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Cheeger sets for unit cube : analytical and numerical solutions for L [infinity] and L² norms

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dc.contributor.advisor Gilbert Strang. en_US
dc.contributor.author Hussain, Mohammad Tariq en_US
dc.contributor.other Massachusetts Institute of Technology. Computation for Design and Optimization Program. en_US
dc.date.accessioned 2008-09-03T15:43:12Z
dc.date.available 2008-09-03T15:43:12Z
dc.date.copyright 2008 en_US
dc.date.issued 2008 en_US
dc.identifier.uri http://hdl.handle.net/1721.1/42455
dc.description Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2008. en_US
dc.description In title on t.p., "L" appears as italic letters and "[infinity]" appears as the symbol. en_US
dc.description Includes bibliographical references (leaves 47-48). en_US
dc.description.abstract The Cheeger constant h(Q) of a domain Q is defined as the minimum value of ...... with D varying over all smooth sub-domains of Q. The D that achieves this minimum is called the Cheeger set of Q. We present some analytical and numerical work on the Cheeger set for the unit cube ... using the ...and the ... norms for measuring IIDII. We look at the equivalent max-flow min-cut problem for continuum flows, and use it to get numerical results for the problem. We then use these results to suggest analytical solutions to the problem and optimize these shapes using calculus and numerical methods. Finally we make some observations about the general shapes we get, and how they can be derived using an algorithm similar to the one for finding Cheeger sets for domains in ... en_US
dc.description.statementofresponsibility by Mohammad Tariq Hussain. en_US
dc.format.extent 48 leaves 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 Computation for Design and Optimization Program. en_US
dc.title Cheeger sets for unit cube : analytical and numerical solutions for L [infinity] and L² norms en_US
dc.type Thesis en_US
dc.description.degree S.M. en_US
dc.contributor.department Massachusetts Institute of Technology. Computation for Design and Optimization Program. en_US
dc.identifier.oclc 240704675 en_US


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