Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2008. / In title on t.p., "L" appears as italic letters and "[infinity]" appears as the symbol. / Includes bibliographical references (leaves 47-48). / 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 ... / by Mohammad Tariq Hussain. / S.M.
| Identifer | oai:union.ndltd.org:MIT/oai:dspace.mit.edu:1721.1/42455 |
| Date | January 2008 |
| Creators | Hussain, Mohammad Tariq |
| Contributors | Gilbert Strang., Massachusetts Institute of Technology. Computation for Design and Optimization Program., Massachusetts Institute of Technology. Computation for Design and Optimization Program. |
| Publisher | Massachusetts Institute of Technology |
| Source Sets | M.I.T. Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 48 leaves, application/pdf |
| 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., http://dspace.mit.edu/handle/1721.1/7582 |
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