Geometric gradient-flow dynamics with singular solutions
| dc.creator | Holm, Darryl D. | |
| dc.creator | Putkaradze, Vakhtang | |
| dc.creator | Tronci, Cesare | |
| dc.date | 2007-04-18 | |
| dc.date | 2008-04-28 | |
| dc.date.accessioned | 2026-07-07T09:35:10Z | |
| dc.date.available | 2026-07-07T09:35:10Z | |
| dc.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. | |
| dc.description | 28 pages, 1 figure, to appear on Physica D | |
| dc.identifier | https://arxiv.org/abs/0704.2369 | |
| dc.identifier | http://arxiv.org/abs/0704.2369 | |
| dc.identifier | doi:10.1016/j.physd.2008.04.010 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159747 | |
| dc.subject | Adaptation and Self-Organizing Systems | |
| dc.subject | Pattern Formation and Solitons | |
| dc.title | Geometric gradient-flow dynamics with singular solutions | |
| dc.type | text |