  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.
