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Center for Nonlinear Studies |
Numerical simulations of physical equations of motion always involve a discretization of time, and the discrete-time behavior is often different from that of the physical equations with the differences increasing with the artificial time-step. It is therefore essential to understand the features of different algorithms, such that optimal properties can be chosen for a given set of problems. Our aim is here to investigate and improve the simulation techniques for systems in thermal equilibrium. We briefly review our (G-JF) recent simple derivation [1] of a stochastic Stormer-Verlet algorithm for the evolution of Langevin equations in a manner that preserves proper configurational sampling (diffusion and Boltzmann distribution) in discrete time. The method, which is as simple as conventional Verlet schemes, has been numerically tested on both low-dimensional nonlinear systems as well as more complex molecular systems with many degrees of freedom [2]. In light of the fundamental artifacts introduced by discrete time, we provide a simple intuitive picture of the benefits of our algorithm, which exhibits configurational sampling statistics nearly independent of the numerical time step. We then introduce a new G-JF companion algorithm for controlling pressure in molecular ensembles; i.e., a barostat for so-called NPT simulations. Drawing on the idea of Andersen, we consider a global variable (a piston), which emulates the dynamics of the simulated volume. However, our description of the dynamics is defined differently and leads to a very simple set of discrete-time equations that can easily be implemented and tested for statistical accuracy. We review the fundamental issues in Molecular Dynamics with periodic boundary conditions, sketch the derivation and motivation for the algorithm, and show favorable comparisons with state-of-the-art algorithms for simulating molecular systems at constant mass, pressure, and temperature. [1] Gronbech-Jensen & Farago, Molecular Physics Vol.111, 983 (2013). [2] Gronbech-Jensen, Hayre, & Farago, Computer Physics Communications, Vol.185, 524 (2014).
Host: Turab Lookman, txl@lanl.gov