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.

/pdf/patterns-and-collective-behavior-in-granular-media-2t8b6sr2ja.pdf

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

Mass transport in a dilute binary mixture of Maxwell molecules under steady shear flow is studied. The analysis is made from an exact perturbation solution of the Boltzmann equation through first order in the concentration gradient. The reference state ~zeroth order approximation ! corresponds to the exact recent solution @Phys. Rev. E52, 3812 ~1995!# of the Boltzmann equation in the uniform shear flow, which holds for arbitrary values of the shear rate. The results show that the mass flux obeys a generalized Fick’s law where, due to the anisotropy of the problem, a mutual diffusion tensor is defined. This tensor is a highly nonlinear function of the shear rate and the parameters of the mixture ~particle masses, concentrations, and force constants !. The calculations presented here extend previous results derived in the limit cases of self-diffusion and tracer particles.@S1063-651X~98!02601-4#

Mutual diffusion in a binary mixture under shear flow

Coupling between shear flow and temperature gradient for the very hard particles interaction

Recently, the color diffusion in uniform shear flow has been analyzed from the Boltzmann equation [V. Garzo and A. Santos, J. Chem. Phys. 97, 2039 (1992)]. Here, the analysis is generalized to allow for a shear‐rate dependence of the color field, which yields a zero‐field limit of the color conductivity tensor identical to the self‐diffusion tensor.

Color conductivity induced by a shear‐rate dependent color field

We get a solution of the Bhatnagar-Gross-Krook (BGK) model kinetic equation by means of a perturbative expansion of a temperature gradient to study the transport properties in a gas with large shear rate. The irreversible fluxes are evaluated exactly to first order in the expansion for Maxwell molecules. The transport coefficients obtained are highly nonlinear functions of the shear rate. This dependence on shear rate is analysed and compared with previous results for several transport coefficients. Finally, we have found a solution for a simple model of constant collision frequency for which a large shear rate coexists with an arbitrary temperature gradient.

Generalized transport coefficients in a gas with large shear rate

The Navier-Stokes transport coefficients for a granular gas of smooth inelastic hard disks or spheres are determined from the inelastic Boltzmann equation by means of Grad's moment method. The shear viscosity η, the thermal conductivity κ and the new transport coefficient μ (not present for elastic collisions) are explicitly obtained as nonlinear functions of the (constant) coefficient of restitution α. The expressions of η, κ, and μ agree with those previously obtained from the Chapman-Enskog method by using the first Sonine approximation. A comparison with previous results derived from Grad's moment method for two and three dimensions is also carried out.

Vicente Garzó

Papers

Mutual diffusion in a binary mixture under shear flow

Coupling between shear flow and temperature gradient for the very hard particles interaction

Color conductivity induced by a shear‐rate dependent color field

Generalized transport coefficients in a gas with large shear rate

Grad's moment method for a low-density granular gas. Navier-Stokes transport coefficients