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Geometric gradient-flow dynamics with singular solutions

Holm, DD, Putkaradze, V and Tronci, C (2008) Geometric gradient-flow dynamics with singular solutions Physica D: Nonlinear Phenomena, 237 (22). pp. 2952-2965.

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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.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Holm, DD
Putkaradze, V
Date : 2008
DOI : 10.1016/j.physd.2008.04.010
Depositing User : Symplectic Elements
Date Deposited : 17 May 2017 12:21
Last Modified : 10 Jun 2019 13:08

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