Mathematical modeling of point defects in materials science

Eric Cancès (1, 2) , Claude Le Bris (1, 2)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
2 MICMAC - Methods and engineering of multiscale computing from atom to continuum

We survey some recent mathematical works we have contributed to that are related to the modeling of defects in materials science at different scales. We emphasize the similarities (need of a reference, often periodic system; renormalization procedure; etc) shared by models arising in different contexts. Our illustrative examples are taken from electronic structure models, atomistic models, homogenization problems. The exposition is pedagogic and deliberately kept elementary. Both theoretical and numerical aspects are addressed.

Mots clés: Modeling of defects; materials science; multiscale science; periodicity; renormalization; electronic structure models; atomistic models; homogenization theory

Domaines: Equations aux dérivées partielles [math.AP]

Eric Cancès, Claude Le Bris. Mathematical modeling of point defects in materials science. Mathematical Models and Methods in Applied Sciences, 2013, 23 (10), pp.1795. ⟨10.1142/S0218202513500528⟩. ⟨hal-00916157⟩