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Title:The role of topological defects and textures in the kinetics of phase ordering
Author(s):Zapotocky, Martin
Doctoral Committee Chair(s):Goldbart, Paul M.
Department / Program:Physics
nematic liquid crystals
topological defects
nematic systems
Abstract:In this thesis, I present the results of a theoretical investigation of ordering processes induced by symmetry-breaking quenches in two physical systems. Both systems investigated possess a rich homotopy structure of the order-parameter space, which results in numerous topologically stable objects being generated during the quench, and influencing the properties of the system during the subsequent approach to equilibrium. The results reported are mostly computational in nature. The two systems investigated are (i) nematic liquid crystals, which support topologically stable abelian (in the uniaxial nematic case) and non-abelian (in the biaxial nematic case) singular defects, and (ii) the 0(3)-symmetric vector (i.e., Heisenberg-type) system in 2 spatial dimensions, which supports topologically stable, but non-singular objectstopological textures. In the case of nematic systems, the numerical investigation concentrates on the phase-ordering proceSs and point defect dynamics following a quench into both the uniaxial and biaxial nematiC phases of a quasi-2-dimensionalliquid crystalline system. The time dependences of the correlation function, structure factor, energy density, and number densities of topological defects are computed. By comparing the growth laws for the characteristic length scales extracted from the order-parameter correlations and from the total number of topological defects in the system, it is determined that weak violations of dynamical scaling occur in the system, even at the latest times studied. The observed scaling violations ~~ attributed to the presence of a logarithmic correction to the asymptotic power-law growth. of the average inter:defect separation. Following the quench to the biaxial nematic phase, there are four topologically distinct defect species ptesent in the system, the populations of which are studied in detail. It is found that only two types of defect are observed in large numbers at late times, and a mechanism for the selection of the prevailing defect species is proposed. In addition to the computational investigation of the phase ordering process in 2-d.imensional nematic systems, analytical derivations of the singular (power-law) short-distance behavior of the contribution to the structure factor (i.e., the light scattering intensity) for all types of topologically stable defects encountered in 2- and 3-d.imensional uniaxial and biaxial nematics are presented. The second system studied-the Heisenberg-type model in 2 spatial dimensionsis first implemented numerically as the discretized 0(3) nonlinear u-model with the standard form of free energy and with purely dissipative dynamics. Two distinct mechanisms for the decay of the order-parameter variations-single texture unwinding, and topological charge annihi1ation-are identified and characterized in this system. It is found that whereas at early times after the quench the annibi1ation process dominates, the unwinding processes become of comparable importance at later times. By·examining the correlations in the order parameter and in the topological charge density, it is shown that dynamical scaling is strongly violated during the phase-ordering process, and multiple characteristic length-scales growing as distinct power-laws in time are identified. In order to study in detail the origins of the observed multi-scaling behavior, the phase-ordering process is then studied within a modified 0(3) nonlinear u-model with an additional free energy term { the· so-called Sk:yrme term, familiar in high-energy physics) that stabilizes the textures against shrinking and unwinding. It is found that this modification influences the multi-scaling properties of the system in a dramatic way, and that with single-texture u.n windings suppressed, the form of the spectrum of exponents characterizing the decay or the moments of the topological charge density distribution can be predicted successfully by a simple two-length-scale argument.
Issue Date:1996
Genre:Dissertation / Thesis
Rights Information:1996 Martin Zapotocky
Date Available in IDEALS:2011-04-21
Identifier in Online Catalog:4015833

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