Discrete, amorphous physical models
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1999.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2005
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| Online Access: | http://hdl.handle.net/1721.1/9345 |
| _version_ | 1826208100970921984 |
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| author | Rauch, Erik, 1974- |
| author2 | Gerald Jay Sussman. |
| author_facet | Gerald Jay Sussman. Rauch, Erik, 1974- |
| author_sort | Rauch, Erik, 1974- |
| collection | MIT |
| description | Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1999. |
| first_indexed | 2024-09-23T14:00:13Z |
| format | Thesis |
| id | mit-1721.1/9345 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T14:00:13Z |
| publishDate | 2005 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/93452019-04-10T16:00:17Z Discrete, amorphous physical models Rauch, Erik, 1974- Gerald Jay Sussman. Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. Electrical Engineering and Computer Science. Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1999. Includes bibliographical references (leaves 25-26). Discrete models of physical phenomena are an attractive alternative to continuous models such as partial differential equations. In discrete models, such as cellular automata, space is treated as having finitely many locations per unit volume. Physical processes are modelled by rules that typically depend on a small number of nearby locations. Such models have the feature that they depend critically on a regular (crystalline) lattice, as well as the global synchronization of all sites. We might well ask, on the grounds of minimalism, whether the global synchronization and crystalline lattice arc inherent in any discrete formulation. Is it possible to do without these conditions and still model physics? Or are they somehow fundamental? We will answer this question by presenting a class of models that are "extremely local" in the sense that the update rule does not depend on synchronization with other sites, or on detailed knowledge of the lattice geometry. All interactions involve only a single pair of sites. The models have the further advantage that they exactly conserve the analog of quantities such as momentum and energy which are conserved in physics. A framework for simulating the asynchronous, parallel model with irregular geometry on a sequential computer will be presented. Evidence will be given that the models agree well qualitatively and quantitatively with continuous differential equations. We will draw parallels between the various kinds of physical models and various computing architectures, and show that the class of models presented corresponds to a new parallel computing architecture known as an amorphous computer. by Erik Rauch. S.M. 2005-08-22T20:29:04Z 2005-08-22T20:29:04Z 1999 1999 Thesis http://hdl.handle.net/1721.1/9345 44416065 eng 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 45 leaves 2490502 bytes 2490262 bytes application/pdf application/pdf application/pdf Massachusetts Institute of Technology |
| spellingShingle | Electrical Engineering and Computer Science. Rauch, Erik, 1974- Discrete, amorphous physical models |
| title | Discrete, amorphous physical models |
| title_full | Discrete, amorphous physical models |
| title_fullStr | Discrete, amorphous physical models |
| title_full_unstemmed | Discrete, amorphous physical models |
| title_short | Discrete, amorphous physical models |
| title_sort | discrete amorphous physical models |
| topic | Electrical Engineering and Computer Science. |
| url | http://hdl.handle.net/1721.1/9345 |
| work_keys_str_mv | AT raucherik1974 discreteamorphousphysicalmodels |