Completed in Summer 2022, this project was my first formal introduction to the standard methods of numerical integration like Euler-Cromer, Leapfrog, RK2 and RK4 (+ some Velocity-Verlet) used in many problems of computational physics. A large part of this project involved understanding the different mathematical approaches used to integrate numerically, along with their implementation in code. I also explored the relative errors propagated by each of these algorithms, and understood the relation between error propagated by an algorithm with the kind of physical system solved for. Checks for total energy and momentum of the system were coded, and important physical and computational limitations of the scope of the project were identified. Finally, I gained key conceptual insights on modelling different kinds of physical systems computationally during the weekly meetings with our project guides, Philip Cherian & Prof. Bikram Phookun. The project ended with a 10-min presentation in front of a few physics students and Prof. Phookun, after which I submitted the code and a project report.
In this project, I studied and computationally modelled the Brownian motion of single particle in the Earth's atmosphere. The relevant differential equation was constructed, solved analytically and verified by three numerical integration methods. Then, I numerically verified Einstein's famous result (1905 paper) which relates the mean square displacement of the particle with time, and explored the relation between Diffusivity & Damping Constant by examining the nature of their log-log plots.