DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:**Maria Cameron, American University

**Title: ***
Computing Transition Paths in Stochastic Systems
*

**Abstract:**
Many processes in nature are modeled using stochastic differential equations.
Examples include thermally-activated small-scale processes in physics and chemistry
such as conformational changes in molecules, chemical reactions, magnetization switches
and nucleation events. Other examples come from such fields as
evolutionary biology and stochastically modeled computer networks.
I will consider two stochastic systems: a system without detailed balance
evolving according to a nongradient stochastic differential, and a stochastic network associated
with the Lennard-Jones-38 cluster. In both cases the noise is small
so that the direct simulation is inefficent. In the first system, I will introduce
a method for computing the quasipotential, a function that
determines the transition rates and transition paths in the case of small noise.
I will present the results of analysis of the second system using three different approches:
the discrete transition path theory approach, the zero-temperature approach, and a heuristic approach.

**Time:** Friday, September 21, 2012, 1:30-2:30 p.m.

**Place:** Planetary Hall (formerly Science and Tech I), Room 242

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491