Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1897795 | Physica D: Nonlinear Phenomena | 2008 | 14 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Darryl D. Holm, Vakhtang Putkaradze, Cesare Tronci,