Stochastic chaos and thermodynamic phase transitions : theory and Bayesian estimation algorithms
Thesis (M. Eng. and S.B.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2008
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| Online Access: | http://hdl.handle.net/1721.1/41649 |
| _version_ | 1811070576811311104 |
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| author | Deng, Zhi-De |
| author2 | Chi-Sang Poon. |
| author_facet | Chi-Sang Poon. Deng, Zhi-De |
| author_sort | Deng, Zhi-De |
| collection | MIT |
| description | Thesis (M. Eng. and S.B.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007. |
| first_indexed | 2024-09-23T08:38:14Z |
| format | Thesis |
| id | mit-1721.1/41649 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T08:38:14Z |
| publishDate | 2008 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/416492019-04-09T18:54:41Z Stochastic chaos and thermodynamic phase transitions : theory and Bayesian estimation algorithms Deng, Zhi-De Chi-Sang Poon. 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 (M. Eng. and S.B.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007. Includes bibliographical references (p. 177-200). The chaotic behavior of dynamical systems underlies the foundations of statistical mechanics through ergodic theory. This putative connection is made more concrete in Part I of this thesis, where we show how to quantify certain chaotic properties of a system that are of relevance to statistical mechanics and kinetic theory. We consider the motion of a particle trapped in a double-well potential coupled to a noisy environment. By use of the classic Langevin and Fokker-Planck equations, we investigate Kramers' escape rate problem. We show that there is a deep analogy between kinetic rate theory and stochastic chaos, for which we propose a novel definition. In Part II, we develop techniques based on Volterra series modeling and Bayesian non-linear filtering to distinguish between dynamic noise and measurement noise. We quantify how much of the system's ergodic behavior can be attributed to intrinsic deterministic dynamical properties vis-a-vis inevitable extrinsic noise perturbations. by Zhi-De Deng. M.Eng.and S.B. 2008-05-19T16:05:15Z 2008-05-19T16:05:15Z 2007 2007 Thesis http://hdl.handle.net/1721.1/41649 219714017 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 200 p. application/pdf Massachusetts Institute of Technology |
| spellingShingle | Electrical Engineering and Computer Science. Deng, Zhi-De Stochastic chaos and thermodynamic phase transitions : theory and Bayesian estimation algorithms |
| title | Stochastic chaos and thermodynamic phase transitions : theory and Bayesian estimation algorithms |
| title_full | Stochastic chaos and thermodynamic phase transitions : theory and Bayesian estimation algorithms |
| title_fullStr | Stochastic chaos and thermodynamic phase transitions : theory and Bayesian estimation algorithms |
| title_full_unstemmed | Stochastic chaos and thermodynamic phase transitions : theory and Bayesian estimation algorithms |
| title_short | Stochastic chaos and thermodynamic phase transitions : theory and Bayesian estimation algorithms |
| title_sort | stochastic chaos and thermodynamic phase transitions theory and bayesian estimation algorithms |
| topic | Electrical Engineering and Computer Science. |
| url | http://hdl.handle.net/1721.1/41649 |
| work_keys_str_mv | AT dengzhide stochasticchaosandthermodynamicphasetransitionstheoryandbayesianestimationalgorithms |