Search

MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
9/1997

A nonlocal anisotropic model for phase transitions. Part II: Asymptotic behaviour of rescaled energies

Giovanni Alberti and Giovanni Bellettini

Abstract

In this paper we study the asymptotic behaviour in the thermodynamic limit of a non local model for phase separation. More precisely we consider the free energy obtained by replacing the usual gradient term in the Cahn-Hilliard model with an interaction energy associated to a positive non-isotropic interaction potential, and then we show that the limit in the sense of Gamma-convergence of suitable rescalings of this energy leads to the classical (non-isotropic) model for surface tension. These functionals appear in statistical mechanics as free energies of Ising systems with Kac potential.

Received:
Apr 22, 1997
Published:
Apr 22, 1997
MSC Codes:
49J45, 49N45, 82B24
Keywords:
phrase transitions, singular perturbations, gamma-convergence, nonlocal integral functionals

Related publications

inJournal
1998 Repository Open Access
Giovanni Alberti and Giovanni Bellettini

A non-local anisotropic model for phase transitions : asymptotic behavior of rescaled energies

In: European journal of applied mathematics, 9 (1998) 3, pp. 261-284