On the estimation of the curvatures and bending rigidity of membrane networks via a local maximum-entropy approach

TL;DR

This paper introduces a meshfree, local maximum entropy method for estimating membrane network curvatures and bending rigidity, validated through numerical benchmarks and molecular dynamics simulations, offering a flexible tool for membrane elasticity analysis.

Contribution

It develops a novel meshfree curvature estimation technique based on local maximum entropy, enabling accurate membrane elasticity predictions from molecular data.

Findings

Accurate curvature estimates for membrane networks.

Convergence properties validated through benchmark problems.

Effective prediction of bending rigidity from local curvature data.

Abstract

We present a meshfree method for the curvature estimation of membrane networks based on the Local Maximum Entropy approach recently presented in (Arroyo and Ortiz, 2006). A continuum regularization of the network is carried out by balancing the maximization of the information entropy corresponding to the nodal data, with the minimization of the total width of the shape functions. The accuracy and convergence properties of the given curvature prediction procedure are assessed through numerical applications to benchmark problems, which include coarse grained molecular dynamics simulations of the fluctuations of red blood cell membranes (Marcelli et al., 2005; Hale et al., 2009). We also provide an energetic discrete-to-continuum approach to the prediction of the zero-temperature bending rigidity of membrane networks, which is based on the integration of the local curvature estimates. The Local Maximum Entropy approach is easily applicable to the continuum regularization of fluctuating membranes, and the prediction of membrane and bending elasticities of molecular dynamics models.