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Register a new userStochastic thermostats: comparison of local and global schemes
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We show that a recently introduced stochastic thermostat [J. Chem. Phys. 126 (2007) 014101] can be considered as a global version of the Langevin thermostat. We compare the global scheme and the local one (Langevin) from a formal point of view and through practical calculations on a model Lennard-Jones liquid. At variance with the local scheme, the global thermostat preserves the dynamical properties for a wide range of coupling parameters, and allows for a faster sampling of the phase-space.
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Many applications in computational science require computing the elements of a function of a large matrix. A commonly used approach is based on the the evaluation of the eigenvalue decomposition, a task that, in general, involves a computing time that scales with the cube of the size of the matrix. We present here a method that can be used to evaluate the elements of a function of a positive-definite matrix with a scaling that is linear for sparse matrices and quadratic in the general case. This methodology is based on the properties of the dynamics of a multidimensional harmonic potential coupled with colored noise generalized Langevin equation (GLE) thermostats. This $f-$thermostat (FTH) approach allows us to calculate directly elements of functions of a positive-definite matrix by carefully tailoring the properties of the stochastic dynamics. We demonstrate the scaling and the accuracy of this approach for both dense and sparse problems and compare the results with other established methodologies.
In this work we compare and characterize the behavior of Langevin and Dissipative Particle Dynamics (DPD) thermostats in a broad range of non-equilibrium simulations of polymeric systems. Polymer brushes in relative sliding motion, polymeric liquids in Poiseuille and Couette flows, and brush-melt interfaces are used as model systems to analyze the efficiency and limitations of different Langevin and DPD thermostat implementations. Widely used coarse-grained bead-spring models under good and poor solvent conditions are employed to assess the effects of the thermostats. We considered equilibrium, transient, and steady state examples for testing the ability of the thermostats to maintain constant temperature and to reproduce the underlying physical phenomena in non-equilibrium situations. The common practice of switching-off the Langevin thermostat in the flow direction is also critically revisited. The efficiency of different weight functions for the DPD thermostat is quantitatively analyzed as a function of the solvent quality and the non-equilibrium situation.
This work presents new parallelizable numerical schemes for the integration of Dissipative Particle Dynamics with Energy conservation (DPDE). So far, no numerical scheme introduced in the literature is able to correctly preserve the energy over long times and give rise to small errors on average properties for moderately small timesteps, while being straightforwardly parallelizable. We present in this article two new methods, both straightforwardly parallelizable, allowing to correctly preserve the total energy of the system. We illustrate the accuracy and performance of these new schemes both on equilibrium and nonequilibrium parallel simulations.
Molecular dynamics simulations require barostats to be performed at constant pressure. The usual recipe is to employ the Berendsen barostat first, which displays a first-order volume relaxation efficient in equilibration but results in incorrect volume fluctuations, followed by a second order or Monte Carlo barostat for production runs. In this paper, we introduce stochastic cell rescaling, a first-order barostat that samples the correct volume fluctuations by including a suitable noise term. The algorithm is shown to report volume fluctuations compatible with the isobaric ensemble and its anisotropic variant is tested on a membrane simulation. Stochastic cell rescaling can be straightforwardly implemented in existing codes and can be used effectively both in equilibration and in production phases.
We report the development of a discontinuous spectral element flow solver that includes the implementation of both spectral difference and flux reconstruction formulations. With this high order framework, we have constructed a foundation upon which to provide a fair and accurate assessment of these two schemes in terms of accuracy, stability, and performance with special attention to the true spectral difference scheme and the modified spectral difference scheme recovered via the flux reconstruction formulation. Building on previous analysis of the spectral difference and flux reconstruction schemes, we provide a novel nonlinear stability analysis of the spectral difference scheme. Through various numerical experiments, we demonstrate the additional stability afforded by the true, baseline spectral difference scheme without explicit filtering or de-aliasing due to its inherent feature of staggered flux points. This arrangement leads to favorable suppression of aliasing errors and improves stability needed for under-resolved simulations of turbulent flows.
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