A numerical strategy for coarse-graining two-dimensional atomistic models at finite temperature: the membrane case

Xavier Blanc (1) , Frédéric Legoll (2, 3)

1 LJLL - Laboratoire Jacques-Louis Lions
2 MICMAC - Methods and engineering of multiscale computing from atom to continuum
3 multi-échelle - Modélisation et expérimentation multi-échelle pour les solides hétérogènes

We present a numerical strategy to compute ensemble averages of coarse-grained two-dimensional membrane-like models. The approach consists in generalizing to these two-dimensional models a one-dimensional strategy exposed in [Blanc, Le Bris, Legoll, Patz, JNLS 2010], which is based on applying the ergodic theorem to Markov chains. This may be considered as a first step towards computing the constitutive law associated to such models, in the thermodynamic limit.

Domaines: Science des matériaux [cond-mat.mtrl-sci]

Xavier Blanc, Frédéric Legoll. A numerical strategy for coarse-graining two-dimensional atomistic models at finite temperature: the membrane case. Computational Materials Science, 2013, 66, pp.84-95. ⟨10.1016/j.commatsci.2012.04.045⟩. ⟨hal-00627294⟩