Mentor: Vikas Aragam
Mentee: Abhay Katyal
Description: This project started with an initial discussion of General Relativity and the metric tensor. The discussion continued with the properties of black holes to draw an analogy to the properties/mechanism of acoustic black holes, which can enhance our understanding of black holes.
Mentor: Kalina Slavkova
Mentee: Dhruva Karkada
Description: I used information theory, dynamical systems theory, and bifurcation theory all to analyze the computational properties of neurons. By using these mathematical frameworks, we can build a theoretic understanding of information processing in the brain and the biophysical mechanisms that control information flow. A stronger theoretical understanding of the brain is an important step towards understanding the deep mysteries of neuroscience and artificial intelligence.
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Mentor: Avik Roy
Mentee: Connor Davis
Description: Using particle physics simulation data, I analyzed a process that created a virtual top-partner particle. I characterized the distribution of its mass, and verified that the mass distribution diverges from a Breit-Wigner distribution for large widths. Additionally, I discovered that despite having infinite standard deviations, the central limit theorem applies to these mass distributions. I also characterized the relationship between the width of the mass distributions and the standard deviation obtained from the sampling distribution of their sample means.
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Project Name: Computational Methods in Astrophysics
Mentor: Luyan Yu
Mentee: Bryce Hobbs
Description: This project focused on various techniques necessary for computational astrophysics, including finite difference methods, spectral decomposition, a Galerkin method, and time integration schemes. These methods were used to develope N-body star cluster simulations, and convection simulations for a practical learning approach and to demonstrate how these methods can be used to approximate physical processes.
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Mentee: Rylee Ross
Description: Explanation of the differences and similarities of Copenhagen Interpretation of Quantum Mechanics especially in their models of the double slit experiment. The problem of definition of Measurement in quantum mechanics and how bohmian mechanics allows wfn to collapse and model this paradox better than standard interpretations.
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Project Name: A Crash Course in Charged Black Holes
Mentor: Nicolas Duran
Mentee: Gina Chen
Description: Pulling from various textbooks about General relativity, I derived parts of the solution for a Reissner-Nordstrom black hole and investigated its properties. We used the metric and spacetime diagrams to learn about what could happen to particles that fall into a charged black hole.
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