547 research outputs found
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 in non-conservative fluid-type systems, of the generic form,
+\int^\infty_0 dt V^{-1} \av{I_\epsilon \exp(t {\cal L})
I}_0 where is a pseudo-streaming operator. It consists of a
sum of an instantaneous transport coefficient , and a time integral
over a time correlation function in a state of thermal equilibrium between a
current and its conjugate current . This formula with
and 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 in complex fluids of the generic form, , i.e.
a sum of an instantaneous transport coefficient , and a time
integral over a time correlation function in a state of thermal equilibrium
between a current and a transformed current . The streaming
operator generates the trajectory of a dynamical variable
when used inside the thermal average . 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 and ,
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
- …