Math @ Duke

Publications [#246892] of JianGuo Liu
Papers Published
 Degond, P; Liu, JG, Hydrodynamics of selfalignment interactions with precession and derivation of the LandauLifschitzGilbert equation,
Mathematical Models & Methods in Applied Sciences, vol. 22 no. SUPPL.1
(2012),
pp. 111400118, ISSN 02182025 [doi]
(last updated on 2018/08/16)
Abstract: We consider a kinetic model of selfpropelled 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 nonconservative equation for the orientation. First, we assume that the alignment interaction is purely local and derive a firstorder system. However, we show that this system may lose its hyperbolicity. Under the assumption of weakly nonlocal interaction, we derive diffusive corrections to the firstorder system which lead to the combination of a heat flow of the harmonic map and LandauLifschitzGilbert dynamics. In the particular case of zero selfpropelling 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.


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