Convexity In The Theory Of Lattice Gases PDF Download
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Author | : Robert B. Israel |
Publisher | : Princeton University Press |
Total Pages | : 257 |
Release | : 2015-03-08 |
Genre | : Science |
ISBN | : 1400868424 |
Download Convexity in the Theory of Lattice Gases Book in PDF, ePub and Kindle
In this book, Robert Israel considers classical and quantum lattice systems in terms of equilibrium statistical mechanics. He is especially concerned with the characterization of translation-invariant equilibrium states by a variational principle and the use of convexity in studying these states. Arthur Wightman's Introduction gives a general and historical perspective on convexity in statistical mechanics and thermodynamics. Professor Israel then reviews the general framework of the theory of lattice gases. In addition to presenting new and more direct proofs of some known results, he uses a version of a theorem by Bishop and Phelps to obtain existence results for phase transitions. Furthermore, he shows how the Gibbs Phase Rule and the existence of a wide variety of phase transitions follow from the general framework and the theory of convex functions. While the behavior of some of these phase transitions is very "pathological," others exhibit more "reasonable" behavior. As an example, the author considers the isotropic Heisenberg model. Formulating a version of the Gibbs Phase Rule using Hausdorff dimension, he shows that the finite dimensional subspaces satisfying this phase rule are generic. Originally published in 1979. 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.
Author | : Barry Simon |
Publisher | : Princeton University Press |
Total Pages | : 534 |
Release | : 2014-07-14 |
Genre | : Science |
ISBN | : 1400863430 |
Download The Statistical Mechanics of Lattice Gases, Volume I Book in PDF, ePub and Kindle
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.
Author | : Barry Simon |
Publisher | : |
Total Pages | : 522 |
Release | : 1993-01-01 |
Genre | : Science |
ISBN | : 9780691087795 |
Download The Statistical Mechanics of Lattice Gases Book in PDF, ePub and Kindle
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.
Author | : Sacha Friedli |
Publisher | : Cambridge University Press |
Total Pages | : 643 |
Release | : 2017-11-23 |
Genre | : Mathematics |
ISBN | : 1107184827 |
Download Statistical Mechanics of Lattice Systems Book in PDF, ePub and Kindle
A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.
Author | : Janusz Je̜drzejewski |
Publisher | : |
Total Pages | : 25 |
Release | : 1999 |
Genre | : |
ISBN | : |
Download Ground States of Lattice Gases with Almost Convex Repulsive Interactions Book in PDF, ePub and Kindle
Author | : Barry Simon |
Publisher | : |
Total Pages | : |
Release | : 1993 |
Genre | : |
ISBN | : |
Download The Statistical Mechanics of Lattice Gases Book in PDF, ePub and Kindle
Author | : GRUBER |
Publisher | : Birkhäuser |
Total Pages | : 419 |
Release | : 2013-11-11 |
Genre | : Science |
ISBN | : 3034858582 |
Download Convexity and Its Applications Book in PDF, ePub and Kindle
This collection of surveys consists in part of extensions of papers presented at the conferences on convexity at the Technische Universitat Wien (July 1981) and at the Universitat Siegen (July 1982) and in part of articles written at the invitation of the editors. This volume together with the earlier volume «Contributions to Geometry» edited by Tolke and Wills and published by Birkhauser in 1979 should give a fairly good account of many of the more important facets of convexity and its applications. Besides being an up to date reference work this volume can be used as an advanced treatise on convexity and related fields. We sincerely hope that it will inspire future research. Fenchel, in his paper, gives an historical account of convexity showing many important but not so well known facets. The articles of Papini and Phelps relate convexity to problems of functional analysis on nearest points, nonexpansive maps and the extremal structure of convex sets. A bridge to mathematical physics in the sense of Polya and Szego is provided by the survey of Bandle on isoperimetric inequalities, and Bachem's paper illustrates the importance of convexity for optimization. The contribution of Coxeter deals with a classical topic in geometry, the lines on the cubic surface whereas Leichtweiss shows the close connections between convexity and differential geometry. The exhaustive survey of Chalk on point lattices is related to algebraic number theory. A topic important for applications in biology, geology etc.
Author | : Anna T. Lawniczak |
Publisher | : American Mathematical Soc. |
Total Pages | : 357 |
Release | : 1996 |
Genre | : Computers |
ISBN | : 0821802585 |
Download Pattern Formation and Lattice gas Automata Book in PDF, ePub and Kindle
Articles review the diverse recent progress in the theory and development of lattice-gas and lattice Boltzmann methods and their applications. It features up-to-date articles, takes an interdisciplinary approach including mathematics, physical chemistry, and geophysics.
Author | : Jeffrey Yepez |
Publisher | : |
Total Pages | : 226 |
Release | : 1995 |
Genre | : Lattice gas |
ISBN | : |
Download Lattice Gas Dynamics Book in PDF, ePub and Kindle
The theory and computation of lattice gas dynamics for viscous fluid hydrodynamics is presented. Theoretical analysis of these exactly conserved, discrete models is done using the Boltzmann approximation, a mean-field theoretical treatment. Theoretical results are then compared to numerical data arrived by exactly computed simulations of simple lattice-gas systems. The numerical simulations presented were carried out on a prototype lattice-gas machine, the CAM-8, which is a virtual finegrained paralled mesh architecture suitable for discrete modeling in arbitrary dimensions. Single speed and multi-speed lattice gases are treated. The new contribution is an integer lattice gas with many particles per momentum state. Comparisons are made between the mean-field theory and numerical experiments for shear viscosity transport coefficient.
Author | : Rudolf Hilfer |
Publisher | : World Scientific |
Total Pages | : 473 |
Release | : 2000-03-02 |
Genre | : Science |
ISBN | : 9814496200 |
Download Applications Of Fractional Calculus In Physics Book in PDF, ePub and Kindle
Fractional calculus is a collection of relatively little-known mathematical results concerning generalizations of differentiation and integration to noninteger orders. While these results have been accumulated over centuries in various branches of mathematics, they have until recently found little appreciation or application in physics and other mathematically oriented sciences. This situation is beginning to change, and there are now a growing number of research areas in physics which employ fractional calculus.This volume provides an introduction to fractional calculus for physicists, and collects easily accessible review articles surveying those areas of physics in which applications of fractional calculus have recently become prominent.