Title:
Thermostated Kac models
Thermostated Kac models
| dc.contributor.advisor | Bonetto, Federico | |
| dc.contributor.author | Vaidyanathan, Ranjini | |
| dc.contributor.committeeMember | Loss, Michael | |
| dc.contributor.committeeMember | de la Llave, Rafael | |
| dc.contributor.committeeMember | Harrell, Evans | |
| dc.contributor.committeeMember | Wiesenfeld, Kurt | |
| dc.contributor.department | Mathematics | |
| dc.date.accessioned | 2016-01-07T17:38:44Z | |
| dc.date.available | 2016-01-07T17:38:44Z | |
| dc.date.created | 2015-12 | |
| dc.date.issued | 2015-11-16 | |
| dc.date.submitted | December 2015 | |
| dc.date.updated | 2016-01-07T17:38:44Z | |
| dc.description.abstract | We consider a model of N particles interacting through a Kac-style collision process, with m particles among them interacting, in addition, with a thermostat. When m = N, we show exponential approach to the equilibrium canonical distribution in terms of the L2 norm, in relative entropy, and in the Gabetta-Toscani-Wennberg (GTW) metric, at a rate independent of N. When m < N , the exponential rate of approach to equilibrium in L2 is shown to behave as m/N for N large, while the relative entropy and the GTW distance from equilibrium exhibit (at least) an "eventually exponential” decay, with a rate scaling as m/N^2 for large N. As an allied project, we obtain a rigorous microscopic description of the thermostat used, based on a model of a tagged particle colliding with an infinite gas in equilibrium at the thermostat temperature. These results are based on joint work with Federico Bonetto, Michael Loss and Hagop Tossounian. | |
| dc.description.degree | Ph.D. | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | http://hdl.handle.net/1853/54446 | |
| dc.language.iso | en_US | |
| dc.publisher | Georgia Institute of Technology | |
| dc.subject | Kinetic theory | |
| dc.subject | Spectral gap | |
| dc.subject | Heat bath | |
| dc.title | Thermostated Kac models | |
| dc.type | Text | |
| dc.type.genre | Dissertation | |
| dspace.entity.type | Publication | |
| local.contributor.advisor | Bonetto, Federico | |
| local.contributor.corporatename | College of Sciences | |
| local.contributor.corporatename | School of Mathematics | |
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| relation.isOrgUnitOfPublication | 85042be6-2d68-4e07-b384-e1f908fae48a | |
| relation.isOrgUnitOfPublication | 84e5d930-8c17-4e24-96cc-63f5ab63da69 | |
| thesis.degree.level | Doctoral |