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

Liu, Jian-Guo; Frouvelle, Amic; Degond, Pierre

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

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https://www.aimsciences.org/book/AM/volume/Volume%208

Date

2012

Titre du colloque

Hyperbolic Problems: Theory, Numerics, Applications

Date du colloque

2012-06

Ville du colloque

Padova

Pays du colloque

ITALY

Métadonnées

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Auteur(s)

Liu, Jian-Guo
Frouvelle, Amic

Degond, Pierre

Résumé (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.

Mots-clés

Smoluchowski equation; equilibrium states