Graduate Seminar Course Math 285J:

Mathematical Aspects of Computational Materials Science



Suggested Final Projects; Numerics Projects and Research Papers

These are all suggestions. Additional, similar projects are possible as well. Please discuss with me any ideas you have.
Each student should have picked a project by Feb. 16. Please come to my office to discuss the choice of your project.

Numerics Pojects

Here is a list of potential numerics project you can do as part of this course, to get a "very good" grade:
  • Write a program for simulating the nearest neighbor two-dimensional Ising model on a square lattice using the Metropolis Monte Carlo technique.
  • Write a program to simulate the formation of a fractal. this phenomena is called dendritic growth. It is also know as DLA. Diffusion limited aggregation. There are different specific problems one can look at and program, and this should be discussed with me.
  • Calculate the ground state energy of the Helium atoms within the independent particle approximation. This is described in Thijssen, "Computational Physics", on pages 51-54.
  • Do a density-functional theory calculation (using the code fhi98md) to calculate the lattice constant of a material of your choice.

    • Research Papers

    Here is a list of possible research papers you can discuss as your final project, to get a "very good" grade:
  • A short seminar about the ideas and implementation of "Hyperdynamics"; the relevant papers are:
    A.F. Voter, J. Chem. Phys. 106, 4665 (1997).
    A.F. Voter, Phys. Rev. Lett. 78, 3908 (1997).

  • A description of Transition State Theory; the "original" paper:
    G.. Vineyard, J. Phys. Chem. Solids 3, 121 (1957).
    A good review is:
    P. Haenggi et al., Rev. Mod. Phys. 62, 251 (1990)

  • Level Sets and Sputter Deposition:
    P.L. O'Sullivan et al., Journ. Appl. Phys. 58, 4061 (2000)

  • Details of Numerical Implementation of Island Dynamics level-set implementation in our group here at UCLA; the most relevant paper is:
    S. Chen et al, Journ. Comp. Phys. 167, 475 (2001)
    I will discuss this model and method in class, but it would be useful if someone (with level set expertise ?) can talk about some of the detailed numerics ...