期刊
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
卷 22, 期 -, 页码 -出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S021820251140001X
关键词
Self-propelled particles; alignment dynamics; precession; hydrodynamic limit; hyperbolicity; diffusion correction; weakly nonlocal interaction; Landau-Lifschitz-Gilbert; spin dynamics
资金
- NSF [DMS 10-11738]
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 Landau-Lifschitz-Gilbert dynamics. In the particular case of zero self-propelling speed, the resulting model reduces to the phenomenological Landau-Lifschitz-Gilbert equations. Therefore the present theory provides a kinetic formulation of classical micro-magnetization models and spin dynamics.
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