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

Multiscale non-adiabatic dynamics with radiative decay, case study on the post-ionization fragmentation of rare-gas tetramers

In this supplementary material, we recollect, for reader's convenience, the general scheme of suggested multiscale model (Sec. 1), and basic informations about approaches used for pilot study: a detailed description of the interaction model (Sec. 2) and dynamical methods used for the dark dynamics step (Sec. 3) reported previously in two preceding studies [1, 2]. In addition, a detailed description of the treatment of radiative processes is also given (Sec. 4).Comment: supplementary material for parent paper; 9 pages, 1 figure; corrected formulae and misleading notation in Sec.4 (pages 7 and 8

Capillary Rise in Nanopores: Molecular Dynamics Evidence for the Lucas-Washburn Equation

When a capillary is inserted into a liquid, the liquid will rapidly flow into it. This phenomenon, well studied and understood on the macroscale, is investigated by Molecular Dynamics simulations for coarse-grained models of nanotubes. Both a simple Lennard-Jones fluid and a model for a polymer melt are considered. In both cases after a transient period (of a few nanoseconds) the meniscus rises according to a $\sqrt{\textrm{time}}$-law. For the polymer melt, however, we find that the capillary flow exhibits a slip length $\delta$, comparable in size with the nanotube radius $R$. We show that a consistent description of the imbibition process in nanotubes is only possible upon modification of the Lucas-Washburn law which takes explicitly into account the slip length $\delta$.Comment: 4 pages 4 figure

Consistent particle-based algorithm with a non-ideal equation of state

A thermodynamically consistent particle-based model for fluid dynamics with continuous velocities and a non-ideal equation of state is presented. Excluded volume interactions are modeled by means of biased stochastic multiparticle collisions which depend on the local velocities and densities. Momentum and energy are exactly conserved locally. The equation of state is derived and compared to independent measurements of the pressure. Results for the kinematic shear viscosity and self-diffusion constants are presented. A caging and order/disorder transition is observed at high densities and large collision frequency.Comment: 7 pages including 4 figure

Particle-Based Mesoscale Hydrodynamic Techniques

Dissipative particle dynamics (DPD) and multi-particle collision (MPC) dynamics are powerful tools to study mesoscale hydrodynamic phenomena accompanied by thermal fluctuations. To understand the advantages of these types of mesoscale simulation techniques in more detail, we propose new two methods, which are intermediate between DPD and MPC -- DPD with a multibody thermostat (DPD-MT), and MPC-Langevin dynamics (MPC-LD). The key features are applying a Langevin thermostat to the relative velocities of pairs of particles or multi-particle collisions, and whether or not to employ collision cells. The viscosity of MPC-LD is derived analytically, in very good agreement with the results of numerical simulations.Comment: 7 pages, 2 figures, 1 tabl

A reduced model for shock and detonation waves. I. The inert case

We present a model of mesoparticles, very much in the Dissipative Particle Dynamics spirit, in which a molecule is replaced by a particle with an internal thermodynamic degree of freedom (temperature or energy). The model is shown to give quantitavely accurate results for the simulation of shock waves in a crystalline polymer, and opens the way to a reduced model of detonation waves

Dissipative Particle Dynamics with energy conservation

Dissipative particle dynamics (DPD) does not conserve energy and this precludes its use in the study of thermal processes in complex fluids. We present here a generalization of DPD that incorporates an internal energy and a temperature variable for each particle. The dissipation induced by the dissipative forces between particles is invested in raising the internal energy of the particles. Thermal conduction occurs by means of (inverse) temperature differences. The model can be viewed as a simplified solver of the fluctuating hydrodynamic equations and opens up the possibility of studying thermal processes in complex fluids with a mesoscopic simulation technique.Comment: 5 page

Evolution of displacements and strains in sheared amorphous solids

The local deformation of two-dimensional Lennard-Jones glasses under imposed shear strain is studied via computer simulations. Both the mean squared displacement and mean squared strain rise linearly with the length of the strain interval $\Delta \gamma$ over which they are measured. However, the increase in displacement does not represent single-particle diffusion. There are long-range spatial correlations in displacement associated with slip lines with an amplitude of order the particle size. Strong dependence on system size is also observed. The probability distributions of displacement and strain are very different. For small $\Delta \gamma$ the distribution of displacement has a plateau followed by an exponential tail. The distribution becomes Gaussian as $\Delta \gamma$ increases to about .03. The strain distributions consist of sharp central peaks associated with elastic regions, and long exponential tails associated with plastic regions. The latter persist to the largest $\Delta \gamma$ studied.Comment: Submitted to J. Phys. Cond. Mat. special volume for PITP Conference on Mechanical Behavior of Glassy Materials. 16 Pages, 8 figure

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