Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The text is a self-contained, comprehensive introduction to the theory of hydrodynamic lattice gases. Lattice-gas cellular automata are discrete models of fluids. Identical particles hop from site to site on a regular lattice, obeying simple conservative scattering rules when they collide. Remarkably, at a scale larger than the lattice spacing, these discrete models simulate the Navier-Stokes equations of fluid mechanics. This book addresses three important aspects of lattice gases. First, it shows how such simple idealised microscopic dynamics give rise to isotropic macroscopic hydrodynamics. Second, it details how the simplicity of the lattice gas provides for equally simple models of fluid phase separation, hydrodynamic interfaces, and multiphase flow. Lastly, it illustrates how lattice-gas models and related lattice-Boltzmann methods have been used to solve problems in applications as diverse as flow through porous media, phase separation, and interface dynamics. Many exercises and references are included.

Hydrodynamics --- Lattice gas --- Cellular automata --- Mathematical models. --- Computer simulation.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Stochastic processes --- Mathematical physics --- Lattice gas --- Statistical mechanics --- Mechanics --- Mechanics, Analytic --- Quantum statistics --- Statistical physics --- Thermodynamics --- Gas, Lattice --- Crystal lattices --- Statistical mechanics. --- Mécanique statistique. --- Lattice gas. --- Gaz réticulaires.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book provides a self-contained introduction to cellular automata and lattice Boltzmann techniques. Beginning with a chapter introducing the basic concepts of this developing field, a second chapter describes methods used in cellular automata modeling. Following chapters discuss the statistical mechanics of lattice gases, diffusion phenomena, reaction-diffusion processes and non-equilibrium phase transitions. A final chapter looks at other models and applications, such as wave propagation and multiparticle fluids. With a pedagogic approach, the volume focuses on the use of cellular automata in the framework of equilibrium and non-equilibrium statistical physics. It also emphasises application-oriented problems such as fluid dynamics and pattern formation. The book contains many examples and problems. A glossary and a detailed bibliography are also included. This will be a valuable book for graduate students and researchers working in statistical physics, solid state physics, chemical physics and computer science.

Statistical physics. --- Cellular automata. --- Diffusion. --- Lattice gas. --- Phase transformations (Statistical physics)

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Hydrodynamics --- Lattice gas --- Cellular automata --- Hydrodynamique --- Automates cellulaires --- Mathematical models. --- Mathematical models. --- Mathematical models. --- Modèles mathématiques --- Modèles mathématiques

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

A state-of-the-art survey of both classical and quantum lattice gas models, this two-volume work will cover the rigorous mathematical studies of such models as the Ising and Heisenberg, an area in which scientists have made enormous strides during the past twenty-five years. This first volume addresses, among many topics, the mathematical background on convexity and Choquet theory, and presents an exhaustive study of the pressure including the Onsager solution of the two-dimensional Ising model, a study of the general theory of states in classical and quantum spin systems, and a study of high and low temperature expansions. The second volume will deal with the Peierls construction, infrared bounds, Lee-Yang theorems, and correlation inequality.This comprehensive work will be a useful reference not only to scientists working in mathematical statistical mechanics but also to those in related disciplines such as probability theory, chemical physics, and quantum field theory. It can also serve as a textbook for advanced graduate students.Originally published in 1993.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Lattice gas --- Statistical mechanics --- Mécanique statistique --- Lattice gas. --- 536.75 --- Mechanics --- Mechanics, Analytic --- Quantum statistics --- Statistical physics --- Thermodynamics --- Gas, Lattice --- Crystal lattices --- Entropy. Statistical thermodynamics. Irreversible processes --- 536.75 Entropy. Statistical thermodynamics. Irreversible processes --- Physics --- Physical Sciences & Mathematics --- Atomic Physics --- Mécanique statistique