurgical purpose due to any physico-chemical constraint can be treated as steam coal and can be used as a blend. So the entire range of all chemical properties are covered under the term steam coal, from lignite to anthracite.

Coal is a biochemical sedimentary rock with very high heterogeneity in chemistry both organic as well inorganic components, different maceral constituents, diverse physical properties. Steam coal if blended to meet the commercial criteria, adds more complexity to the physico-chemical properties. The sampling of such heterogeneous mass is very critical. Many published literatures and standards are available for sampling of coal either addresses hard coal or lignite coal, which are not essentially followed by the industry. The purpose of this paper is to examine ways steam coals are sampled and prepared by the end user laboratory, identify the gap in standard & actual practice and what measures to close the opening existing out of inherent shortcomings or need a change in sampling methods, which can improve the quality of the coal it burns for electric generation, thereby gaining both environmental and economic benefits.

II. Sampling Location An estimation of the true value of the desired parameters of a bulk material, to a certain of degree confidence, through analysis on a few grams of test sample is definitely a daunting problem. Location at which the sample is collected is crucial for its representation to the original coal. Coal can be sampled at various locations in a power plant which depends on the objective of the sampling followed by accessibility to coal and coal handling plant layout and method of sampling. It can be done to understand “Incoming Quality” from the delivery vehicles, conveyer belt, feeder to silo or bunker or stockpile, discharge from crusher; or to know the “As fired” quality by taking samples from silo out let, the pulverizer outlet etc. Both the qualities are important for the plant to monitor the plant efficiency with respect to feed quality irrespective of the blend or storage changes. Most of the power plant use blend of different sources and qualities of coal. It’s not only the chemistry of coal, the physical and mineral matter constituents of coal also play an important role in selecting the sampling point. As far as any standard goes, the sampling location is not stringent although it is essential. All the standards should have been strict on this aspect as it plays a major role in deciding the representativeness of the coal if it is sampled for incoming quality where external agency is involved and commercial aspects are obvious. Even a perfect analytical procedure cannot rectify the problems created by faulty sample collection. A good sampling plan will ensure that the samples obtained will, on average, closely represent the bulk composition of the coal being measured. In addition, the sample must be collected and handled in a such way that its chemical composition does not change by the time it is analyzed. Finally, the sampling must be done with the requirements of the analytical method in mind. It is always good to know as much about the sampling site as possible, especially about the sources of the errors being investigated, and the mechanisms for their isolation. Another important consideration in sampling is the physical environment like weather conditions, air temperature, humidity, wind

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speed, rainfall, from both source as well as the point of sampling etc. Normally any sampling scheme is supposed to conform to relevant national or international standards. However, due to technical, cost and time constraints, very often some modifications are made in the method of sampling jointly by the seller and the purchaser. It is a known fact that about 80% of the total variances involved at the different stages of sample collection, preparation and analysis comes from errors during its collection only. The sampling plan describes the overall aims and objectives; it includes specific and practical instructions on what is going to be sampled, how it will be sampled, at what frequency, what the sample will be analyzed for and by whom. An appropriate sampling plan provides transparency to all users and will not only improve the reliability of the results and the level of assurance; it may also help to reduce costs for analyses and verification.

Here are few criteria that must be followed when sampling to ensure the overall precision and accuracy of the results:  Who is responsible for each step?  Where and when are samples taken?  How are the samples taken? E.g. it might be necessary to first clean the system where residues from previous samples might still be contained, etc.  Which instruments are used, if relevant? Describe automatic sampling equipment, but also describe the tools for manual sampling. It might also be important how samples can be picked out from sufficiently deep in a pile of several meter height.  How will the identity of the samples be ensured?  How are the samples stored (dry, cool, dark, inert atmosphere, etc.)?  How and when are increments combined?  When are the samples analyzed, are remaining samples stored after analysis, etc.?  Ensure that the sample is representative of the bulk material, which means all parts of the material being sampled must have an equal probability of being collected and becoming part of the final sample for analysis,  Make sure that the sample does not undergo any chemical or physical changes after completion of the sampling procedure and during the storage prior to analysis  The sample size must be adequate  Choosing appropriate sampling locations also depends on whether coal is received in a batch or a continuous process.  A sampling point must be reasonably accessible to be an effective location. Sampling cannot be performed from a location that cannot be reached. It should be recognized that the best sampling point may not be accessible and that sampling will need to be performed at the next best point of accessibility. Accessibility and safety are related in that a sampling point may be physically accessible, but sampling from that location may present a risk of injury. Once chosen a sampling location, identify the potential risks associated with that location, take the appropriate safety precautions, and provide protective equipment.  Sampling point has an impact on the granulometry of actual vs collected sample  Chute and belt sampling is most economical and representative  It is always desirable to have a second sampling point for cross verification  Assess variability in coal to be sampled: Variability can be distinguished between o Spatial variability - This term refers to the heterogeneity of a material depending on the location, e.g. the heterogeneity within one single batch o Temporal variability - This term takes into account changes of properties over time,  Based on historical data, any variation in the analytical values for the respective fuel or material does not exceed 1/3 of the uncertainty value to which the operator has to adhere with regard to the activity data determination of the relevant fuel or material III. Sampling Method The sampling of coal, whether performed manually or mechanically must extract a quantity of coal much similar than the original lot but with proportionately the same quality. But coal quality is not always uniform, and variability makes it difficult for representativeness. Preliminary to any laboratory testing of coal, it is imperative that a representative sample be obtained; otherwise, the most carefully conducted analysis is meaningless.

Reliable sampling of a complex mixture such as coal is difficult and handling and preparation of the sample for analysis presents further problems. Variations in coal handling facilities make it practically impossible to publish a set of rules that would apply to every manual sampling situation. The proper collection of the sample involves an understanding and consideration of the minimum number and weight of increments, the particle size distribution of the coal, the physical character and variability of the constituents of coal, and the desired precision. The selection of a sampling method depends upon factors such as the sampling purpose, accuracy desired, accessibility of the site and technical, economic and time constraints. Taking a representative sample

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manually from material that is stationary involves very great difficulties and almost invariably can only be realised in a limited manner. Manual sampling techniques, although subject to errors associated with human discretion, may be avoided to effectively collect samples of definable quantity. Automatic sampling system, once designed, installed and tested for a specific plant application will surely produce representative samples in terms of quality as well as cost.

The sampling error is by far the largest component of the total error in the analysis of coal samples. Generally, 80% of the total error is due to some aspect of sampling [15]. Sampling errors are two types – Random and systematic. Random error covers – isolated changes in process, coal heterogeneity, sample quantity etc. But interestingly random errors move both positive and negative direction around mean value and mostly averages out. However, systematic error mainly caused by inaccuracies in the sampling mechanism. This is known as sampling bias. Every end user of coal should consider the sampling bias, which can be done by a statistical comparison of the data from coal collected by the end user lab method and ASTM Stop-belt technique [16].

Hardly, any such data has been generated by the power plant lab to substantiate the bias in the sampling. This should have been a practice with frequent interval for comparison and establishing the sampling bias and it must be an essential part of the standards with defined frequency for comparison. The sampling personnel should also record coal feed rate, sampling speed, number increment, number of increment per averaging period, sampler dimension, total lot size, maintenance breakdown history.

III.A INDIAN STANDARD (IS) Manual Sampling Indian Standards IS: 436 (Part l/Section 1)-1964 (Reaffirmed 2013) [17] for manual sampling, specifies in paragraph 0.3.4.2: “It may, however, be mentioned that the representativeness of the samples drawn in this manner and hence the reliability of the conclusions is not likely to be assured”.

The IS method covers - sampling from conveyers, sampling from wagons during loading or unloading: (These increments shall be drawn with the help of a suitable scoop or shovel, depending upon the size of the coal, at regular intervals at the time of loading or unloading of the wagons, covering at least 25% of wagons. At every selected point a sample shall be collected by taking the whole section of coal from top to bottom over an area of 30 cm diameter), sampling from ships during loading or unloading, sampling from stock pile (the surface of each sub-lot shall be levelled and one point for approximately every 250 metric tons of material in the sub-lot shall be chosen at random. For doing so, coal from the surface up to a depth of, approximately 50 cm shall be collected at first. The bottom of the hole so formed shall then be covered by a plate and the coal lying on the sides shall be removed up to that plate so that when the hole is dug further {to collect further samples}, the coal from the sides may not fill up the hole by falling down. This procedure is repeated till the bottom is reached.

Rarely this sampling procedure is being followed in totality. The reasons are best known to the institutions carrying out the job. Whatever the possible explanations, if a standard method cannot be practiced in totality, we should think the way out for the alternative solutions and amend the standards accordingly, instead of placing a standard name sake in paper.

Mechanical sampling IS: 436 (Part l/Section 2)-1976 (Reaffirmed 2000) [18] and IS 16143: Part 1-8:2014 [19], for mechanical sampling of coal. Mechanical sampling method has taken reference of IS0 1988-1975 [20], which has been withdrawn by TC/SC: ISO/TC 27/SC 4 and replaced by ISO 18283:2006 [21]. The IS standard also refers to Draft BS 1017: Part 1[22] which was withdrawn in 2008 [23]. The referred BS standard changed to BS 1017: Part 1:1989, and further superseded by BS ISO 13909-1-4:2001[24]. Basically, these ISO standards refers to sampling of hard coal.

III.B ISO STANDARD Manual Sampling ISO 18283 [21] defines the basic terms used in manual sampling of hard coal and coke and describes the general principles of sampling. It specifies procedures and requirements for establishing a manual sampling scheme, methods of manual sampling, sampling equipment, handling and storage of samples, sample preparation and a sampling report. This International Standard applies to manual sampling from fuels in movement. Guidelines for manual sampling from fuels in stationary situations are given in Annex B, but this method of sampling does not provide a representative test sample and the sampling report shall state this.

ISO 18283 does not include sampling of brown coals and lignites, which is described in ISO 5069-1:1983 [25] and ISO 5069-2 [26], nor sampling from coal seams, which is given in ISO 14180[27].

Mechanical sampling Mechanical sampling of hard coal and coke is covered in ISO 13909 [24] (all parts). In India very limited use of mechanical sampler is in practice by power plants or suppliers.

III.C ASTM STANDARD Part of Committee D05 on Coal and Coke, the subcommittee’s six task groups develop and maintain guides, practices, and test methods for sampling of coal and coke derived from coal. For coal sampling ASTM has got following standard test methods -

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

D2234/D2234M: Practice for Collection of a Gross Sample of Coal (followed by D2013 Practice for Preparing Coal Samples for Analysis) [28]  D 4916: Standard Practice for Mechanical Auger Sampling; [29]  D 4702: Standard Guide for Inspecting Crosscut, Sweep-Arm, and Auger Mechanical Coal-Sampling Systems for Conformance with Current ASTM Standards; [30]  D 6543: Standard Guide to the Evaluation of Measurements Made by On-Line Coal Analyzers [31]; and  D 6609: Standard Guide for Part-Stream Sampling of Coal. [32]  D7256/D7256M: Practice for Mechanical Collection and Within-System Preparation of a Gross Sample of Coal from Moving Streams [33]. The new standard ASTM D 7256/7256M is a combination of several previous sampling standards and sample preparation ASTM Standard D 2013—Method of Preparing Coal Samples for Analysis [34]  D 7430: Standard Practice for Mechanical Sampling of Coal [35] Historically, the U S Steel Corporation advise removing full cross sectional cut from a stopped belt conveyor or moving stream, but discourage sampling from railroad cars and other stationary sources [36]. The accuracy of sampling procedure can be checked by running a bias test between stopped belt cut and stationary manual sampling. Both automated and manual sampling can be done at various sampling locations as below with a predefined sampling scheme Sampling from moving streams o Sampling from a falling stream o Sampling from a moving belt o Stopped belt sampling  Sampling from stationary coal o Sampling from stockpiles o Sampling from wagons, barges and ships Table 1 Number and weight of increments for general purpose sampling procedure (ASTM D2234/2234M) Top size, mm 16 50 150 Mechanically cleaned coal† Number of increments 15 15 15 Minimum weight of increments, kg 1 3 7 Raw (uncleaned) coal† Number of increments 35 35 35 Minimum weight of increments, kg 1 3 7

For coal above 150 mm top size, the sampling procedure should be mutually agreed upon in advance by all parties concerned† The fundamental requirements of sampling have been explained in OAR/EPA [37]. If there is any doubt as to the condition of the preparation of the coal (for example, mechanically cleaned coal or raw coal) the number of increments for raw coal shall apply. Similarly, although a coal has been mechanically cleaned, it may still show great variation because of being a blend of two different portions of one seam or a blend of two or many different seams. In such cases, the number of increments should be as specified for raw (uncleaned) coal. Sampling should be carried out by systematically sampling either on a time-‐basis or on a mass-‐basis, or by stratified random sampling. The interval between primary increments (Table 1) depends on the size of the sub-lot and the number of primary increments in the sample, and should be determined in accordance with relevant standards. This interval should not be changed during the sampling of the sub-lot.

Following are the points to be considered in the selection of a sampling method which depends upon factors such as the sampling purpose, accuracy desired, accessibility of the site and technical, economic and time constraints. Precision is the closeness of the data to the true value in given conditions as indicated by the reproducibility of the unbiased results. Sampling precision depends on variability of coal, number of samples from a lot, number of increments comprising each sample, and mass of sample relative to the nominal top size.

The testing laboratory should have the supporting data of its precision.

Table 2 Preference Order of coal sampling procedures and methods Sampling procedure Collection method preference Stopped Belt Cut Full stream cut Part Stream cut Stationary Sampling

Automatic Manual Automatic Manual Automatic Manual Automatic Manual

1 2 3 4 5 6 7 8

Manual Sampling – top size, increment design, plan and lot system, frequency of sampling, how to collect a sample from segregated lot, how to access the center point of stock otherwise its peripheral sample, dimension of sampling tool should be sufficient to allow the largest particle to pass freely into it, the first stage of sampling known as primary increments is the collection of an adequate number of coal portions from positions distributed

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over the entire lot, minimum mass of the gross sample relative to the nominal top size, randomness of check and of course the knowledge, experience and safety of sampler. Manual method of wagon top sampling of large sized coals is not only difficult but also violates some of the fundamental principles of sampling. As per requirement samples are to be drawn from the full depth of the wagons which is impossible to be collected manually. Furthermore, due to size segregation the samples collected from the wagon top does not satisfy the criteria of representativeness of the whole samples. Since the ash and mineral matter distribution in the different size fractions of coal or blended steam coal is not homogeneous, results from the samples which do not reflect the true size distribution of the lot are likely to be biased. More importantly, sample collection by a shovel from the top or bottom discharge is a function of human discretion and not governed by the probability rule. Wagon sampling when practiced in other parts of the globe is done on smaller and uniform sized coals, generally washed and blended, and preferably by auto-mechanical auger systems, not by manual methods which is less prominent in Indian context and possibly the major contributor of deviation in test results among the laboratories (Table 2). Coal samples can also be taken from a moving conveyor belt. Manual sampling from stationary coal such as a coal storage pile or railcars is, sometimes, necessary but this is problematic and less representative. Some standards, such as ISO 13909-1 [24] stipulate that manual sampling should not be exercised in cases where the nominal coal top size is above 63 mm or when the coal flow rate is greater than 100 tons per hour. Certainly, for a manual sampling, when the belt stands still, the calculation takes into consideration the length of the conveyor belt on which the material is sampled.

Mechanical Sampling – material flow rate, sampling speed, particle size distribution, sample cutter speed and dimension, in addition to top size and segregation, lot size and shape, sampling variance, location of sampler etc.

IV. Sample preparation The distribution of mineral matter in coal presents problems for the crushing, grinding, and uniform mixing at each step of the sampling procedure. The various densities of the materials found in coal can easily cause their segregation, especially if there is a wide range of particle sizes. Crushing and grinding coal, or both, from a large particle to a very small particle in one operation tends to produce a wide range of particle sizes and a high concentration of very fine particles. The crushing, grinding, and pulverizing should involve a reasonable number of steps, considering the starting particle size and nature of the coal. The samples obtained by quartering on the cement floor were consistently higher in ash than those obtained from the sampling machine, but when the quartering was done on oil cloth the agreement was very close. This would indicate that the high ash in the quartering samples was due to floor dust but more samples should be obtained by quartering on oil cloth before a definite conclusion can be reached. Care to be taken for – feed size, type of crusher, crusher capacity and uniformity in feed rate and product size, step size reduction with screening and atmospheric equilibration, crusher cleanliness to avoid contamination, proper storage of crushed product to avoid any atmospheric loss, room cleanliness, air flow, room temperature & humidity fluctuations etc. Any such variable, which can impact the physico-chemical properties of coal should be monitored and recorded in the lab and its influence is to be quantified as an error or uncertainty in measurement. To minimize the moisture problem, all standard methods include, when necessary, an air-drying stage in the preparation of the analysis sample so that subsequent handling and analysis will be made on a relatively stable laboratory sample with reference to gain or loss of moisture from or to the laboratory atmosphere. The distribution of mineral matter in coal presents problems for the crushing, grinding, and uniform mixing at each step of the sampling procedure. The various densities of the materials found in coal can easily cause their segregation, especially if there is a wide range of particle sizes.

Too many handling steps will increase the exposure of the coal to air and increase the chance of moisture changes and oxidation in low rank coals.

ASTM Method IV.A Gross Sample In ASTM gross sample is defined as a sample representing a quantity, or lot, of coal and is composed of a number of increments on which neither reduction nor division has been performed.

A lot is a discrete quantity of coal for which the overall quality to a particular precision needs to be determined.

Minimal quantity of sample depends on top size, mineral characteristics, variation in the valuable component content, coal density, grain shape, content, uniformity and size of mineral matters. For quantities of coal up to approximately 1000 tons it is recommended that the one gross sample represent the lot. The number of increments to be taken for the gross sample depends on the type of coal being sampled (35 for raw coal and 15 for mechanically cleaned coal). The size of each increment depends on the top size (granulometry) of the coal being sampled. The ASTM general purpose sampling procedures are designed to give a precision such that if gross samples are taken repeatedly from a lot or consignment and one ash determination is made on the analysis sample from each gross sample, 95 out of 100 of these determinations will fall within ±10 %of the average of all determinations.

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IV.B Laboratory Sample Once a gross sample has been taken, it is reduced in both particle size and quantity to yield a laboratory sample.

The particle size distribution, or nominal top size, of the laboratory sample depends on its intended use in the laboratory and the nature of the tests to be run. The minimum allowable weight of the sample at any stage of reduction depends on the size consist, the variability of the constituents sought, and the degree of precision desired.

IV.C Analysis Sample The subsample is reduced to 100% through a number 60# (250 µm) sieve and then divided to not less than 50 g, which is called the analysis sample and is required for most ASTM laboratory tests.

Many problems may arise during the sampling and sample preparation processes [38], such as  the loss or gain of moisture, due to uncontrolled lab atmosphere  improper mixing of constituents, due granulometry & HGI (in blended coals), feed rate and crusher type  improper crushing and grinding due to mineral matter, feed rate and crusher type etc.  contamination of the sample by equipment improper cleaning  oxidation of coal due to atmospheric exposure  As the crusher wear, the top size of the crushed product will grow and hammer/screen replacement should take place before this exceeds acceptable limits and clearance between wear plates and the rotor assembly can also influence the top size of the crushed product. The major sampling risk of poor crusher inspection & maintenance to the moisture integrity of the coal – either directly through excessive drying or indirectly through improper save sample sizing contributing to sample preparation error.

To minimize the moisture problem, all standard methods include, when necessary, an air-drying stage in the preparation of the analysis sample so that subsequent handling and analysis will be made on a relatively stable laboratory sample with reference to gain or loss of moisture from or to the laboratory atmosphere. [39] Coal is susceptible to oxidation at room temperature, especially the low rank steam coal. Like moisture changes, such oxidation has to be considered in sampling, preparing, and storing samples. Comparison of moisture and ash-free MAF (Kcal/kg) values is often useful for evaluating suspected oxidation problems. Containers should be selected that will hold only the required amount of sample and leave a very minimum of air space. Even when such precautions are taken, the samples change very quickly, so the analysis of a sample should be carried out as soon as possible after it is received.

V. Conclusion In analyzing coal samples for their chemical composition, it is apparent that certain current standard test methods for sampling and sample preparation either require modification or they are not fully applied by the end users of coal. Obtaining a representative sample implies that every particle has a chance of being selected. A correct and representative sample requires that every particle in a lot being sampled is equally represented. A representative sample is collected by taking a definitive number increments, periodically throughout the entire coal lot being sampled. The number and weight of increments required for a desired degree of precision depends on the variability of the coal which increases with increasing impurities. The sampling of coal can take place from either stationary lots or from moving streams. Sampling from stationary lots is particularly problematic because in many cases it is not in compliance with the fundamental sampling principle stipulating that all parts of the lot being sampled must be accessible for physical sampling. Therefore, sampling from moving streams is preferred. The best location for sampling from a moving stream is at the discharge point of a conveyor belt or chute, that is a falling stream where the complete stream can be intersected at regular intervals. However, cross-belt cutters are now more popular and are widely used in the coal industry. Accurate coal sampling of it requires that you obtain all the various size gradients it contains in their proper proportion with each sample increment. While this is impossible to accomplish from a stockpile or from the top of a truck, railcar or barge, it can be accomplished from the surface of a conveyor belt. The stopped belt sampling, when properly executed, is considered as bias free and is recommended by several standards as a reference sampling method when carrying out a bias test procedure. This should have been a practice with frequent interval for comparison and establishing the sampling bias and it must be an essential part of the standards with defined frequency for comparison. Thus, the summary or the total error of sample preparation, excluding the sampling error, consists of the error of the sample division due to the inadequate homogenization during the treatment and error from insufficient number of pieces in the sample, i.e. the inadequate sample mass, as well as the error of the chemical analysis [8]. Since the error from the insufficient sample mass is included in the total error, and because the error resulting from the inaccuracy of the sample division is insuperable, the former error is not possible to determine. Still, a careful operation of the sample division during the homogenization can reduce the specific error to a constant value. Consequently, the variation of the total error from one set to another will be a result of the disproportion between the sample mass and the grain size in the mixture. All sampling systems should be checked for bias, because systematic errors may be introduced. These systematic errors generally are caused by a loss or gain in the mass of increments during collection or by cyclical variations of coal quality at time intervals coinciding with systematic sampling time. Bias testing is

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discussed in certain standards, such as ISO/DIS 13909 Part 8 [24] for bias testing of mechanical samplers and in ASTM D4702 [30] with guidelines for inspecting cross-cut, sweep arm, and auger mechanical sampling systems. Coal analysis, and possibly in most new uses of coal, will require higher standards of quality control and accuracy than are currently quoted in many of the existing standard test methods and practices by the laboratories in India. These factors will become increasingly more important when economic decisions must be made based on the validity, i.e., Accuracy, Bias, Interlab Tolerance, Measurement Uncertainty of coal analysis data ISO’s Published Document – Guide to the Expression of Uncertainty in Measurement (1995) (known as GUM); published in 1993, reprinted with corrections in 1995) [40-42]. It’s worth to mention here that many of the coal testing laboratories are accredited to ISO 17025 "General Requirements for the Competence of Testing and Calibration Laboratories” [43], states that " where applicable, a statement on the estimated uncertainty of measurement; information on uncertainty is needed in test reports when it is relevant to the validity or application of the test results, when a customer's instruction so requires, or when the uncertainty affects compliance to a specification limit; ". It has been seen that the total cost of a sampling system in a coal handling plant is very low in comparison to the overall cost of the plant (less than 1%) is either not included in the system and if included is put out of commission for various reasons which could be easily over-come. Automatic samplers although slightly higher initial cost can save many hours of costly operator-time while producing reliable and representative sample. In most cases investment in sampling system will still be a fraction of what is expended on the analysis, but the analysis can only be as reliable as the sample delivered to the laboratory.

Ultimately, all of us agree to the fact that sampling is not an art but processes and methods that characterize it neither depend on contingent social and ethical values, nor on the individual bias of a scientist but part of science.

VI. References [1]. Stach, E. M. et al. 1982, Stach’s Textbook of Coal Petrology, Borntraeger Brothers, Stuttgart, 535p.

[2]. Grout, F. F., 1909, Composition of Coals, Econ. Geol, 2, p 225, 1907; 4, p 646, 1909; 4, P663, 1909.

[3]. Seyler, S. C, 1924, Chemical Classification of Coal, Fuel in Science and Practice, No 3, p 15, 41,79; Petrology and Classification of Coal, Op. cit., 17, P 177, 200, 235,1938.

[4]. Ralston, O. C., Graphic Studies in Ultimate Coal Analysis of Coal, U. S. Bur. Mines Tech Paper 93.

[5]. Rogers, H. D., 1858, Geol. Pa., Vol 1, 59, 104-109; Vol 2, 2, P 751-775.

[6]. Frazer, Jr., P’ 1877, “Classification of Coals," Am. Inst. Min. Eng., vol. 6, p. 430.

[7]. Campbell, M. R., 1905, "The Classification of Coals," Bulletin Am. Inst. Min. Eng., p. 1033; and "The Classification of Coals," Report of Coal Testing Plant, U. S. Geological Survey, St. Louis, Professional Paper, U. S. Geological Survey No. 48, Part I, pp. 156-173.; Internat. Conf. Bitum. Coal at Pittsburgh, 1926, Vol1, P 632-661 [8]. Parr, S. W.; 1906, The Classification of Coal, Jour. Amer. Chem. Soc., Vol 28, P 1425; Jour. Ind. Eng. Chem., 14, P919, 1922. file:///D:/Paper%204/engineeringexperv00000i00180.pdf [9]. ASTM Standard Classification of Coals by Rank, ASTM D 338, Vol 5.06, 2015, http://www.astm.org/Standards/D388.htm [10]. The Coal Classification System Used by the National Coal Board. Revision of 1964, https://books.google.co.in/books/about/The_Coal_Classification_System_Used_by_t.html?id=DBoIMwEACAAJ&redir_esc=y [11]. International Codification system for medium and high rank coals, 1988, http://www.unece.org/fileadmin/DAM/ie/se/pdfs/codee.pdf [12]. Coal Directory of India, 2011 – 2012, Coal Statistics, p 1.5, http://coal.nic.in/sites/upload_files/coal/files/coalupload/coaldir11-12.pdf [13]. Grading of Indian Coals, http://coal.nic.in/content/coal-grades [14]. ISO Standard 11760, Classification of Coals, International Organization for Standardization,1, Rue deVarembe, Case Postale 56, CH1211, Geneva 20, Switzerland.

[15]. Aresco, S. J and Oring, A. A.; 1965, A study of the precision of coal sampling, sample preparation and analysis, Transactions, Society of Mining Engineers/AIME, Vol 232, P 258-264.

[16]. Annual Book ASTM Standards, Part 26, 1981, P 920 [17]. Indian Standards IS: 436 (Part l/Section 1)-1964 (Reaffirmed 2013) [18]. Indian Standard Methods for Sampling of Coal and Coke Part I Sampling of Coal Section 2 Mechanical Sampling IS: 436 (Part I/Set 2) – 1976, (Reaffirmed 2000) https://law.resource.org/pub/in/bis/S11/is.436.1.2.1976.pdf [19]. BIS IS 16143: Part 1-8:2014 BIS IS 16143-1:2014, Hard Coal and Coke - Mechanical Sampling [20]. ISO 1988:1975, Hard coal – Sampling [21]. ISO 18283:2006, Hard coal and coke — Manual sampling, further amended ISO 18283:2006/Cor.1:2009.

[22]. BS 1017-1:1989, Sampling of coal and coke. Methods for sampling of coal [23]. http://shop.bsigroup.com/ProductDetail/?pid=000000000000211003 [24]. ISO 13909-1-8:2001, Hard coal and coke — Mechanical sampling [25]. ISO 5069-1:1983, (Reviewed 2013) Brown coals and lignites -- Principles of sampling -- Part 1: Sampling for determination of moisture content and for general analysis [26]. ISO 5069/2-1983 (Reviewed 2013) Brown coals and lignites - Principles of sampling - Part 2: Sample preparation for determination of moisture content and for general analysis [27]. ISO 14180:1998, Solid mineral fuels -- Guidance on the sampling of coal seams.

[28]. ASTM D2234/D2234M, 2010, Standard Practice for Collection of a Gross Sample of Coal [29]. ASTM D4916-04, Standard Practice for Mechanical Auger Sampling (Withdrawn 2008) [30]. ASTM D4702-07, Standard Practice for Quality Management of Mechanical Coal Sampling Systems (Withdrawn 2008) [31]. ASTM D6543 – 15, Standard Guide to the Evaluation of Measurements Made by Online Coal Analyzers [32]. ASTM D6609 - 08(2015), Standard Guide for Part-Stream Sampling of Coal [33]. ASTM D7256/D7256M-08, Standard Practice for Mechanical Collection and Within-System Preparation of a Gross Sample of Coal from Moving Streams (Withdrawn 2008) [34]. ASTM D2013 / D2013M – 12, Standard Practice for Preparing Coal Samples for Analysis [35]. ASTM D7430 - 15b, Standard Practice for Mechanical Sampling of Coal [36]. U.S. Steel Corporation, Sampling and Analysis of Coal and Coke, Pittsburgh, PA, 1929, 334pp

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D. Mahapatra, American International Journal of Research in Science, Technology, Engineering & Mathematics, 13(1), December, 2015February, 2016, pp. 01-09 [37]. OAR/EPA (2009) Proposed rule for mandatory reporting of greenhouse gases. Technical support document – The coal sectors, Washington, DC, USA, Office of Air and Radiation, US Environmental Protection Agency, 53 pp (Jan 2009) [38]. Qian Zhu, 2014, Coal sampling and analysis standards, http://www.usea.in/sites/default/files/042014_Coal%20sampling%20and%20analysis%20standards_ccc235.pdf [39]. John T. Riley, 2007, Routine Coal and Coke Analysis: Collection, Interpretation, and Use of Analytical Data, ASTM Stock No. MNL57.

[40]. ISO’s Published Document – Guide to the Expression of Uncertainty in Measurement (1995) (known as GUM); published in 1993, reprinted with corrections in 1995)., [41]. JCGM 104:2009, Evaluation of measurement data – An introduction to the "Guide to the expression of uncertainty in measurement" and related documents, [42]. JCGM 106:2012, Evaluation of measurement data – The role of measurement uncertainty in conformity assessment [43]. ISO 17025-2005, General requirements for the competence of testing and calibration laboratories

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â&#x192;&#x2014; ,đ??&#x2021; â&#x192;&#x2014;â&#x192;&#x2014; ) and Lagrange Formalism for Electron Field in Terms of Strengths (đ??&#x201E; â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; , â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; (đ??&#x201E;Ë&#x160; đ??&#x2021;Ë&#x160;) Dr. Bulikunzira Sylvestre University of Rwanda University Avenue, B.P 117, Butare Telephone number: +250788423056 Abstract: In previous works, spinor Dirac equation for half-spin particle has been written in tensor form,in â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; , đ??ťË&#x160; â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; ). It â&#x192;&#x2014; ) and (đ??¸Ë&#x160; the form of non-linear Maxwellâ&#x20AC;&#x2122;s like equations, through two electromagnetic fields (đ??¸â&#x192;&#x2014; , đ??ť 2 2 â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; â&#x192;&#x2014; â&#x192;&#x2014; â&#x192;&#x2014; â&#x192;&#x2014; â&#x192;&#x2014; â&#x192;&#x2014; has been proved, that the fields (đ??¸ , đ??ť ) and (đ??¸Ë&#x160;, đ??ťË&#x160;) satisfy non-linear conditions đ??¸ = đ??ť and đ??¸ . đ??ť = 0. â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; , đ??ťË&#x160; â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; ) have the same properties as those of the â&#x192;&#x2014; ) and (đ??¸Ë&#x160; Further, it has been proved, that the fields (đ??¸â&#x192;&#x2014; , đ??ť â&#x192;&#x2014; ), components of electromagnetic tensor đ??šđ?&#x153;&#x2021;đ?&#x153;&#x2C6; . On the other hand, it has been proved, that the strengths (đ??¸â&#x192;&#x2014; , đ??ť solution of these non-linear equations for free particle fulfils Maxwellâ&#x20AC;&#x2122;s equations for vacuum (with zero at the right side). In this work, in the development of the above mentioned ideas, we elaborated the Lagrange â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; , â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; â&#x192;&#x2014; ) and (đ??¸Ë&#x160; formalism for electron field in terms of strengths (đ??¸â&#x192;&#x2014; , đ??ť đ??ťË&#x160;).

Keywords: Dirac equation, tensor formalism, Lagrange formalism, strengths.

I. Introduction In previous works, Dirac equation for half-spin particle such as electron has been written in tensor form, through â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; . It has been proved, that the complex vectors â&#x192;&#x2014;â&#x192;&#x2014; and â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; two complex isotropic vectors â&#x192;&#x2014;F = â&#x192;&#x2014;E + iH FË&#x160; = â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; EË&#x160; â&#x2C6;&#x2019; iHË&#x160; 2 â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; satisfy non-linear condition â&#x192;&#x2014;F 2 = 0 and â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; â&#x192;&#x2014;F = â&#x192;&#x2014;E + iH â&#x192;&#x2014;â&#x192;&#x2014; and â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; FË&#x160; = â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; EË&#x160; â&#x2C6;&#x2019; iHË&#x160; FË&#x160; = 0. The last condition is equivalent â&#x192;&#x2014; 2 = 0 and â&#x192;&#x2014;E. â&#x192;&#x2014;H â&#x192;&#x2014; = 0, obtained by separating real and imaginary parts to two conditions for real quantities â&#x192;&#x2014;E 2 â&#x2C6;&#x2019; â&#x192;&#x2014;H 2 â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; , HË&#x160; â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; ) fulfils Maxwellâ&#x20AC;&#x2122;s â&#x192;&#x2014; = 0. Further, it has been proved, that each of the fields (E â&#x192;&#x2014; ,H â&#x192;&#x2014;â&#x192;&#x2014; ) and (EË&#x160; in equality F equations for vacuum (with zero at right side).

In the development of the above ideas, in this work, we shall elaborate the Lagrange formalism for electron field â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; , â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; â&#x192;&#x2014; , â&#x192;&#x2014;H â&#x192;&#x2014; ) and (EË&#x160; in tensor formalism, in terms of strengths (real quantities (E HË&#x160;)).

II. Research Method In previous works, via Cartan map, Dirac equation for electron has been written in tensor form, in the form of â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; , â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; â&#x192;&#x2014; ,H â&#x192;&#x2014;â&#x192;&#x2014; ) and (EË&#x160; non-linear Maxwellâ&#x20AC;&#x2122;s like equations, through two electromagnetic fields (E HË&#x160;).

In this work, starting with the Lagrangian of electron field in spinor formalism and using the same method, based on Cartan map, we shall write the Lagrangian of electron field in tensor formalism, through the strengths â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; , HË&#x160; â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; ). Finally, using Noether's theorem, we shall derive expressions for fundamental dynamical â&#x192;&#x2014; ,H â&#x192;&#x2014;â&#x192;&#x2014; ) and (EË&#x160; (E variables (energy, momentum, charge and spin) conserved in time.

III. Spinor Formulation of Dirac Equation Relativistic particle with spin 1â &#x201E;2 and different from zero rest mass is described by the wave equation, proposed by Dirac in 1928. This equation, written in symmetric form is (γΟ â&#x2C6;&#x201A;Îź â&#x2C6;&#x2019; m)Ď&#x2C6;=0.

(1) Here γΟ are square matrices of 4đ?&#x2018;Ąâ&#x201E;&#x17D; rank, satisfying the relations (Clifford-Dirac algebra) γΟ γν +γν γΟ =2δΟν , (2) Where Îź, ν=0,1,2,3.

It is natural to emphasize, that in general, Dirac matrices γΟ are defined with accuracy to correspondence transformation. Thus, the representation of these matrices can be chosen in different forms. Ordinary, it is commonly used the representation of Dirac matrices in which γ0 is diagonal:

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I 0 ⃗]. γ0 = [ ], γ=[ 0 σ (3) 0 −I −σ ⃗ 0 Here σ ⃗ are second rank Pauli spin matrices, having the form 0 1 0 −i 1 0 σ1 = [ ], σ2 =[ ], σ3 =[ ].

(4) 1 0 i 0 0 −1 This representation is often called the standard representation.

In this representation, Dirac bispinor ψ is written as φ Ψ=( χ ) .

(5) Here φ, χ are tridimensional (but two components) Pauli spinors.

Using formulas (3) and (5), equation (1) can be written in the form of a system of two equations: p φ − (p ⃗σ ⃗ )χ = −m φ { 0 .

(6) p0 χ − (p ⃗σ ⃗ )φ = mχ μ Another representation of Dirac matrices is the spinor representation. In this representation γ -matrices and Dirac bispinor ψ are written in the form 0 I ⃗ ], γ0 =[ ], γ=[0 −σ (7) I 0 ⃗ σ 0 ξ Ψ=( ).

(8) η With the help of formulas (7) and (8), Dirac equation (1) can be written in the form of a system of two equations (p0 + (p ⃗σ ⃗ )) η = mξ { (9) (p0 − (p ⃗σ ⃗ ))ξ = mη.

It follows from equation (1), that each component of the wave function ψ satisfies the Klein-Gordon equation (□ − m2 )ψi = 0.

(10) ∂ 2 ⃗ Where i=1,2,3,4; □= 2-∇ − DˊAlembert operator . ∂t

IV. Lagrangian for Electron Field in Terms of Strengths In previous works, using Cartan map, Dirac equation for electron (γμ ∂μ − m)ψ = 0, has been written in tensor form as follows ⃗ ⃗​⃗​⃗ ⃗​⃗ Fi ) − iD ⃗​⃗ × ⃗F = − m F×Fˊ1⁄2 D0 ⃗F + vi (D √2 (F ⃗ .F ⃗ ˊ)

⃗​⃗ Fˊi ) + iD ⃗​⃗ × ⃗​⃗​⃗ D0⃗​⃗​⃗ Fˊ − vˊi (D Fˊ = −

m

⃗F×Fˊ ⃗​⃗​⃗

√2 (F ⃗ .F ⃗ ˊ) { Where ⃗ =E ⃗ + iH ⃗​⃗ , F ⃗​⃗​⃗ ⃗​⃗​⃗ ⃗​⃗​⃗​⃗ , Fˊ = Eˊ − iHˊ are two complex isotropic vectors, and ⃗ ×H ⃗​⃗ i ∂ E ⃗D ⃗ = − i ⃗∇, D0 = , ⃗v = 2 .

2 ∂t

2

.

(11)

(12)

1⁄2

(13) (14) (15)

⃗E

Here we use the natural system of units in which c=ћ=1.

Separating real and imaginary parts in equations (12), we obtain a system of non-linear Maxwell’s like ⃗​⃗​⃗ , ⃗​⃗​⃗​⃗ ⃗ ,H ⃗​⃗ ) and (Eˊ equations for strengths (E Hˊ) ⃗​⃗

⃗ + ∂H = vi (∇ ⃗ Hi ) + mj rotE a ∂t ⃗ ∂E

⃗​⃗ − rotH ⃗​⃗​⃗ + rotEˊ

∂t ⃗​⃗​⃗​⃗ ∂Hˊ

⃗ Ei ) + mj = −vi (∇ v ⃗ Hˊi ) − mj = −vˊi (∇ a

∂t ⃗​⃗​⃗ ∂Eˊ

⃗​⃗​⃗​⃗ − { rotHˊ

∂t

.

(16)

⃗ Eˊi ) + mj = vˊi (∇ v

Here ja = √2

⃗ ×Eˊ ⃗​⃗​⃗ +H ⃗​⃗ ×Hˊ ⃗​⃗​⃗​⃗ ) cosφ⁄2+(H ⃗​⃗ ×Eˊ ⃗​⃗​⃗ +Hˊ ⃗​⃗​⃗​⃗ ×E ⃗ ) sinφ⁄2 (E 2

2

2

2

⃗ ⃗​⃗​⃗ ⃗​⃗ ⃗​⃗​⃗​⃗ ⃗ ⃗​⃗​⃗ ⃗​⃗ ⃗​⃗​⃗​⃗ ⃗ ⃗​⃗​⃗​⃗ ⃗​⃗​⃗ ⃗H ⃗ ) +2(E ⃗ ⃗​⃗​⃗​⃗ ⃗​⃗​⃗ ⃗H ⃗ )] [(E Eˊ) +(H Hˊ) 2(E Eˊ)(H Hˊ)+(E Hˊ) +(Eˊ Hˊ)(Eˊ

jv = −√2

1⁄4

,

⃗ ×Eˊ ⃗​⃗​⃗ +H ⃗​⃗ ×Hˊ ⃗​⃗​⃗​⃗ ) sinφ⁄2 +(H ⃗​⃗ ×Eˊ ⃗​⃗​⃗ +Hˊ ⃗​⃗​⃗​⃗ ×E ⃗ ) sinφ⁄2 (E 2

2

2

2

⃗ Eˊ ⃗​⃗​⃗ ) +(H ⃗​⃗ Hˊ ⃗​⃗​⃗​⃗ ) 2(E ⃗ Eˊ ⃗​⃗​⃗ )(H ⃗​⃗ Hˊ ⃗​⃗​⃗​⃗ )+(E ⃗ Hˊ ⃗​⃗​⃗​⃗ ) +(Eˊ ⃗​⃗​⃗ ⃗H ⃗ ) +2(E ⃗ Hˊ ⃗​⃗​⃗​⃗ )(Eˊ ⃗​⃗​⃗ ⃗H ⃗ )] [(E ⃗​⃗​⃗ H ⃗​⃗ −E ⃗ Hˊ ⃗​⃗​⃗​⃗ Eˊ ⃗​⃗ Hˊ ⃗​⃗​⃗​⃗ EEˊ+H

φ = tan−1 ⃗ ⃗​⃗​⃗

.

AIJRSTEM 15-808; © 2015, AIJRSTEM All Rights Reserved

1⁄ 4

(17) ,

(18) (19)

Page 11

Bulikunzira Sylvestre., American International Journal of Research in Science, Technology, Engineering & Mathematics, 13(1), December, 2015-February, 2016, pp. 10-13

⃗​⃗​⃗ and ⃗H ⃗​⃗​⃗​⃗ , we obtain a simple system ⃗ //Hˊ In particular, when φ = 0, i.e., ⃗E//Eˊ ⃗​⃗

⃗ + ∂H = vi (∇ ⃗ Hi ) + √2m rotE ∂t

⃗ ×Eˊ ⃗​⃗​⃗ +H ⃗​⃗ ×Hˊ ⃗​⃗​⃗​⃗ E ⃗ ⃗​⃗​⃗ ⃗​⃗ ⃗​⃗​⃗​⃗ (E Eˊ+H Hˊ)

⃗

1⁄2

⃗H ⃗ ×Eˊ ⃗​⃗​⃗ +Hˊ ⃗​⃗​⃗​⃗ ×E ⃗

⃗​⃗ − ∂E = −vi (∇ ⃗ Ei ) + √2m rotH

1⁄2

∂t

⃗ Eˊ ⃗​⃗​⃗ +H ⃗​⃗ Hˊ ⃗​⃗​⃗​⃗ ) (E

⃗​⃗​⃗​⃗

(20)

1⁄2

∂t

⃗​⃗​⃗ ∂Eˊ

.

⃗ ×Eˊ ⃗​⃗​⃗ +H ⃗​⃗ ×Hˊ ⃗​⃗​⃗​⃗ E

⃗​⃗​⃗ + ∂Hˊ = −vˊi (∇ ⃗ Hˊi ) − √2m rotEˊ

⃗ ⃗​⃗​⃗ ⃗​⃗ ⃗​⃗​⃗​⃗ (E Eˊ+H Hˊ)

⃗H ⃗ ×Eˊ ⃗​⃗​⃗ +Hˊ ⃗​⃗​⃗​⃗ ×E ⃗

⃗​⃗​⃗​⃗ − ⃗ Eˊi ) + √2m rotHˊ = vˊi (∇ 1⁄2 ∂t ⃗ Eˊ ⃗​⃗​⃗ +H ⃗​⃗ Hˊ ⃗​⃗​⃗​⃗ ) { (E Spinor Dirac equation (11) can be obtained by variation principle from the Lagrange function L = (ψ ̅γμ ∂μ − mψ ̅ )ψ + h. c.

Using the spinor representation of γμ -matrices, formula (21) can be written in the form L = {ξ+ [p0 ξ − (p⃗ . σ ⃗ )ξ − mξ] + η+ [p0 η + (p ⃗.σ ⃗ )η − mη]}, where ∂ ⃗. p0 = i , p⃗ = −i∇ ∂t Applying Cartan map, formula (22) can be written in vector form as follows ⃗​⃗ Fi ) − iD ⃗​⃗ × ⃗F + L = [D0 ⃗F + vi (D m

⃗F×Fˊ ⃗​⃗​⃗

√2 (F ⃗ Fˊ ⃗​⃗​⃗ ⁄2)

1⁄2

⃗​⃗​⃗ Fˊ

]

(22)

∗

⃗F×Fˊ ⃗​⃗​⃗

m

(21)

1⁄2

√2 (F ⃗ Fˊ ⃗​⃗​⃗ ⁄2)

⃗F

]

∗

⃗ ⃗F ⁄2) (F

1⁄2

⃗​⃗ Fˊi ) + iD ⃗​⃗ × ⃗​⃗​⃗ + [D0 ⃗​⃗​⃗ Fˊ − vˊi (D Fˊ +

∗

.

1⁄2

∗

⃗​⃗​⃗ ⃗​⃗​⃗ (Fˊ Fˊ ⁄2)

(23) Calculating the first term, we obtain

⃗ ⃗​⃗​⃗ ⃗​⃗

⃗​⃗​⃗​⃗

⃗F×Fˊ ⃗​⃗​⃗

m

⃗​⃗ Fi ) − iD ⃗​⃗ × ⃗F + [D0 ⃗F + vi (D

1⁄2

√2 (F ⃗ ⃗​⃗​⃗ Fˊ⁄2)

⃗ F

]

∗

∗

⃗ ⃗F ⁄2) (F

⃗​⃗ 1 ⃗ ∂H {[−E ⃗| 2|E ∂t

=

1⁄2

⃗​⃗

⃗

⃗​⃗​⃗

⃗ Hi ) − ⃗E. ⃗∇ × ⃗E + + ⃗Evi (∇ ⃗ ⃗​⃗​⃗​⃗

⃗​⃗

) ) ⃗ (E×Eˊ+H×Hˊ ⃗​⃗ ∂E ⃗​⃗ ⃗ ⃗​⃗ ⃗ ⃗​⃗ ⃗​⃗ (H×Eˊ−E×Hˊ ⃗​⃗ ∂H ⃗​⃗ ⃗ ⃗​⃗ ⃗ ⃗ √2mE 1⁄2 + H ∂t − H. vi (∇Ei ) − H. ∇ × H + √2mH 1⁄2 ] + i [H ∂t − Hvi (∇Ei ) − H. ∇ × E − ⃗ ⃗​⃗​⃗ ⃗​⃗ Hˊ ⃗​⃗​⃗​⃗ ) (E Eˊ+H

⃗​⃗ √2mH

⃗ Eˊ ⃗​⃗​⃗ +H ⃗​⃗ Hˊ ⃗​⃗​⃗​⃗ ) (E

⃗ ×Eˊ ⃗​⃗​⃗ +H ⃗​⃗ ×Hˊ ⃗​⃗​⃗​⃗ ) (E 1⁄2

⃗ ⃗​⃗​⃗ ⃗​⃗ ⃗​⃗​⃗​⃗ (E Eˊ+H Hˊ)

+ ⃗E

⃗ ∂E ∂t

⃗ Ei ) − ⃗E. ⃗∇ × ⃗H ⃗ + √2mE ⃗ − ⃗E. vi (∇

⃗​⃗ ×Eˊ ⃗​⃗​⃗ −E ⃗ ×Hˊ ⃗​⃗​⃗​⃗ ) (H 1⁄2

⃗ ⃗​⃗​⃗ ⃗​⃗ ⃗​⃗​⃗​⃗ (E Eˊ+H Hˊ)

]}.

(24)

Calculating the second term, we obtain ⃗​⃗ Fˊi ) + iD ⃗​⃗ × ⃗​⃗​⃗ [D0⃗​⃗​⃗ Fˊ − vˊi (D Fˊ + ⃗ ⃗​⃗​⃗

⃗​⃗

⃗​⃗​⃗​⃗

m

⃗F×Fˊ ⃗​⃗​⃗

√2 (F ⃗ Fˊ ⃗​⃗​⃗ ⁄2)

1⁄2

⃗​⃗​⃗ Fˊ

]

∗

∗

⃗​⃗​⃗ ⃗​⃗​⃗ (Fˊ Fˊ ⁄2)

1⁄2

=

⃗​⃗ 1 ⃗​⃗​⃗ ∂Hˊ {[Eˊ ⃗​⃗​⃗ | 2|Eˊ ∂t ⃗​⃗

⃗​⃗​⃗

⃗ ˊvˊi (∇ ⃗ Hˊi ) + ⃗​⃗​⃗ ⃗ × ⃗​⃗​⃗ +E Eˊ. ∇ Eˊ + ⃗​⃗​⃗

⃗ ⃗​⃗​⃗​⃗

⃗​⃗​⃗​⃗

) ) ⃗​⃗​⃗ (E×Eˊ+H×Hˊ ⃗​⃗​⃗​⃗ ∂Eˊ ⃗​⃗​⃗​⃗ ⃗​⃗​⃗​⃗ ⃗ ⃗​⃗​⃗​⃗ ⃗​⃗​⃗​⃗ (H×Eˊ−E×Hˊ ⃗​⃗​⃗​⃗ ∂Hˊ ⃗​⃗​⃗​⃗ ⃗ ⃗ √2mEˊ 1⁄2 − Hˊ ∂t − Hˊ. vˊi (∇Eˊi ) + Hˊ. ∇ × Hˊ − √2mHˊ 1⁄2 ] + i [Hˊ ∂t − Hˊvˊi (∇Eˊi ) − ⃗ ⃗​⃗​⃗ ⃗​⃗ ⃗​⃗​⃗​⃗ (E Eˊ+H Hˊ)

⃗ ⃗​⃗​⃗ ⃗​⃗ ⃗​⃗​⃗​⃗ (E Eˊ+H Hˊ)

⃗ ⃗​⃗​⃗ ⃗​⃗

⃗​⃗​⃗​⃗

⃗​⃗

⃗​⃗​⃗

⃗​⃗​⃗

⃗ ⃗​⃗​⃗​⃗

) ) ⃗​⃗​⃗​⃗ ⃗​⃗​⃗​⃗ (E×Eˊ+H×Hˊ ⃗​⃗​⃗ ∂Eˊ + ⃗​⃗​⃗ ⃗​⃗​⃗ (H×Eˊ−E×Hˊ ⃗ Eˊi ) − ⃗Eˊ. ⃗∇ × ⃗​⃗​⃗​⃗ Hˊ. ⃗∇ × ⃗​⃗​⃗ Eˊ + √2mHˊ Eˊ. vˊi (∇ Hˊ + √2mEˊ 1⁄2 + Eˊ 1⁄2 ]}. ∂t

⃗ ⃗​⃗​⃗ ⃗​⃗ ⃗​⃗​⃗​⃗ (E Eˊ+H Hˊ)

⃗ ⃗​⃗​⃗ ⃗​⃗ ⃗​⃗​⃗​⃗ (E Eˊ+H Hˊ)

(25) Finally, combining formulae (24) and (25), we find the Lagrange function for electron field in terms of strengths ⃗​⃗​⃗ , ⃗H ⃗ , ⃗H ⃗ ) and (Eˊ ⃗ ˊ) in the form (E ⃗ ⃗​⃗​⃗ ⃗​⃗

⃗​⃗

⃗​⃗​⃗​⃗

⃗

) 1 1 ⃗ ∂H + ⃗Evi (∇ ⃗ Hi ) − ⃗E. ⃗∇ × ⃗E + √2mE ⃗ (E×Eˊ+H×Hˊ ⃗​⃗ ∂E − ⃗H ⃗ . vi (∇ ⃗ Ei ) − ⃗H ⃗ . ⃗∇ × ⃗H ⃗ + L = {[ ⃗ (−E 1⁄2 + H 2

|E|

⃗​⃗

⃗​⃗​⃗

∂t

⃗ ⃗​⃗​⃗ ⃗​⃗ ⃗​⃗​⃗​⃗ (E Eˊ+H Hˊ)

⃗ ⃗​⃗​⃗​⃗

∂t

⃗ ⃗​⃗​⃗

⃗​⃗

⃗​⃗

⃗​⃗​⃗​⃗

⃗​⃗​⃗

) ) 1 ⃗​⃗​⃗ ∂Hˊ + ⃗Eˊvˊi (∇ ⃗​⃗​⃗ (E×Eˊ+H×Hˊ ⃗​⃗​⃗​⃗ ∂Eˊ ⃗​⃗​⃗​⃗ ⃗​⃗ (H×Eˊ−E×Hˊ ⃗ Hˊi ) + ⃗​⃗​⃗ ⃗ (Eˊ Eˊ. ⃗∇ × ⃗​⃗​⃗ Eˊ + √2mEˊ √2mH 1⁄2 ) + 2|Eˊ 1⁄2 − Hˊ ∂t − Hˊ. vˊi (∇Eˊi ) + ⃗​⃗​⃗ | ∂t ⃗ ⃗​⃗​⃗ ⃗​⃗ ⃗​⃗​⃗​⃗ (E Eˊ+H Hˊ)

⃗ ⃗​⃗​⃗ ⃗​⃗ ⃗​⃗​⃗​⃗ (E Eˊ+H Hˊ)

⃗​⃗

⃗​⃗​⃗

⃗ ⃗​⃗​⃗​⃗

⃗ ⃗​⃗​⃗ ⃗​⃗

⃗​⃗

⃗​⃗​⃗​⃗

⃗

) ) 1 ⃗​⃗​⃗​⃗ ⃗​⃗​⃗​⃗ (H×Eˊ−E×Hˊ ⃗ × ⃗​⃗​⃗​⃗ ⃗​⃗ ∂H − H ⃗​⃗ vi (∇ ⃗ Ei ) − H ⃗​⃗ . ∇ ⃗ ×E ⃗ − √2mH ⃗​⃗ (E×Eˊ+H×Hˊ ⃗ ∂E − Hˊ. ∇ Hˊ − √2mHˊ 1⁄2 )] + i [ ⃗ (H 1⁄2 + E |E|

⃗ Eˊ ⃗​⃗​⃗ +H ⃗​⃗ Hˊ ⃗​⃗​⃗​⃗ ) (E

⃗​⃗

⃗​⃗​⃗

∂t

⃗ ⃗​⃗​⃗​⃗

) ⃗ . vi (∇ ⃗ Ei ) − E ⃗ .∇ ⃗ ×H ⃗​⃗ + √2mE ⃗ (H×Eˊ−E×Hˊ E 1⁄2 ) + ⃗ Eˊ ⃗​⃗​⃗ +H ⃗​⃗ Hˊ ⃗​⃗​⃗​⃗ ) (E

⃗​⃗​⃗

⃗​⃗

⃗​⃗​⃗​⃗ 1 ⃗​⃗​⃗​⃗ ∂Hˊ (Hˊ ⃗​⃗​⃗ | |Eˊ ∂t ⃗​⃗​⃗

⃗ ⃗​⃗​⃗​⃗

⃗​⃗​⃗ + √2mHˊ ⃗​⃗​⃗​⃗ ⃗ Eˊi ) − ⃗​⃗​⃗​⃗ − ⃗​⃗​⃗​⃗ Hˊvˊi (∇ Hˊ. ⃗∇ × Eˊ

) ⃗​⃗​⃗ ∂Eˊ + Eˊ ⃗​⃗​⃗ . vˊi (∇ ⃗​⃗​⃗ (H×Eˊ−E×Hˊ ⃗ Eˊi ) − E ⃗ ˊ. ∇ ⃗ × ⃗​⃗​⃗​⃗ Eˊ Hˊ + √2mEˊ 1⁄2 )]}. ∂t

∂t

⃗ ⃗​⃗​⃗ ⃗​⃗ Hˊ ⃗​⃗​⃗​⃗ ) (E Eˊ+H

⃗ Eˊ ⃗​⃗​⃗ +H ⃗​⃗ Hˊ ⃗​⃗​⃗​⃗ ) (E

AIJRSTEM 15-808; © 2015, AIJRSTEM All Rights Reserved

⃗ ×Eˊ ⃗​⃗​⃗ +H ⃗​⃗ ×Hˊ ⃗​⃗​⃗​⃗ ) (E 1⁄2

⃗ ⃗​⃗​⃗ ⃗​⃗ Hˊ ⃗​⃗​⃗​⃗ ) (E Eˊ+H

+

(26)

Page 12

Bulikunzira Sylvestre., American International Journal of Research in Science, Technology, Engineering & Mathematics, 13(1), December, 2015-February, 2016, pp. 10-13

V. Fundamental Dynamical Variables On the basis of Noether's theorem, from Lagrangian (26) we can derive expressions for fundamental dynamical variables.

For energy, we have E = â&#x2C6;Ť T00 d3 x, (27) where T00 =

â&#x192;&#x2014; â&#x2C6;&#x201A;L â&#x2C6;&#x201A;E â&#x192;&#x2014; ,0 â&#x2C6;&#x201A;x0 â&#x2C6;&#x201A;E

+

â&#x192;&#x2014;â&#x192;&#x2014; â&#x2C6;&#x201A;L â&#x2C6;&#x201A;H â&#x192;&#x2014;â&#x192;&#x2014; ,0 â&#x2C6;&#x201A;x0 â&#x2C6;&#x201A;H

+

â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; â&#x2C6;&#x201A;L â&#x2C6;&#x201A;EË&#x160; â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; ,0 â&#x2C6;&#x201A;x0 â&#x2C6;&#x201A;EË&#x160;

+

â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; â&#x2C6;&#x201A;L â&#x2C6;&#x201A;HË&#x160; â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; ,0 â&#x2C6;&#x201A;x0 â&#x2C6;&#x201A;HË&#x160;

.

(28)

Replacing expression (26) in formula (28), we obtain â&#x192;&#x2014; â&#x192;&#x2014;â&#x192;&#x2014; â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; i â&#x2C6;&#x201A;HË&#x160; â&#x192;&#x2014; â&#x2C6;&#x201A;E + H â&#x192;&#x2014;â&#x192;&#x2014; â&#x2C6;&#x201A;H) + i (E â&#x192;&#x2014; Ë&#x160; â&#x2C6;&#x201A;EË&#x160; + â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; T00 = (E HË&#x160; ).

(29)

With consideration of the solution for free particle in the form of plane waves 0 â&#x192;&#x2014; =E â&#x192;&#x2014; eâ&#x2C6;&#x2019;2iÎľđ?&#x2019;Śt+2ikâ&#x192;&#x2014; r , E

(30)

â&#x192;&#x2014;| 2|E

0

â&#x2C6;&#x201A;t

â&#x192;&#x2014; Ë&#x160;| 2|E

â&#x2C6;&#x201A;t

â&#x2C6;&#x201A;t

â&#x2C6;&#x201A;t

â&#x2C6;&#x2019;2iÎľđ?&#x2019;Śt+2ikâ&#x192;&#x2014; r

â&#x192;&#x2014;â&#x192;&#x2014; = H â&#x192;&#x2014;â&#x192;&#x2014; e H , 0 â&#x192;&#x2014; â&#x2C6;&#x2019;2iÎľđ?&#x2019;Śt+2ik r â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; EË&#x160; = â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; EË&#x160; e , 0 â&#x192;&#x2014; â&#x2C6;&#x2019;2iÎľđ?&#x2019;Śt+2ik r â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; HË&#x160; = â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; HË&#x160; e , where Îľ = Âą1 is the sign of energy, Îľ = +1 for a particle and Îľ = â&#x2C6;&#x2019;1 for an antiparticle, we find â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; |). â&#x192;&#x2014; | + |EË&#x160; đ??¸ = Îľđ?&#x2019;Ś(|E Similarly, for momentum, we have Pj = â&#x2C6;Ť T0j d3 x, where T0j =

â&#x192;&#x2014; â&#x2C6;&#x201A;L â&#x2C6;&#x201A;E â&#x192;&#x2014; ,0 â&#x2C6;&#x201A;xj â&#x2C6;&#x201A;E

+

â&#x192;&#x2014;â&#x192;&#x2014; â&#x2C6;&#x201A;L â&#x2C6;&#x201A;H â&#x192;&#x2014;â&#x192;&#x2014; ,0 â&#x2C6;&#x201A;xj â&#x2C6;&#x201A;H

+

â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; â&#x2C6;&#x201A;L â&#x2C6;&#x201A;EË&#x160; â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; ,0 â&#x2C6;&#x201A;xj â&#x2C6;&#x201A;EË&#x160;

+

â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; â&#x2C6;&#x201A;L â&#x2C6;&#x201A;HË&#x160; . â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; ,0 â&#x2C6;&#x201A;xj â&#x2C6;&#x201A;HË&#x160;

â&#x2C6;&#x201A;xj

â&#x2C6;&#x201A;xj

â&#x192;&#x2014; Ë&#x160;| 2|E

â&#x2C6;&#x201A;xj

With the formulae (30)-(33), we get â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; |). â&#x192;&#x2014; | + |EË&#x160; P j = kj (|E For charge, we have Q = â&#x2C6;Ť j0 d3 x, where, â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; â&#x2C6;&#x201A;L + â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; â&#x192;&#x2014; â&#x2C6;&#x201A;L + H â&#x192;&#x2014;â&#x192;&#x2014; â&#x2C6;&#x201A;L + EË&#x160; j0 = (E HË&#x160; â&#x192;&#x2014; â&#x192;&#x2014;â&#x192;&#x2014; â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; â&#x2C6;&#x201A;E,0

â&#x2C6;&#x201A;H,0

â&#x2C6;&#x201A;EË&#x160;,0

â&#x2C6;&#x201A;xj

â&#x192;&#x2014; Ă&#x2014;H â&#x192;&#x2014;â&#x192;&#x2014; E â&#x192;&#x2014;| |E

â&#x2C6;&#x2019;

â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; Ă&#x2014;HË&#x160; â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; EË&#x160; â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; | |EË&#x160;

(33) (34) (35)

(37) (38) (39)

â&#x2C6;&#x201A;L ). â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; ,0 â&#x2C6;&#x201A;HË&#x160;

(40)

With consideration of formulae (26) and (30)-(33), we obtain â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; |). â&#x192;&#x2014; | + |EË&#x160; j0 = (|E In the same way, we obtain the following expression for spin pseudo-vector s=

(32)

(36)

Considering expression (26), we find â&#x192;&#x2014; â&#x192;&#x2014;â&#x192;&#x2014; â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; i â&#x2C6;&#x201A;HË&#x160; â&#x192;&#x2014; â&#x2C6;&#x201A;E + â&#x192;&#x2014;H â&#x192;&#x2014; â&#x2C6;&#x201A;H) + i (E â&#x192;&#x2014; Ë&#x160; â&#x2C6;&#x201A;EË&#x160; + â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; T0j = (E HË&#x160; ). â&#x192;&#x2014;| 2|E

(31)

.

(41) (42)

VI. Discussion and Conclusion In previous works, via Cartan map, Dirac equation for electron has been written in tensor form, in the form of â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; , â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; â&#x192;&#x2014; ,H â&#x192;&#x2014;â&#x192;&#x2014; ) and (EË&#x160; non-linear Maxwellâ&#x20AC;&#x2122;s like equations, through two electromagnetic fields (E HË&#x160;). The solution of these non-linear tensor wave equations for free particle in the form of plane waves has been obtained. In this work, using the same method, we found the Lagrange function of electron field in tensor formalism, in terms of â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; , â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; â&#x192;&#x2014; , â&#x192;&#x2014;H â&#x192;&#x2014; ) and (EË&#x160; strengths (E HË&#x160;). Applying Noether's theorem, from the obtained Lagrangian, we derived expressions for fundamental dynamical variables (energy, momentum, charge and spin) conserved in time.

References [1] [2] [3] [4]

S.Bulikunzira, â&#x20AC;&#x153;Tensor formulation of Dirac equation through divisors,â&#x20AC;? Asian Journal of Fuzzy and Applied Mathematics, vol.2, no6, Dec.2014, pp.195-197.

S.Bulikunzira, â&#x20AC;&#x153;Tensor formulation of Dirac equation in standard representation,â&#x20AC;? Asian Journal of Fuzzy and Applied Mathematics, vol.2, no6, Dec.2014, pp.203-208.

F.Reifler, â&#x20AC;&#x153; Vector wave equation for neutrinos,â&#x20AC;? Journal of mathematical physics, vol.25, no4, 1984, pp.1088-1092.

P.Sommers,â&#x20AC;? Space spinors,â&#x20AC;? Journal of mathematical physics, vol.21, no10, 1980, pp.2567-2571.

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ISSN (Print): 2328-3491, ISSN (Online): 2328-3580, ISSN (CD-ROM): 2328-3629 AIJRSTEM is a refereed, indexed, peer-reviewed, multidisciplinary and open access journal published by International Association of Scientific Innovation and Research (IASIR), USA (An Association Unifying the Sciences, Engineering, and Applied Research)

Experimental Investigation on the strength characteristics of Polymer Based GGBFS Concrete Vinaykumar S. Jatti Assistant Professor, Symbiosis Institute of Technology (SIT), Symbiosis International University (SIU), Lavale, Pune-412 115, Maharashtra, INDIA Abstract: Due to the properties like improved bond strength, high compressive strength, fast curing, and resistance to chemical attacks, polymer concrete is been used extensively. This paper evaluates the study of effect of addition of polymer based GGBFS concrete on strength characteristics. An addition of 0%-5% polymer is done with an increment of 0.5%. The strength characteristics such as compressive strength, tensile strength, flexural strength, shear strength are studied for different percentage addition of polymer.

The work is carried out on M30 grade of concrete. 30% and 40% of cement is replaced by GGBFS in all the experimental work. The study concludes that mechanical properties like compressive, tensile, flexural, shear, shows higher values.

Keywords: Polymer concrete; GGBFS; SBR latex; Mechanical properties I. Introduction Disposal of industrial wastes is an issue faced by the manufacturing firm. In particularly, by-product of the iron manufacturing industry faces problem of disposing the slag. The chemical composition of molten slag is close to the cement. The molten slag consists of silicon and aluminum based residue. This slag is water-quenched, which results in the formation of a glassy granulate. Thus obtained glassy granulate is dried and ground to the required size. This is known as ground granulated blast furnace slag (GGBFS). GGBFS is an environmentally friendly construction material and helps in reduction of carbon dioxide gas emission. The characteristic of GGBS includes good water impermeability, resistance to sulphate attack and improved resistance to corrosion. This helps to increase the service life of a structure and reduces the maintenance cost. Thus GGBFS can significantly save natural resources, energy and reduces the efforts for disposal of industrial wastes. Thereby the consumption of cement reduces. Shariq et al. [1] experimentally obtained the compressive strength of cement mortar consisting of 20%, 40 % and 60 % of GGBFS for different types of sand. Further the obtained the compressive strength of concrete with 20%, 40 % and 60 % of GGBFS for two grades of concrete. They found that the compressive strength of mortar increased after 28 days and 150 days with 20% and 40% GGBFS, respectively.

Peter et al. [2] reported that slag with a specific surface area between 4000 cm2/g and 6000 cm2/g would significantly improve the performance of GGBS concretes. Shoubi et al. [3] showed a review on industrial by products such as GGBFS, Silica Fume and PFA as cement replacement on the performance of the concrete, economical, environmental and social aspects. Darquennes et al. [4] studied the effect of different percentages of slag (0 and 42% of the binder mass) on cracking under free and restraint conditions by means of the Temperature Stress Testing Machine. Elsayed [5] studied the effects of mineral admixtures on water permeability and compressive strength of concretes which consists of silica fume (SF) and fly ash (FA). Further they compared the results with ordinary Portland cement concrete without admixtures. Based on the experimental results they found 10% as optimum cement replacement by FA and SF. They found improved compressive strength and permeability of concrete consisting of high slag cement, silica fume and fly ash.

Kogbara et al. [6] explored the potential of GGBFS activated by cement and lime. This work was carried out for stabilization/solidification treatment of a mixed contaminated soil. Martin et al. [7] analyzed the effect of pH and acid type in the concrete. The results showed that the concrete failed in the durability test of waste water infrastructure due to the extraordinarily harsh nature. Ling et al. [8] studied the performance of GGBFS compared it with fresh concrete and hardened concrete. Thus based on the literature it can be seen that GGBFS concrete is characterized by high strength, lower heat of hydration and resistance to chemical corrosion. Also from the literature it can be observed that addition of polymer into the concrete improves the performance of the concrete. Further researchers studied the effect of addition of GGBFS and polymer into the concrete on performance of the concrete. Present study focuses on the effect of different percentage of polymer on GGBFS concrete and optimum percentage of polymer is also obtained.

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Vinaykumar, American International Journal of Research in Science, Technology, Engineering & Mathematics, 13(1), December, 2015February, 2016, pp. 14-17

II. Materials Ordinary Portland Cement (OPC), 43 grade conforming to IS: 8112 – 1989was used. The specific gravity of cement was found to be 3.15. Locally available crushed aggregates and river sand confirming to IS: 383-1970 was used. Specific gravity of crushed aggregate and river sand was 2.60 and 2.61 respectively. In this experimental work, low calcium, ground granulated blast furnace slag from the ACC cement plant, Kudithini, Hospet, India. Confirming to IS: 3812 (Part 1) – 2003 was used. Chemical composition of GGBFS is shown in the Table I. Table I Chemical composition of ground granulated blast furnace slag Chemical

Percentage

Silica

34-35

Aluminum oxide

11-15

Iron oxide

0.29-1.4

Calcium oxide

36-41

Magnesium oxide

6

Potassium oxide

0.39

Sulphate

0.3

Loss on ignition

2.8 Specific gravity = 2.94

The concrete mix M30 investigated in this study is prepared with standard 53 grade Portland cement and polymers which conform to Indian standards. Mix design was carried out according to the IS 10262: 2009. The concrete mixed used for casting the cube, cylinder, beam, L-shape and impact specimen is 1: 1.47: 2.48 by weight and a water cement ratio as 0.45.

The following strength tests are conducted on the casted specimen after 28 days of curing 1.

Compressive strength test on 150 mm x 150 mm x 150 mm cube.

2.

Tensile strength test on ɸ150 mm x 300 mm length cylinder.

3.

Flexural strength test on 100 mm x 100 mm x 500 mm beam.

4.

Impact strength test on ɸ150 mm x 60 mm length cylinder.

5.

Shear strength test on L shaped specimens III. Results and Discussions This section discusses the test results of polymer based GGBFS concrete produced by different dosages of polymer addition after 28 days of curing. Fig. 1 shows the variation of compressive strength for polymer based GGBFS concrete produced by different dosage of polymer addition. It is observed that the compressive strength of polymer based GGBFS concrete go on increasing as the percentage of polymer addition go on increasing up to 2.5%. Beyond this the compressive strength decreases. Thus the higher compressive strength may be achieved by adding 2.5% polymer in GGBFS concrete. Also it is observed that the compressive strength of polymer concrete produced by replacing 30% cement by GGBFS is higher as compared to 40% replacement. It is found that the polymer concrete with 30% replacement cement by GGBFS and 2.5% addition of polymer shows 15% increase in compressive strength as compared to the reference mix. The polymer concrete with 30% replacement of cement by GGBFS shows higher compressive strength to that of 40% replacement for all the percentage addition of polymer. This may be due to the fact that the addition of 2.5% polymer in GGBFS concrete will fill all the pores of concrete and develop a good bond between the particles of cement, sand and aggregates, thereby increasing the strength properties.

Figure 1 Variation of Compressive strength

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Vinaykumar, American International Journal of Research in Science, Technology, Engineering & Mathematics, 13(1), December, 2015February, 2016, pp. 14-17

Fig.2 shows the variation of tensile strength for polymer based GGBFS concrete produced by different dosages of polymer addition. It is observed that the tensile strength of polymer based GGBFS concrete go on increasing as the percentage of polymer addition go on increasing up to 2.5%. Beyond this, the tensile strength decreases.

Thus the higher tensile strength may be achieved by adding 2.5% polymer in GGBFS concrete. Also it is observed that the tensile strength of polymer concrete produced by replacing 30% cement by GGBFS is higher as compared to 40% replacement. It is found that the polymer concrete with 30% replacement cement by GGBFS and 2.5% addition of polymer shows 61% increase in tensile strength as compared to the reference mix.

The polymer concrete with 30% replacement of cement by GGBFS shows higher tensile strength to that of 40% replacement for all the percentage addition of polymer. This may be due to the fact that the addition of 2.5% polymer in GGBFS concrete will fill all the pores of concrete and develop a good bond between the particles of cement, sand and aggregates, thereby increasing the strength properties.

Figure 2 Variation of Tensile strength

Fig.3 shows the variation of flexural strength for polymer based GGBFS concrete produced by different dosage of polymer addition. It is observed that the flexural strength of polymer based GGBFS concrete go on increasing as the percentage of polymer addition go on increasing up to 2.5%. Beyond this, the flexural strength decreases.

Thus the higher flexural strength may be achieved by adding 2.5% polymer in GGBFS concrete. Also it is observed that the flexural strength of polymer concrete produced by replacing 30% cement by GGBFS is higher as compared to 40% replacement. It is found that the polymer concrete with 30% replacement cement by GGBFS and 2.5% addition of polymer shows 23% increase in flexural strength as compared to the reference mix. The polymer concrete with 30% replacement of cement by GGBFS shows higher flexural strength to that of 40% replacement for all the percentage addition of polymer. This may be due to the fact that the addition of 2.5% polymer in GGBFS concrete will fill all the pores of concrete and develop a good bond between the particles of cement, sand and aggregates, thereby increasing the strength properties.

Figure 3 Variation of Flexure strength

Fig.4 shows the variation of shear strength for polymer based GGBFS concrete produced by different dosage of polymer addition. It is observed that the shear strength of polymer based GGBFS concrete go on increasing as the percentage of polymer addition go on increasing up to 2.5%. Beyond this, the shear strength decreases. Thus the higher shear strength may be achieved by adding 2.5% polymer in GGBFS concrete. Also it is observed that the shear strength of polymer concrete produced by replacing 30% cement by GGBFS is higher as compared to

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Vinaykumar, American International Journal of Research in Science, Technology, Engineering & Mathematics, 13(1), December, 2015February, 2016, pp. 14-17

40% replacement. It is found that the polymer concrete with 30% replacement cement by GGBFS and 2.5% addition of polymer shows 61% increase in shear strength as compared to the reference mix. The polymer concrete with 30% replacement of cement by GGBFS shows higher shear strength to that of 40% replacement for all the percentage addition of polymer. This may be due to the fact that the addition of 2.5% polymer in GGBFS concrete will fill all the pores of concrete and develop a good bond between the particles of cement, sand and aggregates, thereby increasing the strength properties.

Figure 4 Variation of shear strength

1.

2.

3.

4.

IV. Conclusions Compressive strength of polymer based GGBFS concrete is higher at 2.5% addition of polymer. Also it can be concluded that the compressive strength of polymer concrete with 30% replacement of cement

by GGBFS is higher as compared to 40% replacement.

Tensile strength of polymer based GGBFS concrete is higher at 2.5% addition of polymer. Also it can be concluded that the tensile strength of polymer concrete with 30% replacement of cement by GGBFS is higher as compared to 40% replacement.

Flexural strength of polymer based GGBFS concrete is higher at 2.5% addition of polymer. Also it can be concluded that the flexural strength of polymer concrete with 30% replacement of cement by GGBFS is higher as compared to 40% replacement.

Shear strength of polymer based GGBFS concrete is higher at 2.5% addition of polymer. Also it can be concluded that the shear strength of polymer concrete with 30% replacement of cement by GGBFS is higher as compared to 40% replacement.

References

[1] [2]

[3]

[4] [5] [6] [7] [8]

M. Shariq, J. Prasad, A. K. Ahuja,“Strength Development of Cement Mortar and Concrete Incorporating GGBFS”, Asian Journal of Civil Engineering (Building and Housing) 9 (1), 2008, pp.61-74 .

W.C. Peter, Leung, H.D.Wong, “Final Report on Durability and Strength Development of Ground Granulated Blast Furnace Slag Concrete”, Geotechnical Engineering Office, Civil Engineering and Development Department, The Government of Hong Kong, 2010.

M. V. Shoubi, A. S. Barough, O. Amirsoleimani, “Assessment of the Roles of Various Cement Replacements in Achieving Sustainable and High Performance Concrete”, International Journal of Advances in Engineering and Technology 6 (1), 2013, pp.68-77.

A. Darquennes, S. Staquet, B. Espion, “Behaviour of Slag Cement Concrete under Restraint Conditions”, European Journal of Environmental and Civil Engineering 15 (5), 2011, pp. 787-798.

A.A. Elsayed, “Influence of Silica Fume, Fly Ash, Super Pozz and High Slag Cement on Water Permeability and Strength of Concrete”, Jordan Journal of Civil Engineering 5 (2), 2011, pp. 245-257.

R. B. Kogbara, A. Al-Tabbaa. “Mechanical and Leaching Behaviour of Slag-Cement and Lime-activated Slag Stabilized/Solidified Contaminated Soil”, Science of the Total Environment 409 (11), 2011, pp. 2325-2335.

M. O’Connell, C. McNally, M. G. Richardson, “Performance of Concrete Incorporating GGBS in Aggressive Wastewater Environments”, Construction and Building Materials 27 (1), 2012, pp. 368-374.

W. Ling, T. Pei, and Y. Yan, “Application of Ground Granulated Blast Furnace Slag in High- Performance Concrete in China”, International Workshop on Sustainable Development and Concrete Technology, Organized by China Building Materials Academy, PRC, 2004, pp. 309-317.

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ISSN (Print): 2328-3491, ISSN (Online): 2328-3580, ISSN (CD-ROM): 2328-3629 AIJRSTEM is a refereed, indexed, peer-reviewed, multidisciplinary and open access journal published by International Association of Scientific Innovation and Research (IASIR), USA (An Association Unifying the Sciences, Engineering, and Applied Research)

HF Propagation Variation on a Path Aligned Along the Mid-latitude Trough During Winter 1

Mfon O. Charles Assistant Lecturer, Physics Department, University of Calabar, Nigeria.

1

Abstract: This work presents observations from an extensive set of measurements of the direction of arrival and signal strength of HF signals propagating on a path (Nurmijärvi to Bruntingthorpe) oriented along the mid-latitude trough with path length 1800km. Signals were radiated on five frequencies between 4.6 and 14.4 MHz and measurements span the period from the 2009 sunspot minimum to July 2014, which is within the present sunspot maximum. Deviations were observed to occur at all frequencies and throughout the period of measurement. The largest deviations were mostly southerly and occurred at the highest frequencies: 11.1 and 14.4 MHz. In general, deviations occurred more in winter than summer. The received signal strengths were greater during summer than winter and the largest signal strengths were produced at the lowest frequency while the largest frequency produced the least signal strengths. There is also an observed effect on the duration and percentage of occurrence of propagation due to the solar cycle.

Keywords: HF propagation, Mid-latitude trough, Winter variations, Sunspot cycles, Nurmijärvi, Bruntinthorpe.

I. INTRODUCTION High-Frequency (HF) radio propagation is made possible through refraction by the ionosphere, and the ionosphere is that part of the atmosphere in which free electrons are sufficiently numerous to influence the propagation of radio waves. The name ionosphere comes from the fact that this region is formed by the ionization of atoms in the atmosphere thereby creating free electrons. The free electrons in the ionosphere cause HF radio waves to be refracted and eventually directed back to earth [1]. It goes on to say that the greater the density of electrons, the higher the frequencies that can be reflected. According to this same source, the ionosphere may have four regions present during the day. These regions are called the D, E, F1 and F2 regions.

Their approximate height ranges are: D region 50 to 90 km; E region 90 to 140 km; F1 region 140 to 210 km; F2 region over 210 km. It goes further to say that at certain times during the solar cycle the F1 region may not be distinct from the F2 region with the two merging to form an F region. At night the D, E and F1 regions become very much depleted of free electrons, leaving only the F2 region available for communications.

These varying characteristics of the ionosphere with respect to time of day, seasons, and solar cycles, make HF prediction and propagation a somewhat difficult task. According to Merriam-Webstar online dictionary, the mid-latitudes are latitudes of the temperate zones or from about 30 to 60 degrees north or south of the equator.

Located within the mid-latitudes is the trough which according to [2], is a major feature of the F-region ionosphere that forms at the boundary between the mid-latitudes and auroral ionospheres, and where the plasma concentration is usually lower compared with regions immediately poleward and equatorward. In terms of time of formation/appearance, the local time extent of the trough is small in summer, centred about midnight, and extends further towards dawn and dusk with progression towards winter [2]. For terrestrial HF radio systems, the electron depletion in the trough region reduces the maximum frequency that can be reflected by the ionosphere along the great circle path (GCP) [3]. Also, in the mid-latitudes, this electron density depletion and subsequent reduction in maximum useable frequency (MUF) often leads to large deviations from GCP [4]. A signal however, can still be reflected from the gradients in the poleward and equatorward walls of the trough or scattered from irregularities embedded in the trough or in the auroral region which lies just poleward of the trough [5]. In [6], it was also affirmed that these reflections from gradients and irregularities in the trough caused the signals to arrive from directions away from the GCP and at times delayed with respect to normal propagation.

Having taken measurements during sunspot maximum in 2001 for a shorter trough path between Uppsala, Sweden and Leicester, it was observed in [7] that the off-GCP signal received (deviations) were majorly to the north, with southerly deviations being much less frequent. These results they however reported were in contrast to a similar experiment conducted near sunspot minimum in 1994 in Canada, during which both southerly and northerly deviations were observed in the 5-15 MHz range, showing variations in DOA with respect to solar

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activity. In [8] deviations were found to occur more often at night especially during the winter and equinoctial months for signal frequencies between 7 and 11.1 MHz and these deviations were large.

Deviations in direction of arrival (DOA) due to the presence of the trough is not only an issue in radio communication systems where directional antennas are employed but also impacts greatly on radiolocation systems for which estimates of a transmitter location are obtained by triangulation from a number of receiving sites [8]. This could cause wrong assumptions for transmitter position, leading to timing and positional errors in navigation systems such as GPS. This work aims to investigate the effects of the mid-latitude trough on signals transmitted during winter within the mid-latitudes by analyzing HF transmissions from Nurmijarvi, Finland (60.5N, 24.65E) to Bruntingthorpe, Leicester, (52.49N, 1.11W) with a path length of 1800km. This work will give HF radio engineers an insight on the behaviour of signals transmitted during winter over this trough path and also see how these effects change with frequency and with solar cycle, thus enabling proper planning and execution of reliable and efficient communications.

II. MATERIALS AND METHOD A. Materials Data obtained from measurements between the trough path (Nurmijärvi to Bruntingthorpe) were collected over the duration spanning the recent solar minimum (2009) to the present (2014) which is within the present solar maximum. These data which contain the received signal strength and direction of arrival were obtained for each year. In each year, the peak month in winter was chosen to represent the winter season. A 10-day transmission data for the chosen month was then used for the analysis.

Figure 1: Map showing the paths employed in the reported measurements, with geographical coordinates.

B. Method The method used to make the measurements has been discussed in detail elsewhere in [7] and [9], and the days for which measurements were made is given later in this section.

Variation in smoothed sunspot number from the previous solar maximum (2001) to the present solar maximum (2014) 160

140

120

Monthly SN

100

80

60

40

20

0 2001

2002

2003

2004

2005

2006

2007

2008 Year

2009

2010

2011

2012

2013

2014

Figure 2: Variation in smoothed sunspot number over a solar cycle. The quantity plotted is the monthly mean international sunspot number downloaded from the Space Weather Prediction Centre, US National Oceanic and Atmospheric Administration in [10].

In deriving the statistics presented in Figs 3a-e and Tables 1 and 2 of this work, propagation is deemed to have occurred if any readily identifiable trace, other than sporadic E, is seen between 00:00-24:00 UT. The sporadic E is a region which is very unpredictable in its time of formation, the area which it covers, the duration for

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Mfon O. Charles., American International Journal of Research in Science, Technology, Engineering & Mathematics, 13(1), December, 2015-February, 2016, pp. 18-27

which it persists, and even in its electron density. For this reason it was excluded, so as to eliminate any false hopes of reflections. Derivation of these statistics presented in Figs 3a-e and Tables 1 and 2 are thoroughly explained in [11]. Also given in [11] is a sample experimental data from which these statistics were obtained.

Measurements used were taken on the following days: 2009: January 1-9, 2010: January 17-26, 2011: January 3-12, 2012: January 11-20, 2013: January 10-19, 2014: January 8-17.

III. RESULTS Results are presented from a solar minimum to the present maximum to observe any variations.

2009

10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2010

10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2011

10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

No of Days

2012 10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2013 10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2014 10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time of Day (UT) Figure 3a: A plot of hourly and yearly occurrence of propagation at 4.6 MHz

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2009 10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2010 10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2011 10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

No of Days

2012 10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2013 10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2014 10 8 6 4 2 0

GCP ND 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

SD

Time of Day (UT) Figure 3b: A plot of hourly and yearly occurrence of propagation at 7 MHz

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Mfon O. Charles., American International Journal of Research in Science, Technology, Engineering & Mathematics, 13(1), December, 2015-February, 2016, pp. 18-27

2009 10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2010 10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2011 10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

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8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

No of Days

2012 10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2013 10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2014 10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time of Day (UT) Figure 3c: A plot of hourly and yearly occurrence of propagation at 8 MHz

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2009

10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2010 10 8 6 4 2 0

GCP ND SD 1

2

3

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9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2011 10 8 6 4 2 0

GCP ND SD 1

2

3

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9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

No of Days

2012 10 8 6 4 2 0

GCP ND SD 1

2

3

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9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2013 10 8 6 4 2 0

GCP ND SD 1

2

3

4

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8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2014 10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time of Day (UT)

Figure 3d: A plot of hourly and yearly occurrence of propagation at 11.1 MHz

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2009

10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2010

10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2011

10 8 6 4 2 0

GCP ND SD

No of Days

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2012

10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

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10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2013

10 8 6 4 2 0

GCP ND SD 1

2

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10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2014 10 8 6 4 2 0

GCP ND SD 1

2

3

4

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6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time of Day (UT) Figure 3e: A plot of hourly and yearly occurrence of propagation at 14.4 MHz IV. OBSERVATIONS AND DISCUSSIONS A. GCP Propagation At 4.6 MHz, GCP propagation occurs almost throughout the whole day but poor around midday, appearing mostly from sunset (16:00 UT) till sunrise 8:00 UT. This is in contrast with summer appearance which is observed to be concentrated around midnight. This observation is consistent with [12] who said that the peak electron density during daytime is greater in winter than in summer for the same SSN (seasonal/winter anomaly). As solar activity increases, its duration and percentage of occurrence around midday worsens, increasing from being absent at 13:00 UT in 2009 to being absent from 09:00 UT to 16:00 UT in 2014.

At 7, 8, 11.1, and 14.4 MHz, GCP propagation occurs mainly during the day and decreases in duration and percentage of occurrence as frequency increases. At these high frequencies, GCP propagation also tends to increase in duration of occurrence as solar activity increases although this is not very obvious in 2013 and 2014.

GCP propagation at these higher frequencies is in line with the assertions made by [12] for daytime in the midlatitudes; when he said that an increase in SSN increases the peak electron density and the layer height of peak

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Mfon O. Charles., American International Journal of Research in Science, Technology, Engineering & Mathematics, 13(1), December, 2015-February, 2016, pp. 18-27

electron density during the daytime. This means that as SSN increases, the critical frequencies of the ionospheric layers increase, allowing higher frequencies to be propagated whether via a GCP or an off-GCP. It can be seen that for each year and on all central frequencies, the duration of no-GCP propagation increases as frequency increases. This goes to show that at a constant electron density, increasing the frequency beyond the critical frequency of the ionosphere will cause the signal to penetrate the ionosphere.

B. Observed Deviations Table 1: Observed yearly deviations at various frequencies for Winter Path: Nurmijarvi-Bruntingthorpe Frequency(MHz)

Northerly Deviations (°n)

Southerly Deviations (°s)

2009 4.6 7 8 14.4

50 80 100 40

40

2010 8

100

11.1

80

60

14.4

40

40

2011 7

20

8

20

8 11.1 14.4

30 30,60,80 140

8 11.1 14.4

20,80 20,40,60

30

2012 180 120

2013

7 8

180 150,160

2014 20 20

Table 2: Percentage Occurrence Statistics by Mode and Bearing for Signal Frequencies of 4.6, 7.0, 8.0, 11.1, and 14.4 MHz

Table 1 shows observed deviations with magnitude over the period of observation. Deviations from GCP occurred both northerly and southerly with the larger occurring mostly southwards of the GCP. Propagation was dominated by the GCP for all years except in 2013 which was dominated by northerly deviations.

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Variation with Frequency Deviations were observed to occur across all observed frequencies but the magnitude of deviation was strongest at the higher frequencies (11.1 and 14.4 MHz) Variation with Solar cycle It can be observed from Table 1 that at each central frequency where southerly deviations occurred, deviations tended to increase in magnitude with increasing solar activity.

Variation in Time of occurrence Table 2 shows that off-GCP propagation occurred all through the day during winter and were somewhat more regular between 22:00 UT and 09:00 UT except in 2013 when gradients in the trough walls and embedded irregularities appeared to be very severe, consequently supporting only off-GCP propagation all day. This is in line with [6], that the trough generally occurs at night during winter and causes signals to arrive well displaced from the GCP. Even though the percentage of occurrence of deviations in 2013 was higher between 10:00 UT and 21:00 UT due to an obvious greater ionisation and thus greater electron density during these hours, deviations were still strong at night between 22:00 UT and 09:00 UT. The winter season also showed a decrease in magnitude of southerly deviations as frequency increases for each year as can be seen in the third column of Table 1.

Although off-GCP propagation is in most cases viewed as a setback in radio communication systems especially in radiolocation systems, it however proved to be useful in providing communications during the periods when GCP propagation was not supported. Table 3 shows that throughout the duration observed, there was always an off-GCP either northerly or southerly occurring during the hours when GCP propagation was not supported. A very extreme case is observed at 14.4 MHz in 2013 when there was no GCP propagation all throughout the period and days of observation.

C. Signal Strength A particularly striking feature is the presence of 2 modes occurring occasionally during winter nights at 4.6 MHz. As seen in Table 3, no off-GCP propagation exists for this frequency. This could then be as a result of the F layer being diffuse due to irregularities (Spread F), thus causing the radio wave to scatter. According to [1], spread F in the mid-latitudes occurs mostly during winter and during the night hours. It goes on to say that at all latitudes; spread F will have a higher tendency of occurring when there is depletion in F region electron density.

As it is known, this is a characteristic feature of the mid-latitude trough.

Traces of 2 to 3 modes with SNRs between the range 8.5dB-12dB are often seen between 09:00 and 15:00 UT at 4.6, 7, and 8 MHz, with the upper limit tending to decrease to 10dB as frequency increases from 4.6 to 8MHz. This is typical of the daytime ionosphere, comprising of the E, F1, and F2 layers from which reflections are all possible. Hence, the higher frequencies are reflected higher up in the ionosphere and as a result return with less signal strengths due to the longer distance covered. The SNRs obtained during winter were less compared to those obtained in summer (8.5dB-15dB) as given in [11].

It is also observed that during solar minimum, daytime multimode propagation occurs mainly at lower frequencies (4.6, 7, and at 8 MHz) but not at the higher frequencies. As solar activity increases however, the higher frequencies (11.1 and 14.4 MHz) begin to exhibit multimode propagation too, especially around midday when the sun is at its peak. This feature was very obvious during winter than in the summer as observed by [11] .

V. CONCLUSION At 4.5 MHz, GCP propagation occurred mainly from sunset till sunrise, decreasing in duration and percentage of occurrence as solar activity increases as was observed too in summer in [11]. At 7, 8, 11.1, and 14.4 MHz, GCP propagation appears mainly during the day and increases with increasing solar activity. For all years, increasing the frequency tends to suppress propagation. Finally, GCP propagation for daytime is greater in duration and percentage during winter compared to that observed in [11] during summer. This winter anomaly is however not consistent for frequencies above 8 MHz Deviations were observed across all frequencies and mostly at night throughout the period of measurement. The largest deviations were mostly southerly and occurred at the highest frequencies: 11.1 and 14.4 MHz. These southerly deviations increase in magnitude with increase in solar activity for each central frequency. In general, deviations occurred more in winter compared to that observed in summer in [11]. Also, comparing with results from [11], the received signal strengths were greater during summer than winter. For both seasons, the largest signal strengths were produced at the lowest frequency while the largest frequency produced the least signal strengths.

REFERENCES [1] [2]

IPS Radio and Space Services, “Introduction to HF radio propagation,” http://www.ips.gov.au/Educational/5/2/2#sect1, 2012. Last Accessed July 23, 2014.

A. Roger, The mid-latitude trough-revisited, in P. Kintner Jr., A.J. Coster, T. Fuller-Rowell, A.J. Mannucci, M. Mendillo, and R. Heelis (Eds.), Midlatitude ionospheric dynamics and disturbances , Washington: The American Geophysical Union, 2013, pp. 25-33.

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E.M. Warrington, A. Bourdillon, E. Benito, C. Bianchi, J. Monilié, M. Muriuki, M. Pietrella, V. Rannou, H. Rothkaehl, H. Saillant, O. Sari, A.J. Stocker, E. Tulunay, Y. Tulunay, and N. Zaalov, “Aspects of HF radio propagation,” Annals of Geophysics, vol. 52(3-4), 2009, pp. 301-321, doi: 10.4401/ag-4577 [4] E.M. Warrington, A.J. Stocker, N. Zaalov, D.R. Siddle, and I.A. Nasyrov, “Propagation of HF radio waves over northerly paths: measurements, simulation and systems aspects,” Annals of Geophysics, vol. 47(2-3), 2004, pp. 1161-1177.

[5] N. Zaalov , H. Rothkaehl, A.J. Stocker, and E.M. Warrington, “Comparison between HF propagation and Demeter satellite measurements within the mid-latitude trough,” Joint Advanced Space Research, vol. 52, 2013, pp. 781-790. doi: 10.1016/j.asr.2013.05.023 [6] A.J. Stocker, E.M. Warrington and D.R. Siddle, “Observations of Doppler spreads on HF signals received over polar cap and through paths at various stages of the solar cycle,” Radio Science, vol. 48(5), 2013, pp. 638-645.

[7] D.R. Siddle, N.Y. Zaalov, A.J. Stocker and E.M. Warrington, “Time of flight and direction of arrival of HF radio signals received over a path along the midlatitude trough: Theoretical considerations,” Radio Science, vol. 39(4), 2004b, RS4009, doi: 10.1029/2004RS003052 [8] D.R. Siddle, A.J. Stocker and E.M. Warrington, “Time of flight and direction of arrival of HF radio signals received over a path along the midlatitude trough: Observations,” Radio Science, vol. 39(4), 2004a, RS4008, doi: 10.1029/2004RS003049 [9] A.J. Stocker, N.Y. Zaalov, E.M. Warrington, and D.R. Siddle,” Observations of HF propagation on a path aligned along the midlatitude trough,” Advances in Space Research, vol. 44(6), 2009, pp. 677-684, doi: 10.1016/j.asr.2008.09.038.

[10] http://www.ngdc.noaa.gov/stp/space-weather/solar-data/solar-indices/sunspot-numbers/international/tables/table_internationalsunspot-numbers_monthly.txt. Last Accessed July 22, 2014.

[11] M.O. Charles, “Observations of HF propagation on a path aligned llong the mid-latitude trough during summer,” American International Journal of Research in Sciences, Technology, Engineering and Mathematics, vol. 13(1), 2016, Accepted for publication.

[12] K. Davis, Ionospheric radio, London: Peter Peregrinus Ltd, 1990.

VI. Acknowledgments The author conducted the reported work as his M.Sc project at the University of Leicester, UK under the supervision of Professor Michael Warrington.

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American International Journal of Research in Science, Technology, Engineering & Mathematics

Available online at http://www.iasir.net

ISSN (Print): 2328-3491, ISSN (Online): 2328-3580, ISSN (CD-ROM): 2328-3629 AIJRSTEM is a refereed, indexed, peer-reviewed, multidisciplinary and open access journal published by International Association of Scientific Innovation and Research (IASIR), USA (An Association Unifying the Sciences, Engineering, and Applied Research)

Synthesis and Characterization of Bismuth Doped Barium Titanate S. Islam, A. Siddika, N. A Ahmed, N. Khatun, S. N. Rahman Industrial Physics Division Bangladesh Council of Scientific and Industrial Research (BCSIR) Dr. Kudrat -i-Khuda Road, Dhaka-1205, BANGLADESH Abstract: The mixture Ba1-xBi2x/3TiO3 was prepared by the standard solid state reaction method. Bi 2O3 was added as a dopant to the powder mixture of Barium Carbonate BaCO3 and Titanium Dioxide TiO2 and sintered at 1150ºC for five hours. The microstructure, dielectric and electric properties of the mixture have been investigated. The dielectric constant increased with increasing Bi 2O3 until it reached the maximum value with 0.6 mol% Bi2O3 additive, and the maximum dielectric loss was found 0.021 for 0.02% Bi2O3 content. The maximum Curie temperature was found 135ºC for 0.02, 0.03, 0.04% Bi content. The frequency dependent dielectric constant (ε) and dielectric loss (tanδ) of the samples at room temperature were collected in the frequency range from 40 Hz to 110MHz. Keywords: Sintering, Microstructure, SEM, Barium titanate, Bismuth doping, Dielectric property, Electrical Resistivity.

I. Introduction Barium Titanate is a very important Perovskite crystal in the world of electronics. The crystal structure is a primitive cube, with the Ba-larger cation in the corner, the Ti-smaller cation in the middle of the cube and oxygen, in the centre of the faces edges [1].Barium Titanate is considered as a Perovskite because of its corner linked oxygen octahedral with a small cation filling the octahedral hole and a large cation filling the dodecahedral hole, so that we can substitute the cations, maintaining the charge balance and keeping the size within the range for particular co-ordination number to improve its physical properties [2]. Its ferroelectric properties are connected with a series of four structural phase transitions having the following sequence upon heating: rhombohedral, orthorhombic, tetragonal and cubic. It has piezoelectric property, so it can be used in the production of transducer. The temperature, at which the phase transition occurs, is known as Curie temperature.

Above this temperature, the ferroelectric property does not exist. The higher Tc resembles the wider stable region for Multilayer capacitor. The property of BaTiO 3 has been widely investigated for many years. In the previous investigation, M.M. Vijatovic´ Petrovic´ et al. synthesized Sb doped BaTiO 3. The influence of Sb doping concentration shifts the temperature phase transition peaks to the lower temperatures and broadens ε –T curves [3]. S. Hao et al. prepared BaTiO3 powders doped with Ag by sol-gel method. The lowest resistivity was found 5.644Ω-m [4].S. Thirumalai et al. synthesized and characterized the microwave assisted BaTiO3 Nanoparticles. They found the tetragonal crystal structure even at lower heating temperature of 1000ºC. The particle size is about 20 nm less for the microwave heated samples than the conventional heating. The dielectric constant values measured at room temperature was relatively higher than that of the conventionally heated product. The dielectric loss values were also relatively lesser for microwave heated samples [5]. TadasRamoška et al. showed that La doped BaTiO3 gives maximally enhanced dielectric constant at low, room and high temperature phase transition [6]. Barium Titanate has higher sintering Temperature, which is 1300ºC. S. Wu et al. investigated Bi doping as a sintering additive, can effectively lower the sintering temperature of BaTiO 3 based ceramics from 1300 ºC to 1130ºC [7]. In this study, we desired to synthesize Bi doped BaTiO3 and analyze its various properties.

II. Materials and Method A.

Experimental Procedure

Polycrystalline samples of BaTiO3 + x wt. % (Bi2O3) (x = 0.01; 0.06) were prepared using a solid state synthesis.

The samples were synthesized from an analytically pure barium carbonate BaCO3, titanium oxide TiO2, and bismuth oxide (Bi2O3) [8]. Mixture of the raw materials was ground in ball mill in ethanol for five hours. The materials were dried and calcined at the temperature of 900˚C for three hours. The powder was made into disklike pellets and then sintered at 1150 ˚C for three hours in a furnace.

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S. Islam et al., American International Journal of Research in Science, Technology, Engineering & Mathematics, 13(1), December, 2015February, 2016, pp. 28-32

B.

Ceramics Characterization

The surface morphology of Bi doped BTO ceramics was determined by scanning electron microscopy (SEM, Hitachi S-3400N).In order to measure the dielectric properties, conductive layer of silver paste (Demetron Leipzegrstr.10, Germany) was painted on the polished ceramic samples as the electrodes. The capacitances of the ceramics were determined by a Good Will LCR-814 LCR meter (20mF to 200pF). The frequency dependence of the capacitances and loss were measured by an Agilent 4294A Precision Impedence Analyzer with frequency range 40 Hz to 110 MHz at room temperature. The dielectric constant was calculated from the capacitance using the following equation



Cd 0A

(1)

where C is the capacitance (F), d the thickness (m), A is the area (m2) and ε0=8.85×10ˉ 12 F mˉ1.

III. Result and Discussion A.

Surface Morphology

The surface SEM investigations were performed on both Bi doped and undoped Barium Titanate samples. The microstructure consists of inter-granular pores and grains of various sizes. Fig.1 (a) shows fairly uniform micrograph of pure BT sample. Micrograph shows some agglomerations as well as small grains but less porous.

In fig.1 (b), the BaTiO3-based ceramics doped with 0.01 mol% Bi2O3 shows similar micro graph like undoped Barium Titanate. As the Bi2O3 content is increased, as shown in Fig. 2(c-g), more porous ceramics are revealed and the morphologies show less dense surface. The average grain size of pure BT was 230.68 nm. The maximum grain size was found 458.2 nm for 0.06% Bi doping.

Figure1 SEM image of Ba1-xBi2x/3TiO3 samples sintered at 1150˚C (a) x = 0.00, (b) x = 0.01 (c) x = 0.02, (d) x = 0.03, (e) x = 0.04, (f) x = 0.05, (g) x = 0.06.

B.

Dielectric Properties

Temperature Dependent Dielectric Properties It is observed from the Table 1 that dielectric constant of BTO ceramics increases significantly with Bi doping.

This might be due to the role of conducting Bismuth ions in BaTiO3 network in the place of Barium ions [2]. In addition, Bi3+ substitutes Ba2+ in BaTiO3, so the ion volume of A-site decreases due to the barium vacancy, which makes a bigger active space for Ti4+. For the increase of electrovalence from +2 to +3 of A-site ion, a residual positive charge appears and the mutual effect between A and B (Ti4+) sites becomes stronger. Thus the

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polarization of Ti4+ is enhanced, and then the dielectric constant increase sharply [5]. The Curie temperature T c, which is the transition temperature from ferroelectric to paraelectric phase, was found to be in the range of 125°C to 135°C. Variation of Curie temperature with doping concentration is given in fig. 2. At T < Tc, the material becomes spontaneously polarized. At T>Tc the dielectric constant is given by Curie Weiss Law [9],

ε=

C (T  TC )

(2)

Decrease in Tc with Bi doping indicates a partial substitution of Ba 2+ ions with Bi3+ into the perovskite lattice [10].

Table 1Effect of Bi doping on Dielectric constant, Dielectric Loss and Curie temperature.

Sample X% 0.00

Dielectric Constant ε(Troom) 12905.3

Dielectric Constant ε(Tc) 13013.9

Dielectric Constant ε(frequency) 975.81

Curie Temperature Tc (°C)

tanδ

125

0.012

0.01

31229.4

31930.2

421.81

125

0.008

0.02

34727.6

35456.1

120.09

135

0.021

0.03

42673.0

44.085.0

839.71

135

0.011

0.04

42687.5

44750.0

230.48

135

0.013

0.05

53014.4

54890.8

539.82

130

0.007

0.06

67585.5

69694.6

803.49

130

0.009

Figure 2 Variation of Curie temperature with Doping Concentration.

Figure 3 Variation of Dielectric Loss with Doping Concentration

138

0.025

Dielectric Loss,tanδ

Curie Temp

136 134 132 130 128 126 124 0

0.05

Doping Concentration

0.02 0.015 0.01 0.005 0

0.05

Doping Concentration

The energy losses which occur in dielectrics are due to dc conductivity and dipole relaxation. The loss factor (tanδ) is the useful indication of the energy loss as heat [9] From the Table 1, it was found that BT with 0.05% Bi showed less dielectric loss while 0.02% doped BT exhibit greater dielectric loss. So it can be concluded that addition of Bismuth could minimize the dielectric loss (Fig. 3).

Frequency Dependent Dielectric Properties The frequency dependence of the dielectric constant of pure and Bi doped BaTiO3 is given in Table 1. The maximum Dielectric Constant with varying frequency was found 3421.81 for 0.01% doping. And the minimum Dielectric constant was 803.49 for 0.06% doping. Higher values of Dielectric Constant are due to the presence of all different types of polarizations, such as dipolar, atomic ionic and electrical polarization [11].

The frequency dependent dielectric loss is given in fig. 4. The maximum dielectric losses are 0.0256, 0.0319, 0.0326, 0.0486, 0.0494, 0.0577, and 0.0593 for pure and 0.01, 0.02, 0.03, 0.04, 0.05, and 0.06% Bi doped BTO. So dielectric loss factor increases with the increase of Bi doping. The dielectric loss corresponding to frequency is due to the ion jump relaxation, ion vibration-deformation loss and electron polarization loss. The ion jump relaxation between two equivalent ion positions is the main contributor to the dielectric loss at moderate frequencies below 105 Hz. So, in this case the dielectric loss was found due to the ion relaxation [12].

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Figure 4 Variation of dielectric loss with frequency for Ba1-xBi2x/3TiO3.

Table 2 Effect of Bi doping on temperature dependent resistivity.

0.06

Sample, X%

Resistivity, ρ (Ω-cm)

0.00

6.77×107

0.01

7

x=0.01 x=0.02

0.04

tanδ

2.98×10

x=0.00

0.05

x=0.03 x=0.04

0.03

0.02

2.19×107

0.03

2.06×107

0.02

0.04

2.00×107

0.01

0.05

1.65×107

0.00

0.06

1.86×107

x=0.05 x=0.06

0.00

100.00

200.00

Frequency

C. Electric Properties Temperature Dependent Electrical Resistivity The temperature dependence of the capacitance and resistivity of pure and Bi doped BaTiO3 is given in Table 2.

The resistivity decreases with the increase of Bi composition, except for x =0.06 composition. That means that the presence of Bi increases the conductivity of BaTiO3. So Bismuth infused BTO shows low PTRC behavior.

Whereas T. Hashishin et al. observed that Barium Titanate with 0.25 mole% and 0.45 mole% Nd additive shows too high resistivity at room temperature which meet the industrial application [12].

Frequency Dependent Electrical Conductivity The frequency dependent electrical conductivity is shown in fig. 5. The maximum value of logσ was found 3.623 Scm⁻¹ for 0.05% Bi Doped BTO and the minimum value of logσ was found 1.121 Scm⁻¹ for 0.04% Bi Doped BTO. In the low frequency region the variation of conductivity is due to the polarization effect and in the intermediate frequency plateau region, conductivity is almost frequency independent and is equal to dc conductivity σdc (fig.5). As only high frequency range was accounted in our observation, so these regions are absent as shown in fig. 6. In this frequency range, conductivity increases with the frequency i.e., only dispersive effect is existent [14]. In fact, the frequency dependence of conductivity or universal dynamic response (UDR) of ionic conductivity is related by the simple expression and is given by the Jonscher’s power law,

 ac   dc  A n

(3)

Where, the σac is the ac conductivity, σdc is the limiting zero frequency conductivity, A is the pre-exponential constant ω = 2πf is the angular frequency and n is the power law exponent, where 0 < n < 1 [14][15].

Figure 6 logσ and logf plots for pure and Bismuth doped BT ceramics

Figure 5 Schematic representation of log conductivity vs. frequency

2.5 x=0.00

logσ

2

x=0.01

1.5

x=0.02 x=0.03

1

x=0.04 x=0.05

0.5

x=0.06 0 0.500

1.000

1.500

2.000

logf

IV. Conclusion The present study describes the synthesis of Bi doped barium titanate by solid state reaction method. Bi doping is used to lower the sintering temperature. In this study the sintering temperature was 1150°C. The microstructure development of Bismuth doped barium titanate was fine grained with grains in the range from 230.68 nm for pure to 458.2nm for 0.06% Bi doped BaTiO3. The grain size is increasing with the Bi2O3doping.

The Temperature dependent resistivity of BaTiO3 base ceramics doped with Bi decreases with the doping

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concentration. The dielectric constant increases with doping concentration but the dielectric loss increases up to 0.02% doping concentration then decreases for increasing doping concentration. The ac electrical conductivity was found maximum for 0.05% Bi doping. The Dielectric Constant with varying frequency changes with the doping concentration and Bi doping increases the dielectric loss factor.

V. References [1]

M. M. Vijatović, J. D. Bobić, B. D. Stojanović, Science of Sintering, 40 (2008) 155- 165.

[2] [3]

Moganti Venkata Someswara Rao, Kocharlakota Venkata Ramesh, Majeti Naga Venkata Ramesh, BonthulaSrinivasa Rao, Advances in Materials Physics and Chemistry, 2013, 3, 77-82.

M.M. Vijatovic´ Petrovic´ , J.D. Bobic´ , J. Banys , B.D. Stojanovic´, Materials Research Bulletin 48 3766–3772.

[4]

S. Hao, D. Fu, J. Li,W. Wang, and B. Shen, International Journal of InorganicChemistry,Volume 2011, Article ID 837091, 4 pages.

[5]

S. Thirumalai, B. P. Shanmugavel, Journal of Microwave Power and Electromagnetic Energy, 45 (3), 2011, pp. 121-127.

[6]

T Ramoška, J Banys, R Sobiestianskas, M. V. petrović, J Bobić, B Stojanović ,Processing and application of ceramics 4[3] (2010) 193198.

[7]

S Wu, X Wei, X Wang, Hongxing Yang and Shunqi Gao, J. Mater. Sci. Technol., 2010, 26(5), 472-476.

[8]

Sitko D., Bąk W., Garbarz-Glos B., Antonova M. and Jankowska-Sumara I; Ukr. J. Phys. Opt. 2012, V13, Suppl. 3.Research. Vol. 13, No. 3, pp. 248~251 (2012).

[9]

M. A. Omar, 1993, Elementary Solid State Physics, Addison Wesley Publishing Company,Inc, page-408.

[10] S. Yasmin, S. Choudhury, M.A Hakim, A. H. Bhuiyan and M. J. Rahman,;Journal of Ceramic Processing Research, Vol.12, No.4,pp 387-391(2010).

[11] P. K. Patel, J. Rani, N. Adhalakha, H. Singh, K. L Yadav; Journal of Physics and Chemistry of Solids, 74(2013), 545-549.

[12] Y.S. Cho, K.H. Yoon; Advanced Electronic and Photonic Materials and Devices, Volume 4: Ferroelectrics and dielectrics; Academic Press.

[13] T. Hashishin, E. Sato, S. Umeki, K. Kojima and J. Tamaki; Material Science and Engineering 18(2011) 092031.

[14] P. Muralidharan, Impedence Spectroscopy; Chapter 4; Investigation of Ac conductivity and electrical modulus of LBS, LPBS and LVP samples.

[15] H. Naceur, A. Megriche, Md. El Maaoui; Oriental Journal of Chemis-try; Vol. 29, No (3): Page. 937-944.

VI. Acknowledgments The authors gratefully acknowledge Director BCSIR laboratories, Dhaka of Bangladesh Council of Scientific and Industrial Research (BCSIR) for doing this research work.

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ISSN (Print): 2328-3491, ISSN (Online): 2328-3580, ISSN (CD-ROM): 2328-3629 AIJRSTEM is a refereed, indexed, peer-reviewed, multidisciplinary and open access journal published by International Association of Scientific Innovation and Research (IASIR), USA (An Association Unifying the Sciences, Engineering, and Applied Research)

Two Way Signal Coordination by Using Simple Progressive System for Three-Signalized Intersections Morugu Srujan Kumar1, Student M.E (Transportation Engineering), Osmania University, Telangana, India.

Bhasker Valkati2, Lecturer, Department of Civil Engineering, Dawadimi, Shaqra University, KSA. Dr.R. Srinivasa Kumar3, Assistant Professor, Department of Civil Engineering, Osmania University, Telangana, India.

Abstract: Secunderabad popularly known as twin city of Hyderabad is located in Indian state of Telangana.

It is one of the largest metropolitan areas in India. As the numbers of vehicles are increasing day by day, major cities like Secunderabad are facing so many problems such as loss of time, increase in fuel consumption, increase in noise pollution and causes long queues which produce inconvenience, frustrations to drivers and road users. The Secunderabad city has too many intersections and too many traffic signals.

The main objective of this study is to optimize the signal timings and coordinate them for continuous flow of traffic. In this study, three adjacent signal intersections were selected to evaluate, optimize and coordinate them. Traffic problems which exist in these intersections are congestion, delay, traffic jam due to heavy traffic volume. All the intersection details such as geometric features, traffic volumes, and signal timings are studied first, and optimized and coordinated along the stretch. The signal coordination is done by Simple Progressive Method. Coordinating the signals showed better results compared to the present conditions.

Keywords: Optimize, Evaluate, Congestion, Traffic volume, Signal Timings, Coordination, etc, I. Introduction Traffic congestion occurs on road networks due to increase in use, slower speeds, longer trip times and increased vehicular queuing. When traffic demand is more, the interaction between the vehicles slows the speed of the traffic stream and results in traffic congestion. As demand approaches the capacity of a road, traffic congestion starts. In areas of high traffic flow, at intersection vehicles attempting to cross or turn left or right causes even more traffic congestion without any control in the traffic flow. Road networks in urban areas frequently intersect thus leading conflict between opposing flows of traffic to delays and accidents.

To overcome these problems over at intersection and where there is heavy traffic flow, to control the vehicular traffic in a discipline manner, traffic signals are installed at intersections and places where the traffic demand is more. Traffic signals allows for the orderly passage of traffic. It allows pedestrians to safely cross busy lane roads and highways without getting run over. Without traffic signals, there would be many accidents and many traffic and pedestrian deaths.

II. Objectives of the Study Based on the above discussion, the present study was taken up with the following objectives: (a).

To identify the signal junctions which are to be coordinated. (b).

To measure road geometrics of the identified road junctions. (c).

To conduct traffic engineering surveys, such as traffic volume, travel time. (d).

To design the traffic signal parameters.

To coordinate the three signalized junction for one-way and two-way coordination.

III. Literature Review Chen Zhao-Meng, Liu Xiao-ming, and Wu Wen-Xiang (2014) proposes a coordinated control method for variable cycle time green wave bandwidth optimization integrated with traffic-actuated control. In the coordinated control, green split is optimized in real time by the measured presence of arriving and/or standing vehicles in each intersection and simultaneously green waves along arterials are guaranteed.

Liqiang Fan (2014) the proper phase difference of traffic signals for adjacent intersections could decrease the time of operational delay. Some theorems show how to minimize the total average delay time for vehicle operating at adjacent intersections under given conditions. If the distance and signal cycles of adjacent intersections satisfy with specific conditions, the total average delay time would achieve zero. If the signal

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cycles of adjacent intersections and the phase difference of them are co-prime numbers, the total average delay time would be a constant.

Byungkyu (Brian) Park and Yin Chen (2012) carried out the study on Signal timing optimization and coordination for improving traffic flow through a series of traffic signals reducing the overall delay at an intersection.

Wei Li, Andrew p. Tarko (2010) studies the impact of arterial signal coordination on the frequency and severity of rear end and right angle collisions – the two types of crashes that are prevalent at signalized intersections – the frequency and severity of which are likely to be affected by signal coordination.

IV. Study Area The study area for this project taken three Signalized junctions (Sweekar Upkaar Signal Junction, SBH Signal Junction, Patny Signal Junction) which are 400m apart from each other. The description of these three junctions and their geometric data is explained below.

Fig. 1 Google Map showing three Signal Junction V. METHODOLOGY Firstly, the signal design is done for the three junctions taking the traffic volume survey and geometric data of these three junctions are collected. The through, left-turn, right-turn movements are counted and signal design is done by Webster method. The green times are calculated with this method. Then, with this the traffic signal coordination is done by simple progressive method. The offset is calculated and the time space diagram can be drawn.

VI. DATA COLLECTION The data collection includes the traffic volume survey by manual count method. The PCU factors are obtained from IRC 106-1990.The Traffic Volumes of the three intersections are given below: Table 1- Sweekar Upkaar Jn Approach JBS

YMCA

SBH Signal Jn

Bowenpally

Movement TH LT RT TH LT RT TH LT RT TH LT RH

(vehicle/hour) 1143 2562 218 275 88 643 600 90 63 460 107 114

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Table 2- SBH Signal Jn Approach Sweekar UpkaarJn YMCA

Patny Signal Jn

Paradise

Movement

(vehicle/hour)

TH LT RT TH LT RT TH LT RT TH LT RH

550 1650 450 556 286 297 380 758 410 256 279 135

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Morugu et al., American International Journal of Research in Science, Technology, Engineering & Mathematics, 13(1), December, 2015February, 2016, pp. 33-38 LT RT TH LT RT TH LT RH

Table 3- Patny Signal Jn Approach

SBH Signal Jn Clock Tower

Movement

(vehicle/hour)

TH LT RT TH

727 589 181 543

BATA

Manju Theatre

1683 291 536 367 357 453 492 243

The average travel time from Sweekar Upkaar junction to Patny signal junction is before signal coordination is 3minutes 12 seconds. The average speed for the stretch is found to be 15.44kmph.

The present signal green times of the three signal junctions are given below: Table 4- Present Signal Timings Junction

Approach

Green time

Sweekar Upkaar Junction

North South East West North South East West North South East West

22 seconds 30 seconds 15 seconds 12 seconds 20 seconds 30 seconds 12 seconds 20 seconds 22 seconds 30 seconds 20 seconds 20 seconds

SBH Signal junction

Patny Signal junction

VII. Data Analysis The traffic volume data collected at field and geometric data such as road widths are used for analysis of signal timings. At each intersection, signal is designed for all the approaches, the green times are found out for every approach as for north, south, east, and west. The signal is designed as per Webster method.

Time lost per cycle = L=∑ (I-a) +∑l The optimum cycle time for minimum delay (Co) is given by: Co= (1.5L+5)/ (1-Y) Effective green time per cycle = Co-L, Green time, g = (y (c₀-L)/(Y) Using the above formulae’s, the green times for every junction for each approach is given as: Table 5- Sweekar Upkaar Signal Junction North

South

East

West

Cycle length (Co) Effective green time per cycle, Co-L Green time

120 seconds

Cycle length (Co)

120 seconds

Effective green time per cycle, Co-L

104 seconds

104 seconds 24 seconds

Green time

32 seconds

Cycle length (Co) Effective green time per cycle, Co-L Green time Cycle length (Co) Effective green time per cycle, Co-L Green time

120 seconds

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104 seconds 18 seconds 120 seconds 104 seconds 30 seconds

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Morugu et al., American International Journal of Research in Science, Technology, Engineering & Mathematics, 13(1), December, 2015February, 2016, pp. 33-38

Table 6- SBH Signal Junction

North

South

East

West

Cycle length (Co)

110 seconds

Effective green time per cycle, Co-L

94 seconds

Green time

23 seconds

Cycle length (Co)

110 seconds

Table 7- Patny Signal Junction Effective green time per cycle, Co-L

116 seconds 100 seconds

Green time

29 seconds

Cycle length (Co)

116 seconds

Effective green time per cycle, Co-L

100 seconds

Green time

36 seconds

Cycle length (Co)

116 seconds

Effective green time per cycle, Co-L

100 seconds

Effective green time per cycle, Co-L

24 seconds 116 seconds 100 seconds

Green time

26 seconds

Cycle length (Co)

Effective green time per cycle, Co-L

94 seconds

Green time

34 seconds

Cycle length (Co)

110 seconds

Effective green time per cycle, Co-L

94 seconds

North

South

East

Green time

14 seconds

Green time

Cycle length (Co)

110 seconds

Cycle length (Co)

Effective green time per cycle, Co-L

94 seconds

Green time

23 seconds

West

VIII. Traffic Signal Coordination After the above Signal design, we have to coordinate the stretch of 800m of inbound traffic from South to North; therefore, the cycle lengths and green time of respective phases are taken for coordination. Before coordination of signals, the following definitions are to be understood.

Time Space Diagram Time space diagram is simply a plot of signal indication as a function of time for two or more signals. The diagram is scaled with respect to distance, so that one may easily plot the vehicle position as position of time.

Through Band The through band is the strip bordered by dark green. This indicates the length of time available for vehicles going a certain speed to travel without stopping.

Bandwidth It is the width of through band in time.

Figure 2-Time Space Diagram for One Way Coordination Offset The offset is the time from when the signal turns green until the succeeding signal turns green. If the offset was zero, then the lights would turn green at the same time.

Offset = distance between intersection (m)/ ideal vehicle speed (m/s) Time Space Diagram for One-way Coordination For the given signal stretch, coordination has to be done, The Average travel time in these junctions is taken as 28kmph, the cycle lengths for Sweekar Upkaar, SBH Signal junction, Patny signal junctions are 120 seconds,

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110 seconds, and 116 seconds, the green time for south leg is 32seconds, 34seconds and 36seconds. Distance between intersections is 400m.

The green time is taken as bandwidth in signal coordination diagram by default and corresponding red, and amber times are indicated. The offset is determined by Offset = 400/ (28* (1000/3600) = 52 seconds.

The time space diagram is adjusted into the bandwidth with 7seconds forward at SBH signal junction for exact coordination. The time interval is taken as 20 seconds on y-axis.

Two-way Signal Coordination Presenting one-way coordination is very simple than two-way coordination. In the above diagram in one-way coordination, the x-axis and y-axis is drawn taking x- axis as time interval of 20 seconds till 620 seconds and yaxis as distance between the intersections at 400m marking horizontal line parallel to x axis, and at 800m parallel to SBH signal junction. At Sweekar Upkaar junction, at 0 seconds the green time is started marking 32 seconds this is called as bandwidth. After 32 seconds is marked, the red time continues, followed by green time and so on. This bandwidth extends through next signal and till third signal; the through band meets from Sweekar Upkaar junction to SBH signal junction at offset of 52 seconds. And there the green time is marked of 34 seconds, followed by red time and so on...up to 3 to 4 cycles. And at third signal junction at 800m with offset of 104 seconds, the green time of 36 seconds is drawn followed by red time and so on. The through band indicates the continuous movement of vehicles without any stopping.

Figure 3-Time space diagram for Two Ways Signal Coordination Presentation One way/ Two-way Coordination Diagram IX. Result  At Sweekar Upkaar Signal Junction, The cycle length is found to be 120 seconds, and effective green time per cycle as 104 seconds, and green time for north approach as 24 seconds.

Green time for south approach as 32 seconds Green time for east approach as 18 seconds Green time for west approach as 30 seconds.  At SBHSignal Junction, The cycle length is found to be 110 seconds, and effective green time per cycle as 94 seconds, and green time for north approach as 23 seconds.

Green time for south approach as 34 seconds Green time for east approach as 14 seconds Green time for west approach as 23 seconds.  At PatnySignal Junction, The cycle length is found to be 116 seconds, and effective green time per cycle as 100 seconds, and green time for north approach as 29 seconds.

Green time for south approach as 36 seconds Green time for east approach as 24 seconds Green time for west approach as 36seconds.

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X. Summary From the above study, the following summary can be drawn, the change in green times for all the three signal junctions is given below, some of the signal timings are changed or increased or decreased accordingly to give more priority to the major corridor Table 8- Green Times of 3 Signal Intersections after Optimization Intersection

Sweekar upkaar junction

SBH Signal junction

Patny Signal junction

Approach

Green time

Improvement in %

Before

After

North

22 seconds

24 seconds

8.3 %

South

30 seconds

32 seconds

6.25%

East

15 seconds

18 seconds

16.67%

West

12 seconds

30 seconds

60%

North

20 seconds

23 seconds

13%

South

30 seconds

34 seconds

11.8%

East

12 seconds

14 seconds

14.28%

West

20 seconds

23 seconds

13%

North

22 seconds

29 seconds

24.13%

South

30 seconds

36 seconds

16.67%

East

20 seconds

24 seconds

16.67%

West

20 seconds

26 seconds

23%

The Traffic Signal Coordination is done by Simple Progressive System. The Progression speed is taken as 28kmph. Therefore, all the vehicles should strictly limit the speed to 28kmph in order pass the green bandwidth.

The distance between junctions is 400m; the offset is taken as 52 seconds from Sweekar Upkaar to SBH Signal junction, and 104 seconds from SBH Signal junction to Patny Signal junction.

The speed of traffic flow is also improved by 45% (28-15.44)/28*100 = 44.85 ≈ 45% XI. CONCLUSIONS The following are the observations and conclusions drawn from the study:  The widths of the road should be increased to improve the efficiency of the road stretch.  The travel time can be reduced considerably due to coordination.  The U turns should not be allowed in middle of the road, at it makes the platoon of vehicles to stop until the vehicle clears the road.  As the distance between the signal intersections are same, the coordination should have allowed during peak hours at inbound in the morning and the outbound in the evening.  The coordination should be used only during peak hours, during non-peak hours it is not useful as it makes other junctions wait which is not efficient during non-peak hours.

References [1] [2] [3] [4] [5] [6]

Chen Zhao-Meng, Liu Xiao-ming, Wu Wen-Xiang (2014), “Optimization Method of Intersection Coordinated Control Based Vehicle Actuated Model,” North China University of Technology, Beijing, China.

Byungkyu (Brian) Park, and Yin Chen (2010), “Quantifying the Benefits of Coordinated Traffic Signal System,”Virginia Transportation Research Council.

Wei Li and Andrew P. Tarko (2010), Safety Consideration in Signal Coordination and Road Design On Urban Streets, International Symposium on Highway Geometric Design, Valencia, Spain.

Keith Riniker, Paul Silberman, Ziada. Sabra (2000), “Signal Timing Optimization Methodologies and Challenges for The City of Baltimore,” MD, USA, Central Business District and Gateway, Transportation Research Board.

IRC: 106-1990, “Guidelines for Capacity of Urban Roads in Plain Areas,” The Indian Road Congress, New Delhi.

Highway Capacity Manual (2000), Transportation Research Board, National Research Council, Washington, D.C.

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ISSN (Print): 2328-3491, ISSN (Online): 2328-3580, ISSN (CD-ROM): 2328-3629 AIJRSTEM is a refereed, indexed, peer-reviewed, multidisciplinary and open access journal published by International Association of Scientific Innovation and Research (IASIR), USA (An Association Unifying the Sciences, Engineering, and Applied Research)

Fingerprint Image De-noising by Various Filters for Different Noise using Wavelet Transform Liton Devnath1, Md. Rafiqul Islam2 Mathematics Discipline, Khulna University, Khulna-9208, Bangladesh

1,2

Abstract: Now a dayâ&#x20AC;&#x2122;s fingerprint image identification is one of the most popular biometric technologies.

The performance of a fingerprint image-matching algorithm depends on the quality of the input fingerprint images. But the images are often corrupted by various types of noises during acquisition and transmission.

Such images have to be cleaned before using in any applications. Image de-noising is basic work for image processing and analysis. Wavelet transforms have become a very powerful tool for de-noising an image. In this paper four types of noise (Gaussian noise , Salt & Pepper noise, Poisson noise and Speckle noise) is used and fingerprint image de-noising performed for different noise by four types of filter ( Mean filter, Median filter, Laplacian filter and Wiener filter) in MATLAB Software . Further results have been compared by PSNR (Peak Signal to Noise Ratio) values for all noises.

Keywords: Mean filter, Median filter, Laplacian filter and Wiener filter, Wavelet transform I. Introduction Image filtering improves the quality of images. The good quality of input fingerprint is important for Automated Fingerprint Identification System (AFIS). Most AFISs are based on minutiae matching [1]. Although the automatic fingerprint recognition and identification have wide and long practical application for image processing and pattern recognition. Several methods have been used to solve the de-noising problems in image analysis. Generally, the de-noising techniques have been categorized into spatial and frequency domain techniques [2, 3, 8]. In spatial domain, adaptive spatial filter is one of the best filtering techniques to restore the heterogeneous pixel characteristics perfectly. Image denoising algorithm consists of few steps; consider two dimensional matrix of an input signal đ?&#x2018;Ľ(đ?&#x2018;Ą) and noisy signal đ?&#x2018;&#x203A;(đ?&#x2018;Ą). Add these components to get noisy data đ?&#x2018;Ś(đ?&#x2018;Ą) i.e, đ?&#x2018;Ś(đ?&#x2018;Ą) = đ?&#x2018;Ľ(đ?&#x2018;Ą) + đ?&#x2018;&#x203A;(đ?&#x2018;Ą) Here the noise can be Gaussian, Salt and pepper, Poissonâ&#x20AC;&#x2122;s and speckle, then apply wavelet transform to get đ?&#x2018;¤(đ?&#x2018;Ą), i.e, đ?&#x2018;&#x160;đ?&#x2018;&#x17D;đ?&#x2018;Łđ?&#x2018;&#x2019;đ?&#x2018;&#x2122;đ?&#x2018;&#x2019;đ?&#x2018;Ą đ?&#x2018;&#x2021;đ?&#x2018;&#x;đ?&#x2018;&#x17D;đ?&#x2018;&#x203A;đ?&#x2018; đ?&#x2018;&#x201C;đ?&#x2018;&#x153;đ?&#x2018;&#x;đ?&#x2018;&#x161;

đ?&#x2018;Ś(đ?&#x2018;Ą) â&#x2020;&#x2019; đ?&#x2018;¤(đ?&#x2018;Ą) Apply filter for different noise by four types of filter (Mean, Median, Laplacian and Wiener), then by inverse wavelet transform to get de-noising image đ?&#x2018;ĽĚ&#x201A;(đ?&#x2018;Ą).

II. Related work Alle Meije Wink et al. (2004) analyses the performance of general wavelet-based de-noising scheme with Gaussian Smoothing. Yong-Hwan Lee et al. (2005) proposed a simple and efficient algorithm for adaptive noise reduction, which combines the linear filtering and thresholding methods in the wavelet transform domain. P. L. Shui et al. (2007) proposed Image de-noising algorithm via best wavelet packet base using Wiener cost function.

A. Buades et al. (2010) focus of his work is, first, to define a general mathematical and experimental methodology to compare and classify classical image de-noising algorithms, second, to propose an algorithm addressing the preservation of structure in a digital image. Sachin D Ruikar et al. (2011) proposed Wavelet Based Image De-noising Technique. This technique is computationally faster and gives better results.

Dr.E.Chandra et al (2011) given a solution for Noise Elimination in fingerprint image using median filter. T. Vidhya et al. (2012) concluded that the fingerprint images are enhanced to a higher quality by de-noising the images using Wavelet based enhancement procedure. Hari Om et al. (2012) proposed An Improved Image Denoising Method Based on Wavelet Thresholding. S. Sutha et al (2013) projected A Comprehensive Study on Wavelet Based Shrinkage Methods for Denoising Natural Images. M. Neelima et al. (2014) project was to study various techniques such as visuShrink, SureShrink, NeighShrink and determine the best one for image denoising. Hani M. Ibrahem ( 2014) presented an efficient switching filter based on cubic B-Spline for removal of salt and pepper noise. The author reported with the PSNR value of 50db with 0.2 noise density. S. Usha et al.

(2015) proposes Performance Analysis of Fingerprint De-noising Using Stationary Wavelet Transform.

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III. Wavelet Transform, Image noise and filters A. Wavelet Transform Wavelet transform gives a full and precise image of the quasi-harmonic componentsâ&#x20AC;&#x2122; dynamics in signal. A wavelet allows one to do multi-resolution analysis, which helps to achieve both time and frequency localization.

Wavelet algorithms process data at different scales or resolutions. As a result, the multi-resolution analysis of the wavelet has good characteristics and advantages in both the space domain and frequency domain.

Nowadays, wavelet analysis has successful applications in bio-medical engineering, signal processing, image processing, video image compression, digital television, image coding, edge detection and other fields [11]. In most of the applications of image processing, it is essential to analyze a digital signal. The wavelet transform is better than Fourier transform because wavelets are localized in both time and frequency whereas the standard Fourier transform is only localized in frequency [6]. Wavelet transform of any function f at frequency a & time b is computed by correlating f with wavelet atom a +â&#x2C6;&#x17E;

đ?&#x2018;Ąâ&#x2C6;&#x2019;đ?&#x2018;? ) đ?&#x2018;&#x2018;đ?&#x2018;Ą đ?&#x2018;&#x17D;

đ?&#x2018;¤đ?&#x2018;&#x201C;(đ?&#x2018;&#x17D;, đ?&#x2018;?) = â&#x2C6;Ťâ&#x2C6;&#x2019;â&#x2C6;&#x17E; đ?&#x2018;&#x201C;(đ?&#x2018;Ą) Ψ (

Wavelet transform is always defined in terms of a â&#x20AC;&#x153;motherâ&#x20AC;? wavelet Ψ and a scaling function đ?&#x153;&#x2018;, along with their dilated and translated versions [4]. The use of wavelet transform on image shows that the transform can analyze the approximation, horizontal, vertical and diagonal components in the fingerprint image [5, 7].

B. Image noise Image noise is random variation of brightness or color information in images, and is usually an aspect of electronic noise. Usually, the noise hides some information about the images and it makes it difficult to diagnose. Image diagnosis is always done after applying image enhancement and de-noising techniques to the original images. There are many types of noises occurs in fingerprint images during acquisition and transmission. Mostly occurred noises are Gaussian noise, Salt and Pepper noise, Poison Noise, Speckle noise and so on [10].

B.1. Gaussian noise This type of noise has a probability density function (PDF) of the normal distribution (also known as Gaussian distribution). It most commonly presents as additive noise to be called additive white Gaussian noise. The general model of amplifier noise is additive, Gaussian, independent at each pixel and independent of the signal intensity. Principal sources of Gaussian noise in digital images arise during acquisition e.g. sensor noise caused by poor brightness or high temperature or electronic circuit noise. Gaussian noise is a major part of the â&#x20AC;&#x153;read noiseâ&#x20AC;? of an image sensor, i.e, of the constant noise level in dark areas of the image [9].

B.2. Salt and pepper noise Impulsive noise is sometimes called salt-and-pepper noise. An image containing salt-and-pepper noise will have dark pixels in bright regions and bright pixels in dark regions. The salt & pepper noise is generally caused by fitting of cameraâ&#x20AC;&#x2122;s sensor cells, by memory cell failure or by combination errors in the image digitizing or transmission. It can be mostly eliminated by using dark frame subtraction, median filtering and interpolating around dark/bright pixels. For an 8 bit/pixel image, the typical intensity value for pepper noise is close to 0 and for salt noise is close to 255 [9].

B.3. Poison Noise This noise is also known as photon shot noise. Poison Noise is typically caused by the variation in the number of photons sensed at a given exposure level. In addition to photon Poison Noise, there can be additional shot noise from the dark leakage current in the image sensor. Shot noise has a root-mean-square value proportional to the square root of the image intensity, and the noises at different pixels are independent of one another. Shot noise follows a Poisson distribution, which except at very low intensity levels approximates a Gaussian distribution.

Since the mean and variance of a Poisson distribution are equal, the image dependent term has a standard deviation if it is assumed that the noise has a unity variance (R. Kaur et al., 2013).

B.4. Speckle noise This type of noise occurs in almost all coherent systems such as SAR (Synthetic Aperture Radar) images, Ultrasound images etc. The source of this noise is random interference between the coherent returns. It increases the mean grey level of a local area. All conventional medical images B-mode ultrasonic have speckle noise and can be an unwanted property since it masks small but diagnostically significant features (Chen et al., 2003). In general, speckle noise commonly referred to data dropout noise. The speckle can also represent some useful information, particularly when it is linked to the laser speckle and to the dynamic speckle phenomenon, where the changes of the speckle pattern, in time, can be a measurement of the surface's activity. Speckle noise follows a gamma distribution function.

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C. Image Filtering Filtering is a technique for modifying or enhancing an image. Image processing operations implemented with filtering include smoothing, sharpening, and edge enhancement. Filtering is a neighborhood operation, in which the value of any given pixel in the output image is determined by applying some algorithm to the values of the pixels in the neighborhood of the corresponding input pixel. In this paper four types of noise is used and fingerprint image de-noising performed for different noise by four types of digital filter. Such as Mean filter, Median filter, Laplacian filter and Wiener filter [9, 10].

C.1. Mean filter Mean filtering is a simple, intuitive and easy to implement method of smoothing images, i.e. reducing the amount of intensity variation between one pixel and the next. It is often used to reduce noise in images. The idea of mean filtering is simply to replace each pixel value in an image with the mean (`average') value of its neighbors, including itself. This has the effect of eliminating pixel values which are unrepresentative of their surroundings. Mean filtering is usually thought of as a convolution filter.

C.2. Median filter Median filtering is similar to the mean or averaging filter since they produce pixel, this is set to an "average" of the pixel values in the surrounding region of the corresponding input pixel. In median filtering, the importance of an output pixel is determined by the median of the surrounding region of pixels rather than the mean. Instead of simply replacing the pixel value with the mean of neighboring pixel values, it replaces it with the median of those values. The median is calculated by first sorting all the pixel values from the surrounding neighborhood into numerical order and then replacing the pixel being considered with the middle pixel value [9]. A major advantage of the median filter over linear filters is that the median filter can eliminate the effect of input noise values with extremely large magnitudes.

C.3. Laplacian filter The Laplacian is a 2-D isotropic measure of the 2nd spatial derivative of an image. The Laplacian of an image highlights regions of rapid intensity change and is therefore often used for edge detection. The Laplacian is often applied to an image that has first been smoothed with something approximating a Gaussian smoothing filter in order to reduce its sensitivity to noise. The Laplacian L(x, y) of an image with pixel intensity values I(x, y) is given by: L(x, y) =

â&#x2C6;&#x201A;2 I â&#x2C6;&#x201A;x2

+

â&#x2C6;&#x201A;2 I â&#x2C6;&#x201A;y2

; This can be calculated using a convolution filter.

C.4. Wiener filter The most important technique for removal of blur in images due to linear motion or unfocussed optics is the Wiener filter. From a signal processing standpoint, blurring due to linear motion in a photograph is the result of poor sampling. Each pixel in a digital representation of the photograph should represent the intensity of a single stationary point in front of the camera. Unfortunately, if the shutter speed is too slow and the camera is in motion, a given pixel will be an amalgam of intensities from points along the line of the camera's motion. This is a two-dimensional analogy to đ??ş(đ?&#x2018;˘, đ?&#x2018;Ł) = đ??š(đ?&#x2018;˘, đ?&#x2018;Ł). đ??ť(đ?&#x2018;˘, đ?&#x2018;Ł) where F is the fourier transform of an "ideal" version of a given image, and H is the blurring function. In this case H is a sinc function: if three pixels in a line contain info from the same point on an image, the digital image will seem to have been convolved with a three-point boxcar in the time domain. If G and H are known, then this technique is inverse filtering [9, 10].

D. Performance Estimation Peak Signal to Noise Ratio (PSNR) PSNR is an engineering term for the ratio between the maximum possible power of a signal and the power of corrupting noise that affects the fidelity of its representation. Because many signals have a very wide dynamic range, PSNR is usually expressed in terms of the logarithmic decibel scale.

2552 ) MSE Where, MSE is mean square error between the original image and the denoised image.

PSNR = 10 â&#x2C6;&#x2122; log10 (

(1)

IV. Performance Analysis After wavelet transform in MATLAB, we adding four types of Noise (Gaussian noise, Salt & Pepper noise, Poisson noise and Speckle noise) to synthesized image. Adding the noise with standard deviation (0.02) and removed those noises using Mean filter, Median filter, Laplacian filter and Wiener filter and comparisons among them. All performance are given below:

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Fig.4.1: Original Image (left), Wavelet Decomposition at level 3(middle), Synthesized Image (right).

Fig.4.2: Gaussian noise (above left), Salt & Pepper noise (above right), Poisson noise (below left), Speckle noise (below right).

Fig.4.3: Removed Gaussian noise by Mean Filter (left), Removed Gaussian noise by Median Filter (right).

Fig.4.4: Removed Gaussian noise by Laplacian Filter (left), Removed Gaussian noise by Wiener Filter (right).

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Fig.4.5: Removed Salt and Pepper noise by Mean Filter (above left), Removed Salt and Pepper noise by Median Filter (above right), Removed Salt and Pepper noise by Laplacian Filter (below left), Removed Salt and Pepper noise by Wiener Filter (below right).

Fig.4.6: Removed Poisson noise by Mean Filter (above left), Removed Poisson noise by Median Filter (above right), Removed Poisson noise by Laplacian Filter (below left), Removed Poisson noise by Wiener Filter (below right).

Fig.4.7: Removed Speckle noise by Mean Filter (left), Removed Speckle noise by Median Filter (right).

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Fig.4.8: Removed Speckle noise by Laplacian Filter (left), Removed Speckle noise by Wiener Filter (right).

Noise Gaussian noise Salt & Pepper noise Poisson noise Speckle noise

Mean Filter 62.9136 62.7369 63.5810 63.2148

PSNR Values by Four Filters Median Filter Laplacian Filter 64.3691 49.9885 64.3860 49.4106 65.8804 49.7048 64.9956 50.0820

Wiener Filter 66.4402 66.6671 67.5685 66.7156

Table 1: PSNR Values by Four Filters The performances of four filters are analyzed using PSNR values of the de-noised (enhanced) image and these values are tabulated in Table 1. From the Table, it is evident that the wavelet enhancement procedure works well than that of the Wiener filter enhancement procedure and from the above Fig. (4.3 to 4.8) we conclude that the median filter gives clearer image than other filters.

V. Conclusion We used the fingerprint image (Fig.4.1) in “jpg” format, adding four noise (Gaussian, Salt & Pepper, Poisson and Speckle) in original fingerprint image with standard deviation (0.02) (Fig.4.2), De-noised all noisy images by four filters and conclude from the results (Table 1) that, the performance of the Wiener Filter after removing noise for all Gaussian noise, Salt and Pepper noise, Poisson noise and Speckle noise is better than Mean filter, Median filter and Laplacian Filter.

References [1] [2] [3] [4] [5] [6] [7] [8] [9]

[10]

T. Vidhya, T. K. Thivakaran, ‘Fingerprint Image Enhancement using Wavelet over Gabor filters’, International Journal of Computer Technology & Applications, Vol 3(3), 2012, pp.1049-1054.

V. Sharan, N. Keshari, T. Mondal, ‘Biomedical Image De-noising and Compression in Wavelet using MATLAB’, International Journal of Innovative Science and Modern Engineering (IJISME), Vol. 2(2), 2014, pp. 9-13.

M. Neelima and M. M. Pasha, ‘Wavelet Transform Based On Image Denoising Using Thresholding Techniques’, International Journal of Advanced Research in Computer and Communication Engineering, Vol. 3(9), 2014, pp. 7906-7908.

M. Misiti, Y. Misiti, G. Oppenheim and J. M. Poggi, ‘Wavelet Toolbox User’s Guide’, The MathWorks, Inc. R2013b, version 4.12, 2013.

D. Maltonie, D. Maio, A. K. Jain, and S. Prabhakar, Handbook of Fingerprint Recognition. Springer-Verlag New York, Inc., 2003.

I. Daubechies, Ten Lectures on Wavelets. Society of Industrial and Applied Mathematics, 1998.

J. Gomes, L. Velho, Image Processing for Computer Graphics and Vision”, Springer-Verlag, 2008.

Y. H. Lee and S. B. Rhee, ‘Wavelet-based Image Denoising with Optimal Filter’, International Journal of Information Processing Systems Vol.1 (1), 2005, pp. 32-36.

Z. Q. Abdullah, ‘Quality Assessment on Medical Image Denoising Algorithm: Diffusion and Wavelet Transform Filters’, A thesis submitted in fulfillment of the requirements for the award of the Degree of Master of Computer Science (Software Engineering), Faculty of Computer Science and Information Technology, Universiti Tun Hussein Onn Malaysia, Springer-Verlag, 2014.

M. Soni1, A. Khare, S. Jain, ‘Problem of Denoising in Digital Image Processing and Its Solving Techniques’, International Journal of Emerging Technology and Advanced Engineering, Vol.4(4), 2014, pp.244-250.M. Unser, ‘8th IEEE Signal Processing Workshop’, 1996, pp. 244-249.

VI. Acknowledgments The authors gratefully acknowledge the helpful comments and suggestions of the reviewers that have improved the presentation.

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ISSN (Print): 2328-3491, ISSN (Online): 2328-3580, ISSN (CD-ROM): 2328-3629 AIJRSTEM is a refereed, indexed, peer-reviewed, multidisciplinary and open access journal published by International Association of Scientific Innovation and Research (IASIR), USA (An Association Unifying the Sciences, Engineering, and Applied Research)

Channel Capacity Analysis of MIMO OFDM System Using Water Filling Algorithm under AWGN and Rayleigh Fading Channel Vipin Kumar1, Dr. Praveen Dhyani2, Anupma3 Research Scholar, Banasthali University, Banasthali, Jaipur (Rajasthan), INDIA 2 Professor & Executive Director, Banasthali University, Jaipur Campus, Jaipur (Rajasthan), INDIA 3 Assistant Professor, PIET, SAMALKHA Haryana, INDIA 1

Abstract: In the paper we have discussed the proposed water filling algorithm which has been used for allocating the power to the MIMO channels so as to enhance the capacity of the MIMO OFDM system. here we have considered MIMO-OFDM system and the channel is assumed to be Flat as under this the convolution integral becomes a simple multiplication operator. Here in this paper we study the comparative analysis of water filling algorithm for both type of channels that is AWGN & Rayleigh fading channel. It can be observed from the graphs that the efficiency of the system is enhanced with the proposed water filling algorithm. It is further seen that there is enhancement in the capacity of a MIMO OFDM system.

Keywords: Multi Input Multi Output (MIMO), water filling, Capacity, outage probability, Signal to Noise Ratio (SNR), Power Budget. Orthogonal Frequency Division Multiplexing (OFDM) I. INTRODUCTION The growing demand on wireless communication services has created the need to support higher and better rate.

Wireless communication systems face high level of ISI that originates from multipath propagation and inherent delay spread. A multipath primarily based technique like orthogonal frequency division multiplexing are often used to eliminate ISI and to boost capability and spectral efficiency (bps/Hz) in wireless system. In addition of this, MIMO systems are promising techniques to extend performance with acceptable bit error rate (BER) by employing a range of antennas. OFDM is best referred to as orthogonal frequency division multiplexing that is used to transmit the signals from one end to another. OFDM may be a broadband multicarrier modulation technique that gives superior performance and advantages over older, additional single-carrier modulation technique as a result of it's a far better match with today’s high-speed knowledge necessities and operation within the ultrahigh frequency and spectrum. it's may be the foremost spectrally economical technique discovered so far, and it mitigates the various drawback of multipath propagation that causes large data errors and loss of signal within the microwave and ultrahigh frequency spectrum. MIMO stands for multiple input and multiple output system .A method wherever signals are transmitted via multiple antennas rather than just one antenna like FDM. This method has the potential of dramatic increase of information transmission in wireless environment for multimedia applications in wireless communications, a high system capacity is required for higher system capacity, and different methods have been proposed in recent years. The multiple input – multiple output system has attracted a lot of research interest due to its potential to increase the system capacity without extra bandwidth like several different communication systems, MIMO-OFDM system has multiple antennas both at the transmitter and receiver end. MIMO system can be used in numerous ways. If we want to require the diversity as an advantage to combat attenuation then we have to send the similar signals through numerous MIMO antennas and at the receiving end all the signals received by MIMO antennas can receive a similar signals traveled through numerous path. During this case the whole received signal should meet up with uncorrelated channels. When MIMO is used for capacity enhancement then we can send completely different set of data that is not a similar set of data like diversity MIMO through number of transmitting antennas and therefore the same number of antennas will receive the signals at the receiving end. To combat the effect of frequency selective fading, MIMO is usually combined with orthogonal frequency-division multiplexing technique. OFDM transforms the frequency-selective fading channels into parallel flat fading sub channels, as long because the cyclic prefix inserted at the start of every OFDM symbol is longer than or equal to the channel length. The channel length means that the length of impulse response of the channel as discrete sequence. The signals on every subcarrier are often simply detected by a time-domain or frequency-domain equalizer.

Otherwise the effect of frequency-selective fading cannot be fully eliminated, and inter-carrier interference and inter-symbol interference are going to be introduced within the received signal.

Our primary motive is to reduce the energy consumed by the circuit and to maximize the capacity of a system and it is possible only if we use multiple MIMO system. So a comparative analysis is done to search out a

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system that is more energy economical. The results here indicate that the capacity of the system increases with the increase in the number of transmit and receive antenna.

The capacity of a MIMO system can further be increased if we know the channel parameters both at the transmitter and at the receiver and assign further power at the transmitter by allocating the power according to the water filling algorithms to all the channels.

II. PROPOSED WATER FILLING ALGORITHM Water filling is a metaphor for the solution of many optimization issues related to channel capacity. In Water filling technique the power for the spatial channels are adjusted based on the channels gain. The channel which has high signal to noise ratio and gain is allotted more power. This More power maximizes the sum of data rates in all sub channels. The data rate in each sub channel is related to the power allocation by Shannonâ&#x20AC;&#x2122;s Gaussian capacity formula C=B log (1+ SNR).

The process of water filling is similar to pouring the water in the vessel. The unshaded portion of the graph represents the inverse of the power gain of a particular channel. The portion representing the shadow represents the Power allocated or the water. shows the maximum water level. The total amount of water filled or power allocated is proportional to the Signal to noise ratio of the channel.

The Capacity of a MIMO system is equal to the algebraic sum of the capacities of all channels mathematically it can be written as: Capacity=â&#x2C6;&#x2018;đ?&#x2018;&#x203A;đ?&#x2018;&#x2013;=1 đ?&#x2018;&#x2122;đ?&#x2018;&#x153;đ?&#x2018;&#x201D;2 (1 + đ?&#x2018;&#x192;đ?&#x2018;&#x153;đ?&#x2018;¤đ?&#x2018;&#x2019;đ?&#x2018;&#x; đ??´đ?&#x2018;&#x2122;đ?&#x2018;&#x2122;đ?&#x2018;&#x153;đ?&#x2018;?đ?&#x2018;&#x17D;đ?&#x2018;Ąđ?&#x2018;&#x2019;đ?&#x2018;&#x2018; â&#x2C6;&#x2014; đ??ť) a) MIMO OFDM SYSTEM MODEL OFDM relies on the idea of multiplexing technique that is frequency-division multiplexing. This is the method of transmission of multiple data streams over a broadband medium. That medium can be radio-frequency spectrum, coax cable, twisted pair, or fiber-optic cable. Every data stream is modulated onto multiple adjacent carriers within the bandwidth of the medium, and each is transmitted at the same time.

Capacity Capacity is the measure of maximum information that can be transmitted reliably over a channel. Claude Elwood Shannon developed the following equation for theoretical channel capacity: đ??śđ?&#x2018; đ?&#x2018;&#x2013;đ?&#x2018; đ?&#x2018;&#x153; = B log (1 + SNR) Where, B = transmission bandwidth, SNR = signal to noise ratio The Shannon capacity of MIMO system depends on the number of antenna. For MIMO the capacity is given by the following equation: Cmimo = NB (1 + SNR) Where, N = minimum of number of transmitting antennas or minimum of number of receiving antennas b) Singular Value Decomposition This techniques decouples the channel matrix in spatial domain in a similar manner to the DFT, decoupling the channel in the frequency domain. If channel matrix H is the the T x R channel matrix. If H has indenpend rows and columns, SVD yields: If H = channel matrix ( T x R channel matrix ) And also have independent rows and columns then singular value decomposition yields: H= U â&#x2C6;&#x2018; đ?&#x2018;&#x2030; â&#x201E;&#x17D; Where U = unitary matrices with dimensions of RxR V = unitary matrices with dimensions of T x T h = hermitian of V Case-1: when T=R (1) â&#x2C6;&#x2018; become a diagonal matrix.

(2) If T>R, is made of RxR diagonal matrix followed by T-R zero column.

(3) If T<R, it is made of T x T diagonal matrix followed by R â&#x20AC;&#x201C; T Zero rows.

(4) This operation is called the singular value decomposition of H Case-2: when T â&#x2030; R (1) the number of spatial channels become restricted to minimum to T and R. (2) if the number of transmit antenna > receive antenna U will be an RxR matrix, (3) V will be a T x T matrix (4) â&#x2C6;&#x2018; will be made of square matrix of order R followed by T â&#x20AC;&#x201C; R zero columns.

Power allocated by the individual channel is given by the Eq. 1, as shown in the following formula

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Power Allocated =

đ?&#x2018;&#x192;đ?&#x2018;Ą+â&#x2C6;&#x2018;đ?&#x2018;&#x203A; đ?&#x2018;&#x2013;=1

1 đ??ťđ?&#x2018;&#x2013;

â&#x2C6;&#x2018;đ??śâ&#x201E;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x2019;đ?&#x2018;&#x2122;đ?&#x2018;

-

1 đ??ťđ?&#x2018;&#x2013;

--------(1)

Where, Pt = power budget of MIMO system H = channel matrix of system c) Algorithm Steps:1.

Take the inverse of the channel gains.

2.

Water filling has nonuniform step structure due to the inverse of the channel gain.

3.

At first, take the sum of the Total Power Pt and the Inverse of the channel gain .It gives the complete area in the waterfilling and inverse power gain.

1 Pt +â&#x2C6;&#x2018;đ?&#x2018;&#x203A;đ?&#x2018;&#x2013;=1 đ??ťđ?&#x2018;&#x2013;

5.

6.

Decide the initial water level by the formula given below by taking the average power allocated (average water Level) 1 đ?&#x2018;&#x192;đ?&#x2018;Ą + â&#x2C6;&#x2018;đ?&#x2018;&#x203A;đ?&#x2018;&#x2013;=1 đ??ťđ?&#x2018;&#x2013; â&#x2C6;&#x2018;đ??śâ&#x201E;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x2019;đ?&#x2018;&#x2122;đ?&#x2018; The power values of each sub channel are calculated by subtracting the inverse channel gain of each channel.

Power Allocated =

đ?&#x2018;&#x192;đ?&#x2018;Ą+â&#x2C6;&#x2018;đ?&#x2018;&#x203A; đ?&#x2018;&#x2013;=1

1 đ??ťđ?&#x2018;&#x2013;

â&#x2C6;&#x2018;đ??śâ&#x201E;&#x17D;đ?&#x2018;&#x17D;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x2019;đ?&#x2018;&#x2122;đ?&#x2018;

-

1 đ??ťđ?&#x2018;&#x2013;

--------(5)

7.

In case the Power allocated value becomes negative stop the iteration process. d) MIMO-OFDM Capacity And Outage Probability Consider a MIMO OFDM system with đ?&#x2018; đ?&#x2018;Ą = transmitting antennas đ?&#x2018; đ?&#x2018;&#x; = receiving antennas The system is represented as Y=hx + n Where X= đ?&#x2018; đ?&#x2018;Ą x 1 transmit vector Y= đ?&#x2018; đ?&#x2018;&#x; x 1 receive vector h = đ?&#x2018; đ?&#x2018;Ą x đ?&#x2018; đ?&#x2018;&#x; channel matrix n= đ?&#x2018; đ?&#x2018;&#x; x 1 AWGN vector at a given instant in time.

The channel capacity is associated to an outage probability. If the channel capacity falls below the outage capacity there is no possibility that the transmitted block of information can be decoded with no errors, in which error coding scheme employed. The outage probability is đ?&#x2018;&#x192;đ?&#x2018;&#x153;đ?&#x2018;˘đ?&#x2018;Ą = đ?&#x2018;&#x192;đ?&#x2018;&#x2021; ( log det(đ??źđ?&#x2018; đ?&#x2018;&#x; + hQâ&#x201E;&#x17D;+ ) < R) Where Q=E[HH+] Q = covariance R = information Rate It is conjectured that đ?&#x2018;&#x192;đ?&#x2018;&#x153;đ?&#x2018;˘đ?&#x2018;Ą đ?&#x2018;&#x2013;đ?&#x2018; minimized by using a uniform power allocation over a subset of the transmit antennas. e) MIMO Channel Configuration MIMO configuration uses multi-element antenna arrays at both transmitter and receiver, which effectively exploits the spatial dimension in addition to time and frequency dimensions.Some limitations on the MIMO capacity are imposed by the number of multipath components or scatterers. For fixed linear matrix channel with additive white Gaussian noise and when the transmitted signal vector is composed of statistically independent equal power components each with a Gaussian distribution and the receiver knows the channel, its capacity is đ?&#x153;&#x152; C = đ?&#x2018;&#x2122;đ?&#x2018;&#x153;đ?&#x2018;&#x201D;2 ( det ( đ??źđ?&#x2018; + H * đ??ťđ??ť )) bits/s/Hz. đ?&#x2018; III. SIMULATION & RESULTS: The capacity of MIMO OFDM system channel is analysed with different combination of transmitting and receiving antennas.the combinations of antennas is shown in the table below.the same combination is considered for both types of channels.

Table 1. Combination of Tx - Rx S.NO 1 2 3 4 5 6

NO.OF TX ANTENNA 1 2 2 3 3 4

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NO.OF RX ANTENNA 1 2 3 2 3 4

TYPE OF CHANNEL AWGN & RAYLEIGH FADING AWGN & RAYLEIGH FADING AWGN & RAYLEIGH FADING AWGN & RAYLEIGH FADING AWGN & RAYLEIGH FADING AWGN & RAYLEIGH FADING

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Figure 1: Channel Capacity with AWGN When BW=10 NO=Ie-6

Figure5: Channel Capacity with AWGN When BW=10 NO=Ie-4

Figure2: Channel Capacity with RFC When BW=10 NO = Ie-6

Figure 6: Channel Capacity with AWGN When BW=20 NO=Ie-4

Figure 3: Channel Capacity with AWGN When BW=20 NO=IE-6

Figure 7: Channel Capacity with AWGN When BW=30 NO=Ie-4

Figure 4: Channel Capacity with AWGN When BW = 30 NO = Ie-6

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Figure 8: Channel Capacity with RFC When BW=20 NO=Ie-6

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Figure 9: Channel Capacity with RFC When BW=30 NO=IE-6

Figure 11: Channel Capacity with RFC WHEN BW=20 NO=Ie-4

Figure 10: Channel Capacity with RFC When BW=10 NO=IE-4

Figure 12: Channel Capacity with RFC When BW=30 NO=IE-4

IV. CONCLUSION In this paper we have described the Mean capacity allocation in a wireless cellular network based on the proposed water filling power allocation in order to enhance the capacity of a MIMO systems with different channel assumptions. It is clear from the result graphs that 4 x 4 MIMO OFDM system provides better channel capacity. So, we can say that a higher order MIMO OFDM system increases the system performance. From the result graph it is also clear that system performance remains approximately same when the combination of antennas is altered.

References [1].

[2].

[3].

[4].

[5].

[6].

[7].

[8].

Remika Ngangbam, R.Anandan, Chitralekha Ngangbam, "MIMO-OFDM based Cognitive Radio Networks Capacity analysis with Water Filling Techniques," International Journal of Computer Science & Communication Networks,Vol 3(3),160-163.

Kuldeep Kumar, Manwinder Singh, "Proposed Water filling Model in a MIMO system," International Journal of Emerging Technology and Advanced Engineering, ISSN 2250-2459, Volume 1, Issue 2, December 2011.

Hemangi Deshmukh,Harsh Goud, "Capacity Analysis of MIMO OFDM System using Water filling Algorithm," International Journal of Advanced Research in Computer Engineering & Technology (IJARCET) Volume 1, Issue 8, October 2012.

G. Scutari, et al., "The MIMO iterative waterfilling algorithm," Signal Processing, IEEE Transactions on, vol. 57, pp.

1917-1935, 2009.

V.Jagan Naveen, K.Murali Krishna and K. RajaRajeswari, “Channel capacity estimation in MIMO-OFDM system using water filling algorithm,”International Journal of Engineering Science and Technology (IJEST) Hemangi Deshmukh , Harsh Goud, “ Capacity Analysis of MIMO OFDM System using Water filling Algorithm,” International Journal of Advanced Research in Computer Engineering & Technology (IJARCET) Volume 1, Issue 8, October 2012 W. Liejun, "An Improved Water-filling Power Allocation Method in MIMO OFDM Systems," Information Technology Journal, vol. 10, pp. 639-647, 2011.

Md. Noor-A-Rahim1, Md. Saiful Islam2, Md. Nashid Anjum3, Md. Kamal Hosain4, and Abbas Z. Kouzani, “Performance Analysis of MIMO-OFDM System Using Singular Value Decomposition and Water Filling Algorithm,” (IJACSA) International Journal of Advanced Computer Science and Applications, Vol. 2,No. 4 ,2011

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ISSN (Print): 2328-3491, ISSN (Online): 2328-3580, ISSN (CD-ROM): 2328-3629 AIJRSTEM is a refereed, indexed, peer-reviewed, multidisciplinary and open access journal published by International Association of Scientific Innovation and Research (IASIR), USA (An Association Unifying the Sciences, Engineering, and Applied Research)

ENERGY ANALYSIS OF DISTILLERY SYSTEMS OF AN ALCOHOL FACTORY BY ENERGY AUDIT Samuel Gebremariam Haile*1, Mukesh Didwania2 Lecturer in Mechanical and Vehicle Engineering Department, Adama Science & Technology University, Adama, Ethiopia.

1,2

Abstract: An Alcohol Factory use furnace oil and electricity as primary source of energy to generate thermal and electric energy to pursue its routine alcohol production. All the thermal energy developed by the boiler is used to evaporate alcohol in the distillery columns. The objective of this paper is to examine the way energy is being used in Alcohol Refining Factory, and identify energy conservation opportunities (ECO) so as to reduce energy costs. The nine energy systems of the factory were inspected to identify energy conservation opportunities (ECOS) and major energy consuming systems of the factory. Out of the nine energy systems, the boiler, distillery columns and pumps, air compressor and their prime movers were found to be major energy consuming systems. To perform the energy audit of these major energy consuming systems, different data were collected by using portable instruments, the instruments installed on major energy systems. Standard energy analysis methods were used to perform the energy audit of the boiler, distillery columns, pumps & air compressor and their prime movers. One of these like Distillery system is discussed in this paper. The energy audit results of the distillery revealed that the energy losses due to convection and radiation losses from distillery columns surfaces. By detailed energy audit of the distillery columns, we find that lot of energy is simply thrown away with the hot effluent. so we conclude that By using different kind of heat exchanger for extracting heat energy by hot fluent, the fermented wine temperature is increased and it reduce steam consumption by the distillery columns. Also By installing a double pipe heat exchanger to recover energy loss due to hot effluent, the life time of the heat exchanger is range 10 to 15 years so we conclude that it is economically feasible ECO. Keywords: Alcohol, Distillation, Distillery columns, ECO, Effluent, Energy Audit, Fermented Wine, Heat.

I. Introduction Figure 1 show alcohol factory and it is a governmental organization which produces potable alcohol and currently it has a distillation capacity of 2,600,000 liters of alcohol per year. This implies the factory has an average production capacity of 8,666 liters of alcohol per day.

Figure 1. Aerial view of the factory

This paper revolves around the energy audit of Distillery system of an alcohol refining factories. The product of the factory alcohol is being used as a raw material in many areas of chemical industries. These include: pharmaceutical purpose, hospital service, production of plastic materials, mixing fuel products, fabrication of paints, production of synthetic rubber, laboratory service, heating purpose, etc. Even though the factory product has high market demand the factory is known to operate with loss in 2004/5 fiscal year due to the fact that the factory uses inefficient energy consuming systems [factory document]. The effluent at a temperature of 90°C is simply channeled to the river. The Problems signify that there are high probabilities of energy conserving opportunities (ECO) in the factory. Therefore it is absolutely essential for the factory to conduct energy auditing.

Energy audit is completed for Boiler, Distillery system and motor and its prime movers and one of them like distillery system is discussed in this paper.

Objective of Audit: The general objective of this paper is to examine the way energy is being used in Alcohol Refining Factory, and identify energy conservation opportunities (ECO) so as to reduce energy costs and prepare an energy & documentation to implement cost effective energy utilization changes and The Specific Objectives of the Research are To clearly identify the types of energy and cost of energy use of the factory, To

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understand how that energy is being used and possibly wasted, To indicate better energy conserving opportunities by assessing the efficiency of its energy consuming devices, To examine energy consuming systems of the factory so the improvements can be quantified in terms of both energy and cost: obtain Sankey diagram of the energy use, To identify and analyze improved operational techniques and / or new equipment that could substantially reduce energy use, energy determine which ones are cost-effective and To prepare an energy action plan.

II. Methodology The methods employed to achieve the objectives of the research by audit are: (i) Literature review (ii) Preliminary data collection of the factory (iii) Inspection of factory energy consuming systems and equipment (iv) Perform desktop analysis (v) Identify feasible Energy Conservation Opportunities (ECOs) (vi) Perform technical feasibility of the identified (ECOs) (vii) Perform economic analysis of the identified (ECOs) (viii) Prepare list of recommended energy conservation measures (ECOs) (ix) Prepare action plan a) Preliminary Energy Audit : Preliminary audit methodology is a relatively quick exercise: (i) Establish energy consumption in the organization (ii) Estimate the scope for saving (iii) Identify the most likely and the easiest areas for attention (iv) Set a â&#x20AC;&#x2DC;reference pointâ&#x20AC;&#x2122; (v) Identify immediate (especially no-/low-cost) improvements/ savings (vi) Identify areas for more detailed study/measurement (vii) Use existing or easily obtained data b) Detailed Energy Audit : A detail audit evaluates the major energy using systems using energy balance based on an inventory of energy using systems, assumptions of current operating conditions and calculation of energy use. From industry to industry the metrology of detail energy audit is flexible and is carried out in the following three phases.

Phase I Pre-Audit - Step 1: Organize energy audit team, Organize instrument and time frame and Familiarization of process or facility activities, Step 2: Conduct brief meeting /awareness program with all divisional head and person concerned Phase II Audit Phase - Step 3: Primary data gathering; Products/service of the facility, Process flow diagram and energy utility diagram, Identify major energy systems of the facility, Step 4: Conduct survey and monitoring and Measurement, Step 5: Analysis of energy use; Energy and material balance and energy lost/waste analysis, Step 6: Identification and development of energy conservation opportunities (ECOS), Step 7: Conduct cost benefit analysis; Conduct technical feasibility, Conduct economic feasibility, Step 8: Prepare energy action plane; Prioritize promising ECOS for implementation, Prepare action plan by low, medium and long term measures, Step 9: Reporting and presentation to the top management. Phase III Post Audit Phase - Step 10: Implementation and follow up.

III. Ethanol production process and the energy input The raw material which is used for producing ethanol is molasses purchased from a Sugar Factory. The procedure and process required for the production of ethanol from molasses include dilution of 80 O brix molasses in to 25O brix and 15O brix molasses syrups, propagation of yeast to facilitate the fermentation process and fermented wine is separated from sludge. By distillation of fermented wine, ethanol can be produced and collected. The energy required to perform these process are thermal energy and electrical energy. The detail procedures and process of ethanol production of the factory are discussed below. Flow diagram of alcohol production is shown in Fig 2.

Figure 2. Production Flow Diagram of Alcohol

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a) The Production Process The main raw material used for the production of ethanol in MAF is molasses. Molasses with black & brown color has 50% of sucrose by mass, average 45-50% alcohol content and 78-83 0brix. Brix is a measure of the amount of sucrose present in the molasses. For example 80 0 Brix molasses contain (80*50) / 100 = 40 % of sucrose by mass. During winter and at night times, the molasses is made to flow with the help of a 5kW pump. b) Distillation Process [1] Distillation is one of the major production processes of ethyl alcohol. It is the processes of boiling different mixtures, at different boiling points, in different columns and condensing the evaporation in order to separate one form the other by fractional distillation. And then the high boiling point fluid will remain at the bottom, the upper goes to the condenser and is cooled partially. This partially cooled fluid again goes to the top of other column.

This process is called reflux. The boiling point of alcohol is 78.2 0C but the boiling point of water is 100 0C. The low boiling point and high volatile property makes alcohol to be easily distilled from water. The process of refining alcohol is called fractional distillation. There are different chemical by products during fermentation such as acetic acid, Aldehyde, and high alcohol ester. If the presence of these chemicals is above the limit, they will cause harmful effects including negative impact in the quality of alcohol produced. Therefore, they are removed in different columns during distillation. It is shown in Figure 3a.

IV. Detailed Energy Audit of distillery system The major thermal energy utilizing equipment of the factory is distillery columns. Distillery columns are energy intensive part of the alcohol manufacturing system. The distillery columns are used to evaporate alcohol from water and other solutions by heating it using super-heated steam produce from the boiler. Distillation of alcohol takes place by using five columns namely distillation column, filtration column, rectification column, Demetalizing column and fusel oil column. The detail of these heating (distillation process) is discussed below.

Distillation column consumes an average of 1.2 kg/s of fermented wine. Fermented wine contains 250brix molasses syrups and other solutions. In this column, the separation of alcohol plus some impurities, which have low boiling points from water and other solutions demands the solution temperature to be raised from room temperature to 900C. Alcohol and some impurities would be sent to the filter column for farther separation of alcohol from impurities. This is accomplished by heating the solution up to 73 0C. The remaining large amount of solution which is at a temperature of 900C is channeled to the river as effluent. After leaving the filter column the solution (alcohol) passes through a series of connected columns for further purification process as shown in Figure 3b.

A. Figure 3 (a) Distillation Process for production of alcohol (b) Energy and mass flow of the distillery columns

a) Collected Data for Conducting Detail Energy Audit of the Distillery Inspection of manufacturing system means inspection of distillation system because it consumes all thermal energy produced by the boiler. Hence, inspection of distillation system is conducted using ultra sonic flow meter, infrared thermometer, tap rule and gage mounted on distillery system. The measured data at the distillery system include: external surface temperatures of the columns, ambient temperatures, length and diameters of the columns, steam consumption of each columns, steam pressure and temperature each columns, these data are presented in Tables 1 and Table 2.

Item Length [m] Outside dia [m] Surface Area[m2] Inside dia.[m] Ambient temp.[0C] Surface temp. [0C] Fluid temp.[ 0C]

Distillation column 10 0.9 28.27 0.82 41.50 86 90

Table 1. Data of Distillation Columns Filtration column Rectification De-metalizing Column column 12 3.73 7.75 1 0.9 0.7 37.7 10.6 17.04 0.92 0.82 0.62 42 40 47.2 76 67 86.5 80 73 95

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Fusel oil column 9.15 0.7 20.12 0.62 42.7 83 95

Data collection method Measured Measured Calculated Measured Measured Measured Gauge

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0.455

0.167

0.341

0.326

0.124

Gauge

1 150

1 150

0.5 100

0.5 100

1 100

Gauge Gauge

Table 2. Data on distillation column solutions Reading Unit 790 Kg/m3 1455 Kg/m3 0 28.34 C

Item Density of ethanol Density of fermented wine Temperature of fermented wine

Data collection method From gauge Catalogue Measured

Ambient temperature of fermentation room

24.21

0

Measured

Volume flow rate of ethanol to filter column

0.00023

m3/s

From gauge

Volume flow rate of fermented wine to distillation column

3000

L / hr

From gauge

Temperature of the effluent

90

0

Measured

Ambient (datum) temperature

25

0

datum

C

C C

b) Pre-Energy Performance Analysis of Distillery Columns In order to perform the energy performance analysis of the distillery columns, the following parameters must be determined: the mass flow rate of effluent, mass flow rate of fermented wine, mass flow rate of steam for each columns, specific heat of fermented wine and effluent. Each parameter is discussed below.

Calculation of Mass Flow Rate of Steam in each Column: The volume flow rate, temperature and pressure of

steam input to each column are read from the gage mounted on the control panel and tabulated in Table 1. Using the gage temperature and pressure of the steam, the density of steam is determined using standard steam table.

The mass flow rate of the steam is calculated by multiplying volume flow rate of the steam by the density. The amount of steam supplied to each column is calculated using equation (1) - (5). 

Mass flow rate of steam consumed by distillation column 3



ms ( dist .)  V s ( dist .) 

1 v@1bar &150 O C

3

= 0.455 m /s * 0.516 kg/m = 0.235 kg/s

(1) 

Mass flow rate of steam consumed by filtration column



ms ( filt .)  V s ( filt .) 

1 v@0.5bar &100 OC

= 0.314 m3/s * 0.293 kg/m3 = 0.092 kg/s

(2) 

Mass flow rate of steam consumed by rectification column



ms ( rect .)  V s ( rect .) 

1 v@1bar &150 OC

= 0.167 m3/s * 0.516 kg/m3 = 0.086 kg/s

(3) 

Mass flow rate of steam consumed by de-metalizing column



ms ( demt .)  V s ( demt .) 

1 v@0.5bar &100 O C

= 0.362 m3/s * 0.293 kg/m3 = 0.106 kg/s

(4) 

Mass flow rate of steam consumed by fuel oil column 3



ms ( fuse.)  V s ( fuse.) 

1 v@1bar &100 O C

3

= 0.124 m /s * 0.589 kg/m = 0.073 kg/s

(5)

The total amount of steam consumed by factory distillery columns is the sum of steam consumed by each column. 











m S (total)  m ( dist.)  m ( filt)  m ( rect )  m ( demt )  m ( fuse) = 0.235 kg/s +0.092 kg/s +0.086 kg/s+ 0.106 kg/s+ 0.073 kg/s = 0.592 kg/s

(6)

Concluding remark on mass balance of the steam

The mass balance of the produced steam consist of operating steam input mass and steam supplied to each distillery columns, vent steam, and steam supplied to de-aerator as output mass. The mass balance of the steam is as shown below.

Input mass (operating) of steam = 0.828 kg/s

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Output mass: Total steam supplied to each distillery columns = 0.592 kg/s, Mass flow rate of vent steam = 0.15 kg/s, Mass flow rate of de-aerator steam = 0.0563 kg/s, Total output mass = 0.7983 kg/s The difference of input and output mass of the steam is 0.0297 kg/s. This difference is due to measuring errors.

Calculation of Mass Flow Rate of Fermented Wine Total amount of fermented wine sent to distillation column from fermented wine tank is 3000 lit/hr [Table 2].

Therefore, the total amount of mass flow rate of fermented wine can be calculated by multiplying the volume flow rate by its density. 



m wine  V wine   wine But



V wine  3000

lit  hr

(7) 1

1000

 0.000833

lit s  3600 3 hr m

m3 ; s

 wine  1455

kg [11] m3

Hence substituting the above data in Equation (7) the mass flow rate of fermented wine is equals to 



3

m wine  V wine   wine = 0.000833m  1455 kg3 = 1.21 s

m

kg s

Calculation of Mass Flow Rate of Ethanol

Total amount of alcohol sent to filtration column from distillation column is 828 lit/hr [Table 2]. Therefore, the total amount of mass flow rate of alcohol can be calculated by multiplying the volume flow rate by its density. 



malcohol  V alcohol   alcohol But



V alcohol  828

(8) 3

lit 1 m   0.00023 hr 1000 lit  3600 s s m3 hr

;

 alcohol  790

kg [11] m3

Hence substituting the above data in Equation (8) the mass flow rate of alcohol is equals to 



malcohol  V alcohol   alcohol = 0.00023

m3 kg kg  790 3 = 0.182 s s m

Estimation of Mass Flow Rate of Effluent

Due to pipe surface corrosion, direct measurement of flow velocity of an effluent is impossible. But assuming no leakage is observed in the distillery columns we can estimate the mass flow rate of the effluent by equating mass in equal mass out in columns using equation (9). 











m s ( total )  m wine  m effl  m alco Or Substituting the results of equation (6 – 8) in (9) the mass flow rate of effluent is 









m effl  ( m s (total )  m wine )  m alco

(9)



m effl  ( m s (total )  m wine )  m alco = (0.592 kg/s +1.21 kg/s)-0.182 kg/s = 0.162 kg/s Calculation of Specific Heat Specific Heat of Effluent The specific heat of effluent during the distillation of alcohol is given by [9]

Cp (eff) = (3.14 + (0.000025(Teff–Tamb)))

(10) Where Teff = Effluent Temperature = 900 C [Table 2], Tamb = Ambient temperature = 250C [Table 2] Substituting the above data in equation (10) the specific heat of the effluent will be = (3.14 + (0.000025(900 –250))) = 3.14 KJ/kg 0C Specific Heat of Fermented Wine According to [9], the specific heat of fermented wine is determined by substituting the values of temperature of fermented wine instead of temperature of the effluent in equation (10).Therefore the specific heat of fermented wine is given by.

Cp (wine) = (3.14 + (0.000025(Twine–Tamb)))

(11)

Where Twine - Fermentation temperature = 28.34 0C [Table 2], Tamb - Ambient temperature = 25 0C [Table 2]

Substituting the above data in equation (11) the specific heat of the fermented wine is given Cp (wine) = (3.14+ (0.000025(28.340C – 250C))) = 3.14 kJ/kg 0C c) Detail Energy Analysis of the Distillery Columns To perform the thermal energy audit of the distillery columns and thereby obtain the net energy loss from the distillation process, thermal energy analysis of the distillery columns must be conducted. The energy analysis is

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based on the energy input and output of the distillery columns. All the input-output energy of the distillery is as shown in figure 4.

Figure 4. Input-output energy of the distillery

Analysis of the Input Energy in the Distillery

As illustrated in Figure 4 steam and fermented wine are the input energy of the distillery columns. The two energy sources of the distillery columns are discussed below.

Steam Energy to the Distillery Columns: one of the major energy sources of the distillery columns is steam energy. The amount of heat energy supplied to the distillery columns can be calculated by multiplying the mass flow rate of steam to each column by its enthalpy. The input steam energy can be obtained using equation (12). 

Q( i ) s  m( i ) s  h( i ) gs

(12)



Where

m ( i ) s - Mass flow rate of steam to columns, h( i ) gs - Enthalpy of super-heated steam at a given temperature

and pressure [Table 3] 

Substitute the values of

m ( i ) s from equation (1) to (5) and the corresponding h(i ) gs

from steam table according to

temperature and pressure values and finally the results are summarized in Table 3 Table 3 Input steam energy in distillation columns Temp. [0C] Pressure [bar] Enthalpy (hgs) kJ/kg Steam (ṁs) [kg/s] 0.235 150 1 2776.4

Heat input [kW] 652.5

Filtration Rectification De-metalizing

0.092 0.086 0.106

100 150 100

0.5 1 0.5

2682.5 2776.4 2682.5

246.79 239 284.34

Fusel oil Total

0.073

100

1

2676.2

195.4 1618.03

Columns Distillation

Energy in the Fermented Wine: The energy of fermented wine is the enthalpy of fermented wine by virtue of its

temperature elevation relative to the ambient temperature of fermentation room. The enthalpy of fermented wine due to its temperature elevation from the ambient temperature fermentation temperature can be obtained using the following equation (13). 

Qwine  m wine  C P ( wine) Twine  Tamb  Where

Qwine  Energy

(13) 

of fermented wine,

m wine  Mass

Specific heat of fermented wine = 3.14 kJ/kg 0C (12),

flow rate of fermented wine =1.21 kg/s (7), Cp

(wine)

-

Twine  Fermentation temperature = 28.34 0C (Table 2),

Tamb  Ambient temperature = 250C (Table 2) Substituting the above data in Equation (13) input energy due to fermented wine is given Qwine = 1.21 kg/s * 3.14 kj/kg 0C (2834 0C - 25 0C) = 12.7 kW Analysis of the Output Energy in the Distillery The energy losses associated with the distillation of alcohol in the distillery columns is indicated in figure 4 include energy loss due to: Energy Loss Due to Effluent: The energy loss due to effluent leaving the distillation column can be obtained using the mass flow rate of effluent and enthalpy change of effluent at effluent temperature relative to the ambient temperature. The analysis is executed using equation (14).

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Qeff  m eff C P ( eff ) Teff  Tamb  

(14) 

Where Q eff = Energy loss with the effluent, m eff  Mass flow rate of effluent = 1.53 kg/s (Eq. 9), C p (eff) = Specific heat of effluent = 3.14 kJ/kg 0C (Eq. 11), Teff = Effluent temperature = 90 0C (Table 2), Tamb = Ambient temperature = 25 0C (Table 2)

Substituting the above data in Equation (15) energy loss with the effluent is given Qeff = 1.53 kg/s * 3.14 kj/kg 0C (90 0C - 25 0C) = 312.3kW Heat loss due to Radiation and Convection from the Distillery Surface: As wind cruises over the distillery surface, energy will be lost from the distillery surface to the wind by convection. In addition, due to difference in temperature between the ambient air and the distillery surface, there is also radiation energy loss. The energy loss due to convection and radiation in watt per unit area of the distillery surface exposed to the ambient temperature condition is given by [4].

Q(i)s = [0.548{(T(i)s / 55.55)4 – (T(i)a / 55.55)4 }+1.957(T(i)s - T(i)a )125 √{(19685V+689)/689 }w/m2 *S(i)A (15) Where T(i)S- Surface temperature of the ith distillery column (Table 1), T (i)a- Local ambient temperature of the ith distillery column (Table 1), S(i)A- Surface area of the ith distillery column(Table 1), V- Wind velocity = 2.56 m/s Substituting the values of the above data from (Table 1) in Equation (15) the total heat loss due to convection and radiation is summarized in Table 4.

Columns

Table 4 Heat loss from distillery surface Ambient temperature (K) Surface temperature (K)

Surface area (m2)

Heat loss (kW)

Distillation

314.5

359

28.27

29.57

Filtration Rectification De-metalizing

313 315 320.2

340 349 359

10.6 37.7 17.04

5.97 28.42 12.31

Fusel oil Total

315.7

356

21.12

19.63 95.90

Heat to Evaporate Alcohol: The heat energy used to perform the evaporation of alcohol from fermented wine can

be found from energy balance of heat entering and leaving the distillery columns.

Heat in steam + Heat in fermented wine = Heat in effluent + Heat loss by radiation and convection + Heat in vapor alcohol Mathematically

Qs + Q wine = Qeff  Qsurf  Qalcoh

(16)

Qalcoh  (QS  Qwine )  (Qsurf  Qeff )

(17)

Substitute the values of Equations (13) to Equation (17) the heat energy carried by evaporation of alcohol is given by Q alcohol = (1619.35 kW + 12.7 kW) – (95.90 kW +312.3 KW) = 1223.9 kW V. Result and discussion The unwanted energy losses are energy loss from distillery surface and energy that is leaving with effluent.

According to detailed energy audit of the distillery columns, 312.3kW of energy is simply thrown away with the effluent. The energy audit results of the distillery revealed that the energy losses due to convection and radiation losses from distillery columns surfaces are 5.86% of input energy. The energy losses due to the heat that is leaving with effluent is 15.86% of the input energy. According to [9], the recommended percentage of heat carried away by the effluent is not greater than 10% of the input energy. This indicates that, the percentage of heat carried away by the effluent in the factory distillery columns is more than the recommended value. From detailed energy audit conducted, this energy conservation opportunities (ECOs) is found: 1. Recovering heat from the hot effluent.

VI. Recommendation a) Technical Evaluation of Recovering Heat from Hot Effluent

According to detailed energy audit of the distillery columns, 312.3kW of energy is simply thrown away with the effluent. But most of alcohol producing factories extracts heat energy from hot effluent by using different types of heat exchangers for preheating fermented wine and thereby reduces their steam consumption. According to [10], using double pipe heat exchangers, for preheating fermented wine by hot effluent, the temperature of fermented wine can be increased from 20 to 30 0C. Thus the factory must be using a heat exchanger to increase their fermented wine temperature in order to reduce steam consumption by the distillery columns. The technical

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evaluation to determining fermented wine temperature when the fermented wine is preheated by hot effluent is discussed below. Let the heat exchanger is counter flow double pipe heat exchanger type.

For counter flow, the outlet temperature of the cooler fluid (fermented wine) can be ether equal or made to exceed the outlet temperature of warmer fluid (effluent). Assuming the outlet temperature of the fermented wine and effluent is equal. So for calculating the effluent temperature the equation is

Teff ( out )  Twine( out )

Teff ( in )  Twine( in )

(18)

(1  R) 

Where Mass flow rate of the effluent = m eff = 1.62 kg/s, Inlet temperature of the effluent = Teff (in ) = 900C, Inlet temperature of wine =

Twine(in ) = 28.34 0C, Specific heat the effluent = c p eff = 3.14 kJ/kg 0C, Specific heat the wine 

= Cp wine= 3.14 kJ/kg 0C, Mass flow rate of the wine = m wine = 1.21kg/s

Substituting the above data in Equation (18) the outlet temperature of the fluid is 51.52 0C, thus the fermented wine temperature will be increased by 23.180C. Using the known mass flow rate and density of the fluids, and the economic range of fluid velocity it is possible to determine the size of the exchanger. b) Economical Evaluation of Recover heat from hot effluent by installation double pipe heat exchanger The economic evaluation and analysis of the feasible energy conservation opportunities involves calculating the energy to be saved, the cost of implementing the energy saving opportunities and determining the payback period of the energy investment. These analyses are performed below.

Energy Saving Analysis: From the results of the energy audit analysis performed so far, it is known that the energy gained by fermented wine at a temperature of 28.340C is 16.03 kW. But using a double pipe heat exchanger to preheat the fermented wine by hot effluent, the temperature of fermented wine can be brought to 51.52 0C. The energy of the fermented wine that could be increased by installing a double pipe heat exchanger is given by 

QNew( wine)  m wine Twine  Tamb 

(19)

Where Q new (wine) = Energy gained by preheated of fermented wine, ṁ wine - Mass flow rate of fermented wine = 1.21 kg/s (Eq.7), Cp wine= Specific heat of fermented wine = 3.14 kJ/kg 0C (Eq.11), Twine-Fermentation temperature = 51.52 0C (Eq.20), T amb- Ambient temperature = 24.12 0C (Table 2) Substituting the above data in Equation (19) the energy gained due to preheated fermented wine is given Q wine = 1.21 kg/s * 3.14 kJ/kg 0C (51.52 0C - 24.12 0C) = 104.10 kW Therefore, the net energy gained due to preheating fermented wine is 104.10 kW – 16.03 kW = 88.07 kW. The equivalent fuel and money saved is 55,107.80 litre and 229,523.99 Ethiopian birr (11034 USD) per year respectively.

Cost Analysis: The cost of a typical double pipe heat exchanger ranges from 50,000 – 60,000 Ethiopian Birr (2400–2500 USD) depending on size, length and feature. An average effective life time of the heat exchanger is 10 years [10].

Payback Period: The payback period can be found by dividing the cost saved with the cost of heat exchanger.

Adding 47% [8], additional cost on the direct average cost of purchasing the heat exchanger for transportation and other related costs, the cost of having the heat exchanger will be 1.47 x 60,000 = 88,200 Ethiopian Birr (4240 USD).

Payback Period = Cost of heat exchanger/Cost Saved = 88,200 Birr/ 229,523.99 Birr per year = 0.4 Years (24) The life time of the heat exchanger is range 10 to 15 years therefore, it is economically feasible ECO. VII. Conclusion According to detailed energy audit of the distillery columns (Recover Heat from Effluent), 259.43kW of energy is simply thrown away with the effluent. But most alcohol producing factories extract heat energy from hot effluent by using different types of heat exchangers for preheating fermented wine so we conclude that by using different kind of heat exchanger for extracting heat energy by hot fluent, the fermented wine temperature is increased by 23.180C and reduce steam consumption by the distillery columns.

By installing a double pipe heat exchanger to recover energy loss due to hot effluent, the technical and economic analysis were conducted which resulted in net energy gain by the fermented wine of 88.07 kW. As a result cost saving is 229,524 Birr (11034 USD) per year; implementation cost is 88,200 Birr (4240 USD) and payback period is 0.4 years and also the life time of the heat exchanger is range 10 to 15 years so we conclude that it is economically feasible ECO.

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VIII. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]

Adrian Beian: Advanced Engineering Thermodynamics, (1998),John Wiley & Sons, Inc,U.S.A. A.Valan Arasu: Turbo Machines, Vikas publishing house pvt.Ltd, New Delhi 2006.

Barney L.Capehart, PhD, CEM; Guide to Energy management, 2nd edition. http//:www.Bureau of Energy Efficiency: Performance Analysis of Boiler.pdf.

Christina Galitsky, Ernest Worrel and Michael Ruth, Energy Efficiency Improvement and cost saving, 2004.

Christopher Russell, C.E.M. Industrial Action Plans for Greater and More Durable Energy Cost Control, 2006.

Energy Efficiency Project Management Handbook, Organized by California energy commission, California, 2000.

W.Berhrens & P.M.Hawranek Manual for the preparation of industrial feasibility studies, newly revised and expanded edition, Vienna, 1991.

How Much Energy Does It Take to Make a Gallon of Ethanol, Institute for Local Self-Reliance, National Office, Washington, DC 2005.

Monthly Reports of production and technical departments of Balezaf Alcohol and Liquor Factory.

Operating and production process manual, Nation Alcohol and Liquor Factory. http:www.clever-books.com/ Clever Books Website. *Samuel Gebremariam Haile and Mukesh Didwania are Lecturer in Mechanical and Vehicle Engineering Department, Adama Science & Technology University, Adama, Ethiopia. Specialized in Thermal Engineering and Samuelâ&#x20AC;&#x2122;s research area is energy engineering and management and Mukesh is working on CFD and heat transfer and interested area is Turbomachinery.

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American International Journal of Research in Science, Technology, Engineering & Mathematics

Available online at http://www.iasir.net

ISSN (Print): 2328-3491, ISSN (Online): 2328-3580, ISSN (CD-ROM): 2328-3629 AIJRSTEM is a refereed, indexed, peer-reviewed, multidisciplinary and open access journal published by International Association of Scientific Innovation and Research (IASIR), USA (An Association Unifying the Sciences, Engineering, and Applied Research)

Genetic Algorithm Approach to Multi-Objective Linear Fractional Programming Problems Savita Mishra Department of Mathematics, The Graduate School College for Women, Sakchi, Jamshedpur,Jharkhand, India-831001 Abstract: Solving multi-objective decisionâ&#x20AC;&#x201C;making problems is, generally, a very difficult goal. In these particular optimization problems, the objectives often conflict across a high-dimensional problem space and may also require extensive computational resources. Genetic Algorithm (GA) is a stochastic heuristic optimization search technique designed following the natural selection process in biological evolution to arrive at optimal or near-optimal solutions to complex decision making problems. In this paper we consider the solution of multi-objective linear-fractional decision-making problems by GA. The GA proposed by us can produce results, which are very close or improved to the results obtained by the existing methods.

Keywords: Multi-objective decision-making (MODM) problems, fractional programming problems, genetic algorithm (GA), optimal solution, compromise solution.

AMS-MSC 2010 NO.: 60J25, 60J27, 60J28 ,90C59.

I. Introduction Multi-objective optimization problems have attracted considerable attention from the scientific and economic community in recent years. Multi-Objective Decision Making (MODM) has been one of the fastest growing problem areas in many disciplines. The multilevel multi-objective system has extensive existences in management fields. Usually, this kind of problem can be solved by multiple mathematical programming.

Although this problem is very relevant in practice, there are few methods available and their quality is hard to determine.

Fractional programming (FP) which has been being used as an important planning tool for the past four decades is applied for a lot of disciplines such as engineering, business, finance, economics etc. FP is generally used for modeling real life problem which has one or more than one objective(s) as a ratio of two functions such as profit/loss, inventory/sales, actual cost/standard cost, output/employee etc. Fractional programs arise in various contexts such as , in investment problems, the firm wants to select a number of projects on which money is to be invested so that the ratio of the profits to the capital invested is maximum subject to the total capital available and other economic requirements which may be assumed to be linear. If the price per unit depends linearly on the output and the capital is a linear function then the problem is reduced to a linear fractional program.

An example of linear fractional programming was first identified and solved by Isbell and Marlow (1956).Their algorithm generates a sequence of linear programs whose solutions converge to the solution of the fractional program in a finite number of iterations. Since then several methods of solutions were developed.

Gilmore and Gomory (1963) modified the simplex method to obtain a direct solution of the problem. Martos (1964) has suggested a simplex-line procedure, while by making a transformation of variables, Charnes and Cooper (1962) have shown that a solution of the problem can be obtained by solving at most two ordinary linear programs. Algorithms based on the parametric form of the problem have been developed by Jagannathan (1966) and Dinkelbach (1967).

After the development of the method by Isbell and Marlow (1956) for solving linear fractional programming problems, various aspects of single objective mathematical programming have been studied quite extensively. It was however realized that almost every real-life problem involves more than one objective. For such problems, the decision makers have to deal with several objectives conflicting with one another, which are to be optimized simultaneously. For example, in transportation problem, one might like to minimize the operating cost, minimize the average shipping time, minimize the production cost and maximize its capacity. Similarly, in production planning, the plant manager might be interested in obtaining a production programme which would simultaneously maximize profit, minimize the inventory of the finished goods, minimize the overtime and minimize the back orders. Several other problems in modern management can also be identified as having multiple conflicting objectives i.e., multi-objective decision-making (MODM) problem. There is pressing need

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to develop approaches to solve such type of multi-objective linear or non-linear fractional programming problems .

Multi-objective linear fractional programming (MOLFP) problems are studied by a few approaches which have appeared in Kornbluth and Steur (1981); Lai (1996); Luhandjula (1984); Sakawa and Yumine (1983).

Luhandjula (1984)proposed a linguist approach to multi objective linear fractional programming by introducing linguistic variables to represent linguistic aspirations of the decision makers .The model of the problem constructed with fuzzy data due to FP approaches [Luhandjula (1984); Sakawa and Yumine (1983)] used to solve MOLFP problems have a difficulty in computation. In the framework of fuzzy decision, Bellman and Zadeh (1970) ;Sakawa and Yumine (1983) presented a fuzzy programming approach for solving multi objective linear fractional programming problem by combined use of the bi-section method and the phase one of simplex methods of linear programming. Multi-level multi-objective linear or non-linear programming problems are new combination problems in the field of multi-level (or multi- objective) decision making problems. Ibrahim (2009) proposed Fuzzy goal programming algorithm for solving decentralized bi-level multi-objective programming problems. Again, Ibrahim (2010) proposed a fuzzy goal programming approach to Solve multi-level multiobjective linear programming problems. Eren and Turan (2013) used Fuzzy multi-objective linear programming approach for optimising a closed-loop supply chain network.

Again for MOLFP, Kornbluth and Steuer (1981) presented two different approaches to MOLFP , based on the weighted Tchebyscheff norm.

In this paper we deal with the MOLFP problems with the essentially cooperative DMs and propose a solution procedure using a genetic algorithm for the problem. GAs was first introduced by Holland [1975] and since then it has been applied to many OR field such as: De Jong (1975); Baker (1985); Goldberg (1989); Michalewicz (1992); Wanga Guangmin et al. (2008); Narang and Arora (2009); Ketabchi et al. (December 2010); Hecheng and Wang (2010) etc. Although various optimization tools are available for MODM problems, the efficiency of these techniques depends to a great extent on the nature of the mathematical formulation of the problem.Some of these traditional techniques, which give accurate results are computationally expansive and become inefficient for a large domain.Genetic Algorithm, which is a population – based search technique Goldberg (1989) has been widely studied, experimented and applied in many fields in engineering worlds.Not only does GAs provide an alternate method to solving problem,it consistently outperforms other tradional methods in the most of the problem link. In general, GAs performs directed random searches through a given set of alternatives with the aim of finding the best alternative with respect to given criteria of goodness. These criteria are required to be expressed in terms of an objective function, which is usually referred to as fitness function. GA search for the best alternative (in the sense of a given fitness function) through ‘chromosomes’ evolution. This paper demonstrates the merit of this technique in deciding optimal solution of multi-objective linear fractional decision-making (MOLFDM) problem taking into cosideration the various constraints and complexities representing the real situation.

The organization of the paper is as follows: following the introduction, this paper presents a brief introduction to MOLFP problem in section-2 and genetic algorithm in section-3. Section-4 and 5 provide the implementation and step by step procedures of the proposed genetic algorithm. Numerical example and a brief discussion are presented in section- 6 and 7 respectively. Section-8 deals with concluding remarks.

II. Multi-objective linear fractional programming (MOLFP) problems A MOLFP problem contains more than one linear fractional objective function and linear or non-linear constraints. Mathematically, a MOLFP problem can be stated as:

Max / Min :

z1 ( x), z 2 ( x), z3 ( x),........ , z P ( x)

subject to n

a j 1

ij

x j (, , )bi ,

i  1,2,..., m

x  0.

Where objective functions z i (x) , i  1,2,........ m. are represented by a linear fractional function:

z i ( x) 

pi ( x) qi ( x )

pi (x) and q i (x ) are linear functions. x is an n  dimensional vector. The problem indicates that there are P numbers of objective functions, which are to be maximized or minimized. The problem contains m number of constraints and n number of decision variables.

Where,

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Most real-world decision problems involve multiple criteria that are often conflict in general and it is sometimes necessary to conduct trade-off analysis in MODM. We can find many instances of decision problem, which are formulated as MODM problem, and in decentralized firm, it is natural that the decision makers behave cooperatively rather than non-cooperatively.

III. Introduction to Genetic Algorithm Genetic algorithm (GA) is search algorithms based on the mechanism of natural selection and natural genetics.

GA is a stochastic heuristic optimization search technique designed following the natural selection process in biological evolution to arrive at optimal or near optimal solutions to complex decision problems. The primary concept behind the use of GAs is the representation of solutions to a problem in an encoded format. These encoded parameters (alleles) are referred to as genes and these are joined to build strings, which represent a potential solution to the problem. These strings of variables are called the chromosomes. Each gene can be represented by a binary string or a real value. The fitness of a chromosome as a candidate solution to a problem is an expression of the objective function represented by it.

The random interaction of the genes in populations under different GA operators constitutes the GA technique [De Jong (1975); Baker (1985); Deb (1995); Holland (1975); Michalewicz (1992)]. The genetic operators used in reproductive process are selection, crossover and mutation.

Selection is the procedure by which chromosomes are chosen for participation in the reproduction process. New points in the search space are generated by crossover and mutation. Crossover is the exchange of important building blocks between two strings that perform well. The number of strings in which material is exchanged is controlled by the crossover probability forming part of the parametric data. Goldberg (1989) and Michalewicz (1992) described various methods of crossover.

Mutation is an important process that permits new genetic material to be introduced to a population. A mutation probability is specified that permits random mutations to be made to individual genes.

An initial population of individuals representing possible solutions is created when this technique is applied to a problem. Each of these individuals has certain characteristics that make them more or less fit as members of the population. The most fit members will have a higher probability of matching than lesser fit members, to produce offsprings that have a significant chance of retaining the desirable attributes of their parents.

This method is very effective at finding optimal or near optimal solutions because of the use of populations of solutions at every iteration, as opposed to single solution, help genetic algorithm to examine the population space, and hence avoid local optimal traps. Also it does not impose many of the limitations required by traditional methods. It is an elegant generate-and- art strategy that can identify and exploit regularities in the environment, and converges on solution that are globally optimal or nearly so.

IV. Procedure of the proposed Genetic Algorithm A. Representation The first step in designing a genetic algorithm for a particular problem is to devise a suitable representation scheme.There are many ways to represent a chromosome, in a GA. Most GAs in used today still used binary chromosome as suggested by Holland in his pioneering effort Holland (1975).The motivation for the use of binary chromosome is that for a given amount of information content, binary strings contains the largest number of schemata and hence provide the GA with the largest space to search and locate similarities between successful chromosomes. Here we use binary vectors as a chromosome to represent real value.

B. Initialization Initially many individual solutions are randomly generated to form an initial population. The population size depends on the nature of the problem. In this paper the process of initialization used by Liu (2002) is followed.

An integer is defined as the number of chromosomes, called pop_size and initialize pop-size chromosome (0)

randomly. Suppose that it is feasible for a decision maker to determine to an interior point x within the constraint set. Let M be an appropriate large positive number so that all the genetic operators are probabilistically complete for the feasible solutions. Select a direction d

n

in R and define a chromosome

x

 M .d if it feasible for the inequality constraints. If not, then we select a random number between 0 x ( 0)  M . d is feasible. To obtain the pop_size initial feasible chromosomes and M until x (1) , x ( 2 ) ,……. x ( pop _ size) , we repeat the process pop_size times. as x

(0)

C. Fitness function and selection strategy During each successive epoch, a proportion of existing population is selected to breed a new generation.

Individual solutions are selected through a fitness-based process. The selection strategy is one of the most important factors in the genetic search. Initially Holland (1975) used the Roulette wheel selection strategy. But

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it has some limitations for example, it only works for the maximization problem and it is not appropriate to apply it to minimization problem because it assigns greater probability to the chromosome that has a greater fitness value. Also in the presence of some super individuals, the Roullet wheel does not work properly. A super individual has a comparatively greater chance to be selected because it has significantly better fitness value.

Consequently, it has relatively large number of off spring and has a tendency to prevent other individual from being selected to contribute to the next generation. Therefore, after a number of generations, a super individual may eliminate other individual and lead to a local optimum.

There are several modified models of Roullet wheel selection such as De Jong (1975) elitist model, expected value model and crowding factor model that try to overcome the restrictions. Baker (1985) proposed a ranking method by mapping individuals to a partially ordered set. The ranking method is a non parametric selection procedure. The population is stored by the fitness values from the best to worst. Ranking methods assign probability to individuals based on their ranks. Therefore, minimization and negativity of the objective function become eligible. Motivated by this analysis we use the normalized geometric Ranking method . In this method, the probability of the i

th

individual being selected is defined by:

P ( Select the i th individual)  a' (1  a) i 1 Where, a is the probability of selecting the best individual, i rank of the individual, a a'  {1  (1  a ) pop _ size } The highest efficiency is regarded as a common benchmark for Decision Making Units (DMUs). This brings about the existence of more than one DMU with the highest score. One may also use Ranking Method Based on Common Weights proposed by Ali Payan et al. (June 2014) or Weighting method by Mishra Savita (2007). The overall balance in decentralized programming problem is seen through the consistency ratio.

Consistency means that the decision maker is exhibiting coherent judgments in specifying the pair wise comparison ( Morteza Rahmami , June 2009 ) of the criteria or alternatives.

D. The crossover The crossover operator is one of the important genetic operators. In the optimization problem with continuous variable, many crossover operators appeared, such as Michalewicz (1992): simple crossover, heuristic crossover and arithmetical crossover. Among them, arithmetical crossover has the most popular application. The paper uses arithmetical crossover which can ensure the off-springs are still in the constraint region and moreover the system is more stable and the variance of the best solution is smaller. The arithmetical crossover can generate two off-springs which are totally linear combined by the father individuals.

Crossover is a genetic operator used to vary the programming of a chromosome or chromosomes from one generation to the next. It is an analogy to reproduction and biological crossover, upon which genetic algorithm are based. The crossover is responsible for the recombination process. It is applied to pairs of chromosomes with a probability, say pc to create new children. We determine the parents for crossover as in Liu (2002). A random number c is generated from the interval [0,1]. The chromosome x

(i )

is selected as a parent if

c  pc . We

i  1 to pop_size times. If x (1) and x ( 2 ) be two parents then the crossover operator (1) ( 2) will produce two children y and y as follows: repeat the process from

y (1)  r.x (1)  (1  r ).x ( 2) y ( 2)  (1  r ).x (1)  r.x ( 2) Where r is a random number generated from (0,1) . Now we check the feasibility of the children chromosomes. If both the children are feasible, then replace the parents by them. If one child is feasible or no children are feasible, we generate the random number until two feasible children are obtained.

E. Mutation Mutation operator performs changes in a single individual. It randomly searches in the neighborhood of a particular solution. Its role is very important to guarantee that the whole search space is reachable.

We define the probability of mutation and use the process similar to that of selecting parents for crossover operation for mutation. Now for each selected parent chromosome, we randomly choose a direction d If

n

in R .

x ( 0)  M . d , where x ( 0)  (x1 , x 2 ,……. x n ) and M is a sufficiently large positive number define

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earlier in the process of initialization, is not feasible, select a number between 0 and

M until it is feasible. If (0) the process fails to produce a feasible solution, we set M  0 and replace the parent x by its (0) child x  M .d .

F. Stopping rule A parameter called number of generation is defined for a GA. As soon as the number of iteration will be equal to the number of generation, the execution will be stopped.

V. Steps of Proposed GAs are as follows: Step-1: Randomly initialize number of chromosome which is equal to the size of the population size (population of feasible trial solution of different decision maker).

Step-2: Apply crossover and mutations scheme as described above to upgrade the chromosomes.

Step-3: For all chromosomes (decision maker), calculate the value of the objectives (each of which is a ratio of two linear functions).

Step-4: According to the value of the objective, calculate the fitness of each chromosome (member).

Step-5: Select the chromosome according to the selection process.

Step-6: Repeat step-1, step-2, step-3, step-4 and step-5.

Step-7: Report the best chromosome as the optimal solution.

Used parameters and their values Parameters Population size Probability of crossover Probability of Mutation Number of Generation

Notations Pop_size pc pm N

Value 50 0.8 0.08 Problem Dependent

VI. Numerical Example The following example considered by Chakraborty and Gupta (2002) is again used to demonstrate the solution procedures and clarify the effectiveness of the proposed approach: Consider the following MOLFP problem Chakraborty and Gupta (2002):

 3x1  2 x2 x1  x2  3 7 x1  2 x2  5 x1  2 x2  1 x1  4 x2  2 x1  3x 2  2 

max z1 max z 2

max z 3

subject to x1  2 x2  1;

2 x1  3x2  15;

x1  9 x2  9;

x1 3,

x2  0 .

Solution: Solution of the above problem obtained by Chakraborty and Gupta [5] using fuzzy mathematical programming is:

x1

x2

z1

z2

z3

3

2

-0.625

1.15

0.785714

z1

z2

z3

The proposed GA gives the solution as:

x1

x2

3.599999 2.599999 -0.608696 1.14760 0.823529 Which is very close or improved to the results obtained by the existing methods Chakraborty and Gupta (2002).

VII. Discussion Multi-objective linear fractional decision making problem is an important branch of Operation Research.

Presently many approaches have been made to solve MODM problems mostly based on fuzzy programming.

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However, it has not yet made a significant break through in the field of MOLFP problem. Following are the advantages and special features of the proposed algorithm to solve MOLFP problem: (1) Multi-objective programming problems have some properties that are more complex than in the usual mathematical programs .Thus solution techniques for this problem have to be rather specialized. Feasible solutions for a MODM problem correspond to members of a particular species, where the fitness of each member is measured by the value of the objective function. Rather than processing a single trial solution at a time, the proposed approach now work with an entire population of trial solution and the population is used to create linking paths between its members and to re-launch the search along these paths.

(2) For each iteration (generation) of a genetic algorithm, the current population consists of the set of trial solutions currently under consideration. These trial solutions are thought of as the currently living members of the species. Some of the youngest members of the population (including especially the fittest members) survive into adulthood and become parents (paired at random) who then have children (new trial solutions) who share some of the features (genes) of both parents.

(3) Since the fittest members of the population are likely to become parents than others, a genetic algorithm tends to generate improving populations of trial solutions as it proceeds. Mutations occasionally occur so that certain children also can acquire features (sometimes desirable features) that are not possessed by either parent. This helps a genetic algorithm to explore a new, perhaps better part of the feasible region than previously considered.

(4) Solution techniques derived in the MODM literature often assume uniqueness, which is done in the exposition of this paper as well. Eventually, survival of the fittest should tend to lead a genetic algorithm to trial solution (the best of any considered) that is at nearly optimal.

(5) This method is very effective at finding optimal or near optimal solution of MOLFP problems.

VIII. Conclusion Since the emergence of multi-objective optimization problems at the beginning of the second decade of the last century, it has become a necessary requirement and has an important role to all areas and fields in the real world. From its early stages, it evolved systematically and scientifically through the genius of scientists and professionals in this field. It had passed through several stages, and it has branched more into various specialized disciplines in the real world.

The GA approach to MOLFP problem proposed by us can produce results which are very close or improved to the results obtained by the existing methods. This approach considers the solution of each DM by randomly pairing up the decision maker (their solutions) .Each pair of DMs (solution) give birth to new feasible trial solutions whose features are a random mixture of the features of the solutions of each decision makers .Unique characteristic of a MODM is reflected by including objective or solutions of each DM. One may use a random process that is biased towards the more fit members. Whenever the random mixture of features and any mutations result in an infeasible solution, this is a miscarriage, so the process of attempting to give birth then is repeated until a child is born that corresponds to a feasible solution.

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Available online at http://www.iasir.net

ISSN (Print): 2328-3491, ISSN (Online): 2328-3580, ISSN (CD-ROM): 2328-3629 AIJRSTEM is a refereed, indexed, peer-reviewed, multidisciplinary and open access journal published by International Association of Scientific Innovation and Research (IASIR), USA (An Association Unifying the Sciences, Engineering, and Applied Research)

Event-Triggered Localization Algorithm Based On Rf with IR Fingerprint and RSSI with PSO Techniques 1

Ahmed Ali Saihood1, Dr. Rakesh Kumar2, Aqeel Mohsin Hamad3 Assistant Lecturer, College of Computer Science and Mathematics, Computer Department University of Thi-Qar Nassirya,Thi-Qar IRAQ 2 Assistant Professor, Department of Computer Science and Engineering National Institute of Technical Teachers Training & Research (Ministry of HRD, Govt. of India) Sector-26, Chandigarh-160019 India 3 Lecturer, College of Computer Science and Mathematics, Computer Department Head of Computer Ceneter University of Thi-Qar Nassirya,Thi-Qar IRAQ

Abstract: Wireless sensor network is the field in which there are mobile sensor nodes. WSNs field is becoming immensely popular with thousands of tiny sensor nodes because of their vast applicability in myriad of applications for e.g. collecting data from unattended hazardous environments, monitoring, emergency rescue operations, and surveillance in military in the hostile, unfavourable terrains. Mobile Wireless Sensor Networks is an arising area for research in contradiction to their well-entrenched predecessor. Such networks are more versatile, flexible than the static sensor networks because in any scenario, the mobile wireless sensor networks can be deployed and contend with brisk topology variations.

In this paper an event-triggered localization algorithm is proposed which is based on Radio Frequency with infrared Frequency fingerprint and RSSI with PSO techniques. The localization algorithm is applied for curtailing the error of average localization for mobile WSN and it also utilized for the escalation speed for transmission of data in Mobile WSN. Keywords: WSN, RF, IF, RSSI, ACO, Event Triggered Localization Algorithm, and PSO Techniques.

I. Introduction Present day WSN is an emerging field of research. Herein, abundant localization algorithms have been prospected for performing localization and aim attention on static sensor network. Wireless sensor network does not advisable for mobile where it consists of the advancement of sensor and network technology. The wireless sensor network is brought in with the movable i.e. mobile sensor nodes popularly known as MWSN (Mobile wireless sensor network). This network gets along sensor nodes that can generally move and then the conventional algorithms for localization for the static sensor networks are not appropriate to MobileWSN. The various applications of MobileWSN appeal for new localization algorithms so the mobile wireless sensor network consists of spatially allocated independent sensors for monitoring environmental conditions for example sound, pressure, temperature etc where for passing their data together via network to the main position.

Rejuvenated networks are inadequate for restrainting sensor activity because they are bi-directional and accordingly upgrading of WSNs was excited by the military operations like surveillance, scrutiny of battlefield.

Here also the networks are utilised in various consumer and industrial applications. The wireless sensor networks subsist of great no. of nodes and every node is able, competent for sensing the surroundings. WSN achieves the uncomplicated calculations where it exchanges information with other sensors and the central unit.

Sensors can be deployed in different ways. There is a peculiar way for deploying sensor nodes in networks; that is uneven distribution of nodes all through a few area of significance where the random network connection in form of topology is builds. Number of previous communication protocol and such networks are achieved and achieved for accomplishing a no. of tasks in distinction for monitoring the legitimate and environmental habitat to home networking, smart battlefields and medical applications. The network may indicate device deterioration for restrainting centre in cooperative. The wireless sensors nodes may be devised to reveal the ground quivering produced through secretive footfalls of filcher and provoke a buzzer. The nearly all applications rely on

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positioning i.e. where for estimation their localization in steady, intent correlative structure. Therefore, designing the decisive and effective algorithms for localization is of immense importance.

1.1 Received Signal Strength Indicator (RSSI) In telecommunication, the Received Signal Strength Indicator is an appraisal of power existing in signal received. It is consistently hidden from the user of the receiver device. Nevertheless, as the strength of signal may alter immensely and the impact range of capabilities in wireless networking (IEEE 802.11) devices generally make the standards accessible to users. Received Signal Strength Indicator is generally performed in the intermediate frequency phase before the IF amplifier and earlier the baseband amplifier, in the zero-IF structure it is accomplished in the baseband signal chain. Output of RSSI is generally a DC analog level. It is provisional strength of signal acknowledged in wireless environs in mercurial units in an IEEE 802.11 system.

The received signal strength indicator is a connotation of the degree of power which is acknowledged and acquired by antenna of receiver side. For this reason the greater the value of RSSI, the stronger the signal. It may also be utilised internally in a wireless networking card for making decision when in the channel the value of radio energy is beneath a certain fixed threshold level that indicate the network card is CTS (clear to send) and once the card is CTS than the packet containing information can be transmitted. The receiver end will observe this RSSI value.

Received Signal Strength Indicator is collected only during the pre-amble phase of receiving of an 802.11 frame that is it is not estimated over the full frame. It is showed in 2009 that RSSI may not inevitably be utilized to accurately gauge distances in a WSN where as the 802.11 standards doesn’t construe any relationship among the value of RSSI and the level of power in dBm or mW. Chipset makers and Vendors support with their own granularity, precision and extend for the certain power that is measured as dBm or mW. They also support with the range of RSSI values which varies from 0 to RSSI_Max. 1.2 ACO (Ant Colony Optimization) ACO is a technique of optimization which was exalted and stimulated through the ant behavior. It is probabilistic technique which is used for resolving the problems relating to computation and such problems can be minimized with verdict of good paths by way of linear representation. This algorithm of optimization is affiliated with the family of ant colony algorithms, in the methods of swarm intellect. The ACO comprises of some meta-heuristic optimizations techniques. This was the first algorithm which intent to pursuit for an optimum path on the basis of the ants demeanor of searching the pathway amidst the food source and colony.

This algorithm was originally proposed by Marco Dorigo in year 1992 during his PhD thesis. Since then earliest idea has been varied for resolving an extensive class of numerical problems, which results, in solving various problems aroused, drawing on distinct facet of the ants behavior.

1.3 PSO (Particle Swarm Optimization) Particle Swarm Optimization is computing technique which amends and improvises a dilemma through repetitively arduous for enhancing aspirant results along view for likely quality estimate. This optimization algorithm optimizes issue by enduring a community of aspirant solutions and intriguing dubbed particles in search-arena bestowing for simple numerical formulas above the position of particle and its velocity.

Every action or movement of particle is affected by its most excellent position known. It is steering anent towards most excellent positions known or location in search-arena that are amended at the time excelling positions are erect by other particles. This anticipated the swarm to be in motion toward the most excellent solutions.

Particle Swarm Optimization was initially ascribed to Eberhart, Shi and Kennedy [1] [2] and was initially designed considering the simulation of communal behavior [3] for depiction of activity of creatures usually a flock of bird either fish school.

PSO technique was made easy and realized for attaining optimization. It is a meta-heuristic because it makes some or no presumptions related to the problem which is being optimized. It may seek very huge areas of candidate solutions. Withal, PSO don’t give assurance of an optimum solution is always erect. More particularly, it doesn’t utilize the acclivity of the problem which is being optimized, that means in Particle Swarm Optimization there is no requirement of the optimization problem to be distinctable as it was required in regular optimization techniques for example, quasi-newton and gradient descent techniques. Accordingly, PSO can also be applicable on problems related to optimization that are; change over time, partially irregular, noisy, many more. Let the no. of particles be Sp in the swarm. In the search-space, each particle is having a position xi ∈ ℝn and Vi∈ ℝn is the velocity. Suppose, Pi be most excellent position known of ‘i’ particle and assume the most excellent position known of the integrated swarm be ‘g’. The algorithm for particle swarm optimization is deliberated below:  For every particle i = 1, ..., Sp carry out:  Load position of particle along consistently dispersed random vector: xi ~ U (bl, bu), where bl is the inferior boundary and bu is the superior boundary of search-arena.  After that load best position known of particle to its primary position such as Pi ← xi  If (f(pi) < f(g)), then amend the best position known of swarm such as g ← Pi

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         

Load velocity of particle as, Vi ~ U(-|bu-bl|, |bu-bl|) Just before completion norm is meet for example no. of repetition accomplished, or result along acceptable target operation count is erect, than reiterate: For every particle that is from i = 1, ..., Sp carry out: And for every dimension D = 1, ..., n carry out: Select arbitrary values as rp, rg ~ U(0,1) After that update the velocity of particle such as Vi,D ← ω Vi,D + φp rp (Pi,D-xi,D) + φg rg (gD-xi,D) After updating velocity, amend position of particle as xi ← xi + Vi But if (f(xi) < f(Pi)) than, amend the best position known of particle such as Pi ← xi And if (f(Pi) < f(g)) then update the best position known of swarm as g ← Pi Finally g possesses the most excellent found result.

II. Related Work This section discussed the research work that has been done in previous years. This is the most promising field of research in which now all researchers are showing interest. A literature review goes beyond the pursuit for information or knowledge and it involves the localization techniques and connection of relationships among the literature and our research field.

Gholami, Vaghefi, and Strome studied the received signal strength on the basis of localization problem, here in this, it transmits power or path loss exponent that is not known to commensurate with the maximum estimator mien an arduous problem of non convex optimization. For avoiding the dilemma in resolving the MLE (maximum estimator) which author used appropriate approximations and specify systematically the problem of localization as a generic trust region sub problem which can be resolved specifically under benign conditions and the imitation results shows the encouraging accomplishment for the proposed techniques which also have plausible complexities as compared with the existent approaches [1].

Patwari, N et al. Proposed the measurement-based statistical models appropriate for representing time-of-arrival, angle-of-arrival, Wideband and ultra-wideband measurements, and Radio Frequency and acoustic media are also altercate. In this paper, by using these configurations researchers shows the computation of Cramer-Rao Bound on position appraisal accuracy desirable for provided coterie of calculations. The paper concisely analysis an extensive and thriving body of algorithms for localization of sensor nodes and was designed for reiterating elemental analytical signal processing imperative to anticipate the new and to built advancement in the state-of-the-art and to a great extent open areas of the sensor network localization research [2]. Chen Meng et al. prospected a peculiar technique for localization of source and for issue tracking in wireless sensor networks where the minimax approximation and semi definite relaxation were applied and they completely transform the traditionally non-linear and non-convex issue within the issues of convex optimization for two distinct models for source localization which involve both consistent distance and RSS. Here, the author designed an agile low-complexity semi definite programming algorithm for two distinct models for source localization. The proposed algorithm in this paper can be utilized either to approximate calculation, estimation of the source location or for initializing standard non-convex maximum likelihood algorithm [3].

Ouyang, R.W et al. suggested convex estimators precisely for problems for the localization based on RSS (Received Signal Strength) and two together co-operative and non-co-operative strategy are deliberated and authors initiated with the localization problem based upon non-co-operative received signal strength and extract non-convex estimator which proximate Maximum Likelihood estimator, nevertheless it has no algorithmic with enduring residual. Technique named semi definite relaxation was imposed to the imitative non-convex estimator also advances a convex estimator for improving the estimation performance. The researchers append both the estimator (ML estimator with the convex estimator) with the result obtained from the convex estimator as the beginning point. The techniques were extended to the problem of cooperative localization and equivalent CRLB (Cramer-Rao Lower Bounds) were imitative as performance criterion their prospected convex estimators acquiesce well with the RSS measurement model. The imitation results certainly manifest their exceptional performance for the wireless localization approach based on RSS [4].

Wang et al. [5] proposed unique techniques for the problem of localization in wireless sensor networks through utilising the RSS (received-signal-strength) calculations. Under commensurate exponential transformation of the traditional measurement model for path loss and the transformation, the problem was reformulated and relatively surrounded by Maximum Likelihood parameter appraisal that indicated as the WLS (weighted least squares) technique. This is utilised for localization of sensor node in both cooperative and non-cooperative schemes and the imitation results verify the efficacy and potency of the approach proposed for both indoor/outdoor situations.

III. Overview Of Term Weighting Schemes Methodology used here in paper involves various phases. The first step is creating a wireless sensor network with significant amount of nodes connected and forming clusters. Then the event triggered localization algorithm with RSSI with PSO is applied. The IF and RF fingerprint are provided as input to this phase where

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localization algorithm with RSSI is applied for estimating the strength of signal along with the position. In the concluding phase the experiments are performed to acquire the extracted location which is required. Different parameters are used for verifying the proposed approach like RMSE, average localization error and energy efficiency. The results obtained will than compared with the results of previous work. The steps involved in methodology; Step1: Create the wireless sensor network with sensor nodes in the form of cluster.

Step2: Code is created for event triggered localization algorithm with RSSI and with PSO. Step3: Code is formed for inputting both IR and RF fingerprint to localization algorithm with RSSI with PSO. Step4: Experiments are performed for verifying the approach.

The flowchart of methodology is shown below; Create Mobile Wireless Sensor Nodes, Clusters and Network System

Apply Event Triggered Localization Algorithm with RSSI (to calculate signal power) WITH PSO

IR Fingerprint

Output

RF Fingerprint Report Extracted Location to required Node/BS

Fig.1 Flowchart IV. Result and Discussion In this section of paper, different parameters are discussed and predicted that are farther used for the comparing the proposed approach in this paper with the approaches formerly used.

A. Performance Measures of WSN Localization: These are used to reconciliation the localization in matlab simulator. Communications system toolbox of Matlab is utilised for implementation operation. Accordingly the computation of the performances and determination is executed on the basis of several criterions such as RMSE, average localization error, and energy effectiveness for comparison with earlier algorithms.

4.1.1 Average localization error: This affirms the accuracy of location which is extracted. It construe that higher the accuracy, lower will be the average localization error.

4.1.2 RMSE (Root mean square error): This parameter is a most commonly used for measuring the differences among values anticipated by an estimator. The values literally observed and if less error is shown than it interpret good accuracy and certainty. Root mean square error can be estimated by using the following equation; đ?&#x2018;&#x20AC; RMSE = sqrt (1/MNâ&#x2C6;&#x2018;đ?&#x2018;&#x161;=1 â&#x2C6;&#x2018;N n=1(R(m, n)F(m, n))) 4.1.3 Energy Efficiency: The efficiency here delineates the life span of network and nodes and if the inadequacy and reduction of energy efficiency decelerate the networkâ&#x20AC;&#x2122;s lifesp an.

B. Experimental Outcomes: Here, in this segment of paper, the experiments are executed and finished. The figures shown below shows the result obtained from the proposed approach. Following figures shows the graphical representation of RMSE, average localization error, and energy efficiency between the previous and proposed approach.

Fig. 2 Graph for comparison of RMSE for previous and proposed work

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Fig 2 shown above shows the graphical comparison of root mean square error for both previous and proposed work. Blue line shows the values for previous work and red line shows the values for proposed work. From the graph it is shown that the value of RMSE in case of proposed work is much lesser than the previous work. That means the proposed approach is more efficient and reliable than the previously used approach.

Fig. 3 and fig. 4 shown below shows the average localization error with IR and RF for proposed approach and previous approach.

Fig. 3 Average Localization Error for proposed work The figure shown above shows the comparison graph where on x axis there is no. of anchor nodes and on y axis average localization error with IR and RF for the approach proposed in this paper.

Fig. 4 Average Localization Error for previous work Fig. 4 shows the graph betwixt the average localization error and no. of anchor nodes with IR and RF for the previous approach. The result obtained after comparing both the graphs concludes that the average localization error in proposed work is less, which makes it more accurate approach than previous.

In following figures the energy efficiency is shown that at both transmit and receive side. Fig. 5 and fig 6 exhibits the energy gps and energy sink simultaneously. For estimating the energy received and energy transmitted following equations are applied. Genuinely, the imitation utilises the radio model of 1 st order for communication model. The equation written in (1) depicts the received energy and equation (2) represents the energy transmitted. Both equations are used to depict the dissipated energy, although a SN receives or transmits a message of l -bit that is the length of message is l. đ??¸đ?&#x2018;&#x;đ?&#x2018;&#x2019;đ?&#x2018;?đ?&#x2018;&#x2013;đ?&#x2018;&#x2019;đ?&#x2018;Łđ?&#x2018;&#x2019; = đ?&#x2018;&#x2122; â&#x2C6;&#x2014; đ??¸đ?&#x2018;&#x2019;đ?&#x2018;&#x2122;đ?&#x2018;&#x2019;đ?&#x2018;?

Eq.1 đ??¸đ?&#x2018;&#x201C;đ?&#x2018;

đ??¸đ?&#x2018;Ąđ?&#x2018;&#x;đ?&#x2018;&#x17D;đ?&#x2018;&#x203A;đ?&#x2018; =

đ?&#x2018;&#x2122; â&#x2C6;&#x2014; (đ??¸đ?&#x2018;&#x2019;đ?&#x2018;&#x2122;đ?&#x2018;&#x2019;đ?&#x2018;? + đ??¸đ?&#x2018;&#x201C;đ?&#x2018; â&#x2C6;&#x2014; đ?&#x2018;&#x2018; 2 ), đ?&#x2018;&#x2013;đ?&#x2018;&#x201C;đ?&#x2018;&#x2018; â&#x2030;¤ â&#x2C6;&#x161; đ??¸

đ?&#x2018;&#x161;đ?&#x2018;?

đ?&#x2018;&#x2122; â&#x2C6;&#x2014; (đ??¸đ?&#x2018;&#x2019;đ?&#x2018;&#x2122;đ?&#x2018;&#x2019;đ?&#x2018;? + đ??¸đ?&#x2018;&#x161;đ?&#x2018;? â&#x2C6;&#x2014; đ?&#x2018;&#x2018; 4 ), đ?&#x2018;&#x2013;đ?&#x2018;&#x201C;đ?&#x2018;&#x2018; > â&#x2C6;&#x161;

đ??¸đ?&#x2018;&#x201C;đ?&#x2018;

Eq. 2

đ??¸đ?&#x2018;&#x161;đ?&#x2018;? { Where, l is the length of message i.e. size of packet and which is taken as 64 and d is the distance travelled or covered by the packet.

Fig. 5 Energy Efficency (Egps)

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In Fig. 5 circle shows the energy received and rectangle shows the energy transmitted at the gps position of all nodes deployed in the WSN. In fig. 6 the graph is between the range and Esink where circles show the energy received by nodes and rectangles show the energy transmitted.

Fig. 6 Energy Efficency (Esink) The experimental results obtained by different parameters shows that the approach proposed here in this paper is more decisive and accurate than the previous work. This is because the root mean square value and average localization error is less in comparison with previous work, which makes this approach a better approach.

V. Conclusion The experimental results obtained in this paper from all the experiments shows that the approach prospected is more efficient as correlated with previous approach. Location of all nodes for the finger print technique along with applying RSSI where infrared fingerprint along with radio frequency fingerprint that will be applied parallel. Accordingly, the event triggered localization algorithm with Received Signal Strength Indi cator is applied for extracting the location and defining the strength of signal. The proposed work in paper is more decisive and potent and is much more effective as compared to the previous system. All the parameters are estimated just to authenticate the efficacy of the system.

VI. Future Scope Although, the results acquired from the technique proposed in this paper are promising but this approach is limited to the number of nodes connected in a wireless sensor network. The work can be extensive on large number of nodes. Future work may involve; the consideration of different localization algorithms for IF and RF fingerprints with received signal strength. The different algorithms can be utilised for optimization for enhancing the accuracy and to propose more efficient approach.

VII. References [1] [2]

[3] [4]

[5] [6] [7] [8] [9] [10]

[11]

[12]

[13]

Gholami. M.R., Vaghefi. R.M., Strom, E.G., "RSS-Based Sensor Localization in the Presence of Unknown Channel Parameters", attended the IEEE transaction on Signal Processing, pp. 3752-3759, Aug.1,2013, TSP.2013.2260330.

Ash, Patwari. N., Hero. A.O., Moses. R.L., Correal. N.S., Kyperountas S. "Locating the nodes: cooperative localization in wireless sensor networks", attended the IEEE transaction on Signal Processing Magazine, IEEE, vol. no.22, pp.54-69, July2005, MSP.2005.1458287.

Chen Meng, Zhi Ding, Dasgupta. S., "A Semidefinite Programming Approach to Source Localization in Wireless Sensor Networks", IEEE transaction on Signal Processing Letters, IEEE, vol. no. 15, pp.253-256, 2008, LSP.2008.916731.

Ouyang. R.W., Wong, A.K.S., Chin Tau Lea, "Received Signal Strength-Based Wireless Localization via Semidefinite Programming: Non-cooperative and Cooperative Schemes", IEEE transaction on Vehicular Technology, vol.no.3, pp.1307-1318, March 2010, TVT.2010.2040096.

Gang Wang, Kehu Yang, "A New Approach to Sensor Node Localization Using RSS Measurements in Wireless Sensor Networks", IEEE transaction on Wireless Communications,vol.no.10,pp.13891395,May2011,TWC.2011.031611.101585.

Meesookho. C., Mitra. U., Narayanan. S., "On Energy-Based Acoustic Source Localization for Sensor Networks", IEEE transaction on Signal Processing, vol.no.56, pp.365-377, Jan. 2008, TSP.2007.900757.

Hing Cheung So, Lanxin Lin, "Linear Least Squares Approach for Accurate Received Signal Strength Based Source Localization", IEEE transaction on Signal Processing, vol.no.59, pp.4035-4040,Aug.2011, TSP.2011.2152400.

Cheung. K.W., So, H.C., Ma. W.K., Chan, Y. T., "Least squares algorithms for time-of-arrival-based mobile location", IEEE transaction on Signal Processing, vol.no.52, pp.1121-1130, April 2004, TSP.2004.823465.

Blatt. D., Hero. A.O. "Energy-based sensor network source localization via projection onto convex sets", IEEE transaction on Signal Processing, vol.no.54, pp.3614-3619, Sept. 2006, TSP.2006.879312.

Chong Liu, Kui Wu, Tian He, "Sensor localization with Ring Overlapping based on Comparison of Received Signal Strength Indicator", Mobile Ad-hoc and Sensor Systems, 2004 IEEE International Conference, pp.516-518, 25-27 Oct. 2004, MAHSS.2004.1392193.

S. Mazuelas, A. Bahillo, R. M. Lorenzo, P. Fernandez, F. A. Lago, E. Garcia, J.Blas, and E. J.Abril, “Robust indoor positioning provided by real-time RSSI values in unmodified WLAN networks,” IEEE J. Sel. Topics Signal Process., vol. 3, no. 5, pp. 821–831, 2009.

M. R. Gholami, S. Gezici, and E. G. Ström, “Improved position estimation using hybrid TW-TOA and TDOA in cooperative networks,” IEEE Trans. Signal Process., vol. 60, no. 7, pp. 3770–3785, Jul. 2012.

A. O. Hero, N. S. Correal, N. Patwari, M. Perkins and O’Dea, “Relative location estimation in wireless sensor networks,” IEEE Trans.

Signal Process., vol. 51, no. 8, pp. 2137–2148, Aug. 2003.

[J. H. Lee and R. M. Buehrer, “Location estimation using differential RSS with spatially correlated shadowing,” in Proc. IEEE GLOBECOM, pp. 1–6, 2009.

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[14] S. Gezici, “A survey on wireless position estimation,” Wireless Pers. Commun., vol. 44, no. 3, pp. 263–282, Feb. 2008.

[15] N. Patwari, “Location estimation in sensor networks,” Ph.D. dissertation, Univ. of Michigan, Ann Arbor, MI, USA, 2005.

[16] A. A. Ahmed, H. Shi, and Y. Shang, “Sharp: A new approach to relative localization in wireless sensor networks,” in Proceedings of the Second International Workshop on Wireless Ad Hoc Networking - Volume 09, ser. ICDCSW ’05. Washington, DC, USA: IEEE Computer Society, 2005, pp. 892–898.

[17] S.K. Udgata, S.L. Sabat and S. Mini, “Sensor deployment in irregular terrain using Artificial Bee Colony algorithm”, Proceedings of IEEE, World Congress on Nature & Biologically Inspired Computing, Coimbatore, pp. 1309-1314, 2009.

[18] M. Romoozi and H.E. Komleh, “A Positioning method in Wireless sensor networks using Genetic algorithms”, International Journal of Digital Content Technology and its Applications, vol. 4, pp. 174 -179, 2010.

[19] Y. Qi, H. Kobayashi, and H. Suda, “Analysis of wireless geolocation in a non-line-of-sight environment,” IEEE Trans. Wireless Commun., vol. 5, no. 3, pp. 672–681, 2006.

[20] N. Patwari, “Location estimation in sensor networks,” Ph.D. dissertation, Univ. of Michigan, Ann Arbor, MI, USA, 2005.

[21] R. Vaghefi, M. Gholami, R. Buehrer, and E. Strom, “Cooperative received signal strength-based sensor localizationwith unknown transmit powers,” IEEE Trans. Signal Process., vol. 61, no. 6, pp. 1389–1403, Mar. 2013.

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[23] S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory. Englewood Cliffs, NJ, USA: Prentice-Hall, 1993.

VIII.Acknowledgments From the depth of my heart I would like to thank my parents for their effort to encourage me to do what best for always.

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ISSN (Print): 2328-3491, ISSN (Online): 2328-3580, ISSN (CD-ROM): 2328-3629 AIJRSTEM is a refereed, indexed, peer-reviewed, multidisciplinary and open access journal published by International Association of Scientific Innovation and Research (IASIR), USA (An Association Unifying the Sciences, Engineering, and Applied Research)

Observations of HF Propagation on a Path Aligned Along the Mid-latitude Trough during Summer 1

Mfon O. Charles Assistant Lecturer, Physics Department, University of Calabar, Nigeria.

1

Abstract: This work presents observations from an extensive set of measurements of the direction of arrival and signal strength of HF signals propagating on a path (Nurmijärvi to Bruntingthorpe) oriented along the mid-latitude trough with path length 1800km. Signals were radiated on five frequencies between 4.6 and 14.4 MHz and measurements span the period from the 2009 sunspot minimum to July 2014, which is within the present sunspot maximum. Deviations were observed to occur at all frequencies and throughout the period of measurement. The largest deviations were mostly southerly and occurred at the highest frequencies: 11.1 and 14.4 MHz. The largest signal strengths were produced at the lowest frequency while the largest frequency produced the least signal strengths, for both paths. There is also an observed effect on the duration and percentage of occurrence of propagation due to the solar cycle.

Keywords: Daily variations, HF propagation, Mid-latitudes trough, Summer variations, Sunspot cycles I. INTRODUCTION High-Frequency (HF) radio propagation is made possible through refraction by the ionosphere, and the ionosphere is that part of the atmosphere in which free electrons are sufficiently numerous to influence the propagation of radio waves. The name ionosphere comes from the fact that this region is formed by the ionization of atoms in the atmosphere thereby creating free electrons. The free electrons in the ionosphere cause HF radio waves to be refracted and eventually directed back to earth [1]. It goes on to say that the greater the density of electrons, the higher the frequencies that can be reflected. According to this same source, the ionosphere may have four regions present during the day. These regions are called the D, E, F1 and F2 regions.

Their approximate height ranges are: D region 50 to 90 km; E region 90 to 140 km; F1 region 140 to 210 km; F2 region over 210 km. It goes further to say that at certain times during the solar cycle the F1 region may not be distinct from the F2 region with the two merging to form an F region. At night the D, E and F1 regions become very much depleted of free electrons, leaving only the F2 region available for communications.

These varying characteristics of the ionosphere with respect to time of day, seasons, and solar cycles, make HF prediction and propagation a rather difficult task. The Merriam-Webstar online dictionary defines the midlatitudes as latitudes of the temperate zones or from about 30 to 60 degrees north or south of the equator.

Located within the mid-latitudes is the trough which is a major feature of the F-region ionosphere that forms at the boundary between the mid-latitudes and auroral ionospheres, and where the plasma concentration is usually lower compared with regions immediately poleward and equatorward [2]. In terms of time of formation, the local time extent of the trough is small in summer, centred about midnight, and extends further towards dawn and dusk with progression towards winter [2]. For terrestrial HF radio systems, the electron depletion in the trough region reduces the maximum frequency that can be reflected by the ionosphere along the great circle path (GCP) [3]. Also, in the mid-latitudes, this electron density depletion and subsequent reduction in maximum useable frequency (MUF) often leads to large deviations from GCP [4]. A signal however, can still be reflected from the gradients in the poleward and equatorward walls of the trough or scattered from irregularities embedded in the trough or in the auroral region which lies just poleward of the trough [5]. In [6], it is also affirmed that these reflections from gradients and irregularities in the trough caused the signals to arrive from directions away from the GCP and at times delayed with respect to normal propagation.

Having taken measurements during sunspot maximum in 2001 for a shorter trough path between Uppsala, Sweden and Leicester, it was observed in [7] that the off-GCP signal received showed characteristics consistent with scattering from field-aligned irregularities in the northern trough wall and/or auroral oval. They also opined that the deviations were majorly to the north, with southerly deviations being much less frequent and coherent.

These results they however reported were in contrast to a similar experiment conducted near sunspot minimum in 1994 in Canada, during which both southerly and northerly deviations were observed in the 5-15 MHz range, showing variations in DOA with respect to solar activity. In [8] deviations were found to occur more often at night especially during the winter and equinoctial months for signal frequencies between 7 and 11.1 MHz but summer deviations however were rare and tended to be smaller in magnitude (<5°) compared to several tens of degrees observed during other seasons.

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Deviations in direction of arrival (DOA) due to the presence of the trough is not only an issue in radio communication systems where directional antennas are employed but also impacts greatly on radiolocation systems for which estimates of a transmitter location are obtained by triangulation from a number of receiving sites [8]. This could cause wrong assumptions for transmitter position, leading to timing and positional errors in navigation systems such as GPS. This work aims to investigate the effects of the mid-latitude trough on signals transmitted during summer by analyzing HF transmissions from Nurmijarvi, Finland (60.5N, 24.65E) to Bruntingthorpe, Leicester, (52.49N, 1.11W) with a path length of 1800km. Findings will give HF radio engineers an insight on signal behaviour during summer over this trough path and also see how these effects change with frequency and with solar cycle, thus enabling proper planning and execution of reliable and efficient communications.

II. MATERIALS AND METHOD A. Materials Data obtained from measurements between the trough path (Nurmijärvi to Bruntingthorpe) were collected over the duration spanning the recent solar minimum (2009) to the present (2014) which is within the present solar maximum. These data which contain the received signal strength and direction of arrival were obtained for each year. In each year, the peak month in summer was chosen to represent the summer season. A 10-day transmission data for the chosen month was then used for the analysis:

Figure 1: Map showing the paths employed in the reported measurements, with geographical coordinates.

B. Method The method used to make the measurements has been discussed in detail elsewhere in [7] and [9], and the days for which measurements were made is given later in this section.

Variation in smoothed sunspot number from the previous solar maximum (2001) to the present solar maximum (2014) 160

140

120

Monthly SN

100

80

60

40

20

0 2001

2002

2003

2004

2005

2006

2007

2008 Year

2009

2010

2011

2012

2013

2014

Figure 2: Variation in smoothed sunspot number over a solar cycle. Quantity plotted is the monthly mean international sunspot number downloaded from the Space Weather Prediction Centre, US National Oceanic and Atmospheric Administration in [10].

In deriving the statistics presented in Figures 4a-e and Tables 1 and 2, propagation is deemed to have occurred if any readily identifiable trace, other than sporadic E, is seen between 00:00-24:00 UT. The sporadic E is a region which is very unpredictable in its time of formation, the area which it covers, the duration for which it persists, and even in its electron density. For this reason it is excluded to remove short-lived reflections.

All strong off-GCP propagation was considered as true reflections whether or not it occurred for up to 50% of the days observed (5 days). Weak off-GCP propagation that occurred for up to 50% of days observed was

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regarded as possible reflections but only the days with strong reflections were included whereas weak off-GCP propagation that did not occur for up to 50% of the days observed were excluded. During some intervals however, the data quality was not sufficient to categorise the direction of arrival and these together with the short-lived deviations that sometimes occur briefly at dawn and dusk, have been excluded.

The total percentage for each mode (GCP, northerly, or southerly deviations) should equal 100% which would indicate that that particular mode existed for 24 hours on all 10 days investigated (i.e. 240 hours) for each season considered.

Finally, for frequencies where there was more than one northerly or southerly reflection (e.g. for 8 MHz in 2013, where there exists two northerly deviations: 60°N and 80°N and for 14.4 MHz in 2013, where there exists two southerly deviations: 110°S and 160°S), the combination of the highest counts for each hour of the day derived from both/all modes as the case may be, was used in computing the percentages presented in Table 2.

This is because the figures presented are only meant to show the times of day during which deviations occurred (regardless of the degree of deviation and number of deviations for each mode), so as to enable the prediction of which modes supported or dominated propagation at various times of the day.

Measurements used were taken on the following days: 2009: June 8-19, 2010: July 1-10, 2011: July 5-14, 2012: July 18-27, 2013: July 13-22, 2014: June 5-16.

Figure 3: A Sample data showing the received SNR (left column) and off-GCP propagation (right column) at 4.6 MHz, 7 MHz, 8 MHz, and 11.1 MHz on June 10, 2009

III. RESULTS Results are presented from a solar minimum to the present solar maximum to observe any perceived variations.

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2009 10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2010

10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2011 10 8 6 4 2 0

GCP ND SD

No of Days

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2012

10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2013

10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2014 10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time of day (UT) Figure 4a: A plot of hourly and yearly occurrence of propagation at 4.6 MHz

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2009 10 8

GCP

6

ND

4

SD

2 0 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2010 10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2011 10 8

GCP

6

ND

4

SD

2 0 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

No of Days

2012 10 8

GCP

6

ND

4

SD

2 0 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2013 10 8

GCP

6

ND

4

SD

2 0 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2014 10 8

GCP

6

ND

4

SD

2 0 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time of day (UT) Figure 4b: A plot of hourly and yearly occurrence of propagation at 7 MHz

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2009 10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2010 10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2011 10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

No of Days

2012 10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2013 10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2014 10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time of day (UT) Figure 4c: A plot of hourly and yearly occurrence of propagation at 8 MHz

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2009 10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2010 10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2011 10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

No of Days

2012 10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2013 10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2014 10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time of day (UT) Figure 4d: A plot of hourly and yearly occurrence of propagation at 11.1 MHz

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2009

10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2010 10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2011 10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

No of Days

2012 10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2013

10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2014 10 8 6 4 2 0

GCP ND SD 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time of day (UT) Figure 4e: A plot of hourly and yearly occurrence of propagation at 14.4 MHz

IV. OBSERVATIONS AND DISCUSSIONS A. GCP Propagation At 4.6 MHz, GCP propagation is centred on midday (19:00 UT to 05:00 UT). Its duration and percentage of occurrence gradually decreases as solar maximum is approached, decreasing from 19:00 UT to 05:00 UT in 2009 to 21:00 UT to 03:00 UT in 2014, thus limiting its occurrence only to hours around midnight.

At 7, 8 MHz, GCP propagation becomes much more apparent during the day, while still existing at night, eventually appearing all through the day at 11.1 and 14.4 MHz. This daytime appearance of GCP propagation at 11.1 and 14.4 MHz is however accompanied with decreasing percentage of occurrence around midnight. This means that as frequency increases, the occurrence time shifts from nighttime to daytime. This will be a result of low frequencies being absorbed by the highly ionised D-layer during daytime. Thus as frequency increases,

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daytime GCP transmission is gradually supported whereas the nighttime ionosphere remains less concentrated with free electrons to reflect these high frequencies. This can be noticed by observing duration of GCP propagation for each year across all frequencies of transmission, using Figs 4a-e.

B. Observed Deviations Table 1: Observed yearly deviations at various frequencies for Summer Path: Nurmijarvi-Bruntingthorpe Frequency(MHz)

Northerly Deviations (°n)

8 14.4

100

Southerly Deviations (°s)

2009 40 2010 40

14.4 2011

60

14.4 2013 8 11.1 14.4

60,80 30

40 110,160

Table 2: Percentage Occurrence Statistics by Mode and Bearing for Signal Frequencies of 4.6, 7.0, 8.0, 11.1, and 14.4 MHz

All frequencies and years without deviations were not included in Tables 1 and 2. Table 1 shows the observed deviations and their magnitude over the period of observation. As observed in Table 1, deviations from the great circle path occurred both from the north (northerly) and from the south (southerly). In general, the larger deviations occurred mostly southwards of the GCP. Despite the deviations, propagation was usually dominated by the GCP for all years except in 2013 when propagation was dominated by northerly deviations.

All figures in Table 2 have been rounded-up or down to the nearest whole number in other to avoid ambiguity.

The figures under the “No Propagation” sub-column are obtained by subtracting the highest occurrence percentage on corresponding sub-columns under GCP, Northerly deviations, and Southerly deviations from 25%, which is the maximum percentage per sub column, making a total of 100% per column.

Variation with Frequency Deviations were observed to occur across all observed frequencies but the magnitude of deviation was strongest at the higher frequencies (11.1 and 14.4 MHz) Variation in Time of occurrence Although off-GCP propagation is in most cases viewed as a setback in radio communication systems especially in radiolocation systems, it however proved to be useful in providing communications during the periods when GCP propagation was not supported. Table 2 shows that throughout the duration observed, there was always an off-GCP either northerly or southerly occurring during the hours when GCP propagation was not supported. A very extreme case is observed at 11.1 MHz and 14.4 MHz in 2013, when there was no GCP propagation all throughout the period and days of observation. There was no obvious variation with solar cycles.

C. Signal Strength Traces of 2 to 3 modes with SNRs between the range 8.5dB-15dB are often seen between 09:00 and 15:00 UT at 4.6, 7, and 8 MHz, with the upper limit (15dB) decreasing to 10.5 dB at 8MHz. This decrease in SNR with increasing frequency is observed for the whole duration of measurements (2009 – 2014), dropping further to

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9dB at 14.4MHz. This is typical of the daytime ionosphere, comprising of the E, F1, and F2 layers from which reflections are all possible. Hence, the higher frequencies are reflected higher up in the ionosphere and as a result return with less signal strengths due to the longer distance covered.

It is observed too that during solar minimum, daytime multimode propagation is only observed at the lower frequencies (4.6, 7, and at 8 MHz) but not at the higher frequencies. As solar activity increases however, the higher frequencies (11.1 and 14.4 MHz) begin to exhibit multimode propagation too, especially around midday when the sun is at its peak. This feature was less obvious in the summer though. The summer was mostly characterised by singlemode signals with a wide SNR (for e.g. a singlemode signal with SNR of 8.5dB to 9.5dB). However, an unusual surge was observed in the SNR of signals obtained in 2013 for all frequencies, rising up to 18 dB at 4.6 MHz and 15 dB at 14.4 MHz V. CONCLUSION At 4.6 MHz, GCP propagation occurs mainly from sunset till sunrise, decreasing in duration and percentage of occurrence as solar activity increases. For this through path, low frequencies are supported only at night while the high frequencies can support GCP propagation during the day. Hence, for daytime transmissions, high frequencies from 7MHz should be employed.

Summer deviations were generally rare and the largest deviations were mostly southerly and occurred at the highest frequencies: 11.1 and 14.4 MHz. These southerly deviations increased in magnitude with increase in solar activity. A very good thing about this rough path is that communications is guaranteed either by northerly or southerly deviations even when there is no possibility of GCP propagation. This is of great advantage for normal radio communication systems that don’t include radiolocations services. Results have shown in Tables 1 and 2 that the time of formation of the trough is not only centred about midnight as suggested by [2], as deviations are observed all through the day, especially towards solar maximum. Finally, the summer season witnessed large SNRs and the largest SNRs were produced at the lowest frequency while the largest frequency produced the least SNRs. REFERENCES [1]

IPS Radio and Space Services, Introduction to HF radio propagation, http://www.ips.gov.au/Educational/5/2/2#sect1, 2012. Last Accessed July 23, 2014.

[2] A. Roger, The mid-latitude trough-revisited, in P. Kintner Jr., A.J. Coster, T. Fuller-Rowell, A.J. Mannucci, M. Mendillo, and R. Heelis (Eds.), Midlatitude ionospheric dynamics and disturbances , Washington: The American Geophysical Union, 2013, pp. 25-33.

[3] E.M. Warrington, A. Bourdillon, E. Benito, C. Bianchi, J. Monilié, M. Muriuki, M. Pietrella, V. Rannou, H. Rothkaehl, H. Saillant, O. Sari, A.J. Stocker, E. Tulunay, Y. Tulunay, and N. Zaalov, “Aspects of HF radio propagation,” Annals of Geophysics, vol. 52(3-4), 2009, pp. 301-321, doi: 10.4401/ag-4577 [4] E.M. Warrington, A.J. Stocker, N. Zaalov, D.R. Siddle, and I.A. Nasyrov, “Propagation of HF radio waves over northerly paths: measurements, simulation and systems aspects,” Annals of Geophysics, vol. 47(2-3), 2004, pp. 1161-1177.

[5] N. Zaalov , H. Rothkaehl, A.J. Stocker, and E.M. Warrington, “Comparison between HF propagation and Demeter satellite measurements within the mid-latitude trough,” Joint Advanced Space Research, vol. 52, 2013, pp. 781-790. doi: 10.1016/j.asr.2013.05.023 [6] A.J. Stocker, E.M. Warrington and D.R. Siddle, “Observations of Doppler spreads on HF signals received over polar cap and through paths at various stages of the solar cycle,” Radio Science, vol. 48(5), 2013, pp. 638-645.

[7] D.R. Siddle, N.Y. Zaalov, A.J. Stocker and E.M. Warrington, Time of flight and direction of arrival of HF radio signals received over a path along the midlatitude trough: Theoretical considerations, Radio Science, vol. 39(4), 2004b, RS4009, doi: 10.1029/2004RS003052 [8] D.R. Siddle, A.J. Stocker and E.M. Warrington, Time of flight and direction of arrival of HF radio signals received over a path along the midlatitude trough: Observations, Radio Science, vol. 39(4), 2004a, RS4008, doi: 10.1029/2004RS003049 [9] A.J. Stocker, N.Y. Zaalov, E.M. Warrington, and D.R. Siddle, Observations of HF propagation on a path aligned along the midlatitude trough,” Advances in Space Research, vol. 44(6), 2009, pp. 677-684, doi: 10.1016/j.asr.2008.09.038.

[10] http://www.ngdc.noaa.gov/stp/space-weather/solar-data/solar-indices/sunspot-numbers/international/tables/table_internationalsunspot-numbers_monthly.txt. Last Accessed July 22, 2014.

VI. Acknowledgments The author conducted the reported work as his M.Sc project at the University of Leicester, UK under the supervision of Professor Michael Warrington.

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Invariant Lagrangian for Electron Field in Terms of Complex Isotropic Vectors Dr. Bulikunzira Sylvestre University of Rwanda University Avenue, B.P 117, Butare, Rwanda Abstract: In previous works, Dirac equation for half-spin particle such as electron has been written in tensor â&#x192;&#x2014; form, in the form of non-linear Maxwell´s like equations, through two complex isotropic vectorsâ&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;đ??š = đ??¸â&#x192;&#x2014; + đ?&#x2018;&#x2013;đ??ť â&#x20AC;˛ â&#x20AC;˛ â&#x20AC;˛ â&#x20AC;˛ â&#x192;&#x2014; â&#x20AC;˛ . It has been proved, that the complex vectors đ??š = đ??¸â&#x192;&#x2014; + đ?&#x2018;&#x2013;đ??ť â&#x192;&#x2014; and â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;đ??š = â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; â&#x192;&#x2014; â&#x20AC;˛ satisfy and â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;đ??š = â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; đ??¸ â&#x2C6;&#x2019; đ?&#x2018;&#x2013;đ??ť đ??¸ â&#x2C6;&#x2019; đ?&#x2018;&#x2013;đ??ť 2 2 2 2 â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; non-linear condition đ??š = 0 and đ??š â&#x20AC;˛ = 0. The condition đ??š = 0 or đ??š â&#x20AC;˛ = 0 is equivalent to two conditions â&#x192;&#x2014; 2 = 0 andâ&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;đ??¸ . đ??ť â&#x192;&#x2014; = 0, obtained by equating to zero separately real and imaginary for real quantities đ??¸â&#x192;&#x2014; 2 â&#x2C6;&#x2019; đ??ť 2 â&#x192;&#x2014; ) and (đ??¸â&#x192;&#x2014; â&#x20AC;˛, đ??ť â&#x192;&#x2014; â&#x20AC;˛) have the same parts in the equalityâ&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;đ??š = 0. Further, it has been proved, that the vectors (đ??¸â&#x192;&#x2014; , đ??ť â&#x192;&#x2014; â&#x192;&#x2014; properties as the vectors(đ??¸ , đ??ť ), components of electromagnetic field.

In this work, in the development of the above ideas, we elaborated the Lagrange formalism for electron field â&#x192;&#x2014; . in tensor formalism, in terms of complex isotropic vectorsđ??š = đ??¸â&#x192;&#x2014; + đ?&#x2018;&#x2013;đ??ť Keywords: Electron field, Invariant Lagrangian, Tensor formalism, Complex isotropic vector.

I. Introduction In previous works, using different methods, in particular, with the help of Cartan map, Dirac equation for halfspin particle, such as electron, has been written in tensor form, in the form of non-linear Maxwell's like â&#x192;&#x2014; =E â&#x192;&#x2014; + iH â&#x192;&#x2014;â&#x192;&#x2014; and â&#x192;&#x2014;â&#x192;&#x2014;F â&#x20AC;˛ = â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; â&#x192;&#x2014;â&#x192;&#x2014; â&#x20AC;˛. It has been proved, that the equations, through two complex isotropic vectors F E â&#x20AC;˛ â&#x2C6;&#x2019; iH â&#x20AC;˛ 2 â&#x20AC;˛ â&#x192;&#x2014; â&#x192;&#x2014; â&#x192;&#x2014; â&#x192;&#x2014; â&#x192;&#x2014;â&#x192;&#x2014; â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; â&#x192;&#x2014; â&#x192;&#x2014; â&#x192;&#x2014;â&#x192;&#x2014; complex vectors F = E + iH and F = E â&#x2C6;&#x2019; iHâ&#x20AC;˛ satisfy non-linear condition F = 0 andâ&#x192;&#x2014;â&#x192;&#x2014;Fâ&#x20AC;˛2 = 0, equivalent to â&#x192;&#x2014; 2 = 0 andâ&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014;E. â&#x192;&#x2014;H â&#x192;&#x2014; = 0, obtained by separating real and imaginary parts in two conditions for real quantities â&#x192;&#x2014;E 2 â&#x2C6;&#x2019; â&#x192;&#x2014;H 2 â&#x192;&#x2014; ,H â&#x192;&#x2014;â&#x192;&#x2014; ) and (E â&#x192;&#x2014; â&#x20AC;˛, H â&#x192;&#x2014;â&#x192;&#x2014; â&#x20AC;˛) have the same properties as the equalityâ&#x192;&#x2014;â&#x192;&#x2014;F = 0. Further, it has been proved, that the vectors (E â&#x192;&#x2014; â&#x192;&#x2014; â&#x192;&#x2014; the vectors(E, H), components of electromagnetic field. For example, under Lorentz relativistic transformations, they are transformed as components of electric and magnetic fields. In addition, it has been proved, that the solution of these non-linear equations for free particle as well fulfils Maxwell's equations for vacuum (with zero at the right side).

In this work, in the development of the above mentioned works, we shall elaborate the Lagrange formalism for â&#x192;&#x2014; =E â&#x192;&#x2014; + iH â&#x192;&#x2014;â&#x192;&#x2014; . electron field in tensor formalism, in terms of complex isotropic vectors F II. Research Method In previous works, via Cartan map, Dirac equation for electron has been written in tensor form, in the form of â&#x192;&#x2014; =E â&#x192;&#x2014; + iH â&#x192;&#x2014;â&#x192;&#x2014; and â&#x192;&#x2014;â&#x192;&#x2014;F â&#x20AC;˛ = â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; â&#x192;&#x2014;â&#x192;&#x2014; â&#x20AC;˛. In non-linear Maxwell's like equations, through two complex isotropic vectors F E â&#x20AC;˛ â&#x2C6;&#x2019; iH this work, using the same method, based on Cartan map, we shall elaborate the Lagrange formalism for electron â&#x192;&#x2014; =E â&#x192;&#x2014; + iH â&#x192;&#x2014;â&#x192;&#x2014; . field in tensor formalism, in terms of complex isotropic vectors F III. Dirac Equation in Tensor Form Relativistic particle with spin 1â &#x201E;2 and different to zero rest mass is described by the wave equation, proposed

by Dirac in 1928. This equation, written in symmetric form has the form (γΟ â&#x2C6;&#x201A;Îź â&#x2C6;&#x2019; m)Ψ=0.

(1) Ο Here γ are square fourth rank matrices, satisfying the relations (Clifford-Dirac algebra) γΟ γν +γν γΟ =2δΟν , (2) where Ο,ν=0,1,2,3.

It is natural to emphasize, that in general, Dirac matrices γΟ are defined with accuracy to correspondence transformation. Thus, the representation of these matrices can be chosen in different forms. Ordinary, it is commonly used the representation of Dirac matrices in which Îł0 is diagonal: I 0 â&#x192;&#x2014;]. Îł0 = [ ], Îł=[ 0 Ď&#x192; (3) 0 â&#x2C6;&#x2019;I â&#x2C6;&#x2019;Ď&#x192; â&#x192;&#x2014; 0

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Bulikunzira Sylvestre, American International Journal of Research in Science, Technology, Engineering & Mathematics, 13(1), December, 2015-February, 2016, pp. 83-86

Here Ď&#x192; â&#x192;&#x2014; are second rank Pauli spin matrices, having the form 0 1 0 â&#x2C6;&#x2019;đ?&#x2018;&#x2013; 1 0 Ď&#x192;1 =[ ] , Ď&#x192;2 = [ ] , Ď&#x192;3 =[ ].

(4) 1 0 đ?&#x2018;&#x2013; 0 0 â&#x2C6;&#x2019;1 This representation is often called the standard representation.

In this representation, Dirac bispinor Ψ is written as Ď&#x2020; Ψ=[ Ď&#x2021; ] .

(5) Here Ď&#x2020;, Ď&#x2021; are tridimensional (but two components) Pauli spinors.

Using formulas (3) and (5), equation (1) can be written in the form of a system of two equations p Ď&#x2020; â&#x2C6;&#x2019; (p â&#x192;&#x2014;Ď&#x192; â&#x192;&#x2014; )Ď&#x2021; = â&#x2C6;&#x2019;mĎ&#x2020; { 0 .

(6) (p p0 Ď&#x2021; â&#x2C6;&#x2019; â&#x192;&#x2014; Ď&#x192; â&#x192;&#x2014; )Ď&#x2020; = mĎ&#x2021; Another representation of Dirac matrices is the spinor representation. In this representation γΟ â&#x2C6;&#x2019; matrices and Dirac bispinor Ψ are written in the form 0 I â&#x192;&#x2014;], Îł0 = [ ] , Îł = [0 â&#x2C6;&#x2019;Ď&#x192; (7) I 0 â&#x192;&#x2014; Ď&#x192; 0 Ξ Ψ=[ ].

(8) Ρ With the help of formulas (7) and (8), Dirac equation (1) can be written in the form of a system of two equations p Ρ + (p â&#x192;&#x2014;Ď&#x192; â&#x192;&#x2014; )Ρ = mΞ { 0 .

(9) p0 Ξ â&#x2C6;&#x2019; (p â&#x192;&#x2014;Ď&#x192; â&#x192;&#x2014; )Ξ = mΡ It follows from equation (1), that each component of the wave function Ψ satisfies the Klein-Gordon equation (â&#x2013;Ą â&#x2C6;&#x2019; m2 )Ψi =0.

(10) â&#x2C6;&#x201A; 2 â&#x192;&#x2014; Where i=1,2,3,4 and â&#x2013;Ą = 2 â&#x2C6;&#x2019; â&#x2C6;&#x2021; â&#x2C6;&#x2019; DË&#x160; Alembert operator. â&#x2C6;&#x201A;t With the help of Cartan map, Dirac equation (1) has been written in tensor form, through two complex isotropic â&#x192;&#x2014;â&#x192;&#x2014; and â&#x192;&#x2014;FË&#x160;= â&#x192;&#x2014;EË&#x160;-iH â&#x192;&#x2014;â&#x192;&#x2014; Ë&#x160; as follows vectors â&#x192;&#x2014;F= â&#x192;&#x2014;E+iH â&#x192;&#x2014; â&#x192;&#x2014; â&#x192;&#x2014;â&#x192;&#x2014; â&#x192;&#x2014;F)v â&#x192;&#x2014; Ă&#x2014; â&#x192;&#x2014;F = â&#x2C6;&#x2019; m FĂ&#x2014;F1Ë&#x160;â &#x201E;2 D0 â&#x192;&#x2014;F + (D â&#x192;&#x2014; â&#x20AC;&#x201C; i â&#x192;&#x2014;D â&#x2C6;&#x161;2 (F â&#x192;&#x2014; .F â&#x192;&#x2014; Ë&#x160;)

{

â&#x192;&#x2014; Ë&#x160; â&#x2C6;&#x2019; (D â&#x192;&#x2014;â&#x192;&#x2014; F â&#x192;&#x2014; Ë&#x160;)v â&#x192;&#x2014;â&#x192;&#x2014; Ă&#x2014; F â&#x192;&#x2014;Ë&#x160; = â&#x2C6;&#x2019; D0 F â&#x192;&#x2014;Ë&#x160; +iD D0 =

Here

â&#x192;&#x2014;â&#x192;&#x2014; = D â&#x192;&#x2014; = v

i â&#x2C6;&#x201A; 2 â&#x2C6;&#x201A;t i 2

J

.

â&#x192;&#x2014; Ă&#x2014;F â&#x192;&#x2014;Ë&#x160; F

(11)

1 â &#x201E;2 â&#x2C6;&#x161;2 (F â&#x192;&#x2014; .F â&#x192;&#x2014; Ë&#x160;)

,

â&#x192;&#x2014; , â&#x2C6;&#x2021;

=

J0

m

â&#x192;&#x2014;EĂ&#x2014;H â&#x192;&#x2014;â&#x192;&#x2014; â&#x192;&#x2014;â&#x152;&#x2030; â&#x152;&#x2C6;E

2

.

Here we use the natural system of units in which c=ħ=1.

Separating real and imaginary parts, the system of equations (11) can be represented in the form of a system of â&#x192;&#x2014; , â&#x192;&#x2014;H â&#x192;&#x2014; ) and (E â&#x192;&#x2014; Ë&#x160;, â&#x192;&#x2014;H â&#x192;&#x2014; Ë&#x160;) non-linear Maxwell's like equations for strengths (E â&#x192;&#x2014;â&#x192;&#x2014;

â&#x192;&#x2014; + â&#x2C6;&#x201A;H = vi (â&#x2C6;&#x2021; â&#x192;&#x2014; Hi ) + mja rotE â&#x2C6;&#x201A;t â&#x192;&#x2014;

â&#x192;&#x2014;â&#x192;&#x2014; â&#x2C6;&#x2019; â&#x2C6;&#x201A;E = â&#x2C6;&#x2019;vi (â&#x2C6;&#x2021; â&#x192;&#x2014; Ei ) + mjv rotH â&#x2C6;&#x201A;t â&#x192;&#x2014;â&#x192;&#x2014;

â&#x192;&#x2014; Ë&#x160; + â&#x2C6;&#x201A;HË&#x160; = â&#x2C6;&#x2019;vi Ë&#x160;(â&#x2C6;&#x2021; â&#x192;&#x2014; Hi Ë&#x160;) â&#x2C6;&#x2019; mja rotE â&#x2C6;&#x201A;t â&#x192;&#x2014;Ë&#x160; â&#x2C6;&#x201A;E

â&#x192;&#x2014;â&#x192;&#x2014; Ë&#x160; â&#x2C6;&#x2019; { rotH

â&#x2C6;&#x201A;t

.

(12)

â&#x192;&#x2014; Ei Ë&#x160;) + mjv = vi Ë&#x160;(â&#x2C6;&#x2021;

Here ja = â&#x2C6;&#x161;2

â&#x192;&#x2014; Ă&#x2014;E â&#x192;&#x2014; Ë&#x160;+H â&#x192;&#x2014;â&#x192;&#x2014; Ă&#x2014;H â&#x192;&#x2014;â&#x192;&#x2014; Ë&#x160;) cosĎ&#x2020;â &#x201E;2+(H â&#x192;&#x2014;â&#x192;&#x2014; Ă&#x2014;E â&#x192;&#x2014; Ë&#x160;+H â&#x192;&#x2014;â&#x192;&#x2014; Ë&#x160;Ă&#x2014;E â&#x192;&#x2014; ) sinĎ&#x2020;â &#x201E;2 (E 2

2

2

1â &#x201E;4

2

,

(13)

â&#x192;&#x2014;E â&#x192;&#x2014; Ë&#x160;) +(H â&#x192;&#x2014;â&#x192;&#x2014; H â&#x192;&#x2014;â&#x192;&#x2014; Ë&#x160;) +2(E â&#x192;&#x2014;E â&#x192;&#x2014; Ë&#x160;)(H â&#x192;&#x2014;â&#x192;&#x2014; H â&#x192;&#x2014;â&#x192;&#x2014; Ë&#x160;)+(E â&#x192;&#x2014;H â&#x192;&#x2014;â&#x192;&#x2014; Ë&#x160;) +(E â&#x192;&#x2014; Ë&#x160;H â&#x192;&#x2014;â&#x192;&#x2014; ) +2(E â&#x192;&#x2014;H â&#x192;&#x2014;â&#x192;&#x2014; Ë&#x160;)(E â&#x192;&#x2014; Ë&#x160;H â&#x192;&#x2014;â&#x192;&#x2014; )] [(E

ja = -â&#x2C6;&#x161;2

â&#x192;&#x2014; Ă&#x2014;E â&#x192;&#x2014; Ë&#x160;+H â&#x192;&#x2014;â&#x192;&#x2014; Ă&#x2014;H â&#x192;&#x2014;â&#x192;&#x2014; Ë&#x160;) sinĎ&#x2020;â &#x201E;2 +(H â&#x192;&#x2014;â&#x192;&#x2014; Ă&#x2014;E â&#x192;&#x2014; Ë&#x160;+H â&#x192;&#x2014;â&#x192;&#x2014; Ë&#x160;Ă&#x2014;E â&#x192;&#x2014; ) cosĎ&#x2020;â &#x201E;2 (E 2

2

2

2

1â &#x201E;4

,

(14)

â&#x192;&#x2014;E â&#x192;&#x2014; Ë&#x160;) +(H â&#x192;&#x2014;â&#x192;&#x2014; H â&#x192;&#x2014;â&#x192;&#x2014; Ë&#x160;) +2(E â&#x192;&#x2014;E â&#x192;&#x2014; Ë&#x160;)(H â&#x192;&#x2014;â&#x192;&#x2014; H â&#x192;&#x2014;â&#x192;&#x2014; Ë&#x160;)+(E â&#x192;&#x2014;H â&#x192;&#x2014;â&#x192;&#x2014; Ë&#x160;) +(E â&#x192;&#x2014; Ë&#x160;H â&#x192;&#x2014;â&#x192;&#x2014; ) +2(E â&#x192;&#x2014;H â&#x192;&#x2014;â&#x192;&#x2014; Ë&#x160;)(E â&#x192;&#x2014; Ë&#x160;H â&#x192;&#x2014;â&#x192;&#x2014; )] [(E â&#x192;&#x2014; Ë&#x160;H â&#x192;&#x2014;â&#x192;&#x2014; â&#x2C6;&#x2019;E â&#x192;&#x2014;H â&#x192;&#x2014;â&#x192;&#x2014; Ë&#x160; E â&#x192;&#x2014;â&#x192;&#x2014; H â&#x192;&#x2014;â&#x192;&#x2014; Ë&#x160; EEË&#x160;+H

Ď&#x2020; = arctg â&#x192;&#x2014; â&#x192;&#x2014;

. â&#x192;&#x2014; Ë&#x160; and â&#x192;&#x2014;H â&#x192;&#x2014; //H â&#x192;&#x2014;â&#x192;&#x2014; Ë&#x160;, we find a simple system In particular, if Ď&#x2020; =0, i.e., â&#x192;&#x2014;E//E

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(15)

Page 84

Bulikunzira Sylvestre, American International Journal of Research in Science, Technology, Engineering & Mathematics, 13(1), December, 2015-February, 2016, pp. 83-86 â&#x192;&#x2014;â&#x192;&#x2014;

â&#x192;&#x2014; + â&#x2C6;&#x201A;H = vi (â&#x2C6;&#x2021; â&#x192;&#x2014; Hi ) + â&#x2C6;&#x161;2 m rotE â&#x2C6;&#x201A;t

â&#x192;&#x2014;EĂ&#x2014;E â&#x192;&#x2014; Ë&#x160;+H â&#x192;&#x2014;â&#x192;&#x2014; Ă&#x2014;H â&#x192;&#x2014;â&#x192;&#x2014; Ë&#x160; â&#x192;&#x2014;E â&#x192;&#x2014; Ë&#x160;+H â&#x192;&#x2014;â&#x192;&#x2014; H â&#x192;&#x2014;â&#x192;&#x2014; Ë&#x160;) (E

â&#x192;&#x2014;

â&#x192;&#x2014;â&#x192;&#x2014; â&#x2C6;&#x2019; â&#x2C6;&#x201A;E = â&#x2C6;&#x2019;vi (â&#x2C6;&#x2021; â&#x192;&#x2014; Ei ) + â&#x2C6;&#x161;2 m rotH â&#x2C6;&#x201A;t

1â &#x201E;2

â&#x192;&#x2014;â&#x192;&#x2014; Ă&#x2014;E â&#x192;&#x2014; Ë&#x160;+H â&#x192;&#x2014;â&#x192;&#x2014; Ë&#x160;Ă&#x2014;H â&#x192;&#x2014;â&#x192;&#x2014; Ë&#x160; H â&#x192;&#x2014;E â&#x192;&#x2014; Ë&#x160;+H â&#x192;&#x2014;â&#x192;&#x2014; H â&#x192;&#x2014;â&#x192;&#x2014; Ë&#x160;) (E

â&#x192;&#x2014;â&#x192;&#x2014;

â&#x192;&#x2014; Ë&#x160; + â&#x2C6;&#x201A;HË&#x160; = â&#x2C6;&#x2019;vi Ë&#x160;(â&#x2C6;&#x2021; â&#x192;&#x2014; Hi Ë&#x160;) â&#x2C6;&#x2019; â&#x2C6;&#x161;2 m rotE â&#x2C6;&#x201A;t

â&#x192;&#x2014;Ë&#x160; â&#x2C6;&#x201A;E

1â &#x201E;2

â&#x192;&#x2014;EĂ&#x2014;E â&#x192;&#x2014; Ë&#x160;+H â&#x192;&#x2014;â&#x192;&#x2014; Ă&#x2014;H â&#x192;&#x2014;â&#x192;&#x2014; Ë&#x160; â&#x192;&#x2014;E â&#x192;&#x2014; Ë&#x160;+H â&#x192;&#x2014;â&#x192;&#x2014; H â&#x192;&#x2014;â&#x192;&#x2014; Ë&#x160;) (E

.

(16)

1â &#x201E;2

â&#x192;&#x2014;â&#x192;&#x2014; Ă&#x2014;E â&#x192;&#x2014; Ë&#x160;+H â&#x192;&#x2014;â&#x192;&#x2014; Ë&#x160;Ă&#x2014;H â&#x192;&#x2014;â&#x192;&#x2014; Ë&#x160; H

â&#x192;&#x2014;â&#x192;&#x2014; Ë&#x160; â&#x2C6;&#x2019; â&#x192;&#x2014; Ei Ë&#x160;) + â&#x2C6;&#x161;2 m rotH = vi Ë&#x160;(â&#x2C6;&#x2021; 1â &#x201E;2 â&#x2C6;&#x201A;t â&#x192;&#x2014;E â&#x192;&#x2014; Ë&#x160;+H â&#x192;&#x2014;â&#x192;&#x2014; H â&#x192;&#x2014;â&#x192;&#x2014; Ë&#x160;) (E { It is obvious, that if the rest mass of the particle equals zero, this system splits into two independent systems of â&#x192;&#x2014; , â&#x192;&#x2014;H â&#x192;&#x2014; ) and (E â&#x192;&#x2014; Ë&#x160;, â&#x192;&#x2014;H â&#x192;&#x2014; Ë&#x160;), equivalent to two Weyl's equations in spinor formalism. equations for fields (E IV. Lagrange Formalism for Electron Field in Tensor Formalism Spinor Dirac equation (1) can be obtained by variation principle from the following Lagrange function Ě&#x2026; γΟ â&#x2C6;&#x201A;Îź Ψ)-mΨ Ě&#x2026; Ψ+h.c.

L = i (Ψ (17) Using formulas (7) and (8), formula (17) can be rewritten in the form â&#x192;&#x2014; )Ξ + imΡ] + Ρ+ [â&#x2C6;&#x201A;0 Ρ + (Ď&#x192; â&#x192;&#x2014; )Ρ + imΞ]}+c.h. , L = i {Ξ+ [â&#x2C6;&#x201A;0 Ξ â&#x2C6;&#x2019; (Ď&#x192; â&#x192;&#x2014; .â&#x2C6;&#x2021; â&#x192;&#x2014; .â&#x2C6;&#x2021; (18) or L = {Ξ+ [p0 Ξ + (p â&#x192;&#x2014; .Ď&#x192; â&#x192;&#x2014; )Ξ â&#x2C6;&#x2019; mΡ] + Ρ+ [p0 Ρ â&#x2C6;&#x2019; (p â&#x192;&#x2014; .Ď&#x192; â&#x192;&#x2014; )Ρ â&#x2C6;&#x2019; mΞ]}+c.h. .

(19) Here đ?&#x153;&#x2022; â&#x192;&#x2014; . p0 = i , p â&#x192;&#x2014; =-iâ&#x2C6;&#x2021; (20) đ?&#x153;&#x2022;đ?&#x2018;Ą Here the natural system of units in which c=ħ=1 has been used.

With the help of Cartan map, formula (19) can be written in vector form as follows L= m

â&#x192;&#x2014;â&#x2C6;&#x2014; F 1â &#x201E;2

â&#x192;&#x2014; â&#x192;&#x2014;Fâ&#x2C6;&#x2014; â &#x201E;2) (F

â&#x192;&#x2014;FĂ&#x2014;F â&#x192;&#x2014;Ë&#x160;

1â &#x201E; 2 â&#x2C6;&#x161;2 (F â&#x192;&#x2014;F â&#x192;&#x2014; Ë&#x160;)

â&#x192;&#x2014;â&#x192;&#x2014; Fi ) â&#x2C6;&#x2019; iD â&#x192;&#x2014;â&#x192;&#x2014; Ă&#x2014; â&#x192;&#x2014;F + [D0 â&#x192;&#x2014;F + vi (D

â&#x192;&#x2014; Ă&#x2014;F â&#x192;&#x2014;Ë&#x160; F

m

â&#x2C6;&#x161;2 (F â&#x192;&#x2014; â&#x192;&#x2014;FË&#x160;)

1â &#x201E;2

]+

â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; FË&#x160; â&#x2C6;&#x2014;

â&#x2C6;&#x2014; 1â &#x201E;2

â&#x192;&#x2014; Ë&#x160;F â&#x192;&#x2014; Ë&#x160; â &#x201E;2 ) (F

â&#x192;&#x2014;â&#x192;&#x2014; FË&#x160;i ) + iD â&#x192;&#x2014;â&#x192;&#x2014; Ă&#x2014; â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; [D0â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; FË&#x160; â&#x2C6;&#x2019; vË&#x160;i (D FË&#x160; +

]+c.h. .

(21) â&#x2C6;&#x2014;

It is clear, that varying the Lagrange function (21) over fields â&#x192;&#x2014;F â&#x2C6;&#x2014; and â&#x192;&#x2014;â&#x192;&#x2014;â&#x192;&#x2014; FË&#x160; , we obtain the system of equations (11), equivalent to spinor Dirac equation (1).

Principal Dynamical Variables On the basis of Noetherâ&#x20AC;&#x2122;s theorem, from Lagrangian (21), we can derive expressions for principal dynamical variables conserved in time.

For energy we have the formula Î&#x2022; = â&#x2C6;Ť T 00 d3 x, (22) where T 00 =

â&#x192;&#x2014; â&#x192;&#x2014;Ë&#x160; â&#x2C6;&#x201A;L â&#x2C6;&#x201A;F â&#x2C6;&#x201A;L â&#x2C6;&#x201A;F + â&#x192;&#x2014; â&#x192;&#x2014; ,0 â&#x2C6;&#x201A;x0 â&#x2C6;&#x201A;F â&#x2C6;&#x201A;F Ë&#x160;,0 â&#x2C6;&#x201A;x0

.

(23)

Replacing formula (21) in formula (23), we obtain â&#x192;&#x2014;

T

00

=i

â&#x192;&#x2014; â&#x2C6;&#x2014; â&#x2C6;&#x201A;F) (F â&#x2C6;&#x201A;t 1â &#x201E;2

â&#x192;&#x2014; â&#x192;&#x2014;Fâ&#x2C6;&#x2014; â &#x201E;2) 2(F

â&#x2C6;&#x2014; â&#x192;&#x2014; â&#x192;&#x2014; Ë&#x160; â&#x2C6;&#x201A;FË&#x160;) (F â&#x2C6;&#x201A;t

+i

â&#x2C6;&#x2014;

â&#x192;&#x2014; Ë&#x160;F â&#x192;&#x2014; Ë&#x160; â &#x201E;2 ) 2(F

1â &#x201E;2

.

(24)

Using expressions for vectors â&#x192;&#x2014;F and â&#x192;&#x2014;FË&#x160; â&#x192;&#x2014; = (E â&#x192;&#x2014; 0 + iH â&#x192;&#x2014;â&#x192;&#x2014; 0 ) e2iÎľđ?&#x2019;Śtâ&#x2C6;&#x2019;2ikâ&#x192;&#x2014;râ&#x192;&#x2014; , F 0 0 â&#x192;&#x2014; Ë&#x160; = (E â&#x192;&#x2014; Ë&#x160; â&#x2C6;&#x2019; iH â&#x192;&#x2014;â&#x192;&#x2014; Ë&#x160; ) e2iÎľđ?&#x2019;Śtâ&#x2C6;&#x2019;2ikâ&#x192;&#x2014;râ&#x192;&#x2014; , F

(25) (26)

we find â&#x192;&#x2014; | + |E â&#x192;&#x2014; Ë&#x160;|) . Î&#x2022; = Îľ (|E Here đ?&#x153;&#x20AC; = Âą1 is the sign of energy.

For momentum vector, we have Pj = â&#x2C6;Ť T 0j d3 x, where T 0j =

â&#x192;&#x2014; â&#x192;&#x2014;Ë&#x160; â&#x2C6;&#x201A;L â&#x2C6;&#x201A;F â&#x2C6;&#x201A;L â&#x2C6;&#x201A;F + â&#x192;&#x2014; â&#x192;&#x2014; ,0 â&#x2C6;&#x201A;xj â&#x2C6;&#x201A;F â&#x2C6;&#x201A;F Ë&#x160;,0 â&#x2C6;&#x201A;xj

(27)

(28) .

(29)

With consideration of formula (21), we obtain 0j

T = i

â&#x192;&#x2014; â&#x2C6;&#x201A;xj

â&#x2C6;&#x2014; â&#x192;&#x2014; â&#x192;&#x2014; Ë&#x160; â&#x2C6;&#x201A;FË&#x160;) (F

â&#x192;&#x2014; â&#x2C6;&#x2014; â&#x2C6;&#x201A;F ) (F 1â &#x201E;2

â&#x192;&#x2014;F â&#x192;&#x2014; â&#x2C6;&#x2014; â &#x201E;2) 2(F

+i

â&#x2C6;&#x201A;xj

â&#x2C6;&#x2014;

â&#x192;&#x2014; Ë&#x160;F â&#x192;&#x2014; Ë&#x160; â &#x201E;2 ) 2(F

1â &#x201E;2

.

(30)

Replacing formulas (25)-(26) into formula (30), we find

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⃗ (|E ⃗P = k ⃗ | + |E ⃗ ˊ|) .

Similarly, for charge, we have Q= ∫ j0 d3 x, where ∗ ⃗ ∗ ∂L∗ − ∂L ⃗F + ⃗Fˊ j0 = {F ⃗ ,0 ∂F

⃗ ,0 ∂F

(31) (32) ∂L ∗

⃗ ˊ ,0 ∂F

−

∂L ⃗Fˊ} ⃗ ˊ,0 ∂F

.

(33)

With consideration of formula (21), we obtain j0 =

⃗ ∗F ⃗) (F

∗

1⁄2 +

⃗F ⃗ ∗ ⁄2 ) 2(F

⃗ ˊ ⃗Fˊ) (F 1⁄2

∗

.

(34)

⃗ ˊF ⃗ ˊ ⁄2 ) 2(F

Using formulas (25)-(26), we find ⃗ | + |E ⃗ ˊ| . j0 = |E For spin pseudo vector, we obtain ⃗S = i [

⃗ ×F ⃗∗ F 1⁄2

2 (F ⃗ ⃗F∗ ⁄2)

(35) ⃗ ˊ×F ⃗ˊ F

+

∗

∗

⃗ ˊF ⃗ ˊ ⁄2 ) (F

1⁄2

].

Considering formulas (25)-(26), we find ⃗ ⃗​⃗ ⃗ ⃗​⃗ ⃗S = E×H-Eˊ×Hˊ . ⃗| |E

⃗ ˊ| |E

(36)

(37)

V. Discussion and Conclusion In previous works, using Cartan map, Dirac equation for electron has been written in tensor formalism, in the ⃗​⃗ and ⃗​⃗F ′ = ⃗​⃗​⃗ form of non-linear Maxwell's like equations, through two complex isotropic vectors ⃗F = ⃗E + iH E′ − ⃗​⃗ ′. In this work, using the same method, we elaborated the Lagrange formalism for electron field in tensor iH formalism, in terms of complex isotropic vectors. The Lagrange function for electron field previously written ⃗ =E ⃗ + iH ⃗​⃗ and ⃗​⃗F ′ = ⃗​⃗​⃗ ⃗​⃗ ′. On the through spinors has been rewritten through complex isotropic vectors F E ′ − iH basis of Noether's theorem, we derived expressions for fundamental dynamical variables (energy, momentum, ⃗ , ⃗H ⃗ ) and(E ⃗ ′, ⃗H ⃗ ′). charge, spin) conserved in time and we expressed them through strengths (E References [1] [2] [3] [4] [5]

S.Bulikunzira, “Tensor formulation of Dirac equation through divisors,” Asian Journal of Fuzzy and Applied Mathematics, vol.2, no6, Dec. 2014, pp.195-197.

S.Bulikunzira, “Tensor formulation of Dirac equation in standard representation,” Asian Journal of Fuzzy and Applied Mathematics, vol.2, no6, Dec. 2014, pp.203-208.

S.Bulikunzira, “Formulation of conservation laws of current and energy for neutrino field in tensor formalism,” Asian Journal of Fuzzy and Applied Mathematics, vol.3, no1, Feb.2015, pp.7-9.

F.Reifler., “Vector wave equation for neutrinos,” Journal of mathematical physics, vol.25, no4, 1984, pp.1088-1092.

P.Sommers,” Space spinors,” Journal of mathematical physics, vol.21, no10, 1980, pp.2567-2571.

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ISSN (Print): 2328-3491, ISSN (Online): 2328-3580, ISSN (CD-ROM): 2328-3629 AIJRSTEM is a refereed, indexed, peer-reviewed, multidisciplinary and open access journal published by International Association of Scientific Innovation and Research (IASIR), USA (An Association Unifying the Sciences, Engineering, and Applied Research)

Effect of Electrification in Presence of Non- Uniform Heat Source/Sink on Unsteady Boundary Layer Flow and Heat Transfer in a Fluid With Suspended Particulate Matter (SPM) Over An Inclined Stretching Sheet Runu Sahu, S.K.Mishra Senior Lecturer,Vivekananda Institute of Technology, Chhatabara, Bhubaneswar, Odisha, INDIA Adjunct Professor, Center for Fluid Dynamics Research, CUTM, Paralakhemundi, Odisha, INDIA Abstract: The present study of unsteady laminar two dimensional boundary layer flow and heat transfer with suspended particulate matter (SPM) over an inclined stretching sheet considers electrification of particles, heat due to conduction and viscous dissipation for both the fluid as well as particle phases in presence of heat source/sink . The governing partial differential equations have been reduced to a set of non linear ordinary differential equations by using suitable similarity transformation and then solved numerically using Runge Kutta based shooting technique. The effects of non dimensional parameters namely electrification parameter, unsteady parameter, heat source/sink parameter, volume fraction, diffusion parameter and angle of inclination on non dimensional velocity, temperature ,skin friction and Nusselt number are discussed and presented through graphs and tables. A comparison of the present result with existing literature is found to be in good agreement .It is interesting to note that the electrification of particles enhance the skin friction and heat transfer rate .

AMSW classification 76T10, 76T15 Keywords: Volume fraction, Interaction parameter, Dusty fluid, unsteady flow and heat transfer, Boundary layer flow, Numerical solution. Non uniform heat source/sink Nomenclature Eckert number Froud number Grashof number Prandtl number Temperature at large distance from the wall.

Temperature of particle phase.

Wall temperature Stretching sheet velocity Specific heat of fluid Specific heat of particles Thermal conductivity of particle , velocity component of the particle along x-axis and y-axis A the positive constant c stretching rate g acceleration due to gravity k thermal conductivity of fluid l characteristic length T temperature of fluid phase. u,v velocity component of fluid along x-axis and y-axis x,y cartesian coordinate non- uniform heat source/sink K* mean absorption co-efficient A*& B* the parameters of the space and temperature dependent internal heat source/sink.

Greek Symbols: Volume fraction Fluid particle interaction parameter Volumetric coefficient of thermal expansion The Stefan Bolzman constant & Density of the fluid& particle phase

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Material density η similarity variable θ fluid phase temperature Dust phase temperature Dynamic viscosity of fluid ν kinematic viscosity of fluid Ratio of specific heat Relaxation time of particle phase Thermal relaxation time i.e. the time required by the dust particle to adjust its temperature relative to the fluid.

Velocity relaxation time i.e. the time required by the dust particle to adjust its velocity relative to the fluid. ε diffusion parameter ω density ratio Angle of inclination I. Introduction The MHD laminar boundary layer flow over a stretching sheet has noticeable application in glass blowing continuous casting, paper production, hot rolling, wire drawing ,drawing of plastic films, metal and polymer extrusion, metal spinning and spinning of fibers. During its manufacturing process a stretched sheet interacts with the ambient fluid thermally and mechanically. Both the kinematics of stretching and the simultaneous heating of cooling during such process have a decisive influence on the quality of the final products.

Sakiadis [18] in1961 have developed the flow field due to a flat surface, which is moving with a constant velocity in a quiescent fluid. Then many researchers extended the above study with the effect of heat transfer .Tsou et.al [24] have studied the effect of heat transfer and experimentally confirmed the numerical result of Sakiadis .Grubka et.al [6] have investigated the temperature field in the flow over a stretching surface when subject to uniform heat flux . Ramesh et.al. [5] have investigated the momentum and heat transfer characteristics in hydromagnetic flow of dusty fluid over an inclined stretching sheet with non uniform heat source/sink .Mohammad et.al [11] have developed the steady MHD free convection, heat and mass transfer flow of an incompressible electrically conducting fluid past an inclined stretching sheet under the influence of an applied uniform magnetic field with Hall current and radiation effect. Ali et al.[9] have investigated the heat and mass transfer of a steady flow of an incompressible electrically conducting fluid over an inclined stretching plate under the influence of an applied uniform magnetic field with heat generation and suction and effect of hall current. Alam et.al [14] have studied numerically the effect of viscous dissipation and chemical reaction on MHD free convective heat and mass transfer flow along an inclined permeable stretching sheet with suction.

Mohammad et al.[12] have analyzed the steady hydro magnetic flow of an incompressible electrically conducting fluid over an inclined stretching sheet . Ali et.al [13] have studied the Hall Effect on the study MHD boundary layer flow over an incompressible fluid of combined heat and mass transfer over a moving inclined plate in a porous medium with suction and viscous dissipation. Alam et.al [10] have studied numerically the influence of chemical reaction and heat source/sink on MHD free convective heat and mass transfer flow of a viscous, incompressible and electrically conducting fluid over an inclined stretching sheet.

In the present investigation the focus is made on the electrifications of particles due to tribo electrification. To the author’s knowledge no consulted effort has been made to show the effect of electrification of particles along with particle and particle interaction as well as heat generation / absorption on the boundary layer flow over an inclined stretching sheet. Again the effect parameters like electrification parameter, unsteady parameter, heat source/sink parameter, volume fraction, diffusion parameter, Grashof number; fluid particle interaction parameter and angle of inclination etc on boundary layer characteristics and heat transfer have been discussed.

II. Flow Analysis of the Problem and solution Consider an unsteady two dimensional laminar boundary layer flow of an incompressible viscous dusty fluid along an inclined plate with an acute angle .The flow is generated by the action of two equal and opposite forces along the x-axis and y-axis being normal to the flow .The sheet being stretched with the velocity U w(x) along the x-axis, keeping the origin fixed in the fluid of ambient temperature . Both the fluid and the dust particle clouds are suppose to be static at the beginning. The dust particles are assumed to be spherical in shape and uniform in size and number density of the dust particle is taken as a constant throughout the flow. The sketch of the physical configuration and coordinate system shown are in Figure-1.

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Figure1: Geometrical configuration of the flow problem.

Soo [21] has studied the effect of electrification on the dynamics of a particulate system. At low temperature, electrification of solid particles occurs because of impact with the wall. Even a very slight charge on the solid particles will have a pronounced effect on concentration distribution in the flow of a gas-solid system. Although electric charge on the solid particles can be excluded by definition in theoretical analysis or when dealing truly with a boundless system, electrification of the solid particles always occurs when contact and separation are made between the solid particles and a wall of different materials or similar materials but different surface condition. The electric charges on the solid particles cause deposition of the solid particles on a wall in a more significant manner than the gravity effect and are expected to affect the motion of a metalized propellant and its product of reaction through a rocket nozzle and the jet at the exit of the nozzle. The charged solid particles in the jet of a hot gas also effect radio communications.

As a general statement, any volume element of charge species, with charge experiences an instantaneous force given by the Lorentz force law, (A) Where

is the magnetic flux density. The current densities in corona discharge are so low that the magnetic

force term can be omitted, as this term is many orders of magnitude smaller than the Coulomb term .

The ion drift motion arises from the interaction of ions, constantly subject to the Lorentz force (A) with the dense neutral fluid medium. This interaction produces an effective drag force on the ions. The drag force is in equilibrium with the Lorentz force so that the ion velocity in a field is limited to , where is the mobility of the ion species. The drag force on the ions has an equal and opposite reaction force acting on the neutral fluid molecules via this ion-neutral molecules interaction, the force on the ions is transmitted directly to the fluid medium, so the force on the fluid particles is also given by equation (A). The above analyses motivated to present study of this paper. Here the particles will be allowed to diffuse through the carrier fluid i.e. the random motion of the particles shall be taken into account because of the small size of the particles. This can be done by applying the kinetic theory of gases and hence the motion of the particles across the streamline due to the concentration and pressure diffusion. We have considered the terms related to the heat added to the system to slip-energy flux in the energy equation of particle phase. The momentum equation for particulate phase in normal direction, heat due to conduction and viscous dissipation in the energy equation of the particle phase have been considered for better understanding of the boundary layer characteristics. The effects of electrification, non uniform heat sour/sink, volume fraction of particles on skin friction, heat transfer and other boundary layer characteristics also have been studied. The governing equations of unsteady two dimensional boundary layer incompressible flows of dusty fluids are given by Equation of continuity (1) (2) Momentum equations:

(3) (4) (5) Energy equations:

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(6)

(7) With boundary conditions (8) Where is the density ratio in the main stream.

In order to solve (6) and (7), we consider non 窶電imensional temperature boundary conditions as follows (9) For most of the gases

if

Introducing the following non dimensional variables in equation (1) to (7) , ,

, Where

, M=

Where and are the parameters of the space and the temperature dependent internal heat source/sink. It is to be noted that and are positive heat source and negative to internal heat sink. is the space-and temperature-dependent internal heat generation/absorption (non-uniform heat source/sink) which can be expressed as (10) a is the positive constant which measures the unsteadiness with boundary condition c is the stretching rate and being a positive constant, is the specific heat of fluid phase. k is the thermal conductivity, is the fluid particle interaction parameter. is the volumetric coefficient of thermal expansion, is the kinematic viscosity .

A is the positive constant.

The equations (1) to (7) become (11)

(12) (13) (14)

(15)

(16) With boundary conditions AIJRSTEM 15-852; ﾂｩ 2015, AIJRSTEM All Rights Reserved

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(17) Solution of the problem: Here in this problem the value of are not known but are given. We use Shooting method to determine the value of .We have supplied and . The improved value of is determined by utilizing linear interpolation formula. Then the value of is determined by using Runge-Kutta method. If is equal to up to a certain decimal accuracy, then i.e is determined, otherwise the above procedure is repeated with until a correct is obtained. The same procedure described above is adopted to determine the correct values of .

The essence of shooting technique to solve a boundary value problem is to convert the boundary value problem into initial value problem. In this problem the missing value of and for different set of values of parameter are chosen on hit and trial basis such that the boundary condition at other end i.e. the boundary condition at infinity are satisfied. A study was conducting to examine the effect of step size as the appropriate values of step size â&#x2C6;&#x2020;Ρ was not known to compare the initial values of and .If they agreed to about 6 significant digits, the last value of used was considered the appropriate value; otherwise the procedure was repeated until further change in did not lead to any more change in the value of and .The step size â&#x2C6;&#x2020;Ρ =0.1 has been found to ensure to be the satisfactory convergence criterion of 1 .The solution of the present problem is obtained by numerical computation after finding the infinite value for ď ¨. It has been observed from the numerical result that the approximation to and are improved by increasing the infinite value of ď ¨ which is finally determined as ď ¨ =5.0 with a step length of 0.125 beginning from ď ¨ = 0. Depending upon the initial guess and number of steps N. the values of and are obtained from numerical computations which are given in table â&#x20AC;&#x201C;2 for different parameters.

III. Result and Discussion The transformed (11) to (16) with boundary conditions (17) were solved numerically using Runge Kutta fourth order method with help of shooting technique. Solution of these equations was obtained by using FORTRAN software and the value of velocity profile, wall temperature gradient F(0), G(0),H(0) and θp(0) are given in table-2. We expressed graphically for velocity profile and temperature profile in both fluid and dust phase. In order to check the accuracy of our present numerical solution procedure used a comparison of wall temperature gradient đ?&#x153;&#x192;â&#x20AC;˛(0) is made with those reported by with G.K. Ramesh[5] & Tsai [25] for various values of Pradtl number Pr & B* in absence of other parameters which are given in table-1.Our present results are in a good agreement with the previous results.

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Figure-2&3 illustrate the variation of velocity profiles and temperature profiles θp with η for various values of β. It is observed from the figures that the effect of increasing values of β is to increase the velocity distribution and the temperature distribution θp of dust phase respectfully. Fig -4 &5 illustrate the variation and temperature profiles θp with η for various values of A. It is observed from the

of velocity profiles

figures that the effect of increasing values of A is to increase the velocity distribution profiles θp of dust phase. Fig -6, illustrates the variation of velocity profiles

and the temperature

with η for various values of α. It

is observed from the figure that the effect of increasing values of α is to decrease the velocity distribution of dust phase. Fig -7, illustrates the variation of temperature profiles θp with η for various values of α. It is observed from the figure that the temperature distribution increases for the increasing values of α .Fig.-8 depicts the variation of temperature profiles θ versus η for different value of A*.It is observed that the temperature distribution θ increases for the increasing values of A*. Fig -9 depicts the variation of temperature profiles θp versus η for different value of A*.It is observed that the temperature distribution decreases for the increasing values of A*. Fig.-10 depicts the variation of temperature profiles θ versus η for different value of B*.It is observed that the temperature distribution θ increases for the increasing values of B*. Fig -11, illustrates the variation of temperature profiles θp with η for various values of B*. It is observed that the temperature distribution decreases for the increasing values of B*. Fig -12, presents the variation of velocity distribution with η for various values of Ec. It is observed from the figure that the velocity distribution increases. Fig -13&14 illustrate the variation of temperature profiles θ and

decreases as Ec

with η for various values of Ec. It

is observed from the figures that the fluid and particle phase temperature distributions θ and increase for increasing values of Ec. Fig -15, depicts the variation of temperature profile θ with η for various values of Pr. It is observed from the figure that the temperature distribution θ decreases for increasing values of Pr. Fig -16 depicts the variation of temperature profiles with η for various values of Pr. It is observed from the figure that the effect of increasing values of Pr is to increase dust phase temperature velocity profiles

. Fig -17 illustrates the variation of

with η for various values of Gr. It is observed from the figure that the effect of increasing

values of Gr is to decrease the velocity distribution

. Fig -18, illustrates the variation of temperature profile

with η for various values of Gr. It is observed from the figure that the temperature distribution

increases as

Gr increases. Fig -19&20 depicts the variation of velocity profiles and the temperature profile with η for various values of M. It is observed from the figures that the effect of increasing values of M is to increase the velocity distribution and the temperature distribution of dust phase respectfully.

Table 1: We investigate the comparison value of 0, Q/M = 0, and Ec = 0 B*

Pr

-2 -3 -4

2 3 4

for various values of Pr and B*when β= 0, Gr = 0, A* =

Tsai et al (25) -2.4859 -3.0281 -3.5851

Ramesh et.al(5) -2.4859

-3.0281 -3.5851

Present study

-2.4859 -3.0282 -3.5851

IV. Conclusion The several physical parameters found to affect the problem under consideration are the fluid particle interaction parameter, local Grashof number, heat source/sink parameter, Prandtl number, Eckert number angle of inclination and electrification particles. Some of the important observations of our analysis are reported as follows i. Both velocity and temperature profiles of dust phase increase for increasing value of unsteady parameter A.

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ii.

iii.

iv. v. vi. vii. viii. ix. x. xi.

β 0.01 0.02 0.03 0.01

Increasing value of Ec is enhancing the temperature of both fluid and particle phase which indicates that the heat energy is generated in fluid due to frictional heating also the velocity of particle phase decrease on the increase of Ec. The thermal boundary layer thickness of fluid phase decreases and temperature profile of particle phase increases on the effect of Pr. The temperature decreases at a faster rate for higher values of Pr which implies the rate of cooling is faster in case of higher prandtl number.

The thermal boundary layer thickness and momentum boundary layer thickness of particle phases are increasing for increased values of electrification parameter M. Increasing β increase the velocity and temperature distributions of the particle phase.

The momentum boundary layer thickness of dust phase decrease for the increasing values of Gr but the thermal boundary layer thickness of dust phase increases for the enhanced value of Gr. We have investigated the problem assuming the values , γ=1.0 and Temperature distribution θ of fluid phase increases with increasing value of A*and B* but temperature profiles θp of dust phase decreases with the increase of A*and B*.

The velocity profiles decrease but temperature profiles increase on dust phase for increasing value of parameter .

The kin friction and heat transfer rate decreases with increase of α but increases with increase of electrification parameter M. The wall velocity gradient increases but the wall temperature gradient decreases due to presence of A*&B*.

Table-2 Values of wall velocity gradient - (0),temperature gradient , F(0),G(0),H(0) and θp(0)are given as ,for different values of , , ,M ,A*,B* A and α .

Ec 1.0

Gr 0.01

Pr 0.71

M 0.010

A* 0.3

B* 0.3

A 0.23

α 30°

0.01

0.71

0.010

0.3

0.3

0.23

30°

0.01

0.5 1.0 2.0 1.0

0.71

0.010

0.3

0.3

0.23

30°

0.01

1.0

0.01 0.02 0.03 0.01

0.010

0.3

0.3

0.23

30°

0.01

1.0

0.01

0.1 0.71 1.0 0.71

0.3

0.3

0.23

30°

0.01

1.0

0.01

0.71

0.010 0.015 0.017 0.010

0.3

0.23

30°

0.01

1.0

0.01

0.71

0.010

0.1 0.2 0.3 0.3

0.23

30°

0.01

1.0

0.01

0.71

0.010

0.3

0.1 0.2 0.3 0.3

30°

0.01

1.0

0.01

0.71

0.010

0.3

0.3

0.23 0.25 0.27 0.23

[1]

Abdul R, Nadeem S. [2013] “Heat transfer analysis of the boundary layer flow over a vertical exponential stretching cylinder”.

Global journal of Science Frontier Research Mathematics and Decision Science.13 (1); 73-85.

B.J.Gireesha,G.S.Roopa and C.S.Bagewadi (2013), “Boundary Layer flow of an unsteady Dusty fluid and Heat Transfer over a stretching surface with non uniform heat source/sink ” , Applied Mathematics,2011 ,3,726-735. (http://www.SciRP.org/Journal/am) ,Scientific Research.

B.J.Gireesha,Manjunatha,S.Bagewadi,C.S.[2011b].Unsteady hydromagnetics boundary layer flow and heat transfer of dusty fluid overa stretching sheet . Afrika Matematika, 22, (Article in Press).

Chamkha AJ,Aly Am, Mansour MA, [2010].Similarity solution for unsteady heat and mass transfer from a stretching surface embedded in a porous medium with suction / injection & chemical reach one effects . Chem Engng comm. 197,846-858.

G.K.Ramesh , B.J.Gireesh and C.S.Bagewadi,[2012] “Heat Transfer in M.H.D Dusty Boundary Layer flow of over an inclined stretching surface with non uniform heat source/sink ” ,Hindawi Publishing Corporation , Advances in Mathematical Physics,volume-Article ID 657805,13 pages.

Grubka L.J. and Bobba K.M (1985), “Heat Transfer characteristics of a continuous stretching surface with variable temperature” , Int.J.Heat and Mass Transfer , vol.107,pp.248-250 , 1985.

30° 60° 90°

(0) 1.07188 1.072709 1.073650 1.075845 1.075691 1.075461 1.071791 1.064989 1.059445 1.062833 1.071791 1.071976 1.071791 1.069891 1.069273 1.071791 1.071623 1.071591 1.072044 1.071768 1.071741 1.071791 1.078291 1.084973 1.071791 1.075488 1.071791

-F(0) 0.00491 0.000137 0.005705 0.05527 0.00969 0.05608 0.00969 0.05591 0.012183 0.00953 0.00969 0.00976 0.00969 0.006567 0.013899 0.00964 0.00982 0.00969 0.0101 0.00975 0.00969 0.00969 0.000232 0.007735 0.00969 0.00969 0.00969

-G(0) 0.766561 0.764864 0.763070 0.378367 0.376445 0.370319 0.376445 0.375671 0.375497 0.377100 0.376445 0.376363 0.376445 0.380996 0.381510 0.376604 0.376161 0.376445 0.376512 0.376293 0.376445 0.376445 0.351302 0.328362 0.376445 0.376445 0.376445

H(0) 0.210055 0.208016 0.205129 0.581997 0.337132 0.094875 0.337132 0.362472 0.348535 0.349306 0.337132 0.351176 0.337132 0.305790 0.286868 0.356816 0.369380 0.337132 0.346910 0.355616 0.337132 0.337132 0.316802 0.302853 0.337132 0.619445 0.337132

0.613722 0.614023 0.614020 0.746804 0.614295 0.334849 0.614295 0.619293 0.622047 0.729127 0.744295 0.784269 0.614295 0.617062 0.616229 0.730764 0.671606 0.614295 0.756001 0.689092 0.614295 0.614295 0.630609 0.647933 0.614295 0.611463 0.614295

p(0) 0.009695 0.012449 0.015152 0.014472 0.017225 0.025167 0.017225 0.01847 0.25048 0.012214 0.017225 0.019363 0.017225 0.018121 0.017992 0.017501 0.017507 0.017225 0.017006 0.017094 0.017225 0.017225 0.017664 0.016829 0.017225 0.018874 0.017225

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BIOGRAPHICAL NOTES Runu Sahu was born in Gangapur of district Ganjam; Odisha, India in 1976.She obtained the M.Sc. from K. K. College (Autonomous) Berhampur and M.Phil. Degree in Mathematics from Berhampur University, Berhampur Odisha, India. She is working as Sr. Lecturer in Mathmetics department in Vivekananda Institute of Technology BBSR under BPUT University and she is continuing her research work since 2009 till now. Her field of interest covers the areas of application of boundary layer, heat/mass transfer and dusty fluid flows.

Dr.Saroj Kumar Mishra was born in Narsinghpur of Cuttuck District, Odisha, India on 30th june 1952.He received his M.Sc. degree in Mathematics (1976) and Ph.D in Mathematics in 1982 on the research topic “Dynamics of two phase flow” from IIT Kharagpur, India .

Currently he is working as Adjunct Professor of Mathematics at Centre for Fluid Dynamics Research, CUTM, Paralakhemundi, and Odisha, India. He has authored and coauthored 50 research papers published in national and international journal of repute. He has completed one Major Research project and one Minor Research project sponsored by UGC, New Delhi, India. He has attended/presented the papers in national, international conferences. He is a member of several bodies like Indian Science Congress Association, Indian Mathematical Society, ISTAM, OMS, and BHUMS etc. His research interest includes the area of fluid dynamics, dynamics of dusty fluid particularly, in boundary layer flows, heat transfer, MHD, FHD and flow through porous media. His research interest also covers the nano fluid problems, existence and stability of problems and other related matters. Ten students have already awarded Ph.D degree under his guidance and another six students are working under his supervision.

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