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Diffusion in a continuum model of self-propelled particles with alignment interaction

Pierre Degond Tong Yang

Statistics Theory and Methods mathscidoc:1912.43945

Mathematical Models and Methods in Applied Sciences, 20, 1459-1490, 2010.9
In this paper, we provide the O() corrections to the hydrodynamic model derived by Degond and Motsch from a kinetic version of the model by Vicsek and co-authors describing flocking biological agents. The parameter stands for the ratio of the microscopic to the macroscopic scales. The O() corrected model involves diffusion terms in both the mass and velocity equations as well as terms which are quadratic functions of the first-order derivatives of the density and velocity. The derivation method is based on the standard ChapmanEnskog theory, but is significantly more complex than usual due to both the non-isotropy of the fluid and the lack of momentum conservation.
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@inproceedings{pierre2010diffusion,
  title={Diffusion in a continuum model of self-propelled particles with alignment interaction},
  author={Pierre Degond, and Tong Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210825435843509},
  booktitle={Mathematical Models and Methods in Applied Sciences},
  volume={20},
  pages={1459-1490},
  year={2010},
}
Pierre Degond, and Tong Yang. Diffusion in a continuum model of self-propelled particles with alignment interaction. 2010. Vol. 20. In Mathematical Models and Methods in Applied Sciences. pp.1459-1490. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210825435843509.
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