8. M1-Computational Physics

Computational methods for physics

Lecturer

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

Web site

See     cours.u-cergy.fr/M1-Computational Physics
or cours.cyu.fr ▸ M1–Computational physics.

Syllabus – Chapters selected among:

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

Recommended books

• 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)

Grades

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.

Lecture notes, projects, deadlines

See web site, above.

Suggestions for last project

• 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