We present an overview of the lattice Boltzmann method (LBM), a parallel and efficient algorithm for simulating single-phase and multiphase fluid flows and for incorporating additional physical complexities. The LBM is especially useful for modeling complicated boundary conditions and multiphase interfaces. Recent extensions of this method are described, including simulations of fluid turbulence, suspension flows, and reaction diffusion systems.

Lattice boltzmann method for fluid flows

The calculation of rate coefficients is a discipline of nonlinear science of importance to much of physics, chemistry, engineering, and biology. Fifty years after Kramers' seminal paper on thermally activated barrier crossing, the authors report, extend, and interpret much of our current understanding relating to theories of noise-activated escape, for which many of the notable contributions are originating from the communities both of physics and of physical chemistry. Theoretical as well as numerical approaches are discussed for single- and many-dimensional metastable systems (including fields) in gases and condensed phases. The role of many-dimensional transition-state theory is contrasted with Kramers' reaction-rate theory for moderate-to-strong friction; the authors emphasize the physical situation and the close connection between unimolecular rate theory and Kramers' work for weakly damped systems. The rate theory accounting for memory friction is presented, together with a unifying theoretical approach which covers the whole regime of weak-to-moderate-to-strong friction on the same basis (turnover theory). The peculiarities of noise-activated escape in a variety of physically different metastable potential configurations is elucidated in terms of the mean-first-passage-time technique. Moreover, the role and the complexity of escape in driven systems exhibiting possibly multiple, metastable stationary nonequilibrium states is identified. At lower temperatures, quantum tunneling effects start to dominate the rate mechanism. The early quantum approaches as well as the latest quantum versions of Kramers' theory are discussed, thereby providing a description of dissipative escape events at all temperatures. In addition, an attempt is made to discuss prominent experimental work as it relates to Kramers' reaction-rate theory and to indicate the most important areas for future research in theory and experiment.

Reaction-rate theory: fifty years after Kramers

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

Since the subject of traffic dynamics has captured the interest of physicists, many surprising effects have been revealed and explained. Some of the questions now understood are the following: Why are vehicles sometimes stopped by ``phantom traffic jams'' even though drivers all like to drive fast? What are the mechanisms behind stop-and-go traffic? Why are there several different kinds of congestion, and how are they related? Why do most traffic jams occur considerably before the road capacity is reached? Can a temporary reduction in the volume of traffic cause a lasting traffic jam? Under which conditions can speed limits speed up traffic? Why do pedestrians moving in opposite directions normally organize into lanes, while similar systems ``freeze by heating''? All of these questions have been answered by applying and extending methods from statistical physics and nonlinear dynamics to self-driven many-particle systems. This article considers the empirical data and then reviews the main approaches to modeling pedestrian and vehicle traffic. These include microscopic (particle-based), mesoscopic (gas-kinetic), and macroscopic (fluid-dynamic) models. Attention is also paid to the formulation of a micro-macro link, to aspects of universality, and to other unifying concepts, such as a general modeling framework for self-driven many-particle systems, including spin systems. While the primary focus is upon vehicle and pedestrian traffic, applications to biological or socio-economic systems such as bacterial colonies, flocks of birds, panics, and stock market dynamics are touched upon as well.

Traffic and related self-driven many-particle systems

The goal of this survey is to review recent developments in the hydro­ dynamic stability theory of spatially developing flows pertaining to absolute/convective and local/global instability concepts. We wish to dem­ onstrate how these notions can be used effectively to obtain a qualitative and quantitative description of the spatio-temporal dynamics of open shear flows, such as mixing layers, jets, wakes, boundary layers, plane Poiseuille flow, etc. In this review, we only consider open flows where fluid particles do not remain within the physical domain of interest but are advected through downstream flow boundaries. Thus, for the most part, flows in "boxes" (Rayleigh-Benard convection in finite-size cells, Taylor-Couette flow between concentric rotating cylinders, etc.) are not discussed. Further­ more, the implications of local/global and absolute/convective instability concepts for geophysical flows are only alluded to briefly. In many of the flows of interest here, the mean-velocity profile is non-

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Local and global instabilities in spatially developing flows

In this paper we develop a formalism for calculating the autocorrelation function of a dynamical variable in terms of a well‐defined memory function. Guided by simple physical arguments, an ansatz is adopted for the functional form of the memory function. This ansatz asserts that the memory of dynamical coherence decays exponentially. It is found that:(a) Despite the monotonic exponential decay of the memory function, the autocorrelation function deduced can display negative regions in some circumstances and decay monotonically in other circumstances.(b) The form of the autocorrelation function deduced is identical with that obtained from two other very different analyses, suggesting that the major properties of the function are of general validity.(c) The computed linear momentum autocorrelation function and power spectrum for liquid Ar are in good agreement with the computer experiments of Rahman.(d) The computed dipolar autocorrelation function reproduces all the features of the experimentally determin...

/pdf/on-the-calculation-of-autocorrelation-functions-of-dynamical-58p670xtko.pdf

On the Calculation of Autocorrelation Functions of Dynamical Variables

Lattice gas automata for reactive systems

1. Introduction 2. Basic ideas 3. Microdynamics: general formalism 4. Microdynamics: various examples 5. Equilibrium statistical mechanics 6. Macrodynamics: Chapman-Enskog method 7. Linearized hydrodynamics 8. Hydrodynamic fluctuations 9. Macrodynamics: projectors approach 10. Hydrodynamic regimes 11. Lattice gas simulations 12. Guide for further reading Appendix. Mathematical details.

Lattice Gas Hydrodynamics

I t is our pleasure to welcome Jean Pierre Boon and Constantino Tsallis as guests Editors for the present Special Issue of Europhysics News on “Nonextensive Statistical Mechanics”. They did a great job not only in selecting an impressive set of distinguished authors but also in writing the introductory Editorial and in each being a co-author of one of the contributions. The subject is difficult and could not go without a higher proportion of equations than usual in EPN: our thanks go to the EPN designer who had to face a heavier task than usual. It is sometimes necessary to address arduous developments to cover recent progress in Physics. This time, EPN will ask its readers to make an effort. It is always rewarding. The guests Editors were so efficient that the collected material passes largely the size of a standard EPN issue. We are grateful to the Publisher for accepting to accommodate all the articles in a single volume. It will make of this Special Issue the general reference work on “nonextensive statistical mechanics”. Back to the usual mix of wide-ranging Features and News next time! The Editors

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Special issue overview Nonextensive statistical mechanics: new trends, new perspectives

/pdf/boundaries-in-lattice-gas-flows-4yjeh608tl.pdf

Jean-Pierre Boon

Papers

On the Calculation of Autocorrelation Functions of Dynamical Variables

Lattice gas automata for reactive systems

Lattice Gas Hydrodynamics

Special issue overview Nonextensive statistical mechanics: new trends, new perspectives

Boundaries in lattice gas flows