Classification of Nonlinear Vibrations in Symmetric Molecules : Equivariant Degree Method

dc.contributor.advisorKrawcewicz, Wieslaw
dc.creatorBerezovik, Irina
dc.date.accessioned2020-10-09T17:17:17Z
dc.date.available2020-10-09T17:17:17Z
dc.date.created2019-05
dc.date.issued2019-05
dc.date.submittedMay 2019
dc.date.updated2020-10-09T17:17:18Z
dc.description.abstractThis dissertation is devoted to the study of nonlinear periodic vibrations of a group of particles within symmetric molecular conformations governed by the Lennard-Jones and Coulomb forces. In particular, the author investigates nonlinear vibrational modes of oscillations for molecules with tetrahedral and dihedral configurations of atoms. Using the gradient equivariant degree, the author provides the full topological classification of the periodic solutions with both temporal and spatial symmetries for the above configurations. In the process, the general formulae for processing the equivariant spectral data of the linearized system and obtaining the critical frequencies of the particle motions are devised. The obtained frequencies constitute the set of all critical periods for small amplitude periodic solutions emerging from a given stationary symmetric orbit of solutions. The evaluated equivariant invariants provide a complete list of the spatio-temporal symmetries of the periodic solutions emerging from the ground state symmetric equilibria. The proposed method can be applied to study nonlinear vibrations in other symmetric molecules with general force fields.
dc.format.mimetypeapplication/pdf
dc.identifier.urihttps://hdl.handle.net/10735.1/9000
dc.language.isoen
dc.rights©2019 Irina Berezovik. All rights reserved.
dc.subjectVibration
dc.subjectNonlinear oscillations
dc.subjectAtoms
dc.titleClassification of Nonlinear Vibrations in Symmetric Molecules : Equivariant Degree Method
dc.typeDissertation
dc.type.materialtext
thesis.degree.departmentMathematics
thesis.degree.grantorThe University of Texas at Dallas
thesis.degree.levelDoctoral
thesis.degree.namePHD

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