The Dynamics of Hamiltonian Lattices With Application to Hollomon Oscillators

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dc.contributor.authorZholmaganbetova, Aigerim
dc.contributor.editorBountis, Anastasios
dc.date.accessioned2019-08-29T09:48:42Z
dc.date.available2019-08-29T09:48:42Z
dc.date.issued2019-05-29
dc.descriptionMaster of Science Thesis in Applied Mathematics Department of Mathematics, School of Science and Technology Nazarbayev University Astana 010000, Kazakhstanen_US
dc.description.abstractMany problems in theoretical physics are expressed in the form of Hamiltonian systems. Among these the first to be extensively studied were low-dimensional, possessing as few as two (or three) degrees of freedom. In the last decades, however, great attention has been devoted to Hamiltonian systems of high dimensionality. The most famous among them are the ones that deal with the dynamics and statistics of a large number N of mass particles connected with nearest neighbor interactions. At low energies E, these typically execute quasiperiodic motions near some fundamental stable periodic orbits (SPOs) which represent nonlinear continuations of the N normal mode solutions of the corresponding linear system. However, as the energy is increased, these solutions destabilize causing the motion in their vicinity to drift into chaotic domains, thus giving rise to important questions concerning the systems behavior in the thermodynamic limit, where E and N diverge with E=N = constant. One of the open problems in Hamiltonian dynamics, therefore, examines the relation between local (linear) stability properties of simple periodic solutions of Hamiltonian systems, and the more “global” dynamics. In this thesis, after reviewing the main results on these topics for the case of N-particle Fermi-Pasta-Ulam Hamiltonians, I proceed to apply the corresponding methods to a lattice of Hollomon oscillators, which are of interest to applications in problems of nonlinear elasticity.en_US
dc.identifier.urihttp://nur.nu.edu.kz/handle/123456789/4199
dc.language.isoenen_US
dc.publisherNazarbayev University School of Science and Technologyen_US
dc.rightsAttribution-NonCommercial-ShareAlike 3.0 United States*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/us/*
dc.subjectResearch Subject Categories::MATHEMATICS::Applied mathematicsen_US
dc.titleThe Dynamics of Hamiltonian Lattices With Application to Hollomon Oscillatorsen_US
dc.typeMaster's thesisen_US
workflow.import.sourcescience

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