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Smoothed Dissipative Particle Dynamics (SDPD) is a mesoscopic method which allows to select the level of resolution at which a fluid is simulated. In this work, we study the consistency of the resulting thermodynamic properties as a function of the size of the mesoparticles, both at equilibrium and out of equilibrium. We also propose a reformulation of the SDPD equations in terms of energy variables. This increases the similarities with Dissipative Particle Dynamics with Energy conservation and opens the way for a coupling between the two methods. Finally, we present a numerical scheme for SDPD that ensures the conservation of the invariants of the dynamics. Numerical simulations illustrate this approach.
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Dissipative particle dynamics (DPD) belongs to a class of models and computational algorithms developed to address mesoscale problems in complex fluids and soft matter in general. It is based on the notion of particles that represent coarse-grained portions of the system under study and allow, therefore, to reach time and length scales that would be otherwise unreachable from microscopic simulations. The method has been conceptually refined since its introduction almost twenty five years ago. This perspective surveys the major conceptual improvements in the original DPD model, along with its microscopic foundation, and discusses outstanding challenges in the field. We summarize some recent advances and suggests avenues for future developments.
The algorithm for the DPD fluid, the dynamics of which is conceptually a combination of molecular dynamics, Brownian dynamics and lattice gas automata, is designed for simulating rheological properties of complex fluids on hydrodynamic time scales. This paper calculates the equilibrium and transport properties (viscosity, self-diffusion) of the thermostated DPD fluid explicitly in terms of the system parameters. It is demonstrated that temperature gradients cannot exist, and that there is therefore no heat conductivity. Starting from the N-particle Fokker-Planck, or Kramers equation, we prove an H-theorem for the free energy, obtain hydrodynamic equations, and derive a non-linear kinetic equation (the Fokker-Planck-Boltzmann equation) for the single particle distribution function. This kinetic equation is solved by the Chapman-Enskog method. The analytic results are compared with numerical simulations.
The algorithm for Dissipative Particle Dynamics (DPD), as modified by Espagnol and Warren, is used as a starting point for proving an H-theorem for the free energy and deriving hydrodynamic equations. Equilibrium and transport properties of the DPD fluid are explicitly calculated in terms of the system parameters for the continuous time version of the model.
We present exact and asymptotic results for clusters in the one-dimensional totally asymmetric exclusion process (TASEP) with two different dynamics. The expected length of the largest cluster is shown to diverge logarithmically with increasing system size for ordinary TASEP dynamics and as a logarithm divided by a double logarithm for generalized dynamics, where the hopping probability of a particle depends on the size of the cluster it belongs to. The connection with the asymptotic theory of extreme order statistics is discussed in detail. We also consider a related model of interface growth, where the deposited particles are allowed to relax to the local gravitational minimum.
This article presents a new numerical scheme for the discretization of dissipative particle dynamics with conserved energy. The key idea is to reduce elementary pairwise stochastic dynamics (either fluctuation/dissipation or thermal conduction) to effective single-variable dynamics, and to approximate the solution of these dynamics with one step of a Metropolis-Hastings algorithm. This ensures by construction that no negative internal energies are encountered during the simulation, and hence allows to increase the admissible timesteps to integrate the dynamics, even for systems with small heat capacities. Stability is only limited by the Hamiltonian part of the dynamics, which suggests resorting to multiple timestep strategies where the stochastic part is integrated less frequently than the Hamiltonian one.
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