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A note on phase transitions for the Smoluchowski equation with dipolar potential

Pierre Degond Institut de Math´ematiques de Toulouse Amic Frouvelle Universit´e de PARIS-DAUPHINE Jian-Guo Liu Duke University

Mathematical Physics mathscidoc:1702.22003

2014.1
In this note, we study the phase transitions arising in a modified Smoluchowski equation on the sphere with dipolar potential. This equation models the competition between alignment and diffusion, and the modification consists in taking the strength of alignment and the intensity of the diffusion as functions of the order parameter. We characterize the stable and unstable equilibrium states. For stable equilibria, we provide the exponential rate of convergence. We detail special cases, giving rise to second order and first order phase transitions, respectively. We study the hysteresis diagram, and provide numerical illustrations of this phenomena.
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@inproceedings{pierre2014a,
  title={A note on phase transitions for the Smoluchowski equation with dipolar potential},
  author={Pierre Degond, Amic Frouvelle, and Jian-Guo Liu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208100558308276308},
  year={2014},
}
Pierre Degond, Amic Frouvelle, and Jian-Guo Liu. A note on phase transitions for the Smoluchowski equation with dipolar potential. 2014. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208100558308276308.
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