Download or read book The Mathematical Theory of Thermodynamic Limits written by Isabelle Catto and published by Oxford University Press. This book was released on 1998 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: The thermodynamic limit is a mathematical technique for modeling crystals or other macroscopic objects by considering them as infinite periodic arrays of molecules. The technique allows models in solid state physics to be derived directly from models in quantum chemistry. This book presents new results, many previously unpublished, for a large class of models and provides a survey of the mathematics of thermodynamic limit problems. The authors both work closely with Fields Medal-winner Pierre-Louis Lion, and the book will be a valuable tool for applied mathematicians and mathematical physicists studying nonlinear partial differential equations.
Download or read book Thermodynamic Formalism written by David Ruelle and published by Cambridge University Press. This book was released on 2004-11-25 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reissued in the Cambridge Mathematical Library this classic book outlines the theory of thermodynamic formalism which was developed to describe the properties of certain physical systems consisting of a large number of subunits. It is aimed at mathematicians interested in ergodic theory, topological dynamics, constructive quantum field theory, the study of certain differentiable dynamical systems, notably Anosov diffeomorphisms and flows. It is also of interest to theoretical physicists concerned with the conceptual basis of equilibrium statistical mechanics. The level of the presentation is generally advanced, the objective being to provide an efficient research tool and a text for use in graduate teaching. Background material on mathematics has been collected in appendices to help the reader. Extra material is given in the form of updates of problems that were open at the original time of writing and as a new preface specially written for this new edition by the author.
Download or read book Singular Limits in Thermodynamics of Viscous Fluids written by Eduard Feireisl and published by Birkhäuser. This book was released on 2017-11-24 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about singular limits of systems of partial differential equations governing the motion of thermally conducting compressible viscous fluids. "The main aim is to provide mathematically rigorous arguments how to get from the compressible Navier-Stokes-Fourier system several less complex systems of partial differential equations used e.g. in meteorology or astrophysics. However, the book contains also a detailed introduction to the modelling in mechanics and thermodynamics of fluids from the viewpoint of continuum physics. The book is very interesting and important. It can be recommended not only to specialists in the field, but it can also be used for doctoral students and young researches who want to start to work in the mathematical theory of compressible fluids and their asymptotic limits." Milan Pokorný (zbMATH) "This book is of the highest quality from every point of view. It presents, in a unified way, recent research material of fundament al importance. It is self-contained, thanks to Chapter 3 (existence theory) and to the appendices. It is extremely well organized, and very well written. It is a landmark for researchers in mathematical fluid dynamics, especially those interested in the physical meaning of the equations and statements." Denis Serre (MathSciNet)
Download or read book Nonequilibrium Statistical Thermodynamics written by Bernard H. Lavenda and published by Courier Dover Publications. This book was released on 2019-04-17 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops in detail the statistical foundations of nonequilibrium thermodynamics, based on the mathematical theory of Brownian motion. Author Bernard H. Lavenda demonstrates that thermodynamic criteria emerge in the limit of small thermal fluctuations and in the Gaussian limit where means and modes of the distribution coincide. His treatment assumes the theory of Brownian motion to be a general and practical model of irreversible processes that are inevitably influenced by random thermal fluctuations. This unifying approach permits the extraction of widely applicable principles from the analysis of specific models. Arranged by argument rather than theory, the text is based on the premises that random thermal fluctuations play a decisive role in governing the evolution of nonequilibrium thermodynamic processes and that they can be viewed as a dynamic superposition of many random events. Intended for nonmathematicians working in the areas of nonequilibrium thermodynamics and statistical mechanics, this book will also be of interest to chemical physicists, condensed matter physicists, and readers in the area of nonlinear optics.
Download or read book Mathematical Statistical Mechanics written by Colin J. Thompson and published by Princeton University Press. This book was released on 2015-03-08 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: While most introductions to statistical mechanics are either too mathematical or too physical, Colin Thompson's book combines mathematical rigor with familiar physical materials. Following introductory chapters on kinetic theory, thermodynamics, the Gibbs ensembles, and the thermodynamic limit, later chapters discuss the classical theories of phase transitions, the Ising model, algebraic methods and combinatorial methods for solving the two-dimensional model in zero field, and some applications of the Ising model to biology. 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.
Download or read book Thermodynamic Limit for a System with Dipole dipole Interactions written by E. R. Smith and published by . This book was released on 1975 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Mathematical Theory of Dilute Gases written by Carlo Cercignani and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: The idea for this book was conceived by the authors some time in 1988, and a first outline of the manuscript was drawn up during a summer school on mathematical physics held in Ravello in September 1988, where all three of us were present as lecturers or organizers. The project was in some sense inherited from our friend Marvin Shinbrot, who had planned a book about recent progress for the Boltzmann equation, but, due to his untimely death in 1987, never got to do it. When we drew up the first outline, we could not anticipate how long the actual writing would stretch out. Our ambitions were high: We wanted to cover the modern mathematical theory of the Boltzmann equation, with rigorous proofs, in a complete and readable volume. As the years progressed, we withdrew to some degree from this first ambition- there was just too much material, too scattered, sometimes incomplete, sometimes not rigor ous enough. However, in the writing process itself, the need for the book became ever more apparent. The last twenty years have seen an amazing number of significant results in the field, many of them published in incom plete form, sometimes in obscure places, and sometimes without technical details. We made it our objective to collect these results, classify them, and present them as best we could. The choice of topics remains, of course, subjective.
Download or read book Quantum Theory and Its Stochastic Limit written by Luigi Accardi and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: Well suited as a textbook in the emerging field of stochastic limit, which is a new mathematical technique developed for solving nonlinear problems in quantum theory.
Download or read book Statistical Mechanics of Lattice Systems written by Sacha Friedli and published by Cambridge University Press. This book was released on 2017-11-23 with total page 643 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.
Download or read book On the Symptotic Exactness of Thomas Fermi Theory in the Thermodynamic Limit written by Pedro Balodis Matesanz and published by . This book was released on 1998 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Density Functional Theory written by Eric Cancès and published by Springer Nature. This book was released on 2023-07-18 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: Density functional theory (DFT) provides the most widely used models for simulating molecules and materials based on the fundamental laws of quantum mechanics. It plays a central role in a huge spectrum of applications in chemistry, physics, and materials science.Quantum mechanics describes a system of N interacting particles in the physical 3-dimensional space by a partial differential equation in 3N spatial variables. The standard numerical methods thus incur an exponential increase of computational effort with N, a phenomenon known as the curse of dimensionality; in practice these methods already fail beyond N=2. DFT overcomes this problem by 1) reformulating the N-body problem involving functions of 3N variables in terms of the density, a function of 3 variables, 2) approximating it by a pioneering hybrid approach which keeps important ab initio contributions and re-models the remainder in a data-driven way. This book intends to be an accessible, yet state-of-art text on DFT for graduate students and researchers in applied and computational mathematics, physics, chemistry, and materials science. It introduces and reviews the main models of DFT, covering their derivation and mathematical properties, numerical treatment, and applications.
Download or read book Challenges to The Second Law of Thermodynamics written by Vladislav Capek and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: The advance of scienti?c thought in ways resembles biological and geologic transformation: long periods of gradual change punctuated by episodes of radical upheaval. Twentieth century physics witnessed at least three major shifts — relativity, quantum mechanics and chaos theory — as well many lesser ones. Now, st early in the 21 , another shift appears imminent, this one involving the second law of thermodynamics. Over the last 20 years the absolute status of the second law has come under increased scrutiny, more than during any other period its 180-year history. Since the early 1980’s, roughly 50 papers representing over 20 challenges have appeared in the refereed scienti?c literature. In July 2002, the ?rst conference on its status was convened at the University of San Diego, attended by 120 researchers from 25 countries (QLSL2002) [1]. In 2003, the second edition of Le?’s and Rex’s classic anthology on Maxwell demons appeared [2], further raising interest in this emerging ?eld. In 2004, the mainstream scienti?c journal Entropy published a special edition devoted to second law challenges [3]. And, in July 2004, an echo of QLSL2002 was held in Prague, Czech Republic [4]. Modern second law challenges began in the early 1980’s with the theoretical proposals of Gordon and Denur. Starting in the mid-1990’s, several proposals for experimentally testable challenges were advanced by Sheehan, et al. By the late 1990’s and early 2000’s, a rapid succession of theoretical quantum mechanical ? challenges were being advanced by C ́ apek, et al.
Download or read book Mathematical Foundations of Classical Statistical Mechanics written by D.Ya. Petrina and published by CRC Press. This book was released on 2002-04-11 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph considers systems of infinite number of particles, in particular the justification of the procedure of thermodynamic limit transition. The authors discuss the equilibrium and non-equilibrium states of infinite classical statistical systems. Those states are defined in terms of stationary and nonstationary solutions to the Bogolyubov equations for the sequences of correlation functions in the thermodynamic limit. This is the first detailed investigation of the thermodynamic limit for non-equilibrium systems and of the states of infinite systems in the cases of both canonical and grand canonical ensembles, for which the thermodynamic equivalence is proved. A comprehensive survey of results is also included; it concerns the properties of correlation functions for infinite systems and the corresponding equations. For this new edition, the authors have made changes to reflect the development of theory in the last ten years. They have also simplified certain sections, presenting them more systematically, and greatly increased the number of references. The book is aimed at theoretical physicists and mathematicians and will also be of use to students and postgraduate students in the field.
Download or read book The Porous Medium Equation written by Juan Luis Vazquez and published by Oxford University Press. This book was released on 2007 with total page 647 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Heat Equation is one of the three classical linear partial differential equations of second order that form the basis of any elementary introduction to the area of PDEs, and only recently has it come to be fairly well understood. In this monograph, aimed at research students and academics in mathematics and engineering, as well as engineering specialists, Professor Vazquez provides a systematic and comprehensive presentation of the mathematical theory of the nonlinear heatequation usually called the Porous Medium Equation (PME). This equation appears in a number of physical applications, such as to describe processes involving fluid flow, heat transfer or diffusion. Other applications have been proposed in mathematical biology, lubrication, boundary layer theory, andother fields. Each chapter contains a detailed introduction and is supplied with a section of notes, providing comments, historical notes or recommended reading, and exercises for the reader.
Download or read book On the Asymptotic Exactness of Thomas Fermi Theory in the Thermodynamic Limit written by Pedro Balodis Matesanz and published by . This book was released on 1998 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Homogenization Theory for Multiscale Problems written by Xavier Blanc and published by Springer Nature. This book was released on 2023-04-29 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a pedagogic and comprehensive introduction to homogenization theory with a special focus on problems set for non-periodic media. The presentation encompasses both deterministic and probabilistic settings. It also mixes the most abstract aspects with some more practical aspects regarding the numerical approaches necessary to simulate such multiscale problems. Based on lecture courses of the authors, the book is suitable for graduate students of mathematics and engineering.
Download or read book Quantum Mathematical Physics written by Walter Thirring and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a new edition of Volumes 3 and 4 of Walter Thirring’s famous textbook on mathematical physics. The first part is devoted to quantum mechanics and especially to its applications to scattering theory, atoms and molecules. The second part deals with quantum statistical mechanics examining fundamental concepts like entropy, ergodicity and thermodynamic functions.
