Dissipative particle dynamics
Encyclopedia
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 to avoid the lattice artifacts of the so-called 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 to ensure the proper thermal equilibrium state.
DPD is an off-lattice 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.
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 non-bonded 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.
flow properties of the fluid to its microscopic structure. Such DPD applications range from modelling the rheological properties of concrete to simulating liposome formation in biophysics. Other recent three-phase phenomena such as dynamic wetting.
The state-of-the-art in DPD was captured in a CECAM workshop in 2008. Innovations to the technique presented there include DPD with energy conservation; non-central 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
.
Cellular automaton
A cellular automaton is a discrete model studied in computability theory, mathematics, physics, complexity science, theoretical biology and microstructure modeling. It consists of a regular grid of cells, each in one of a finite number of states, such as "On" and "Off"...
and to tackle hydrodynamic time and space scales beyond those available with molecular dynamics
Molecular dynamics
Molecular dynamics is a computer simulation of physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a period of time, giving a view of the motion of the atoms...
(MD). It was subsequently reformulated and slightly modified by Español to ensure the proper thermal equilibrium state.
DPD is an off-lattice 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.
Equations
The total non-bonded force acting on a DPD particle i is given by a sum over all particles j that lie within a fixed cut-off distance, of three pairwise-additive 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 non-bonded 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
Particle number
The particle number of a thermodynamic system, conventionally indicated with the letter N, is the number of constituent particles in that system. The particle number is a fundamental parameter in thermodynamics which is conjugate to the chemical potential. Unlike most physical quantities, particle...
, 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 Beowulf-style cluster. Because the non-bonded forces are short-ranged 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 particle-particle interactions that require inter-processor communication be much smaller than the number of particle-particle 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 cut-off 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 non-NewtonianNon-Newtonian fluid
A non-Newtonian fluid is a fluid whose flow properties differ in any way from those of Newtonian fluids. Most commonly the viscosity of non-Newtonian fluids is not independent of shear rate or shear rate history...
flow properties of the fluid to its microscopic structure. Such DPD applications range from modelling the rheological properties of concrete to simulating liposome formation in biophysics. Other recent three-phase phenomena such as dynamic wetting.
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"The state-of-the-art in DPD was captured in a CECAM workshop in 2008. Innovations to the technique presented there include DPD with energy conservation; non-central 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
Molecular dynamics
Molecular dynamics is a computer simulation of physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a period of time, giving a view of the motion of the atoms...
.
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 StudioMaterials StudioMaterials Studio is software for simulating and modeling materials developed and distributed by Accelrys, a company specializing in research software for computational chemistry, bioinformatics, cheminformatics, molecular simulation, and quantum mechanics....
: Materials Studio - Modeling and simulation for studying chemicals and materials, Accelrys Software Inc. - DL_MESO: Open-source mesoscale simulation software.
- GPIUTMD: Graphical processors for Many-Particle Dynamics
- LAMMPSLAMMPSLAMMPS is a molecular dynamics program from Sandia National Laboratories.. LAMMPS makes use of MPI for parallel communication and is a free open-source code, distributed under the terms of the GNU General Public License.LAMMPS was originally developed under a Cooperative Research and Development...
- ESPResSoEspressoEspresso is a concentrated beverage brewed by forcing a small amount of nearly boiling water under pressure through finely ground coffee. Espresso is widely known throughout the world....
- DPDmacs
- SciDPD in the MAPS suite of Scienomics