Kinetic models of heterogeneous dissipation

Details Kinetic models of heterogeneous dissipation Kinetic models of heterogeneous dissipation

2007-12-03

arxiv.org/abs/0712.0397v1

Nonlinear Sciences

Adaptation and Self-Organizing Systems

28 pages, 2 figures. Submitted to J. Phys. A

Scientific paper

10.1088/1751-8113/41/34/344010

We suggest kinetic models of dissipation for an ensemble of interacting oriented particles, for example, moving magnetized particles. This is achieved by introducing a double bracket dissipation in kinetic equations using an oriented Poisson bracket, and employing the moment method to derive continuum equations for magnetization and density evolution. We show how our continuum equations generalize the Debye-Hueckel equations for attracting round particles, and Landau-Lifshitz-Gilbert equations for spin waves in magnetized media. We also show formation of singular solutions that are clumps of aligned particles (orientons) starting from random initial conditions. Finally, we extend our theory to the dissipative motion of self-interacting curves.

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