New Green-Kubo formulas for transport coefficients in hard sphere-, Langevin fluids and the likes

We present generalized Green-Kubo expressions for thermal transport coefficients $\mu$ in non-conservative fluid-type systems, of the generic form, $\mu$ $= \mu_\infty$ +\int^\infty_0 dt V^{-1} \av{I_\epsilon \exp(t {\cal L}) I}_0 where $\exp(t{\cal L})$ is a pseudo-streaming operator. It consists of a sum of an instantaneous transport coefficient $\mu_\infty$, and a time integral over a time correlation function in a state of thermal equilibrium between a current $I$ and its conjugate current $I_\epsilon$. This formula with $\mu_\infty \neq 0$ and $I_\epsilon \neq I$ covers vastly different systems, such as strongly repulsive elastic interactions in hard sphere fluids, weakly interacting Langevin fluids with dissipative and stochastic interactions satisfying detailed balance conditions, and "the likes", defined in the text. For conservative systems the results reduce to the standard formulas.Comment: 7 pages, no figures. Version 2: changes in the text and references adde

Foundations of Dissipative Particle Dynamics

We derive a mesoscopic modeling and simulation technique that is very close to the technique known as dissipative particle dynamics. The model is derived from molecular dynamics by means of a systematic coarse-graining procedure. Thus the rules governing our new form of dissipative particle dynamics reflect the underlying molecular dynamics; in particular all the underlying conservation laws carry over from the microscopic to the mesoscopic descriptions. Whereas previously the dissipative particles were spheres of fixed size and mass, now they are defined as cells on a Voronoi lattice with variable masses and sizes. This Voronoi lattice arises naturally from the coarse-graining procedure which may be applied iteratively and thus represents a form of renormalisation-group mapping. It enables us to select any desired local scale for the mesoscopic description of a given problem. Indeed, the method may be used to deal with situations in which several different length scales are simultaneously present. Simulations carried out with the present scheme show good agreement with theoretical predictions for the equilibrium behavior.Comment: 18 pages, 7 figure

Thermodynamically admissible form for discrete hydrodynamics

We construct a discrete model of fluid particles according to the GENERIC formalism. The model has the form of Smoothed Particle Hydrodynamics including correct thermal fluctuations. A slight variation of the model reproduces the Dissipative Particle Dynamics model with any desired thermodynamic behavior. The resulting algorithm has the following properties: mass, momentum and energy are conserved, entropy is a non-decreasing function of time and the thermal fluctuations produce the correct Einstein distribution function at equilibrium.Comment: 4 page

Generalized Green-Kubo formulas for fluids with impulsive, dissipative, stochastic and conservative interactions

We present a generalization of the Green-Kubo expressions for thermal transport coefficients $\mu$ in complex fluids of the generic form, $\mu= \mu_\infty +\int^\infty_0 dt V^{-1} _0$, i.e. a sum of an instantaneous transport coefficient $\mu_\infty$, and a time integral over a time correlation function in a state of thermal equilibrium between a current $J$ and a transformed current $J_\epsilon$. The streaming operator $\exp(t{\cal L})$ generates the trajectory of a dynamical variable $J(t) =\exp(t{\cal L}) J$ when used inside the thermal average $_0$. These formulas are valid for conservative, impulsive (hard spheres), stochastic and dissipative forces (Langevin fluids), provided the system approaches a thermal equilibrium state. In general $\mu_\infty \neq 0$ and $J_\epsilon \neq J$, except for the case of conservative forces, where the equality signs apply. The most important application in the present paper is the hard sphere fluid.Comment: 14 pages, no figures. Version 2: expanded Introduction and section II specifying the classes of fluids covered by this theory. Some references added and typos correcte

Efficient numerical integrators for stochastic models

The efficient simulation of models defined in terms of stochastic differential equations (SDEs) depends critically on an efficient integration scheme. In this article, we investigate under which conditions the integration schemes for general SDEs can be derived using the Trotter expansion. It follows that, in the stochastic case, some care is required in splitting the stochastic generator. We test the Trotter integrators on an energy-conserving Brownian model and derive a new numerical scheme for dissipative particle dynamics. We find that the stochastic Trotter scheme provides a mathematically correct and easy-to-use method which should find wide applicability.Comment: v

On the microscopic foundation of dissipative particle dynamics

Mesoscopic particle based fluid models, such as dissipative particle dynamics, are usually assumed to be coarse-grained representations of an underlying microscopic fluid. A fundamental question is whether there exists a map from microscopic particles in these systems to the corresponding coarse-grained particles, such that the coarse-grained system has the same bulk and transport properties as the underlying system. In this letter, we investigate the coarse-graining of microscopic fluids using a Voronoi type projection that has been suggested in several studies. The simulations show that the projection fails in defining coarse-grained particles that have a physically meaningful connection to the microscopic fluid. In particular, the Voronoi projection produces identical coarse-grained equilibrium properties when applied to systems with different microscopic interactions and different bulk properties.Comment: First revisio

Vapour-liquid coexistence in many-body dissipative particle dynamics

Many-body dissipative particle dynamics is constructed to exhibit vapour-liquid coexistence, with a sharp interface, and a vapour phase of vanishingly small density. In this form, the model is an unusual example of a soft-sphere liquid with a potential energy built out of local-density dependent one-particle self energies. The application to fluid mechanics problems involving free surfaces is illustrated by simulation of a pendant drop.Comment: 8 pages, 6 figures, revtex

Non-affine motion and selection of slip coefficient in constitutive modeling of polymeric solutions using a mixed derivative

Constitutive models for the dynamics of polymer solutions traditionally rely on closure relations for the extra stress or related microstructural variables (e.g., conformation tensor) linking them to flow history. In this work, we study the eigendynamics of the conformation tensor within the GENERIC framework in mesoscopic computer simulations of polymer solutions to separate the effects of nonaffine motion from other sources of non-Newtonian behavior. We observe that nonaffine motion or slip increases with both the polymer concentration and the polymer chain length. Our analysis allows to uniquely calibrate a mixed derivative of the Gordon-Schowalter type in macroscopic models based on a micro-macromapping of the dynamics of the polymeric system. The presented approach paves the way for better polymer constitutive modeling in multiscale simulations of polymer solutions, where different sources of non-Newtonian behavior are modelled independently