Geodesic
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

Braides, Andrea1 ; Scilla, Giovanni2
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, Tome 351 (2013) no. 21-22, pp. 803-806.

Voir la notice de l'article provenant de la source Numdam

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.10.008

Braides, Andrea 1 ; Scilla, Giovanni 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 
@article{CRMATH_2013__351_21-22_803_0,
     author = {Braides, Andrea and Scilla, Giovanni},
     title = {Nucleation and backward motion of discrete interfaces},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {803--806},
     publisher = {Elsevier},
     volume = {351},
     number = {21-22},
     year = {2013},
     doi = {10.1016/j.crma.2013.10.008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2013.10.008/}
}
TY  - JOUR
AU  - Braides, Andrea
AU  - Scilla, Giovanni
TI  - Nucleation and backward motion of discrete interfaces
JO  - Comptes Rendus. Mathématique
PY  - 2013
SP  - 803
EP  - 806
VL  - 351
IS  - 21-22
PB  - Elsevier
UR  - http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2013.10.008/
DO  - 10.1016/j.crma.2013.10.008
LA  - en
ID  - CRMATH_2013__351_21-22_803_0
ER  - 
%0 Journal Article
%A Braides, Andrea
%A Scilla, Giovanni
%T Nucleation and backward motion of discrete interfaces
%J Comptes Rendus. Mathématique
%D 2013
%P 803-806
%V 351
%N 21-22
%I Elsevier
%U http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2013.10.008/
%R 10.1016/j.crma.2013.10.008
%G en
%F CRMATH_2013__351_21-22_803_0
Braides, Andrea; Scilla, Giovanni. Nucleation and backward motion of discrete interfaces. Comptes Rendus. Mathématique, Tome 351 (2013) no. 21-22, pp. 803-806. doi : 10.1016/j.crma.2013.10.008. http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2013.10.008/

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

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

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

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

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

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

Cité par Sources :