Computer Physics

This module is an introduction to the use of computer tools in physics: it involves analyzing a phenomenon, idealizing/modeling it, then studying it on a computer. Critical interpretation of results is also included. Examples are chosen in relation to other current subjects in the course.

To acquire: Physics of random walk and diffusion; describing and solving non-linear dynamical systems (examples from population theory and analytical mechanics); implementing simple algorithms to solve a problem in Physics; simple Python programming and code verification; producing scientific results in the form of synthetic graphs in order to compare numerical results with theoretical predictions; critical discussion of numerical results with knowledge of potential sources of error.

notions of programming (an imperative language, ideally Python); vector and matrix calculations; notions of mathematical analysis (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); notion of numerical error; formulation of the theory in terms of dynamical systems; analysis of linear stability of fixed points and classification; link with matrix diagonalization (eigenvalues, eigenvectors); examples from population dynamics, oscillation physics, etc.

Computer representation of a diffusive process: random walk (microscopic) vs. diffusion equation (macroscopic); statistical study of the random walk on the 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, diffusion-limited fractal growth process, etc.).

A central aim is to learn the different techniques available and to 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 the two approaches mutually, or discover possible limitations and weaknesses (approximations, lack of sufficient statistics, programming errors, numerical errors, etc.).