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Center for Nonlinear Studies |
We present a new, simple simulation technique for systems in thermal equilibrium. We briefly review our GJF stochastic Størmer-Verlet algorithm for the evolution of Langevin equations in a manner that preserves proper configurational sampling (diffusion and Boltzmann distribution) in discrete time. The resulting 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 ensembles with many degrees of freedom. Additionally, we present a recent solution to the "velocity-problem", and we show a simple approach for achieving accurate measures also for kinetic sampling. We show exact analytic results for linear systems, and demonstrate the applicability of the method for both nonlinear and complex systems, which can be accurately simulated at any time step within the stability limit. The method [1] is in the standard form of a Verlet-type algorithm, and is therefore easy to implement and validate in existing codes, including Molecular Dynamics.
[1] Gronbech Jensen and Gronbech-Jensen, "Accurate configurational and kinetic statistics in discrete-time Langevin systems", Molecular Physics (2019)[1] Gronbech Jensen and Gronbech-Jensen, "Accurate configurational and kinetic statistics in discrete-time Langevin systems", Molecular Physics (2019), https://doi.org/10.1080/00268976.2019.1570369.
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