We investigate the hydrodynamic properties of a fluid simulated with a mesoscopic solvent model. Two distinct regimes are identified, the "particle regime" in which the dynamics is gas-like, and the "collective regime" where the dynamics is fluid-like. This behavior can be characterized by the Schmidt number, which measures the ratio between viscous and diffusive transport. Analytical expressions for the tracer diffusion coefficient, which have been derived on the basis of a molecularchaos assumption, are found to describe the simulation data very well in the particle regime, but important deviations are found in the collective regime. These deviations are due to hydrodynamic correlations. The model is then extended in order to investigate self-diffusion in colloidal dispersions. We study first the transport properties of heavy point-like particles in the mesoscopic solvent, as a function of their mass and number density. Second, we introduce excluded-volume interactions among the colloidal particles and determine the dependence of the diffusion coefficient on the colloidal volume fraction for different solvent mean-free paths. In the collective regime, the results are found to be in good agreement with previous theoretical predictions based on Stokes hydrodynamics and the Smoluchowski equation.

Hydrodynamic interactions in complex fluids are investigated by the multiparticle-collision-dynamics algorithm, a mesoscopic simulation technique. The diffusive dynamics of simple fluids is studied, and the diffusion coefficient is calculated as a function of the mean free path of a particle. For small mean free paths, we observe strong effects due to hydrodynamic interactions among the fluid particles. These results are then used to study the dynamics of short polymer chains in solution. For an appropriate choice of the mean free path of the solvent, we obtain excellent agreement of our simulation results with the predictions of Zimm theory for the center-of-mass diffusion coefficient and the relaxation times of the Rouse modes.

We study the dynamics of flexible polymer chains in solution by combining multiparticle-collision dynamics (MPCD), a mesoscale simulation method, and molecular-dynamics simulations. Polymers with and without excluded-volume interactions are considered. With an appropriate choice of the collision time step for the MPCD solvent, hydrodynamic interactions build up properly. For the center-of-mass diffusion coefficient, scaling with respect to polymer length is found to hold already for rather short chains. The center-of-mass velocity autocorrelation function displays a long-time tail which decays algebraically as (Dt)(-3/2) as a function of time t, where D is the diffusion coefficient. The analysis of the intramolecular dynamics in terms of Rouse modes yields excellent agreement between simulation data and results of the Zimm model for the mode-number dependence of the mode-amplitude correlation functions.

The effect of the hydrodynamic interaction on the dynamics of flexible and rod-like polymers in solution is investigated. The solvent is simulated by the multi-particle-collision dynamics (MPCD) algorithm, a mesoscale simulation technique. The dynamics of the solvent is studied and the self-diffusion coefficient is calculated as a function of the mean free path of a particle. At small mean free paths, the hydrodynamic interaction strongly influences the dynamics of the fluid particles. This solvent model is then coupled to a molecular dynamics simulation algorithm. We obtain excellent agreement between our simulation results for a flexible polymer and the predictions of Zimm theory. The study of the translational diffusion coefficient of rod-like polymers confirms the predicted chain-length dependence. In addition, we study the influence of shear on the structural properties of rod-like polymers. For shear rates exceeding the rotational relaxation time, the rod-like molecule aligns with the shear flow, leading to an orientational symmetry breaking transverse to the flow direction. The comparison of the obtained shear rate dependencies with theoretical predictions exhibits significant deviations. The properties of the orientational tensor and the rotational velocity are discussed in detail as a function of shear rate.

Hopping motion of particles on linear chains under the influence of bias is considered where the transition rates represent arbitrary potentials. An exact expression for the stationary current is given and verified by numerical simulations. It exhibits rectification effects for nonsymmetric potentials in the regime of strong bias. Applications to two-and three-dimensional systems are indicated. ͓S1063-651X͑97͒50909-3͔ PACS number͑s͒: 05.40.ϩj, 68.35.Fx, 87.22.Fy The motion of particles in nonsymmetric potentials under the influence of stochastic forces is of great current interest for several reasons. One problem is to understand the conditions under which unidirectional motion of the particles can occur. Apparently, there is a connection of this problem to the second law of thermodynamics ͓1,2͔. In addition, there are interesting relations between this model and, e.g., biological systems ͓2-8͔ or surface diffusion problems ͓9,10͔. There is agreement that under the influence of thermal noise a particle in a static nonsymmetric potential without bias will not move uniformly in one direction. In the presence of fluctuating external forces with sufficiently long correlation times, however, unidirectional motion can arise; that is, such potentials exhibit rectification properties with respect to the slowly varying components of the external force. Most of the previous work in this area is based on continuous diffusion models that are defined in terms of Langevin-type equations of motion ͓2-5,7,8,11-13͔. However, the apparent relevance of such models to problems of transport on microscopic scales suggest a treatment that at least in principle can account for a specific microscopic environment. The simplest microscopic models may be defined as hopping models for particles on linear chains with discrete binding sites and potential barriers in between.From this point of view we investigate in this paper the hopping motion of particles in a one-dimensional discrete model without inversion symmetry under the influence of an arbitrary bias in one direction. We will give a quantitative description of rectification effects that can appear in the region of nonlinear response. Rectification effects from a rate equation model for carrier-mediated transport through channels of biological membranes have been discussed previously ͓14͔. Here we treat hopping of particles in an arbitrary sequence of barriers and trapping sites under periodic boundary conditions. Hence, our calculations are also valid for periodic repetitions of potential structures without inversion symmetry. We emphasize that our derivations give a microscopic description of rectification effects of hopping motion through nonsymmetric potentials. Possible applications of our model are outlined at the end of this paper.Consider a chain consisting of Nϩ1 sites lϭ0, . . . ,N with site energies E l , where we assume periodic boundary conditions, i.e., E 0 ϭE N . In the stationary situation, the current between site l and lϩ1 is given in terms of the site occupation p...