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Nicolas G. Hadjiconstantinou. Péraud, Jean-Philippe M. (Jean-Philippe Michel) Massachusetts Institute of Technology. Dept. of Materials Science and Engineering. Massachusetts Institute of Technology. Department of Materials Science and Engineering 2012-03-16T16:04:10Z 2012-03-16T16:04:10Z 2011 2011 http://hdl.handle.net/1721.1/69799 777956342 Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Materials Science and Engineering, 2011. Cataloged from PDF version of thesis. Includes bibliographical references (p. 95-97). Computational studies in kinetic transport are of great use in micro and nanotechnologies. In this work, we focus on Monte Carlo methods for phonon transport, intended for studies in microscale heat transfer. After reviewing the theory of phonons, we use scientific literature to write a Monte Carlo code solving the Boltzmann Transport Equation for phonons. As a first improvement to the particle method presented, we choose to use the Boltzmann Equation in terms of energy as a more convenient and accurate formulation to develop such a code. Then, we use the concept of control variates in order to introduce the notion of deviational particles. Noticing that a thermalized system at equilibrium is inherently a solution of the Boltzmann Transport Equation, we take advantage of this deterministic piece of information: we only simulate the deviation from a nearby equilibrium, which removes a great part of the statistical uncertainty. Doing so, the standard deviation of the result that we obtain is proportional to the deviation from equilibrium. In other words, we are able to simulate signals of arbitrarily low amplitude with no additional computational cost. After exploring two other variants based on the idea of control variates, we validate our code on a few theoretical results derived from the Boltzmann equation. Finally, we present a few applications of the methods. by Jean-Philippe M. Péraud. S.M. 97 p. eng Massachusetts Institute of Technology M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 Materials Science and Engineering. Low variance methods for Monte Carlo simulation of phonon transport Thesis application/pdf false Publication unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="00245225-3a78-45ba-813a-e665ee71274a"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Language>eng</Language> <Title>Low variance methods for Monte Carlo simulation of phonon transport</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2011</PublicationDate> <Authors> <Author> <DisplayName>Péraud, Jean-Philippe M. (Jean-Philippe Michel)</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>http://dspace.mit.edu/handle/1721.1/7582</License> <Keyword>Materials Science and Engineering.</Keyword> <Abstract>Computational studies in kinetic transport are of great use in micro and nanotechnologies. In this work, we focus on Monte Carlo methods for phonon transport, intended for studies in microscale heat transfer. After reviewing the theory of phonons, we use scientific literature to write a Monte Carlo code solving the Boltzmann Transport Equation for phonons. As a first improvement to the particle method presented, we choose to use the Boltzmann Equation in terms of energy as a more convenient and accurate formulation to develop such a code. Then, we use the concept of control variates in order to introduce the notion of deviational particles. Noticing that a thermalized system at equilibrium is inherently a solution of the Boltzmann Transport Equation, we take advantage of this deterministic piece of information: we only simulate the deviation from a nearby equilibrium, which removes a great part of the statistical uncertainty. Doing so, the standard deviation of the result that we obtain is proportional to the deviation from equilibrium. In other words, we are able to simulate signals of arbitrarily low amplitude with no additional computational cost. After exploring two other variants based on the idea of control variates, we validate our code on a few theoretical results derived from the Boltzmann equation. Finally, we present a few applications of the methods.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>