I may have some codes from which you could use to start.
A good project would be a novel application with one of these codes.

• ground state properties of molecules (MOLE)
• ground state properties of solids (QUCU)
• path integral calculations for bosons (UPI)
• classical MC and MD for 2 or 3 dimensional liquids, plasmas and polymers (LAMMPS)

However, you will be responsible for figuring out how these codes work.

A LIST OF IDEAS:

• Implement an order(N) method (it goes like N asymptotically) for computing the long range Coulomb interaction and compare its timing and accuracy to the usual Ewald method. (find when it is worth using) Alternatively, do a literature search and find out what is being used in practice and compare the various order (N) methods. Is there any hope for Monte Carlo Order (N) methods where particles are moved one at a time instead of all together?
• Simulate a system of quadrapoles on an fcc lattice. This is a simple model for the rotation of solid hydrogen. One can do this either classically or quantum mechanically. Additionally one may want to consider para-ortho alloy. There should be many interesting phase transitions.
• Test the ideas of quasi-random numbers on a hard problem, i.e. an integral that is not feasible with a grid-based method) and compare to Monte Carlo efficiencies. (see Computers in Physics Nov. 1989 )
• In variational Monte Carlo, try doing a random walk in parameter space to find the minimum energy or variance. Try an determine good rules for moving the parameters. Alternatively, is the energy minimization or the variance minimization sharper? Which has the smallest errors for the optimal parameters?


• Visualize the liquid-solid interface of a simple system and learn something about the dynamics of melting and freezing.
• Try and directly calculate the difference in energy of a Li and Li+ atom using correlated sampling (or some related method) applied to variational wavefunctions and compare the efficiency to two separate calculations.
• Write a Path Integral code to simulate an isolated He or H₂ molecule. Verify that the code gives the correct result in the high temperature and low temperature limit. Find out whether molecular dynamics or monte carlo is more efficient OR Study various approximations for the high temperature density matrix.


• Do a literature study of the special techniques that are used to simulate water with an aim to answering some of the following questions: Are quantum nuclear effects important? Is it important that the water molecule have internal motion? How well is the inter-water potential known? What experimental properties can and cannot be calculated from first principles? Is MC or MD better for calculating static properties of water? What special MC transition rules have been invented? Do you have any special finite-size effects in water? How big are they? I don't expect either a review article or for you to rewrite a review article that you find but a synthesis of the state of knowledge of how to simulate water.
• Model the growth of bacterial colonies using methods invloving random walks. Consider the diffusion of nutrients, movement of the bacteria, reproduction, and local communication. A good place to start is the article by Ben-Jacob et al, Nature 368, 46 (1994).
• Try and develop a multiparticle moving scheme for a simple monte carlo application that improves the rate of convergence over that of single particle moves. You could try a simple liquid or Ising model application, where it has been traditional to move the particles sequentially. Test whether moving the particles sequentially or at random works better.
• Try out the histogram method for computing detailed properties of a phase transition. (Ferrenberg and Landau, PRB 44, 5081, 1991) Compare to the method of Lee and Kosterlitz, Phys. Rev. B43, 3265 (1991).
• Further develop your MD code to treat an Argon surface.
• Implement one of the methods discussed in class to perform a temperature controled simulation. (Find something interesting to study using the temperature control.)
• Study strains on grain boundaries in Si using an empirical potential. You could also look at dislocations and vacancies.
• Write an MD code for molecules, implementing SHAKE for constraints.

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October 1998 by David Ceperley .