A Stable Finite Difference Method for the Elastic Wave Equation on Complex Geometries with Free Surfaces

A stable and explicit second order accurate finite difference method for the elastic wave equation in curvilinear coordinates is presented. The discretization of the spatial operators in the method is shown to be self-adjoint for free-surface, Dirichlet and periodic boundary conditions. The fully discrete version of the method conserves a discrete energy to machine precision

Minimum Energy Path to Membrane Pore Formation and Rupture

We combine dynamic self-consistent field theory with the string method to calculate the minimum energy path to membrane pore formation and rupture. In the regime where nucleation can occur on experimentally relevant time scales, the structure of the critical nucleus is between a solvophilic stalk and a locally thinned membrane. Classical nucleation theory fails to capture these molecular details and significantly overestimates the free energy barrier. Our results suggest that thermally nucleated rupture may be an important factor for the low rupture strains observed in lipid membranes

A General Perfectly Matched Layer Model for Hyperbolic-Parabolic Systems

This paper describes a very general absorbing layer model for hyperbolic-parabolic systems of partial differential equations. For linear systems with constant coefficients it is shown that the model possesses the perfect matching property, i.e., it is a perfectly matched layer (PML). The model is applied to two linear systems: a linear wave equation with a viscous damping term and the linearized Navier–Stokes equations. The resulting perfectly matched layer for the viscous wave equation is proved to be stable. The paper also presents how the model can be used to construct an absorbing layer for the full compressible Navier–Stokes equations. For all three applications, numerical experiments are presented. Especially for the linear problems, the results are very promising. In one experiment, where the performance of a “hyperbolic PML” and the new hyperbolic-parabolic PML is compared for a hyperbolic-parabolic system, an improvement of six orders of magnitude is observed. For the compressible Navier–Stokes equations results obtained with the presented layer are competitive with existing methods