STUDENT RESEARCH
Researching Research
Complex concepts explained by student experts ADINKRAS? OAM-ENTANGLED PHOTONS? CRYPTOBEILIC TETRACYCLES?
While Harvey Mudd College recognizes the importance of studentfaculty research, what’s sometimes less recognizable are the descriptive terms within that research. We chose four thesis projects presented during the College’s annual Presentation Days research celebration that included interesting—if not head-scratching—terms, and then asked the authors to explain.
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Free Electrons Dense Plasma Electron Trajectories
Above: An illustration of the stochastic heating process. Charts: Examples of simulation results showing the electron gaining energy in the duration of the laser pulse.
Stochastic heating The firefly is an example of a coupled oscillator found in nature, as the flashing of one firefly encourages another to flash in response.
Coupled oscillator Alec Dunton ’16, mathematics “Topological Data Analysis for Systems of Coupled Oscillators”
An oscillator is an object that exhibits periodic behavior, like a flashing firefly or a swinging pendulum. An oscillator is called “coupled” when its behavior is tied to that of another or many other oscillators. They are of strong interest in the mathematics community because of their ubiquity in nature and utility in modeling phenomena—think: bullfrogs croaking out of phase or a pacemaker entraining the beating of a heart. “I learned about the model with which I was most concerned during my research, the Kuramoto model, as a sophomore in an ordinary differential equations class with my advisor Andrew Bernoff,” says Dunton. “A year later, I began a summer research
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HARVEY MUDD COLLEGE
project on the application of techniques from topological data analysis to systems of coupled oscillators governed by the equation derived by Yoshiki Kuramoto. “I am not sure if I will continue work on this specific subject, but I may revisit it at some point while working toward my PhD at UCLA,” says Dunton, who graduated with High Distinction and received the Stavros Busenberg Prize in Applied Mathematics. “My interests tend to be about data science in general, and coupled oscillators have served as an interesting topic with real-world applications to which to apply techniques from computational topology.”
Xin Zhang ’16, physics “Computational Modeling of Multi-Pass Stochastic Heating”
In stochastic heating, a laser frees electrons from the atoms in a solid (ionizes the solid into plasma) and then heats the electrons by repeatedly pulling them out of the solid and throwing them back in. “By heating the electrons to energies high enough that they can escape from the solid, we can indirectly transfer laser energy to the ions in the solid,” says Zhang, who graduated with Distinction and is pursuing her doctorate in fusion studies at Princeton’s Plasma Physics Lab. “This could lead to small-scale fusion reactions, which could then be used as a clean, alternative energy source.” A good analogy, she says, is picking up a bouncy ball from the floor and throwing it back down. By punching it back down every time it bounces up, eventually the ball has a lot more energy than it started
with, bouncing much higher. This simple comparison belies the complexity of the concept, however. “I learned about [stochastic heating] from my research advisor Professor of Physics Tom Donnelly, who painstakingly explained the concept to me at least five times in the first three years of my college career,” says Zhang. “And then, it took me a couple of reads on papers and other textbooks to really understand it.” For complex research, Zhang has a critical piece of advice: Take your time, read and be patient. “It takes a lot of background knowledge to understand the big picture, the motivation and the formulation of a research question,” she says. “After that, you can try to understand the technical details.”