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dc.contributor.authorGrigo, Alexanderen_US
dc.date.accessioned2009-08-26T17:30:41Z
dc.date.available2009-08-26T17:30:41Z
dc.date.issued2009-05-18en_US
dc.identifier.urihttp://hdl.handle.net/1853/29610
dc.description.abstractIn this thesis we consider mathematical problems related to different aspects of hard sphere systems. In the first part we study planar billiards, which arise in the context of hard sphere systems when only one or two spheres are present. In particular we investigate the possibility of elliptic periodic orbits in the general construction of hyperbolic billiards. We show that if non-absolutely focusing components are present there can be elliptic periodic orbits with arbitrarily long free paths. Furthermore, we show that smooth stadium like billiards have elliptic periodic orbits for a large range of separation distances. In the second part we consider hard sphere systems with a large number of particles, which we model by the Boltzmann equation. We develop a new approach to derive hydrodynamic limits, which is based on classical methods of geometric singular perturbation theory of ordinary differential equations. This method provides new geometric and dynamical interpretations of hydrodynamic limits, in particular, for the of the dissipative Boltzmann equation.en_US
dc.publisherGeorgia Institute of Technologyen_US
dc.subjectBilliardsen_US
dc.subjectBoltzmann equationen_US
dc.subject.lcshHamiltonian systems
dc.subject.lcshStatistical mechanics
dc.subject.lcshErgodic theory
dc.subject.lcshDynamics
dc.subject.lcshTransport theory
dc.titleBilliards and statistical mechanicsen_US
dc.typeDissertationen_US
dc.description.degreePh.D.en_US
dc.contributor.departmentMathematicsen_US
dc.description.advisorCommittee Chair: Bunimovich, Leonid; Committee Member: Bonetto, Federico; Committee Member: Chow, Shui-Nee; Committee Member: Cvitanovic, Predrag; Committee Member: Weiss, Howarden_US


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