Nucleation and backward motion of discrete interfaces

Andrea Braides; Giovanni Scilla

doi:10.1016/j.crma.2013.10.008

Partial differential equations/Calculus of variations

Nucleation and backward motion of discrete interfaces
[Nucléation et mouvement en arrière des interfaces discrètes]

Présenté par : Haïm Brézis

Andrea Braides ¹ ; Giovanni Scilla ²

¹ Dipartimento di Matematica, Università di Roma ‘Tor Vergata’, via della Ricerca Scientifica 1, 00133 Roma, Italy
² Dipartimento di Matematica ‘G. Castelnuovo’, ‘Sapienza’ Università di Roma, piazzale Aldo Moro 5, 00185 Roma, Italy

Comptes Rendus. Mathématique, Volume 351 (2013) no. 21-22, pp. 803-806.

Résumé
Abstract

Nous utilisons une approximation discrète du mouvement par la courbure cristalline pour définir une évolution des ensemples à partir dʼun seul point (nucléation) selon un critère de « maximisation » du périmètre, ce qui donne fomallement une version du mouvement en arrière par courbure cristalline. Cette évolution dépend de lʼapproximation choisie.

We use a discrete approximation of the motion by crystalline curvature to define an evolution of sets from a single point (nucleation) following a criterion of “maximization” of the perimeter, formally giving a backward version of the motion by crystalline curvature. This evolution depends on the approximation chosen.

Reçu le : 2013-10-07
Accepté le : 2013-10-14
Publié le : 2013-11-01

DOI : 10.1016/j.crma.2013.10.008

Affiliations des auteurs :

Andrea Braides ¹ ; Giovanni Scilla ²

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     title = {Nucleation and backward motion of discrete interfaces},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {803--806},
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     doi = {10.1016/j.crma.2013.10.008},
     language = {en},
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Andrea Braides; Giovanni Scilla. Nucleation and backward motion of discrete interfaces. Comptes Rendus. Mathématique, Volume 351 (2013) no. 21-22, pp. 803-806. doi : 10.1016/j.crma.2013.10.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.10.008/

Bibliographie
Cité par

[1] R. Alicandro; A. Braides; M. Cicalese Phase and anti-phase boundaries in binary discrete systems: a variational viewpoint, Netw. Heterog. Media, Volume 1 (2006), pp. 85-107

[2] F. Almgren; J.E. Taylor Flat flow is motion by crystalline curvature for curves with crystalline energies, J. Differ. Geom., Volume 42 (1995) no. 1, pp. 1-22

[3] F. Almgren; J.E. Taylor; L. Wang Curvature driven flows: a variational approach, SIAM J. Control Optim., Volume 50 (1983), pp. 387-438

[4] A. Braides Approximation of Free-Discontinuity Problems, Lecture Notes in Mathematics, vol. 1694, Springer-Verlag, Berlin, 1998

[5] A. Braides Local Minimization, Variational Evolution and Γ-Convergence, Lecture Notes in Mathematics, vol. 2094, Springer-Verlag, Berlin, 2013

[6] A. Braides; M.S. Gelli; M. Novaga Motion and pinning of discrete interfaces, Arch. Ration. Mech. Anal., Volume 95 (2010), pp. 469-498

[7] A. Braides, G. Scilla, Nucleation and backward motion of anisotropic discrete interfaces, in preparation.

[8] J.E. Taylor Motion of curves by crystalline curvature, including triple junctions and boundary points (R.E. Greene; S.T. Yau, eds.), Differential Geometry, Proceedings of Symposia in Pure Mathematics, vol. 54 (part 1), 1993, pp. 417-438

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