The Equilibrium of a Velocity-Verlet Type Algorithm for DPD With Finite Time Steps

Gibson, Jonathan B.; Chen, K.; Chynoweth, S.

doi:10.1142/s0129183199000176

Cited by 36 publications

(24 citation statements)

References 19 publications

(18 reference statements)

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“…The largest error in the computation of g(r) occurs when r is small. A velocity autocorrelation function (see (6)) is plotted in Figure 7, together with comparisons of computations for ∆t = 0.02, 0.04 with a well-resolved computation. Method V gives poor results for computations of the velocity autocorrelation function.…”

Section: Computations We Evaluate Three Numerical Methodsmentioning

confidence: 99%

“…Many papers have used a modified version of the velocity Verlet method (defined in section 2.1) to do this [8,5,6,24]. The velocity Verlet scheme itself is a method for solving the Hamiltonian equations for H(q, p) = 1 2 p 2 + V (q) and consists of iterating the following for a time step ∆t:…”

mentioning

confidence: 99%

“…The velocity autocorrelation function (6) and the radial distribution function (the density of the average number of particles distance r from a fixed particle normalized by the density under the uniform distribution with the same density of particles) are two important averages that should be reproduced correctly by the numerical methods. In section 3, we describe computations of velocity autocorrelation and radial distribution functions.…”

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confidence: 99%

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Splitting for Dissipative Particle Dynamics

Shardlow¹

2003

SIAM J. Sci. Comput.

135

176

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Abstract. We study numerical methods for dissipative particle dynamics, a system of stochastic differential equations for simulating particles interacting pairwise according to a soft potential at constant temperature where the total momentum is conserved. We introduce splitting methods and examine the behavior of these methods experimentally. The performance of the methods, particularly temperature control, is compared to the modified velocity Verlet method used in many previous papers.

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Section: Computations We Evaluate Three Numerical Methodsmentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Splitting for Dissipative Particle Dynamics

Shardlow¹

2003

SIAM J. Sci. Comput.

135

176

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“…Dissipative Particle Dynamics, which has become quite popular in the soft-matter community [44][45][46][47][48][49][50][51][52][53][54][55][56], was developed to address the computational limitations of MD. A very soft interparticle potential, representing coarse-grained aggregates of molecules, enables a large time step to be used.…”

Section: Dissipative Particle Dynamics (Dpd)mentioning

confidence: 99%

Lattice Boltzmann Simulations of Soft Matter Systems

Dünweg¹,

Ladd²

2008

Advances in Polymer Science

201

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This article concerns numerical simulations of the dynamics of particles immersed in a continuum solvent. As prototypical systems, we consider colloidal dispersions of spherical particles and solutions of uncharged polymers. After a brief explanation of the concept of hydrodynamic interactions, we give a general overview of the various simulation methods that have been developed to cope with the resulting computational problems. We then focus on the approach we have developed, which couples a system of particles to a lattice-Boltzmann model representing the solvent degrees of freedom. The standard D3Q19 lattice-Boltzmann model is derived and explained in depth, followed by a detailed discussion of complementary methods for the coupling of solvent and solute. Colloidal dispersions are best described in terms of extended particles with appropriate boundary conditions at the surfaces, while particles with internal degrees of freedom are easier to simulate as an arrangement of mass points with frictional coupling to the solvent. In both cases, particular care has been taken to simulate thermal fluctuations in a consistent way. The usefulness of this methodology is illustrated by studies from our own research, where the dynamics of colloidal and polymeric systems has been investigated in both equilibrium and nonequilibrium situations.

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“…It has been recently observed that various integration schemes commonly used in classical MD lead to distinct deviations from the true equilibrium behavior, including deviations from the temperature predicted by the fluctuation-dissipation theorem, and artificial structures observed in the radial distribution function. 7,[11][12][13][14] These findings demonstrate the serious practical problems associated with the use of DPD and raise concerns regarding its future application to large-scale simulations of soft systems.…”

Section: Introductionmentioning

confidence: 95%

Integration schemes for dissipative particle dynamics simulations: From softly interacting systems towards hybrid models

Vattulainen¹,

Karttunen²,

Besold³

et al. 2002

The Journal of Chemical Physics

176

141

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We examine the performance of various commonly used integration schemes in dissipative particle dynamics simulations. We consider this issue using three different model systems, which characterize a variety of different conditions often studied in simulations. Specifically we clarify the performance of integration schemes in hybrid models, which combine microscopic and meso-scale descriptions of different particles using both soft and hard interactions. We find that in all three model systems many commonly used integrators may give rise to surprisingly pronounced artifacts in physical observables such as the radial distribution function, the compressibility, and the tracer diffusion coefficient. The artifacts are found to be strongest in systems, where interparticle interactions are soft and predominated by random and dissipative forces, while in systems governed by conservative interactions the artifacts are weaker. Our results suggest that the quality of any integration scheme employed is crucial in all cases where the role of random and dissipative forces is important, including hybrid models where the solvent is described in terms of soft potentials. Regarding the integration schemes, the best overall performance is found for integrators in which the velocity dependence of dissipative forces is taken into account, and particularly good performance is found for an approach in which velocities and dissipative forces are determined self-consistently. Remaining temperature deviations from the desired limit can be corrected by carrying out the self-consistent integration in conjunction with an auxiliary thermostat, in a manner that is similar in spirit to the well-known Nosé-Hoover thermostat. Further, we show that conservative interactions can play a significant role in describing the transport properties of simple fluids, in contrast to approximations often made in deriving analytical theories. In general, our results illustrate the main problems associated with simulation methods in which dissipative forces are velocity dependent, and point to the need to develop new techniques to resolve these issues.

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The Equilibrium of a Velocity-Verlet Type Algorithm for DPD With Finite Time Steps

Cited by 36 publications

References 19 publications

Splitting for Dissipative Particle Dynamics

Splitting for Dissipative Particle Dynamics

Lattice Boltzmann Simulations of Soft Matter Systems

Integration schemes for dissipative particle dynamics simulations: From softly interacting systems towards hybrid models

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