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Register a new userThe G-JF Thermostat for Accurate Configurational Sampling in Soft-Matter Simulations
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Added by
Niels Gronbech-Jensen
Publication date
2016
fields
Physics
and research's language is
English
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We implement the statistically sound G-JF thermostat for Langevin Dynamics simulations into the ESPREesSo molecular package for large-scale simulations of soft matter systems. The implemented integration method is tested against the integrator currently used by the molecular package in simulations of a fluid bilayer membrane. While the latter exhibits deviations in the sampling statistics that increase with the integration time step dt, the former reproduces near-correct configurational statistics for all dt within the stability range of the simulations. We conclude that, with very modest revisions to existing codes, one can significantly improve the performance of statistical sampling using Langevin thermostats.
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We have linked together two contributions in the development of configurational thermostats, the BT thermostat and the SDC scheme. We have shown that recently proposed configurational thermostats are generalized and enriched in both understanding and content by the SDC scheme. We have presented the stochastic counterpart to the configurational thermostat.
We expand on the previously published Gr{o}nbech-Jensen Farago (GJF) thermostat, which is a thermodynamically sound variation on the St{o}rmer-Verlet algorithm for simulating discrete-time Langevin equations. The GJF method has been demonstrated to give robust and accurate configurational sampling of the phase space, and its applications to, e.g., Molecular Dynamics is well established. A new definition of the discrete-time velocity variable is proposed based on analytical calculations of the kinetic response of a harmonic oscillator subjected to friction and noise. The new companion velocity to the GJF method is demonstrated to yield correct and time-step-independent kinetic responses for, e.g., kinetic energy, its fluctuations, and Green-Kubo diffusion based on velocity autocorrelations. This observation allows for a new and convenient Leap-Frog algorithm, which efficiently and precisely represents statistical measures of both kinetic and configurational properties at any time step within the stability limit for the harmonic oscillator. We outline the simplicity of the algorithm and demonstrate its attractive time-step-independent features for nonlinear and complex systems through applications to a one-dimensional nonlinear oscillator and three-dimensional Molecular Dynamics.
Simulations of systems with quenched disorder are extremely demanding, suffering from the combined effect of slow relaxation and the need of performing the disorder average. As a consequence, new algorithms, improved implementations, and alternative and even purpose-built hardware are often instrumental for conducting meaningful studies of such systems. The ensuing demands regarding hardware availability and code complexity are substantial and sometimes prohibitive. We demonstrate how with a moderate coding effort leaving the overall structure of the simulation code unaltered as compared to a CPU implementation, very significant speed-ups can be achieved from a parallel code on GPU by mainly exploiting the trivial parallelism of the disorder samples and the near-trivial parallelism of the parallel tempering replicas. A combination of this massively parallel implementation with a careful choice of the temperature protocol for parallel tempering as well as efficient cluster updates allows us to equilibrate comparatively large systems with moderate computational resources.
By means of Metropolis Monte Carlo simulations of a coarse-grained model for flexible polymers, we investigate how the integrated autocorrelation times of different energetic and structural quantities depend on the temperature. We show that, due to critical slowing down, an extremal autocorrelation time can also be considered as an indicator for the collapse transition that helps to locate the transition point. This is particularly useful for finite systems, where response quantities such as the specific heat do not necessarily exhibit clear indications for pronounced thermal activity.
We show how to derive a simple integrator for the Langevin equation and illustrate how it is possible to check the accuracy of the obtained distribution on the fly, using the concept of effective energy introduced in a recent paper [J. Chem. Phys. 126, 014101 (2007)]. Our integrator leads to correct sampling also in the difficult high-friction limit. We also show how these ideas can be applied in practical simulations, using a Lennard-Jones crystal as a paradigmatic case.
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