 Dissipative particle dynamics

Dissipative particle dynamics (DPD) is a stochastic simulation technique for simulating the dynamic and rheological properties of simple and complex fluids. It was initially devised by Hoogerbrugge and Koelman ^{[1]}^{[2]} to avoid the lattice artifacts of the socalled lattice gas automata and to tackle hydrodynamic time and space scales beyond those available with molecular dynamics (MD). It was subsequently reformulated and slightly modified by Español ^{[3]} to ensure the proper thermal equilibrium state.
DPD is an offlattice mesoscopic simulation technique which involves a set of particles moving in continuous space and discrete time. Particles represent whole molecules or fluid regions, rather than single atoms, and atomistic details are not considered relevant to the processes addressed. The particles’ internal degrees of freedom are integrated out and replaced by simplified pairwise dissipative and random forces, so as to conserve momentum locally and ensure correct hydrodynamic behaviour. The main advantage of this method is that it gives access to longer time and length scales than are possible using conventional MD simulations. Simulations of polymeric fluids in volumes up to 100 nm in linear dimension for tens of microseconds are now common.
Contents
Equations
The total nonbonded force acting on a DPD particle i is given by a sum over all particles j that lie within a fixed cutoff distance, of three pairwiseadditive forces:
where the first term in the above equation is a conservative force, the second a dissipative force and the third a random force. The conservative force acts to give beads a chemical identity, while the dissipative and random forces together form a thermostat that keeps the mean temperature of the system constant. A key property of all of the nonbonded forces is that they conserve momentum locally, so that hydrodynamic modes of the fluid emerge even for small particle numbers. Local momentum conservation requires that the random force between two interacting beads be antisymmetric. Each pair of interacting particles therefore requires only a single random force calculation. This distinguishes DPD from Brownian dynamics in which each particle experiences a random force independently of all other particles. Beads can be connected into ‘molecules’ by tying them together with soft (often Hookean) springs. The most common applications of DPD keep the particle number, volume and temperature constant, and so take place in the NVT ensemble. Alternatively, the pressure instead of the volume is held constant, so that the simulation is in the NPT ensemble.
Parallelization
In principle, simulations of very large systems, approaching a cubic micron for milliseconds, are possible using a parallel implementation of DPD running on multiple processors in a Beowulfstyle cluster. Because the nonbonded forces are shortranged in DPD, it is possible to parallelize a DPD code very efficiently using a spatial domain decomposition technique. In this scheme, the total simulation space is divided into a number of cuboidal regions each of which is assigned to a distinct processor in the cluster. Each processor is responsible for integrating the equations of motion of all beads whose centres of mass lie within its region of space. Only beads lying near the boundaries of each processor's space require communication between processors. In order to ensure that the simulation is efficient, the crucial requirement is that the number of particleparticle interactions that require interprocessor communication be much smaller than the number of particleparticle interactions within the bulk of each processor's region of space. Roughly speaking, this means that the volume of space assigned to each processor should be sufficiently large that its surface area (multiplied by a distance comparable to the force cutoff distance) is much less than its volume.
Applications
A wide variety of complex hydrodynamic phenomena have been simulated using DPD, the list here is necessarily incomplete. The goal of these simulations often is to relate the macroscopic nonNewtonian flow properties of the fluid to its microscopic structure. Such DPD applications range from modelling the rheological properties of concrete^{[4]} to simulating liposome formation in biophysics^{[5]}. Other recent threephase phenomena such as dynamic wetting.^{[6]}
Further reading
The full trace of the developments of various important aspects of the DPD methodology since it was first proposed in the early 1990s can be found in "Dissipative Particle Dynamics: Introduction, Methodology and Complex Fluid Applications  A Review"^{[7]}
The stateoftheart in DPD was captured in a CECAM workshop in 2008.^{[8]} Innovations to the technique presented there include DPD with energy conservation; noncentral frictional forces that allow the fluid viscosity to be tuned; an algorithm for preventing bond crossing between polymers; and the automated calibration of DPD interaction parameters from atomistic molecular dynamics.
References
 ^ P. J. Hoogerbrugge and J. M. V. A. Koelman. Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics. Europhysics Letters, 19(3):155–160, JUN 1 1992
 ^ J. M. V. A. Koelman and P. J. Hoogerbrugge. Dynamic simulations of hardsphere suspensions under steady shear. Europhysics Letters, 21(3):363–368, JAN 20 1993
 ^ P. Español and P. B. Warren. Statisticalmechanics of dissipative particle dynamics. Europhysics Letters, 30(4):191–196, MAY 1 1995
 ^ James S. Sims and Nicos S. Martys: Modelling the Rheological Properties of Concrete
 ^ Petri Nikunen, Mikko Karttunen, and Ilpo Vattulainen: Modelling Liposome formation in biophysics
 ^ B. Henrich, C. Cupelli, M. Moseler, and M. Santer": An adhesive DPD wall model for dynamic wetting, Europhysics Letters 80 (2007) 60004, p.1
 ^ Moeendarbary et al. (2009). "Dissipative Particle Dynamics: Introduction, Methodology and Complex Fluid Applications  A Review" (Subscription required). International Journal of Applied Mechanics (World Scientific Journals) 1 (4): 737–763. Bibcode 2009IJAM...01..737M. doi:10.1142/S1758825109000381. http://www.worldscinet.com/ijam/01/0104/S1758825109000381.html.
 ^ Dissipative Particle Dynamics: Addressing deficiencies and establishing new frontiers, CECAM workshop, July 16–18, 2008, Lausanne, Switzerland.
Available packages
Some available simulation packages that can (also) perform DPD simulations are
 Culgi: A multiscale modeling tool for chemist, Culgi BV.
 Fluidix: The Fluidix simulation suite available from OneZero Software.
 Materials Studio: Materials Studio  Modeling and simulation for studying chemicals and materials, Accelrys Software Inc.
 DL_MESO: Opensource mesoscale simulation software.
 GPIUTMD: Graphical processors for ManyParticle Dynamics
 LAMMPS
 ESPResSo
 DPDmacs
 SciDPD in the MAPS suite of Scienomics
External links
Categories: Condensed matter physics
 Soft matter
 Computational fluid dynamics
 NonNewtonian fluids
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