Master of Physics 1 — University of Cergy Pontoise

Computational methods for physics

C Oguey ( oguey @ u-cergy.fr ) CM 12h, TD 18h

See cours.u-cergy.fr/course/view.php?id=17750

or cours.u-cergy.fr ▸ M1 ▸ Master Physique 1 ▸ M1–Numerical methods
for physics.

- Solving Ordinary Differential Equations
- Molecular Dynamics
- Finite difference methods for PDEs
- Time dependent Schrödinger equation – wave packets
- Fourier transform
- Non-linear PDEs: solitons, KdV, Ginzburg-Landau, sine-Gordon
- Introduction to Finite Elements Methods

- W Press, SA Teukolsky, WT Vetterling, BP Flannery: Numerical recipes: the art of scientific computing 3d ed. (Cambridge UP 2007)
- R Landau, M Paez, C Bordeianu, Computational physics: problem solving with computers 3d ed. (Wiley 2015)

Based on projects, each on a physical subject involving numerical methods.

In a concise report, < 8 pages, explain your treatment of the problem, the method
used and the results or solution, including comments and critical analysis. Provide all
your code listings in separate files.

Assessment is based on the report + program for two projects, and on the oral
presentation of one of the projects.

See web site cours.u-cergy.fr/course/view.php?id=17750

- Diffusion or Poisson equation by Fourier transform.
- KdV equation: non-linearity – soliton propagation and interaction.
- Ginzburg-Landau equation: coarsening – scaling regime or limit – correspondence with microscopic models?
- Turing’s model of chemical reactions: enhancer/inhibitor system – pattern formation.

Tools and examples for simple animation here.

C. Oguey, Jan. 2019