Hydrodynamics of self-alignment interactions with precession and derivation of the Landau-Lifschitz-Gilbert equation


Journal Article

We consider a kinetic model of self-propelled particles with alignment interaction and with precession about the alignment direction. We derive a hydrodynamic system for the local density and velocity orientation of the particles. The system consists of the conservative equation for the local density and a non-conservative equation for the orientation. First, we assume that the alignment interaction is purely local and derive a first-order system. However, we show that this system may lose its hyperbolicity. Under the assumption of weakly nonlocal interaction, we derive diffusive corrections to the first-order system which lead to the combination of a heat flow of the harmonic map and LandauLifschitzGilbert dynamics. In the particular case of zero self-propelling speed, the resulting model reduces to the phenomenological LandauLifschitzGilbert equations. Therefore the present theory provides a kinetic formulation of classical micromagnetization models and spin dynamics. © 2012 World Scientific Publishing Company.

Full Text

Duke Authors

Cited Authors

  • Degond, P; Liu, JG

Published Date

  • April 1, 2012

Published In

Volume / Issue

  • 22 / SUPPL.1

International Standard Serial Number (ISSN)

  • 0218-2025

Digital Object Identifier (DOI)

  • 10.1142/S021820251140001X

Citation Source

  • Scopus