Absorbing Boundary Conditions for Molecular Dynamics and Multiscale Modeling

We present an application of differential equation based local absorbing boundary conditions to molecular dynamics. The absorbing boundary conditions result in the absorbtion of the majority of waves incident perpendicular to the bounding surface. We demonstrate that boundary conditions developed for the wave equation can be applied to molecular dynamics. Comparisons with damping material boundary conditions are discussed. The concept is extended to the formulation of an atomistic-continuum multiscale scheme with handshaking between the regions based on absorbing boundary conditions. The multiscale model is effective in minimizing spurious reflections at the interface

Reactive Boundary Conditions as Limits of Interaction Potentials for Brownian and Langevin Dynamics

A popular approach to modeling bimolecular reactions between diffusing molecules is through the use of reactive boundary conditions. One common model is the Smoluchowski partial absorption condition, which uses a Robin boundary condition in the separation coordinate between two possible reactants. This boundary condition can be interpreted as an idealization of a reactive interaction potential model, in which a potential barrier must be surmounted before reactions can occur. In this work we show how the reactive boundary condition arises as the limit of an interaction potential encoding a steep barrier within a shrinking region in the particle separation, where molecules react instantly upon reaching the peak of the barrier. The limiting boundary condition is derived by the method of matched asymptotic expansions, and shown to depend critically on the relative rate of increase of the barrier height as the width of the potential is decreased. Limiting boundary conditions for the same interaction potential in both the overdamped Fokker-Planck equation (Brownian Dynamics), and the Kramers equation (Langevin Dynamics) are investigated. It is shown that different scalings are required in the two models to recover reactive boundary conditions that are consistent in the high friction limit where the Kramers equation solution converges to the solution of the Fokker-Planck equation.Comment: 23 pages, 2 figure