  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.
