After rewriting my SoP a lot of times I think I have finally completed a draft which is quite good. I hope you all agree and if not please tell me why.
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My purpose in life is to expand our body of knowledge of how the universe operates. To realize this purpose my goal in graduate school is to conduct theoretical research that is at the intersection of Cosmology and Particle Physics. Some topics I would like to further explore are cosmic inflation, the expansion of the universe and the effects of modified gravity. These phenomena and problems compel me because they have profound implications for all observed length scales in physics.
To achieve this goal I want to perform research at the Center for Cosmology and Particle Physics. I’m attracted to the the CCPP because the creators of the DGP model are there. It was this model, and others in modified gravity, that convinced me to pursue Particle Cosmology due to their sheer creativity. Currently I would like to work with either Professor X or Y. Professor X's work on large, extra dimensions interests me because it can answer a question I always had: why is K so much larger than G? I also would be interested to be part of Professor Y's research on distinguishing between modified gravity and dark energy. After completing graduate school, I eventually want to become a professor of physics.
As an undergrad, I honed my mathematical modeling and research skills by working with Professor V of the Applied Physics Department in nonlinear dynamics. At the start, I knew nothing about nonlinear dynamics or numerical methods. However, through self study in a few weeks, I learned Mathematica and was familiar with the field. My job was to model the motion of a Physical Double Pendulum we built in the lab and discern its route to chaos. Using Lagrangian Mechanics and Rayleigh dissipation functions, I created a model to match its motion. I couldn't continue this research due to difficulties in attaining a high camera for future use. In hindsight, I would have treated our model pendulum as a system with three degrees of freedom, because it oscillated when it rotated, and treated the support to which it was attached as an energy sink. This third degree of freedom would be a harmonic oscillator, that drew energy away from the other two.
After finding a parameter (which if set to zero) made the system integrable, I created a Poincare sections simulation and observed that, as the parameter increased, the KAM invariant tori disintegrated in an unusual way. They collapsed into themselves to form periodic orbits and if increased slightly further exploded into a sea of points. As this parameter starts off at zero the motion begins as quasiperiodic; it then abruptly becomes periodic, and if increased, further chaotic. I concluded I was observing an unexpected route to chaos. While doing research I learned much of the advanced mathematics of classical mechanics. This math included SU(2) symmetry, Birkhoff Gustavson perturbation theory, Lie Algebra, topology and some differential geometry. The mathematics I learned aided me in interpreting my results and give me a strong foundation to learn and conduct research in other fields of physics.
In college, I took and passed three graduate physics classes including Professor Z's dynamic class. Taking these classes prepared me to complete the required course work of graduate school so I can proceed afterward to conduct research. Even though I learned plenty of technical skills as an undergrad, the most important thing I learned was how to persevere through tragedy and stress. Tragically, in the spring of 2015 my father died. Despite the emotional distress, I completed 29 credits of coursework to graduate on time while working two jobs and conducting research. My undergraduate experience prepared me to overcome any challenge whether it be academic or personal. Using my technical skills and the shown ability to persevere to get the job done I’ll pass the required classes and succeed in conducting research at the frontier of physics."
