Going with the Flow: a Lagrangian approach to self-similar dynamics and its consequences

Simple item page
dc.creatorAronson, D. G.
dc.creatorBetelu, S. I.
dc.creatorKevrekidis, I. G.
dc.date2001-11-23
dc.date2001-12-06
dc.date.accessioned2026-07-07T05:33:46Z
dc.date.available2026-07-07T05:33:46Z
dc.descriptionWe present a systematic computational approach to the study of self-similar dynamics. The approach, through the use of what can be thought of as a ``dynamic pinning condition" factors out self-similarity, and yields a transformed, non-local evolution equation. The approach, which is capable of treating both first and second kind self-similar solutions, yields as a byproduct the self-similarity exponents of the original dynamics. We illustrate the approach through the porous medium equation, showing how both the Barenblatt (first kind) and the Graveleau (second kind) self-similar solutions arise in this framework. We also discuss certain implications of the dynamics of the transformed equation (which we will name "MN-dynamics"); in particular we discuss the discrete-time implementation of the approach, and connections with time-stepper based methods for the "coarse" integration/bifurcation analysis of microscopic simulators.
dc.description14 pages, 2 figure
dc.identifierhttps://arxiv.org/abs/nlin/0111055
dc.identifierhttp://arxiv.org/abs/nlin/0111055
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/80122
dc.subjectAdaptation and Self-Organizing Systems
dc.subjectPattern Formation and Solitons
dc.titleGoing with the Flow: a Lagrangian approach to self-similar dynamics and its consequences
dc.typetext

Files

Collections

arXiv