SUMMER JOB INFO - 2001
Employer: C. Soteros,Dept. of Mathematics & Statistics, UofS (see web page at: http://math.usask.ca/~soteros)
Position: Summer Research Assistant
Location: Saskatoon, SK
Project Objectives and Activities:
The lattice models of Statistical Mechanics have proved to be simple but powerful and useful models for studying the phase-change behaviour and equilibrium properties of large systems of interacting particles. These models have had many applications in physics, chemistry and biology. One of the most important methods used for studying such models is Markov Chain Monte Carlo (MCMC) computer simulation. From MCMC computer simulations one can obtain statistical estimates of quantities of interest, such as the average energy of the system. However, in order to obtain reliable estimates, it is necessary to run numerous simulations (at different temperatures) with each simulation running for millions of time steps. On a single workstation, such a computer experiment could take up to a year to complete. However, recent advances in the theory of MCMC have made it possible to more readily run such computer simulations on a parallel computer and hence cut down on the completion time of an experiment considerably. The goal of this project will be to modify an existing MCMC computer program so that it can run on the 12 node parallel computer cluster recently purchased by myself and A. Smolyakov (Physics) with an NSERC equipment grant. The computer program is designed to study the entanglement complexity (the probability of knotting and linking) of a large polymer system (modelled by a long chain or walk on a lattice). With the modified program, it is expected that it will be possible to study much larger polymer systems than previously possible and that it will be possible to obtain better estimates of, for example, the knotting probability of a ring polymer as a function of polymer length.
Tasks that the student will be responsible for:
The student will use probability, statistics, combinatorial analysis, basic topology, and computer programs to estimate the entanglement properties of a polymer system. The computer work will involve the use of statistical software such as Splus, the C programming language, and learning the batch queue and operating systems specific to the 12 node parallel computer cluster.