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 et al. (2010) [6], 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.

► We aim at computing ensemble averages for two-dimensional membrane-like models.
► The strategy is a coarse-graining approach.
► We identify a Markov chain structure in the variables involved.
► Applying the law of large numbers for Markov chains reduces the number of variables.
► This allows to design a computational method much cheaper than classical MC methods.