No abstract

The force autocorrelation function of an infinitely massive Brownian particle is studied with a molecular dynamics simulation. The plateau time problem, the calculation of the friction coefficient, and the relationship between the stochastic and real force are discussed.

We present a model for treating solid boundaries of a DPD fluid. The basic idea is to model the stick boundary conditions by assuming that a layer of DPD particles is stuck on the boundary. By taking a continuum limit of this layer effective dissipative and stochastic forces on the fluid DPD particles are obtained. The boundary model is tested by a simulation of planar Couette flow which allows the performance of vicosimetric measurements. We analyze the conditions that ensure a proper stick boundary condition for an impenetrable wall, comparing with previous methods used.

By using the standard theory of coarse graining based on Zwanzig's projection operator, we derive the dynamic equations for discrete hydrodynamic variables. These hydrodynamic variables are defined in terms of the Delaunay triangulation. The resulting microscopically derived equations can be understood, a posteriori, as a discretization on an arbitrary irregular grid of the Navier-Stokes equations. The microscopic derivation provides a set of discrete equations that exactly conserves mass, momentum, and energy and the dissipative part of the dynamics produces strict entropy increase. In addition, the microscopic derivation provides a practical implementation of thermal fluctuations in a way that the fluctuation-dissipation theorem is satisfied exactly. This paper points toward a close connection between coarse-graining procedures from microscopic dynamics and discretization schemes for partial differential equations.

We propose a coarse-graining procedure for a fluid system that allows us to discuss from a conceptual point of view different "mesoscopic" approaches to hydrodynamic problems. Dissipative Particle Dynamics (DPD) and Smoothed Particle Dynamics (SPS) are discussed simultaneously within this framework. In particular, we give physical meaning to the weight function used in SPD. The close analogy between DPD and SPD suggests a synthesis of both approaches that overcomes the conceptual shortcomings of both.