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Low variance methods for Monte Carlo simulation of phonon transport

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 dc.contributor.advisor Nicolas G. Hadjiconstantinou. en_US dc.contributor.author Péraud, Jean-Philippe M. (Jean-Philippe Michel) en_US dc.contributor.other Massachusetts Institute of Technology. Dept. of Materials Science and Engineering. en_US dc.date.accessioned 2012-03-16T16:04:10Z dc.date.available 2012-03-16T16:04:10Z dc.date.copyright 2011 en_US dc.date.issued 2011 en_US dc.identifier.uri http://hdl.handle.net/1721.1/69799 dc.description Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Materials Science and Engineering, 2011. en_US dc.description Cataloged from PDF version of thesis. en_US dc.description Includes bibliographical references (p. 95-97). en_US dc.description.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. en_US dc.description.statementofresponsibility by Jean-Philippe M. Péraud. en_US dc.format.extent 97 p. en_US dc.language.iso eng en_US dc.publisher Massachusetts Institute of Technology en_US dc.rights 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. en_US dc.rights.uri http://dspace.mit.edu/handle/1721.1/7582 en_US dc.subject Materials Science and Engineering. en_US dc.title Low variance methods for Monte Carlo simulation of phonon transport en_US dc.type Thesis en_US dc.description.degree S.M. en_US dc.contributor.department Massachusetts Institute of Technology. Dept. of Materials Science and Engineering. en_US dc.identifier.oclc 777956342 en_US
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