Some problems in the dynamics of spatially extended systems

"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."

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Year dc:date

2011

Author dc:creator

• Puri, Sanjay

Contributors dc:contributor

• Oono, Yoshitsugu

• dynamics of spatially extended systems
• non-trivial spatial dependence
• perturbed sine-Gordon equation

Statement dc:rights

• 1988 Sanjay Puri

Language dc:language

en

Identifier

3471834

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/23900