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

Perfectly Matched Layers for Coupled Nonlinear Schr\"{o}dinger Equations with Mixed Derivatives

This paper constructs perfectly matched layers (PML) for a system of 2D Coupled Nonlinear Schr\"odinger equations with mixed derivatives which arises in the modeling of gap solitons in nonlinear periodic structures with a non-separable linear part. The PML construction is performed in Laplace Fourier space via a modal analysis and can be viewed as a complex change of variables. The mixed derivatives cause the presence of waves with opposite phase and group velocities, which has previously been shown to cause instability of layer equations in certain types of hyperbolic problems. Nevertheless, here the PML is stable if the absorption function $\sigma$ lies below a specified threshold. The PML construction and analysis are carried out for the linear part of the system. Numerical tests are then performed in both the linear and nonlinear regimes checking convergence of the error with respect to the layer width and showing that the PML performs well even in many nonlinear simulations.Comment: v.3: A typo in equ (5.4) correcte