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Author: Peter Ashcroft Publisher: Springer ISBN: 3319412132 Category : Science Languages : en Pages : 175
Book Description
This thesis explores several interdisciplinary topics at the border of theoretical physics and biology, presenting results that demonstrate the power of methods from statistical physics when applied to neighbouring disciplines. From birth-death processes in switching environments to discussions on the meaning of quasi-potential landscapes in high-dimensional spaces, this thesis is a shining example of the efficacy of interdisciplinary research. The fields advanced in this work include game theory, the dynamics of cancer, and invasion of mutants in resident populations, as well as general contributions to the theory of stochastic processes. The background material provides an intuitive introduction to the theory and applications of stochastic population dynamics, and the use of techniques from statistical physics in their analysis. The thesis then builds on these foundations to address problems motivated by biological phenomena.
Author: Peter Ashcroft Publisher: Springer ISBN: 3319412132 Category : Science Languages : en Pages : 175
Book Description
This thesis explores several interdisciplinary topics at the border of theoretical physics and biology, presenting results that demonstrate the power of methods from statistical physics when applied to neighbouring disciplines. From birth-death processes in switching environments to discussions on the meaning of quasi-potential landscapes in high-dimensional spaces, this thesis is a shining example of the efficacy of interdisciplinary research. The fields advanced in this work include game theory, the dynamics of cancer, and invasion of mutants in resident populations, as well as general contributions to the theory of stochastic processes. The background material provides an intuitive introduction to the theory and applications of stochastic population dynamics, and the use of techniques from statistical physics in their analysis. The thesis then builds on these foundations to address problems motivated by biological phenomena.
Author: David A. Lavis Publisher: Springer ISBN: 9401794308 Category : Science Languages : en Pages : 801
Book Description
Most interesting and difficult problems in equilibrium statistical mechanics concern models which exhibit phase transitions. For graduate students and more experienced researchers this book provides an invaluable reference source of approximate and exact solutions for a comprehensive range of such models. Part I contains background material on classical thermodynamics and statistical mechanics, together with a classification and survey of lattice models. The geometry of phase transitions is described and scaling theory is used to introduce critical exponents and scaling laws. An introduction is given to finite-size scaling, conformal invariance and Schramm—Loewner evolution. Part II contains accounts of classical mean-field methods. The parallels between Landau expansions and catastrophe theory are discussed and Ginzburg--Landau theory is introduced. The extension of mean-field theory to higher-orders is explored using the Kikuchi--Hijmans--De Boer hierarchy of approximations. In Part III the use of algebraic, transformation and decoration methods to obtain exact system information is considered. This is followed by an account of the use of transfer matrices for the location of incipient phase transitions in one-dimensionally infinite models and for exact solutions for two-dimensionally infinite systems. The latter is applied to a general analysis of eight-vertex models yielding as special cases the two-dimensional Ising model and the six-vertex model. The treatment of exact results ends with a discussion of dimer models. In Part IV series methods and real-space renormalization group transformations are discussed. The use of the De Neef—Enting finite-lattice method is described in detail and applied to the derivation of series for a number of model systems, in particular for the Potts model. The use of Pad\'e, differential and algebraic approximants to locate and analyze second- and first-order transitions is described. The realization of the ideas of scaling theory by the renormalization group is presented together with treatments of various approximation schemes including phenomenological renormalization. Part V of the book contains a collection of mathematical appendices intended to minimise the need to refer to other mathematical sources.
Author: E. Atlee Jackson Publisher: Courier Corporation ISBN: 0486149390 Category : Science Languages : en Pages : 272
Book Description
Key features include an elementary introduction to probability, distribution functions, and uncertainty; a review of the concept and significance of energy; and various models of physical systems. 1968 edition.
Author: Carolyn M. Van Vliet Publisher: World Scientific ISBN: 9812704779 Category : Science Languages : en Pages : 987
Book Description
This book encompasses our current understanding of the ensemble approach to many-body physics, phase transitions and other thermal phenomena, as well as the quantum foundations of linear response theory, kinetic equations and stochastic processes. It is destined to be a standard text for graduate students, but it will also serve the specialist-researcher in this fascinating field; some more elementary topics have been included in order to make the book self-contained.The historical methods of J Willard Gibbs and Ludwig Boltzmann, applied to the quantum description rather than phase space, are featured. The tools for computations in the microcanonical, canonical and grand-canonical ensembles are carefully developed and then applied to a variety of classical and standard quantum situations. After the language of second quantization has been introduced, strongly interacting systems, such as quantum liquids, superfluids and superconductivity, are treated in detail. For the connoisseur, there is a section on diagrammatic methods and applications.In the second part dealing with non-equilibrium processes, the emphasis is on the quantum foundations of Markovian behaviour and irreversibility via the Pauli-Van Hove master equation. Justifiable linear response expressions and the quantum-Boltzmann approach are discussed and applied to various condensed matter problems. From this basis the Onsager-Casimir relations are derived, together with the mesoscopic master equation, the Langevin equation and the Fokker-Planck truncation procedure. Brownian motion and modern stochastic problems such as fluctuations in optical signals and radiation fields briefly make the round.
Author: Gene Mazenko Publisher: Wiley-VCH ISBN: Category : Mathematics Languages : en Pages : 638
Book Description
A completely modern approach to statistical mechanics Gene Mazenko presents an introduction to statistical mechanics from the modern condensed matter physics point of view. Emphasizing symmetry principles, conservation laws, and the consequences of broken symmetry, all of which are crucial to a fundamental understanding of statistical physics, this volume discusses the role of broken translational symmetry in treating solids.Professor Mazenko develops a firm basis for the choice of macrovariables or thermodynamic variables, stressing the importance of Nambu-Goldstone modes. He develops this theory beyond the usual examples of simple fluids with discussions of magnets, superfluids, and solids. Based on the author's more than 30 years of experience with this subject, Equilibrium Statistical Mechanics: * Develops the structure of statistical mechanics and thermodynamics from fundamentals * Highlights the approach of coarse graining in statistical mechanics * Discusses ergodic theory and information theory * Treats phase transitions in a number of specific applications * Includes copious examples and end-of-chapter problems * Gives full development to the rich history of this topic Look for Mazenko's forthcoming volumes, Fluctuations, Order, and Defects; Nonequilibrium Statistical Mechanics; and Field Theory Methods in Statistical Mechanics. Combined with this self-contained volume, these works span the entire graduate-level program.
Author: Horacio S Wio Publisher: World Scientific Publishing Company ISBN: 9814434639 Category : Science Languages : en Pages : 336
Book Description
This book aims to provide a compact and unified introduction to the most important aspects in the physics of non-equilibrium systems. It first introduces stochastic processes and some modern tools and concepts that have proved their usefulness to deal with non-equilibrium systems from a purely probabilistic angle. The aim is to show the important role played by fluctuations in far-from-equilibrium situations, where noise can promote order and organization, switching among non-equilibrium states, etc. The second part adopts a more historical perspective, retracing the first steps taken from the purely thermodynamic as well as from the kinetic points of view to depart (albeit slightly) from equilibrium. The third part revisits the path outlined in the first one, but now undertakes the mesoscopic description of extended systems, where new phenomena (patterns, long-range correlations, scaling far from equilibrium, etc.) are observed. This book is a revised and extended version of an earlier edition published in 1994. It includes topics of current research interest in far-from-equilibrium situations like noise-induced phenomena and free energy-like functionals, surface growth and roughening, etc. It can be used as an advanced textbook by graduate students in physics. It also covers topics of current interest in other disciplines and interdisciplinary approaches in engineering, biophysics, and economics, among others. The level of detail in the book is enough to capture the interest of the reader and facilitate the path to more learning by exploring the modern research literature provided. At the same time, the book is also complete enough to be self-contained for those readers who just need an overview of the subject.
Author: Werner Ebeling Publisher: World Scientific ISBN: 9810213824 Category : Science Languages : en Pages : 344
Book Description
This book presents both the fundamentals and the major research topics in statistical physics of systems out of equilibrium. It summarizes different approaches to describe such systems on the thermodynamic and stochastic levels, and discusses a variety of areas including reactions, anomalous kinetics, and the behavior of self-propelling particles.
Author: Peter Ashcroft
Author: Peter Ashcroft
Author: J.K. Bhattacharjee
Author: David A. Lavis
Author: Michael Plischke
Author: E. Atlee Jackson
Author: Vladimir Privman
Author: Carolyn M. Van Vliet
Author: Gene Mazenko
Author: Horacio S Wio
Author: Werner Ebeling