My primary research interest is in stochastic processes derived from randomized billiard dynamical systems.  My current project uses these billiard Markov processes to model gas-surface interactions.  We use them to study applications in chemical engineering such as gas diffusion, non-equilibrium steady state behavior, and stochastic thermodynamics.  This work involves both computer based simulation and traditional theorem proving.  We seek a theory of probabilistic mechanics to compliment the success of statistical mechanics.

My Research Statement

Random Billiards with Wall Temperature and Associated Markov Chains, with Renato Feres, Nonlinearity 25 (2012) 2503-2541, arXiv:1202.2387

From Billiards to Thermodynamics, with Tim Chumley and Renato Feres, Computers and Mathematics with Applications, 65 (2013),
no.10, 1596–1613, arXiv:1207.5878

Stochastic Motion of Thermally Active Psrticles, with Tim Chumley and Renato Feres, in preparation