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Dissipative particle dynamics

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DPD was initially devised by Hoogerbrugge and Koelman to avoid the lattice artifacts of lattice gas automata and to tackle hydrodynamic time and space scales beyond those available with molecular dynamics (MD). It was subsequently reformulated by P. Español, who derived it with a Langevin equation framework and demonstrated that the fluctuation-dissipation relation must hold in order for DPD to sample canonical ensemble at equilibrium, thereby laying the theoretical foundation of the method. A series of new DPD algorithms with reduced computational complexity and better control of transport properties has emerged in recent years. Some of them chose randomly a pair particle for applying DPD thermostating thus reducing the computational complexity.

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:

fi=∑j≠i(FijC+FijD+FijR)

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.

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