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

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

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