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

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.