## PHYS 8990 Topic

### Biological Applications of Statistical Mechanics

*H.B. Schuttler*

My group is pursuing research in two major areas: strongly correlated electron physics and biological applications of statistical mechanics. In the strongly corrlated electron area, we are presently working on the implementation of Monte Carlo simulation methods for the evaluation of self-consistent Feynman diagram expansions. In the biological stat. mech. area, we are pursuing efforts to model gene regulation and biochemical/metabolic processes observed in living cells by means of ensembles of chemical rate equation models.

In both research areas, Monte Carlo simulation techniques are very important and they also provide a convenient way to introduce students to the respective subjects. There are two projects for incoming graduate students to work on:

(A) Monte Carlo evaluation of self-energy diagrams in the Hubbard model

(B) Ensemble equilibration and sampling for a simplified 3-gene model of the "Repressilator" in E. coli.

In both projects, the student will first be introduced to Markov-chain based random sample generation. The student will then be asked to write a simple Metropolis Monte Carlo code to generate random samples from discrete ("loaded dice") and 1-D continuous probabability distributions (with plenty of help from the instructor). The student will then be given an existing self-energy diagram code, in Project (A), or an exisiting ensemble simulation code, in Project (B), to run a small simulation, make graphical displays of some of the simulation results and interpret the results.