用局部最大熵方法估计膜网络的曲率和抗弯刚度
On the estimation of the curvatures and bending rigidity of membrane networks via a local maximum-entropy approach
摘要：
我们提出了一种无网格方法的膜网络的曲率估计的基础上，最近提出的局部最大熵方法（阿罗约和奥尔蒂斯，2006年）。通过平衡节点数据对应的信息熵的最大化和形状函数的总宽度的最小化来进行网络的连续正则化。通过对基准问题的数值应用来评估给定曲率预测过程的准确性和收敛性质，所述基准问题包括红细胞膜波动的粗粒度分子动力学模拟（Marcelli等人，2005; Hale等人，2009年）。我们还提供了一个充满活力的离散到连续的方法来预测膜网络的零温弯曲刚度，这是基于局部曲率估计的集成。局部最大熵方法可方便地应用于波动膜的连续正则化，以及分子动力学模型的膜弹性和弯曲弹性的预测。
英文摘要：
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.
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