2007/04/30 by Darryl D. Holm, Vakhtang Putkaradze, Cesare Tronci · 3 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Fluid Dynamics and Turbulent Flows #Mathematical Biology Tumor Growth #Nonlinear Dynamics and Pattern Formation #nlin.AO #nlin.PS
paper · pdf · doi:10.1016/j.physd.2008.04.010
28 pages, 1 figure, to appear on Physica D
openalex publication_date 2008/04/27 · arxiv created 2008/04/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.