2004 Prépublication d'Orsay numéro 2004-46 (24/11/2004)



THE INITIAL DRIFT OF A 2D DROPLET AT ZERO TEMPERATURE.

CERF, Raphael - Modélisation Stochastique et Statistique, Université Paris-Sud, Bât. 425, 91405 Orsay cedex
LOUHICHI, Sana - Modélisation Stochastique et Statistique, Université Paris-Sud, Bât. 425, 91405 Orsay cedex


Mots Clés : 2D Ising model; Glauber dynamics; Zero temperature; Markov process; Mean curvature; Velocity.

Classification MSC : 60K35; 82C22


Resumé :

Abstract :
We consider the 2D stochastic Ising model evolving according to the Glauber dynamics at zero temperature. We compute the initial drift for droplets which are discretizations of smooth domains. A specific spatial average of the derivative at time~$0$ of the volume variation of a droplet close to a boundary point is equal to its curvature multiplied by a direction dependent coefficient. For a boundary point having a tangent with angle $\theta$, this coefficient is equal to $-\frac{\textstyle 1}{\textstyle 2}|\cos 2\theta|$.

Article : Fichier Postscript
Contact : Sana.Louhichi@math.u-psud.fr