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

TL;DR

This paper introduces a numerical method for coarse-graining 2D membrane models at finite temperature, extending a 1D approach based on ergodic theorems to facilitate the computation of ensemble averages and constitutive laws.

Contribution

The paper generalizes a 1D ergodic theorem-based strategy to 2D membrane models, enabling efficient computation of ensemble averages in the thermodynamic limit.

Findings

Successfully extends 1D coarse-graining method to 2D membranes.

Provides a numerical framework for computing ensemble averages.

Lays groundwork for deriving constitutive laws for membrane models.

Abstract

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.