Computer Physics

This module provides an introduction to the use of computer tools in physics: analyzing a phenomenon, idealizing/modeling it, and then studying it on a computer. Critical interpretation of the results is also part of the module. The examples discussed are chosen in relation to other current topics in the course.

To be acquired: Physics of random walks and diffusion; description and resolution of nonlinear dynamic systems (examples from population theory and analytical mechanics); implementation of simple algorithms to solve a problem in physics; simple Python programming and code verification; production of scientific results in the form of summary graphs in order to compare numerical results with theoretical predictions; critical discussion of numerical results with knowledge of potential sources of error.

programming concepts (an imperative language, ideally Python); vector and matrix calculations; mathematical analysis concepts (limits, differentiation, integrals, differential equations).

Recommended prerequisites: Python (imperative programming); familiarity with a Linux system

CCI

Idealization of a physical phenomenon, either in the form of equations or a process to be represented on a computer.

Numerical solution of a system of differential equations using simple algorithms (Euler vs. improved Euler, Runge-Kutta); computer implementation and verification using physical intuition (e.g., conservation laws); concept of numerical error; formulation of the theory in terms of dynamic systems; analysis of the linear stability of fixed points and classification; link with matrix diagonalization (eigenvalues, eigenvectors); examples from population dynamics, oscillation physics, etc.

Computer representation of a diffusion process: random walk (microscopic) vs. diffusion equation (macroscopic); statistical study of random walk on a computer and comparison with theory: diffusion constant, position distribution and its evolution over time, etc.; acquisition and interpretation of a histogram; comparison with more complex models without simple analytical predictions (e.g., random walk with persistence, fractal growth process limited by diffusion, etc.)

A central goal is to learn the different techniques available and critically compare the results obtained by numerical and theoretical approaches in order to: 1) better understand the laws that motivated the theoretical model and 2) validate both approaches mutually, or discover possible limitations and weaknesses (approximations, lack of sufficient statistics, programming errors, numerical errors, etc.). etc.).