N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

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Fluctuation-dissipation: Response theory in statistical physics

Granular materials are ubiquitous in our daily lives. While they have been the subject of intensive engineering research for centuries, in the last two decades granular matter has attracted significant attention from physicists. Yet despite major efforts by many groups, the theoretical description of granular systems remains largely a plethora of different, often contradictory concepts and approaches. Various theoretical models have emerged for describing the onset of collective behavior and pattern formation in granular matter. This review surveys a number of situations in which nontrivial patterns emerge in granular systems, elucidates important distinctions between these phenomena and similar ones occurring in continuum fluids, and describes general principles and models of pattern formation in complex systems that have been successfully applied to granular systems.

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Patterns and collective behavior in granular media: Theoretical concepts

▪ Abstract The recent avalanche of research activity in the field of granular matter has yielded much progress. The use of state-of-the-art (and other) computational and experimental methods has led to the discovery of new states and patterns and enabled detailed tests of theories and models. The application of statistical mechanical methods and phenomenology has contributed to the understanding of the microscopic a nd macroscopic properties of granular systems. Some previously open problems seem to be solved. Fluidized granular systems (rapid granular flows), recently referred to as granular gases, are often modeled by hydrodynamic equations of motion, some of which are based on systematic expansions applied to the pertinent Boltzmann equation. The undeniable success of granular hydrodynamics is somewhat surprising in view of the lack of scale separation in these systems and the neglect of certain correlations in most derivations of the hydrodynamic equations. Microstructures have been recognized as key ...

Rapid granular flows

A linear stability analysis of the hydrodynamic equations with respect to the homogeneous cooling state is performed to study the conditions for stability of a suspension of solid particles immersed in a viscous gas. The dissipation in such systems arises from two different sources: inelasticity in particle collisions and viscous friction dissipation due to the influence of gas phase on solid particles. The starting point is a suspension model based on the (inelastic) Enskog kinetic equation where the effect of the interstitial gas phase on the dynamics of grains is modeled via a viscous drag force. The study is carried out in two different steps. First, the transport coefficients of the system are obtained by solving the Enskog equation by means of the Chapman-Enskog method up to first order in spatial gradients. Once the transport properties are known, then the corresponding linearized hydrodynamic equations are solved to get the dispersion relations. In contrast to previous studies [V. Garzo \emph{et al.}, Phys. Rev. E \textbf{93}, 012905 (2016)], the hydrodynamic modes are \emph{analytically} obtained as functions of the parameter space of the system. As expected, linear stability shows $d-1$ transversal (shear) modes (where $d$ is the dimensionality of the system) and a longitudinal "heat" mode to be unstable with respect to long enough wavelength excitations. The results also show that the main effect of gas phase is to decrease the value of the critical length $L_c$ (beyond which the system becomes unstable) with respect to its value for a dry granular fluid. Comparison with direct numerical simulations for $L_c$ shows a good agreement for conditions of practical interest.

Instabilities in granular gas-solid flows

The Boltzmann equation for $d$-dimensional inelastic Maxwell models is considered to analyze transport properties for monodisperse gas-solid suspensions. The influence of the interstitial gas phase on the dynamics of solid particles is modeled via a viscous drag force. The Chapman-Enskog method is applied to solve the inelastic Boltzmann equation to first order in the deviations of the hydrodynamic fields from their values in the homogeneous cooling state. Explicit expressions for the Navier-Stokes transport coefficients are \emph{exactly} obtained in terms of both the coefficient of restitution and the friction coefficient characterizing the amplitude of the external force. The conditions under which a hydrodynamic regime independent of the initial conditions is reached are widely discussed. Finally, the results derived here are compared with those previously obtained for inelastic hard spheres in steady state conditions by using the so-called first Sonine approximation.

Inelastic Maxwell models for monodisperse gas-solid flows

We study in this work the dynamics of a granular impurity immersed in a low-density granular gas of identical particles For description of the kinetics of the granular gas and the impurity particles we use the rough hard sphere collisional model We take into account the effects of non-conservation of energy upon particle collision We find an (approximate) analytical solution of the pertinent kinetic equations for the single-particle velocity distribution functions that reproduces reasonably well the properties of translational/rotational energy non-equipartition We assess the accuracy of the theoretical solution by comparing with computer simulations For this, we use two independent computer data sets, from molecular dynamics (MD) and from Direct Simulation Monte Carlo method (DSMC) Both approach well, with different degrees, the kinetic theory within a reasonable range of parameter values

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Vicente Garzó

Papers

Instabilities in granular gas-solid flows

Inelastic Maxwell models for monodisperse gas-solid flows

Thermal properties of an impurity immersed in a granular gas of rough hard spheres