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Geometric gradient-flow dynamics with singular solutions

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 نشر من قبل Cesare Tronci
 تاريخ النشر 2008
  مجال البحث فيزياء
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The gradient-flow dynamics of an arbitrary geometric quantity is derived using a generalization of Darcys 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.



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