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#### Mathematical Physicsmathscidoc:1702.22006

Mathematical Models and Methods in Applied Sciences, 22, (1), 2012.4
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 non-local 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 micromagnetization models and spin dynamics.
Self-propelled particles; alignment dynamics; precession; hydrodynamic limit; hyperbolicity; diffusion correction; weakly nonlocal interaction; Landau–Lifschitz–Gilbert; spin dynamics Read More: http://www.worldscientific.com/doi/abs/10.1142/S021820251140001X
```@inproceedings{pierre2012hydrodynamics,
title={Hydrodynamics of self-alignment interactions with precession and derivation of the Landau-Lifschitz-Gilbert equation},
author={Pierre Degond, and Jian-Guo Liu},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208230115886465333},
booktitle={Mathematical Models and Methods in Applied Sciences},
volume={22},
number={1},
year={2012},
}
```
Pierre Degond, and Jian-Guo Liu. Hydrodynamics of self-alignment interactions with precession and derivation of the Landau-Lifschitz-Gilbert equation. 2012. Vol. 22. In Mathematical Models and Methods in Applied Sciences. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208230115886465333.