Geometric order parameter equations

Darryl D. Holm; Vakhtang Putkaradze

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arXiv · nlin/0608011

Geometric order parameter equations

Darryl D. Holm·Vakhtang Putkaradze

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Abstract

Aggregation of particles whose interaction potential depends on their mutual orientation is considered. The aggregation dynamics is derived using a version of Darcy's law and a variational principle depending on the geometric nature of the physical quantities. The evolution equations that result separate into two classes: either characteristic equations, or gradient flow equations. We derive analytical solutions of both types of equations which are collapsed (clumped) states and show their dynamical emergence from smooth initial conditions in numerical simuations.

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Darryl D. Holm, Vakhtang Putkaradze. 2006-08-07. Geometric order parameter equations. https://arxiv.org/abs/nlin/0608011

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