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.
","abstract_html":"<p>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.</p>","abstract_has_math":false,"creators":["Chumley, Timothy"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Renato Feres"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-04-25T07:00:00Z","date_published":"2013-04-25T07:00:00Z","updated_at":"2026-07-24T06:13:14Z","subjects":["Mathematics"],"languages":["English (en)"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.7936/K7Q23XB7"],"render_values":[{"text":"https://doi.org/10.7936/K7Q23XB7","href":"https://doi.org/10.7936/K7Q23XB7","code":true}]}]},"links":{"outbound_url":"https://openscholarship.wustl.edu/etd/1092","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Renato Feres"]},{"key":"dc:creator","label":"Author","values":["Chumley, Timothy"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2013-08-26T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English (en)"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://openscholarship.wustl.edu/etd/1092"]},{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.7936/K7Q23XB7"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["Limit Theorems for Random Billiard Models"]}]}],"canonical_facts":{"dc:contributor":["Renato Feres"],"dc:creator":["Chumley, Timothy"],"dc:date.available":["2013-08-26T07:00:00Z"],"dc:description.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.
"],"dc:identifier":["https://openscholarship.wustl.edu/etd/1092"],"dc:identifier.doi":["https://doi.org/10.7936/K7Q23XB7"],"dc:language":["English (en)"],"dc:subject":["Mathematics"],"dc:title":["Limit Theorems for Random Billiard Models"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T06:13:14Z"}