Computer Physics

This module constitutes an introduction to the approach of using computer tools in Physics: it is a question of analyzing a phenomenon, of idealizing/modeling it, then of studying it on computer. The critical interpretation of the results is also part of it. The examples are chosen in relation with the other current subjects in the training.

To be acquired: Physics of random walk and diffusion; description and solution of nonlinear dynamical 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 synthetic graphs in order to confront 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 of a process to be represented on a computer.

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

Representation of a diffusive process on computer: random walk (microscopic) vs. diffusion equation (macroscopic); statistical study of the random walk on computer and confrontation with the theory: diffusion constant, distribution of positions and its evolution in time, etc.; acquisition and interpretation of a histogram; confrontation with more complex models without simple analytical predictions (e.g. random walk with persistence, diffusion-limited fractal growth process, etc)

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