Computational Physics
Contents
- Ordinary differential equations
- Partial differential equations
- Stochastic differential equations
- Monte-Carlo modeling and Metropolis algorithm
Literature: general
- Press, Flannery, Teukolsky, Vetterling
Numerical Recipes
- Landau, Paez, Bordeianu A survey of computational physics
- Gould, Tobochnik
An introduction to computer simulation methods : applications to physical systems
- Pang Introduction to computational physics
- Koonin Computational physics
- Scherer Computational physics
- Potter Computational physics
Literature:special
- Leimkuhler, Reich Simulating Hamiltonian dynamics
- Ames Numerical methods for partial differential equations
- Fornberg A practical guide to pseudospectral methods
- Newman, Barkema Monte Carlo Method
- Landau, Binder A guide to Monte Carlo simulations in statistical physics
Procedure
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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
- 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)
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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.
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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
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Simulated Annealing
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2D Ising model
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Stochastic Resonance
Partial differential equations
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Korteveg-de Vries equations and Tsunamis
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Convection
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Turbulence on a falling liquid film
Ordinary differential equations
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Star trek
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Fermi-Pasta-Ulam paradox