الصفحة 1
الصفحة 1
Vorticity, Statistical Mechanics, and Monte Carlo Simulation
This book is drawn from across many active fields of mathematics and physics, and has connections to atmospheric dynamics, spherical codes, graph theory, constrained optimization problems, Markov Chains, and Monte Carlo methods. It addresses how to access interesting, original, and publishable research in statistical modeling of large-scale flows and several related fields. The authors f this book explicitly reach around the major branches of mathematics and physics, showing how the use of a few straightforward approaches can create a cornucopia of intriguing questions and the tools to answer them. In reading this book, the reader will learn how to research a topic and how to understand statistical mechanics treatments of fluid dynamics.
Transport Coefficients of Fluids
Until recently the formal statistical mechanical approach offered no practicable method for computing the transport coefficients of liquids, and so most practitioners had to resort to empirical fitting formulas. This has now changed, as demonstrated in this innovative monograph. The author presents and applies new methods based on statistical mechanics for calculating the transport coefficients of simple and complex liquids over wide ranges of density and temperature. These molecular theories enable the transport coefficients to be calculated in terms of equilibrium thermodynamic properties, and the results are shown to account satisfactorily for experimental observations, including even the non-Newtonian behavior of fluids far from equilibrium.
The Statistical Mechanics of Financial Markets
The random-walk technique, well known in physics, is also the basic model in finance, upon which are built, for example, the Black-Scholes theory of option pricing and hedging, plus methods of portfolio optimization. Here the underlying assumptions are assessed critically. Using empirical financial data and analogies to physical models such as fluid flows, turbulence, or superdiffusion, the book develops a more accurate description of financial markets based on random walks. With this approach, novel methods for derivative pricing and risk management can be formulated. Computer simulations of interacting-agent models provide insight into the mechanisms underlying unconventional price dynamics. It is shown that stock exchange crashes can be modelled in ways analogous to phase transitions and earthquakes, and sometimes have even been predicted successfully.
The Lace Expansion and its Applications ; Ecole d'Eté de Probabilités de Saint-Flour XXXIV - 2004
The lace expansion is a powerful and flexible method for understanding the critical scaling of several models of interest in probability, statistical mechanics, and combinatorics, above their upper critical dimensions. These models include the self-avoiding walk, lattice trees and lattice animals, percolation, oriented percolation, and the contact process. This volume provides a unified and extensive overview of the lace expansion and its applications to these models. Results include proofs of existence of critical exponents and construction of scaling limits. Often, the scaling limit is described in terms of super-Brownian motion.
The Fermi-Pasta-Ulam Problem : A Status Report
This volume reviews the current understanding of this paradox without trying to force coherence on differing perspectives on the same problem by various groups or approaches. The contributions comprise studies of one-dimensional chains, descriptions of numerical methods, heuristic theories, addressing the "long standing and controversial problem of distinguishing chaos from noise in signal analysis," metastability, the relation of the FPU motions with the integrable equations, approaches using methods of perturbation theory and the proof of the applicability of KAM theory in FPU chains with energy very close to a minimum. For the convenience of the reader the original work of FPU is reprinted in an appendix.
Tensile Fracturing in Rocks : Tectonofractographic and Electromagnetic Radiation Methods
The book’s subject matter is divided over six chapters, which are briefly described below. Chapter 1 summarizes current key concepts in fracture physics. It starts with a pr- entation of the elastic theory of fracture, and concentrates on the results of linear el- tic fracture mechanics. The chapter touches also upon other fracture properties, e.g., crack nucleation, dynamic fracturing and slow fracturing processes. Nucleation is - dressed by statistical mechanics methods incorporating modern approaches of th- mal and fiber bundle processes. The analyses of dynamic fracturing and slow fract- ing focus on the differences, as compared to the linear elastic approach. The cont- versy in interpreting experimental dynamic results is highlighted, as are the surface morphology patterns that emerge in fracturing and the non-Griffith crack extension criterion in very slow fracturing processes.
String Theory : from Gauge Interactions to Cosmology ; Proceedings of the NATO Advanced Study Institute on String Theory: From Gauge Interactions to Cosmology, Cargèse, France, from 7 to 19 June 2004
String Theory is our current best candidate for the unification of all fundamental forces, including gravity, in a consistent quantum framework. In this collection of lectures delivered at the Cargèse Summer School "String Theory: from Gauge Interactions to Cosmology'', world leading experts provide an up-to-date survey of the latest developments in this topic, including the gauge/gravity correspondence, superstring cosmology and cosmic strings, topological string theory and matrix models, physics beyond the standard model and the landscape of vacua of string theory, conformal field theory and critical phenomena in statistical mechanics.
Statistical Physics : An Introduction
Provides a comprehensive presentation of the basics of statistical physics. The first part explains the essence of statistical physics. In the second part, statistical mechanics is applied to various systems which. The book also features applications to quantum dynamics, thermodynamics, the Ising model and the statistical dynamics of free spins.
Statistical Mechanics
The completely revised new edition of the classical book on Statistical Mechanics covers the basic concepts of equilibrium and non-equilibrium statistical physics. In addition to a deductive approach to equilibrium statistics and thermodynamics based on a single hypothesis - the form of the microcanonical density matrix - this book treats the most important elements of non-equilibrium phenomena. Intermediate calculations are presented in complete detail. Problems at the end of each chapter help students to consolidate their understanding of the material. Beyond the fundamentals, this text demonstrates the breadth of the field and its great variety of applications.
Séminaire de Probabilités XLI = Probability Seminar XLI
Stochastic processes are as usual the main subject of the Séminaire, with contributions on Brownian motion (fractional or other), Lévy processes, martingales and probabilistic finance. Other probabilistic themes are also present: large random matrices, statistical mechanics. The contributions in this volume provide a sampling of recent results on these topics. All contributions with the exception of two are written in English language.
Quantum Field Theory I : Basics in Mathematics and Physics : A Bridge between Mathematicians and Physicists
This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists ranging from advanced undergraduate students to professional scientists. The book tries to bridge the existing gap between the different languages used by mathematicians and physicists. For students of mathematics it is shown that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which is beyond the usual curriculum in physics.
Planar Ising Correlations
Examines in detail the correlations for the two-dimensional Ising model in the infinite volume or thermodynamic limit and the sub- and super-critical continuum scaling limits. Steady progress in recent years has been made in understanding the special mathematical features of certain exactly solvable models in statistical mechanics and quantum field theory, including the scaling limits of the 2-D Ising (lattice) model, and more generally, a class of 2-D quantum fields known as holonomic fields.
Physical Theory and its Interpretation : Essays in Honor of Jeffrey Bub
The essays in this volume were written by leading researchers on classical mechanics, statistical mechanics, quantum theory and relativity. The papers cover a number of central topics in the foundations of physics, including the role of symmetry principles in classical and quantum physics (papers by Butterfield and by Healey), Einstein's hole argument in general relativity (Korte), quantum mechanics and special relativity (Hemmo and Berkovitz, Brown and Timpson), quantum correlations (Glymour, Redei), quantum logic (Demopoulos, Isham, Stairs), and quantum probability and information (Gudder, Pitowsky).
Phase Resetting in Medicine and Biology : Stochastic Modelling and Data Analysis
Presents a new theoretical approach to phase resetting and stimulation-induced synchronization and desynchronization in a population of oscillators. The author uses stochastic methods from statistical mechanics and applies his theory to models of practical importance in physiology and neuroscience. He makes the book accessible to readers not familiar with the mathematical formalism. The results are presented and additionally explained without formulae, particularly with a view to the interests of neuroscientists. The author also proposes improvements to stimulation techniques as used by neurologists and neurosurgeons in the context of Parkinson's disease and MEG/EEG data analysis. The book is written for researchers and graduate students but it can also benefit medical practitioners.
Open Quantum Systems III : Recent Developments
Present in a self-contained way the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications. Volume III is devoted to recent developments and applications. The topics discussed include the non-equilibrium properties of open quantum systems, the Fermi Golden Rule and weak coupling limit, quantum irreversibility and decoherence, qualitative behaviour of quantum Markov semigroups and continual quantum measurements.
Open Quantum Systems II : The Markovian Approach
These books present in a self-contained way the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications. Volume II is dedicated to the Markovian formalism of classical and quantum open systems. A complete exposition of noise theory, Markov processes and stochastic differential equations, both in the classical and the quantum context, is provided. These mathematical tools are put into perspective with physical motivations and applications.
Open Quantum Systems I : The Hamiltonian Approach
These books present in a self-contained way the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications. This Volume, I the Hamiltonian description of quantum open systems is discussed. This includes an introduction to quantum statistical mechanics and its operator algebraic formulation, modular theory, spectral analysis and their applications to quantum dynamical systems.
Modern Hematology : Biology and Clinical Management
The first chapters of this book contain a self-contained introduction to path integrals in Euclidean quantum mechanics and statistical mechanics. The resulting high-dimensional integrals can be estimated with the help of Monte Carlo simulations based on Markov processes. The most commonly used algorithms are presented in detail so as to prepare the reader for the use of high-performance computers as an “experimental” tool for this burgeoning field of theoretical physics. Several chapters are then devoted to an introduction to simple lattice field theories and a variety of spin systems with discrete and continuous spins, where the ubiquitous Ising model serves as an ideal guide for introducing the fascinating area of phase transitions. As an alternative to the lattice formulation of quantum field theories, variants of the flexible renormalization group methods are discussed in detail. Since, according to our present-day knowledge, all fundamental interactions in nature are described by gauge theories, the remaining chapters of the book deal with gauge theories without and with matter.
Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena
Model reduction and coarse-graining are important in many areas of science and engineering. How does a system with many degrees of freedom become one with fewer? How can a reversible micro-description be adapted to the dissipative macroscopic model? These crucial questions, as well as many other related problems, are discussed in this book. Specific areas of study include dynamical systems, non-equilibrium statistical mechanics, kinetic theory, hydrodynamics and mechanics of continuous media, (bio)chemical kinetics, nonlinear dynamics, nonlinear control, nonlinear estimation, and particulate systems from various branches of engineering. The generic nature and the power of the pertinent conceptual, analytical and computational frameworks helps eliminate some of the traditional language barriers, which often unnecessarily impede scientific progress and the interaction of researchers between disciplines such as physics, chemistry, biology, applied mathematics and engineering. All contributions are authored by experts, whose specialities span a wide range of fields within science and engineering.
Mathematical Physics of Quantum Mechanics : Selected and Refereed Lectures from QMath9
At the QMath9 meeting, young scientists learn about the state of the art in the mathematical physics of quantum systems. Based on that event, this book offers a selection of outstanding articles written in pedagogical style comprising six sections which cover new techniques and recent results on spectral theory, statistical mechanics, Bose-Einstein condensation, random operators, magnetic Schrödinger operators and much more. For postgraduate students, Mathematical Physics of Quantum Systems serves as a useful introduction to the research literature. For more expert researchers, this book will be a concise and modern source of reference.
