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 / ConférenceExternal document link
https://www.aimsciences.org/book/AM/volume/Volume%208Date
2012Conference title
Hyperbolic Problems: Theory, Numerics, ApplicationsConference date
2012-06Conference city
PadovaConference country
ITALYMetadata
Show full item recordAbstract (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 statesRelated items
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