Physics and Mathematics
Since I was a child I have been highly interested in theoretical physics and the application of mathematics to the real world. This page has a collection of various problems I have modelled using physics and mathematics.
Travelling Salesman Problem Using QAOA and Classical Algorithms
This project for the University of Waterloo Institute of Quantum Computing (IQC) focuses on implementing and comparing classical algorithms with the Quantum Approximate Optimization Algorithm (QAOA) using the Maxcut algorithm for solving the Traveling Salesman Problem (TSP).
Measuring the Wettability of Different Ferrofluid
Concentrations
Submission to the Journal of Undergraduate Engineering Physics and Physics Experiments at Queen's University (JUEPPEQ) and will be published in the 5th edition of the journal. The goal of this experiment was to observe and quantify how the wettability of ferrofluid changes
when exposed to different strengths of non-uniform magnetic fields.
Modeling Air-Craft Harmonics
Two different approaches to choosing which damper to put on an aircraft to reduce wing deflection. The first, approach uses the relation between a second order non-homogenous differential equation and its amplitude to find an optimal damper. The second confirms the choice by displaying the deflection plots.
Quantum Computing in Python
In this project, I solved the Quantum Computing Codebooks produced by Xanadu using the python library PennyLane. The repository includes solutions to the introduction modules T, I, and A, as well as Grover's Module. There is also an example of using Grover's algorithm compared to a conventional searching/sorting algorithm.
Additionally, I included my final report for a course on quantum computing, which includes a presentation on Grover's Algorithm.
Analyzing Non-Divergent Sets
This project involved creating and visualizing modified versions of the Mandelbrot set and Julia set, which are both well-known mathematical objects in the field of complex dynamics. The Mandelbrot set is a classic example of a recursive function that can be broken down into intricate fractal patterns. The modified Mandelbrot set and Julia set were generated using a complex recursive algorithm. To visualize the sets, a threshold was set at 100 and points that lie within the set were plotted on a scatter plot.
Computing Complex Surfaces
A paper and lecture written for Professor Kaveh Mousavand at Queen's University as an extension of Advanced Vector Calculus. The paper describes methods for calculating surface areas derived from first principles.
Computational Engineering Physics
Using numerical methods to solve physics, mathematics and engineering problems utilizing Python. Topics include numerical differentiation and integration, root finding and optimization problems, linear systems of equations, finite-element modelling, Fourier and other transforms and Monte Carlo simulations.
The Heat Death of the Universe
A short film and presentation on the heat death of the universe for a Thermodynamics class. Includes several worked examples of entropy and an interview with Professor Aaron Vincent.