Coarse‐graining molecular dynamics models using an extended Galerkin projection method

Abstract

SUMMARYWe present a new framework for coarse‐graining molecular dynamics models for crystalline solids. The reduction method is based on a Galerkin projection to a subspace, whose dimension is much smaller than that of the full atomistic model. To effectively reduce artificial reflections of phonons at the interface, we construct extended subspaces with increasing accuracy by adding more coarse‐grained variables near the interface between lattice defects and the surrounding region. This approach is equivalent to the generalized Langevin model. But it eliminates the need to precompute the memory function, a well‐known practical difficulty. Further, the variational formulation preserves the stability of the molecular models. Copyright © 2014 John Wiley & Sons, Ltd.

An Atomistic/Continuum Coupling Method Using Enriched Bases

“…Both integrals can be further approximated by standard quadrature formulas. Interested readers may find earlier discussions on quadrature approximations in [18,29,32,17] for static problems and [24,56] for dynamics problems.…”

“…This part is equivalent to the local QC method. In fact, this procedure for approximating the forces has been implemented in [24,56], although in different settings.…”

On the Asymptotic Behavior of the Kernel Function in the Generalized Langevin Equation: A One-Dimensional Lattice Model

“…The GLEs have opened up a new paradigm in molecular modeling. Numerous attempts have been made to derive the GLEs from the full molecular models, and the models have been applied to solid-gas interface [2,1], protein dynamics [5,14,27,43,44], crystalline solids [24,33,34], etc. In general, little is known about the mathematical properties of the memory kernel.…”

From generalized Langevin equations to Brownian dynamics and embedded Brownian dynamics

“…In contrast to the Langevin dynamics (1), the GLE includes a historydependent friction term and a correlated Gaussian noise. The memory term often comes from a coarse-graining step, e.g., 2,[8][9][10][11]15,16,19,22,[25][26][27]29,30,32,34,40,43,46 , which has also been an recent emerging area of interest in molecular modeling. Among the many approximation schemes [6][7][8]12,20,23,32,34 for the GLE model, the BD model (3) is clearly the simplest.…”