Some problems in the dynamics of spatially extended systems
Puri, Sanjay
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https://hdl.handle.net/2142/23900
Description
Title
Some problems in the dynamics of spatially extended systems
Author(s)
Puri, Sanjay
Issue Date
1988
Doctoral Committee Chair(s)
Oono, Yoshitsugu
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
dynamics of spatially extended systems
non-trivial spatial dependence
perturbed sine-Gordon equation
Language
en
Abstract
"In this thesis, we study some representative problems in the dynamics of systems which have a non-trivial spatial dependence.
In the first chapter, we study the perturbed sine-Gordon equation and the ""Painleve test of integrability."" We present results of our numerical studies of the d.c. driven, damped sine-Gordon equation. We also present a nonperturbative proof of the persistence of soliton-like (""soliton"") and antisoliton-like (""antisoliton"") solutions of the d.c. driven, damped sineGordon equation. Subsequently, we describe the so-called ""Painleve test of integrability."" We apply this test to the d.c. driven, damped sine-Gordon equation, which is shown to be nonintegrable in the Painleve sense.
In the second chapter, we present computationally efficient Cell-Dynamical System (CDS) models of phase ordering dynamics. We present results of our numerical studies on these models for
(a)
The nonconserved order parameter case without and with noise;
(b)
The conserved order parameter case with a critical quench (without and with noise), an off-critical quench in the unstable regime (without noise), and the nucleation regime (without noise).
Results on these systems have been obtained inexpensively in terms of
computer time usage. Consequently, we have been able to see stages in the process which have not been numerically accessed so far. Specifically, we demonstrate that the scaled form factor appears to approach an asymptotic regime in which the effects of noise are irrelevant, in accordance with the generally held theoretical view."
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