8.1 Suggested Topics

Below is a list of suggested topics, and they are only weakly suggested. You can do almost anything else as long as you find it reasonably interesting. This could be using one of the codes provided by me or F&S, or your own code. You will write a short “report” (just a few pages, maybe a figure or two), and give a short presentation about your project. The goal in both cases is to document and demonstrate what you learned in doing the project, not so much to document and demonstrate anything new.

• Monte-Carlo simulations:

  • Suggested exercises for the Ising magnet (Sec. 3.2)
  • Orientational correlation functions in 2D dumbbells (Sec. 3.5)
  • Various displacement methods in MC simulation of LJ fluid
  • Orientational correlation in LJ Dumbbells in 3D (Sec. 3.7)

• Molecular dynamics simulations:

  • Structure in a liquid made of particle of two different sizes. Modify mdlj.c to handle a particle-specific value of \(\sigma \). Let there be two types of particles, \(A\) and \(B\), and let \(\sigma _A = \sigma = \sigma _B/2\). For any pair \(ij\), the \(\sigma \) used in evaluating the potential is \(\sigma _{ij} = 1/2(\sigma _i+\sigma _j)\). Modify rdf.c to compute the \(AA\), \(BB\), and \(AB\) radial distribution functions at a few compositions and overall densities.
  • Obstacles: Compute the effect on the diffusivity in a Lennard-Jones fluid at a given temperature and density by the presence of fixed obstacles in the domain which interact with the particles. These obstacles could be other particles which do not move, or “lines” of Lennard-Jones potential (See Sec. 10.1) arrayed on some grid or randomly. A relationship between \(\mathscr {D}/\mathscr {D_0}\) and \(\rho _{\rm obs}\), where \(\rho _{\rm obs}\) is the density of obstacles, might be interesting to see.
  • Any of the suggested exercises involving Stillinger-Weber silicon (Sec. 7.1)
• Case Study 15 from F&S: The overlapping distribution method for computing \(\mu _{\rm ex}\).
• Optimization: Apply one or more of the techniques in Appendix F to one of the Lennard-Jones codes (mclj.c or mdlj.c), and compare the performance to the standard \(N^2\) algorithm.