2007/12/03 by Darryl D. Holm, Vakhtang Putkaradze, Cesare Tronci · 1 citation
Materials Science · Physics and Astronomy · #Material Dynamics and Properties #Random lasers and scattering media #Theoretical and Computational Physics #nlin.AO #nlin.PS
paper · pdf · doi:10.1088/1751-8113/41/34/344010
28 pages, 2 figures. Submitted to J. Phys. A
arxiv created 2007/12/03 · openalex publication_date 2008/08/11 · arxiv updated 2009/12/01 · openalex created_date 2020/11/23 · openalex updated_date 2026/06/11
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.