Kinetic models of heterogeneous dissipation
arXiv:0712.0397 · doi:10.1088/1751-8113/41/34/344010
Abstract
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.
28 pages, 2 figures. Submitted to J. Phys. A
References in corpus (8)
- Aggregation of finite size particles with variable mobility
- Formation of clumps and patches in self-aggregation of finite size particles
- Chapman-Enskog derivation of the generalized Smoluchowski equation
- The directional contact distance of two ellipsoids: Coarse-grained potentials for anisotropic interactions
- Vlasov moments, integrable systems and singular solutions
- Formation and Evolution of Singularities in Anisotropic Geometric Continua
- Geometric dissipation in kinetic equations
- Rotating Concentric Circular Peakons