Geometric gradient-flow dynamics with singular solutions

Details Geometric gradient-flow dynamics with singular solutions Geometric gradient-flow dynamics with singular solutions

2007-04-18

arxiv.org/abs/0704.2369v2

Nonlinear Sciences

Adaptation and Self-Organizing Systems

28 pages, 1 figure, to appear on Physica D

Scientific paper

10.1016/j.physd.2008.04.010

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.

Affiliated with

Also associated with

No associations

Rating

Geometric gradient-flow dynamics with singular solutions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Geometric gradient-flow dynamics with singular solutions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geometric gradient-flow dynamics with singular solutions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-405383