Computational Physics


Contents

  1. Ordinary differential equations
  2. Partial differential equations
  3. Stochastic differential equations
  4. Monte-Carlo modeling and Metropolis algorithm

Literature: general

  1. Press, Flannery, Teukolsky, Vetterling Numerical Recipes
  2. Landau, Paez, Bordeianu A survey of computational physics
  3. Gould, Tobochnik An introduction to computer simulation methods : applications to physical systems
  4. Pang Introduction to computational physics
  5. Koonin Computational physics
  6. Scherer Computational physics
  7. Potter Computational physics

Literature:special

  1. Leimkuhler, Reich Simulating Hamiltonian dynamics
  2. Ames Numerical methods for partial differential equations
  3. Fornberg A practical guide to pseudospectral methods
  4. Newman, Barkema Monte Carlo Method
  5. Landau, Binder A guide to Monte Carlo simulations in statistical physics

Procedure

  1. Preliminary discussion:
    Here you have to demonstrate (i) Understanding of the physical problem, (ii) Understanding of the numerical methods, (iii) What you expect to obtain, (iv) How you want to validate the results, (v) How you plan to present the results, (vi) Estimation of the computer erquirements (memory, CPU time) and a strategy to achieve an optimal performance
  2. Implementation and Computations:
    You are free to choose your operating system and program language. (Do not hesitate to contact me in case of problems, I am however are mostly oriented to C under LINUX)
  3. Report:
    Shortly go through items (i),(ii),(iv),(vi) above. Present the results mainly in graphical form, possibly with errorbars. The main report should be some 4-5 pages, add the listing of your code as appendix.
  4. In choosing the projects keep balance between deterministic and stochastic methods (it is not allowed to have all the projects from one topic below)

Problem sets

Stochastic
  1. Simulated Annealing
  2. 2D Ising model
  3. Stochastic Resonance
Partial differential equations
  1. Korteveg-de Vries equations and Tsunamis
  2. Convection
  3. Turbulence on a falling liquid film
Ordinary differential equations
  1. Star trek
  2. Fermi-Pasta-Ulam paradox