We critically review dissipative particle dynamics (DPD) as a mesoscopic simulation method. We have established useful parameter ranges for simulations, and have made a link between these parameters and χ-parameters in Flory-Huggins-type models. This is possible because the equation of state of the DPD fluid is essentially quadratic in density. This link opens the way to do large scale simulations, effectively describing millions of atoms, by firstly performing simulations of molecular fragments retaining all atomistic details to derive χ-parameters, then secondly using these results as input to a DPD simulation to study the formation of micelles, networks, mesophases and so forth. As an example application, we have calculated the interfacial tension σ between homopolymer melts as a function of χ and N and have found a universal scaling collapse when σ/ρkBTχ0.4 is plotted against χN for N>1. We also discuss the use of DPD to simulate the dynamics of mesoscopic systems, and indicate a possible problem with the timescale separation between particle diffusion and momentum diffusion (viscosity).

PACS. 02.70 -c -Computational techniques.PACS. 51.10+y -Kinetic and transport theory of gases.Abstract. -The stochastic differential equations corresponding to the updating algorithm of Dissipative Particle Dynamics (DPD), and the corresponding Fokker-Planck equation are derived. It is shown that a slight modification to the algorithm is required before the Gibbs distribution is recovered as the stationary solution to the Fokker-Planck equation. The temperature of the system is then directly related to the noise amplitude by means of a fluctuation-dissipation theorem. However, the correspondingly modified, discrete DPD algorithm is only found to obey these predictions if the length of the time step is sufficiently reduced. This indicates the importance of time discretisation in DPD.

PACS. 82.70 -Disperse systems. PACS. 64.75 -Solubility, segregation, and mixing.Abstract. -A new treatment of the phase behaviour of a colloid + nonadsorbing polymer mixture is described. The calculated phase diagrams show marked polymer partitioning between coexisting phases, an effect not considered in the usual effective-potential approaches to this problem. We also predict that under certain conditions an area of three-phase coexistence should appear in the phase diagram.Introduction. -Phase separation in colloidal suspensions, induced by the addition of nonadsorbing polymer, is a phenomenon of fundamental interest and considerable technological importance. A theoretical explanation was first advanced by Asakura and Oosawa [1], and also independently by Vrij [2], based on the exclusion of polymer from the region between two colloid particles when their surface-surface separation becomes smaller than the diameter of a free polymer coil. The resulting imbalance in osmotic pressure gives rise to an effective attractive «depletion» force between the colloid particles [3,4]. At high enough concentration of polymer this depletion force causes the suspension to separate into colloid-poor and colloid-rich phases. In the latter the particles can, depending on conditions (see below), be in either liquidlike or crystalline spatial arrangements.To predict the phase diagram of a colloid + polymer mixture, most workers to date have adopted an approach in which the depletion potential (an effective pair potential) is added to the parent interparticle potential; thermodynamic perturbation theory is then used to calculate phase stability boundaries [5,6]. Although experimental studies [6,7] show qualitative agreement with the predictions of these calculations, an important reservation

Bistable biochemical switches are widely found in gene regulatory networks and signal transduction pathways. Their switching dynamics are difficult to study, however, because switching events are rare, and the systems are out of equilibrium. We present a simulation method for predicting the rate and mechanism of the flipping of these switches. We apply it to a genetic switch and find that it is highly efficient. The path ensembles for the forward and reverse processes do not coincide. The method is widely applicable to rare events and nonequilibrium processes.