Andrew Binder

Andrew Binder, Mitchell Luskin, Danny Perez et al.

Spatial multiscale methods have established themselves as useful tools for extending the length scales accessible by conventional statics (i.e., zero temperature molecular dynamics). Recently, extensions of these methods, such as the finite-temperature quasicontinuum (hot-QC) or Coarse-Grained Molecular Dynamics (CGMD) methods, have allowed for multiscale molecular dynamics simulations at finite temperature. Here, we assess the quality of the long-time dynamics these methods generate by considering canonical transition rates. Specifically, we analyze the transition state theory (TST) rates in CGMD and compare them to the corresponding TST rate of the fully atomistic system. The ability of such an approach to reliably reproduce the TST rate is verified through a relative error analysis, which is then used to highlight the major contributions to the error and guide the choice of degrees of freedom. Finally, our analytical results are compared with numerical simulations for the case of a 1-D chain.

Andrew Binder, Tony Lelièvre, Gideon Simpson

Metastability is a common obstacle to performing long molecular dynamics simulations. Many numerical methods have been proposed to overcome it. One method is parallel replica dynamics, which relies on the rapid convergence of the underlying stochastic process to a quasi-stationary distribution. Two requirements for applying parallel replica dynamics are knowledge of the time scale on which the process converges to the quasi-stationary distribution and a mechanism for generating samples from this distribution. By combining a Fleming-Viot particle system with convergence diagnostics to simultaneously identify when the process converges while also generating samples, we can address both points. This variation on the algorithm is illustrated with various numerical examples, including those with entropic barriers and the 2D Lennard-Jones cluster of seven atoms.