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

Liu, Jian-Guo; Frouvelle, Amic; Degond, Pierre (2012), A note on phase transitions for the Smoluchowski equation with dipolar potential, Hyperbolic Problems: Theory, Numerics, Applications, 2012-06, Padova, ITALY

Type
Communication / Conférence
External document link
https://www.aimsciences.org/book/AM/volume/Volume%208
Date
2012
Conference title
Hyperbolic Problems: Theory, Numerics, Applications
Conference date
2012-06
Conference city
Padova
Conference country
ITALY
Metadata
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Author(s)
Liu, Jian-Guo
Frouvelle, Amic cc
Degond, Pierre
Abstract (EN)
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.
Subjects / Keywords
Smoluchowski equation; equilibrium states

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