Author's School

Graduate School of Arts & Sciences

Author's Department/Program

Mathematics

Language

English (en)

Date of Award

Spring 4-25-2013

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Chair and Committee

Renato Feres

Abstract

The central objects of study in this dissertation are random billiard systems. These are Markov chain systems with general state spaces derived from deterministic billiard systems by selecting one or more dynamical variables and replacing them with random variables with fixed probability distributions. In particular, we study two specific model systems; one which models gas diffusion through cylindrical channels whose walls have a microscopic structure, and another which models a minimalistic heat engine. The main results for the gas diffusion model, a series of probabilistic limit theorems, allow us to express transport characteristics such as mean exit times of the gas from the channel in terms of characteristics of the channel walls. Preliminary results for the heat engine model present some beginning steps in the study of stochastic thermodynamics of billiard-like mechanical systems.

DOI

https://doi.org/10.7936/K7Q23XB7

Comments

Permanent URL: http://dx.doi.org/10.7936/K7Q23XB7

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