Elimination of time step effects in DPD

Abstract

PACS. 02.70.Ns -Molecular dynamics and particle methods. PACS. 05.40.-a -Fluctuation phenomena, random processes, noise, and Brownian motion. PACS. 66.20.+d -Viscosity of liquids; diffusive momentum transport.Abstract. -The equilibrium statistics of quantities computed by means of DPD (dissipative particle dynamics) are usually very sensitive to the time step used in the simulation. In this letter we show how to eliminate this sensitivity by considering the irreversible dynamics in DPD as the limiting case of a thermostat that leaves Maxwell-Boltzmann distribution invariant even for finite time steps. The remaining dependency on time step is solely due to the discretization of the conservative part of the dynamics and is independent of the thermostat.Introduction. -Dissipation particle dynamics (DPD) is a particle-based simulation technique. It was originally proposed to simulate fluids on a mesoscopic scale [1]. A DPD particle models a blob of atoms that have effective, soft interactions. By means of dissipative and fluctuating pair-forces, the equilibrium state of the system is made to satisfy the Boltzmann distribution. Alternatively, one can view upon DPD as a thermostatic scheme in a molecular dynamics (MD) code. In this case, the (conservative) interactions need not be soft.Because DPD is particle-based, it does not have problems associated with the use of a grid such as, e.g., lattice Boltzmann simulations. It is Galilean invariant and momentum is conserved. This is different from Brownian dynamics, Stokesian dynamics and the Andersen thermostat. Different from to the Nosé-Hoover thermostat, the DPD thermostating occurs locally in space through pair interactions. Therefore, the dynamics is expected to be more realistic.A drawback of DPD is that the results of the simulation depend on the chosen time step. None of the DPD schemes proposed up to now give the exact Boltzmann distribution when a finite time step is used. Lowe [2] has introduced a scheme that is similar to the Andersen thermostat, but considers relative velocities of nearby pairs instead of the velocity of individual particles. This scheme gives the Boltzmann distribution, even for finite time steps. It has similar characteristics as DPD, but is not equivalent. In this paper we show how to generalise the ideas of Lowe. The resulting scheme always gives correct equilibrium statistics and reduces to the DPD equations in the limit of zero time step.

Pressure driven flow of polymer solutions in nanoscale slit pores

“…Therefore, within DPD, the hydrodynamic interaction is well developed within the time scale of polymer motion. As noted recently by Peters [36], the Schmidt number in a coarse-grained model is in fact ill-defined, since in the Schmidt number, D 0 corresponds to the diffusion coefficient of single particle, not coarse-grained fluid elements. Our current findings provide further testimony to the effectiveness of the dissipative particle dynamics approach in simulating polymer flow in a variety of situations including in nano-channels.…”

Bottom-up derivation of an effective thermostat for united atoms simulations of water

“…This argument is valid regardless of the projection, as long as the projected dynamics truly follows the DPD ansatz. Types of projections that can be considered are for example clustering collections of freely moving particles into single DPD beads, which is the way DPD is commonly viewed [15,19,20,23,24,25], or DPD used as a thermostat for united atoms coarse-graining [5,26,27]. In the former case, the stochastic and dissipative interactions result from the internal motion of the microscopic particles inside the DPD beads, whereas for the latter case, these interactions result from the internal atomistic motion not explicitly simulated in the coarse-grained particles.…”

Computer simulation of aqueous block copolymer assemblies: Length scales and methods

“…Warren 41 recently reviewed the technique. Many improvements have been implemented within the DPD framework in the last few years, such as modifications in the integrators to eliminate the sensitivity to timestep size 42 and extension beyond the usual constant volume ensemble to a constant pressure ensemble. 43 Murat and Grest were perhaps the first group to incorporate polymer-solvent interactions by performing MD simulations using a coarse-grain model with a mapping of one monomer per site and a coupling to a heat bath.…”