Theory Projects

I completed these projects on my own time or for an academic class. These are any projects completed primarily on pen+paper or using code/software.

Piezo Tunable Microlens - MEMS Final Paper

My final paper on designing a piezoelectrically actuated microlens using for my microelectromechanical systems (MEMS) class I took in the fall of 2022. Based around the poLight TLens, our microlens design uses a piezoelectric membrane to control the shape of a deformable material, thus allowing for precise focal length control of a lens system. In this project, I took charge of making finite element simulations with COMSOL Multiphysics to simulate the piezoelectric effect coupled with solid mechanical deformation.

Tunable Microlens Final Paper

image credits: poLight TLens

Plasma Physics/Aurora Borealis - Fluid Mechanics Final Project

A presentation for my introduction to fluid mechanics mechanical engineering course at Columbia in the Fall of 2021. The final project was an opportunity for students to make a <5 minute presentation on particular aspects of fluid mechanics that weren't covered in the course. Having recently worked directly with plasmas on the reactor project, I was curious to learn about the theoretical framework that physicists use to describe the dynamics of plasmas.

Quantum Simulation and Computing Final Paper

My final paper on simulating the ground state of the Fermi-Hubbard model for my quantum simulation and computing class I took in the spring of 2022. The Fermi-Hubbard model describes electron correlation effects in solids, and can be used to model Mott (metal-insulator) phase transitions. This project allowed me to expand my knowledge and interest in the field of solid state and condensed matter physics, while also learning the process of developing my own simulation on quantum hardware.

Quantum Computing Final Research Paper

image credits: wikimedia creative commons

Particle Physics Research Paper

My research during the summer of 2020 culminated in a paper recently published in Physical Review D.

Aligning a Majorana fermion’s anapole moment with an external current through photon emission mediated by the fermion’s generalized polarizabilities

Senior Honors Thesis - Nonlinear Schrödinger Equation

The nonlinear Schrödinger equation is a partial differential equation that describes a handful of physical phenomena. I study it here in the context of quantum mechanics. I offer background into differential equations and quantum mechanics. I show my work in reducing the nonlinear Schrödinger equation into an efficiently solvable form using the complete memory approximation. I found that the reduced order model is both accurate and much more efficient than a direct numerical solution.

Complete thesis: www.pugetsound.edu/files/resources/hall-kobi.pdf

Github Code: https://github.com/kobihall/Renormalized_Mori_Zwanzig

GitHub Raytracing Experiments

Musings and experiments with Euclidean and non-Euclidean Ray Tracings. Both are works in progress, the non-euclidean version much more so. Learning computer graphics, compute shaders, GPU acceleration, and Vulkan API.

www.github.com/kobihall/Euclidean-Raytracing

www.github.com/kobihall/NonEuclideanRenderingEngine-nere

Sophomore Mathematics Class Paper on Geodesics

At the end of my upper-division Differential Equations class my sophomore year (fall 2018) I had the option to write a paper on a differential equation that interested me. I taught myself some of the mathematics surrounding general relativity, so writing about the geodesic equation really interested me.

INTRODUCTION: In this paper we describe the geodesic problem in differential geometry and general relativity. In its simplest form, a geodesic is the shortest path between two points. In certain contexts this definition does not exactly match the goal of a geodesic. It then makes sense to generally define the geodesic with an analogy. Imagine a bug on the surface of a sphere. It may move in any direction on the sphere, but it may not move off of the sphere. The world the bug experiences is effectively two-dimensional. However, its two dimensional world is ”embedded” in the third dimension. Read the complete Geodesic Research Paper

image credits: wikimedia creative commons
click on image to see animation

Sudoku in Java

An introductory Sudoku game I wrote as a final project for my intro CS class at UPS. The program generates unique Sudoku boards, has a rudimentary Sudoku solver, and a user interface to play generated games.

www.github.com/kobihall/Sudoku

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