Geometric gradient-flow dynamics with singular solutions

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

The gradient-flow dynamics of an arbitrary geometric quantity is derived using a generalization of Darcy's Law. We consider flows in both Lagrangian and Eulerian formulations. The Lagrangian formulation includes a dissipative modification of fluid mechanics. Eulerian equations for self-organization of scalars, 1-forms and 2-forms are shown to reduce to nonlocal characteristic equations. We identify singular solutions of these equations corresponding to collapsed (clumped) states and discuss their evolution.
28 pages, 1 figure, to appear on Physica D

Keywords

Adaptation and Self-Organizing Systems, Pattern Formation and Solitons

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/159747

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0704.2369
 http://arxiv.org/abs/0704.2369
 doi:10.1016/j.physd.2008.04.010

Collections

arXiv