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Static Conceptual Fracture Modeling: Preparing for Simulation and Development
by Ronald A. NelsonModelling of flow in naturally fractured reservoirs is quickly becoming mandatory in all phases of oil and gas exploration and production. Creation of a Static Conceptual Fracture Model (SCFM) is needed as input to create flow simulations for today and for prediction of flow into the future. Unfortunately, the computer modelers tasked with constructing the gridded fracture model are often not well versed in natural fracture characterization and are often forced to make quick decisions as to the input required by the software used to create these models. Static Conceptual Fracture Modelling: Preparing for Simulation and Development describes all the fracture and reservoir parameters needed to create the fracture database for effective modelling and how to generate the data and parameter distributions. The material covered in this volume highlights not only natural fracture system quantification and formatting, but also describes best practices for managing technical teams charged with creating the SCFM. This book will become a must on the shelf for all reservoir modelers.
Statics and Dynamics of Weakly Coupled Antiferromagnetic Spin-1/2 Ladders in a Magnetic Field
by Pierre BouillotThis thesis shows how a combination of analytic and numerical techniques, such as a time dependent and finite temperature Density Matrix Renormalization Group (DMRG) technique, can be used to obtain the physical properties of low dimensional quantum magnets with an unprecedented level of accuracy. A comparison between the theory and experiment then enables these systems to be used as quantum simulators; for example, to test various generic properties of low dimensional systems such as Luttinger liquid physics, the paradigm of one dimensional interacting quantum systems. Application of these techniques to a material made of weakly coupled ladders (BPCB) allowed the first quantitative test of Luttinger liquids. In addition, other physical quantities (magnetization, specific heat etc.), and more remarkably the spins-spin correlations - directly measurable in neutron scattering experiments - were in excellent agreement with the observed quantities. We thus now have tools to quantitatiively assess the dynamics for this class of quantum systems.
Stationary Diffraction by Wedges: Method of Automorphic Functions on Complex Characteristics (Lecture Notes in Mathematics #2249)
by Alexander Komech Anatoli MerzonThis book presents a new and original method for the solution of boundary value problems in angles for second-order elliptic equations with constant coefficients and arbitrary boundary operators. This method turns out to be applicable to many different areas of mathematical physics, in particular to diffraction problems in angles and to the study of trapped modes on a sloping beach. Giving the reader the opportunity to master the techniques of the modern theory of diffraction, the book introduces methods of distributions, complex Fourier transforms, pseudo-differential operators, Riemann surfaces, automorphic functions, and the Riemann–Hilbert problem. The book will be useful for students, postgraduates and specialists interested in the application of modern mathematics to wave propagation and diffraction problems.
Statistical Analysis in Climate Research
by Hans Von Storch Francis W. ZwiersClimatology is, to a large degree, the study of the statistics of our climate. The powerful tools of mathematical statistics therefore find wide application in climatological research. The purpose of this book is to help the climatologist understand the basic precepts of the statistician's art and to provide some of the background needed to apply statistical methodology correctly and usefully. The book is self contained: introductory material, standard advanced techniques, and the specialised techniques used specifically by climatologists are all contained within this one source. There are a wealth of real-world examples drawn from the climate literature to demonstrate the need, power and pitfalls of statistical analysis in climate research. Suitable for graduate courses on statistics for climatic, atmospheric and oceanic science, this book will also be valuable as a reference source for researchers in climatology, meteorology, atmospheric science, and oceanography.
Statistical Analysis of Climate Extremes
by Manfred MudelseeThe risks posed by climate change and its effect on climate extremes are an increasingly pressing societal problem. This book provides an accessible overview of the statistical analysis methods which can be used to investigate climate extremes and analyse potential risk. The statistical analysis methods are illustrated with case studies on extremes in the three major climate variables: temperature, precipitation, and wind speed. The book also provides datasets and access to appropriate analysis software, allowing the reader to replicate the case study calculations. Providing the necessary tools to analyse climate risk, this book is invaluable for students and researchers working in the climate sciences, as well as risk analysts interested in climate extremes.
Statistical Analysis of Geographical Data: An Introduction
by Simon James DadsonStatistics Analysis of Geographical Data: An Introduction provides a comprehensive and accessible introduction to the theory and practice of statistical analysis in geography. It covers a wide range of topics including graphical and numerical description of datasets, probability, calculation of confidence intervals, hypothesis testing, collection and analysis of data using analysis of variance and linear regression. Taking a clear and logical approach, this book examines real problems with real data from the geographical literature in order to illustrate the important role that statistics play in geographical investigations. Presented in a clear and accessible manner the book includes recent, relevant examples, designed to enhance the reader’s understanding.
STATISTICAL ANALYSIS OF MASSIVE DATA STREAMS: Proceedings of a Workshop
by Committee on Applied Theoretical StatisticsMassive data streams—large quantities of data that arrive continuously—are becoming increasingly commonplace in many areas of science and technology. Consequently development of analytical methods for such streams is of growing importance. To address this issue, the National Security Agency asked the NRC to hold a workshop to explore methods for analysis of streams of data so as to stimulate progress in the field. This report presents the results of that workshop. It provides presentations that focused on five different research areas where massive data streams are present: atmospheric and meteorological data; high-energy physics; integrated data systems; network traffic; and mining commercial data streams. The goals of the report are to improve communication among researchers in the field and to increase relevant statistical science activity.
Statistical Analysis of Natural Disasters and Related Losses
by V. F. Pisarenko M. V. RodkinThe study of disaster statistics and disaster occurrence is a complicated interdisciplinary field involving the interplay of new theoretical findings from several scientific fields like mathematics, physics, and computer science. Statistical studies on the mode of occurrence of natural disasters largely rely on fundamental findings in the statistics of rare events, which were derived in the 20th century. With regard to natural disasters, it is not so much the fact that the importance of this problem for mankind was recognized during the last third of the 20th century - the myths one encounters in ancient civilizations show that the problem of disasters has always been recognized - rather, it is the fact that mankind now possesses the necessary theoretical and practical tools to effectively study natural disasters, which in turn supports effective, major practical measures to minimize their impact. All the above factors have resulted in considerable progress in natural disaster research. Substantial accrued material on natural disasters and the use of advanced recording techniques have opened new doors for empirical analysis. However, despite the considerable progress made, the situation is still far from ideal. Sufficiently complete catalogs of events are still not available for many types of disasters, and the methodological and even terminological bases of research need to be further developed and standardized. The present monograph summarizes recent advances in the field of disaster statistics, primarily focusing on the occurrence of disasters that can be described by distributions with heavy tails. These disasters typically occur on a very broad range of scales, the rare greatest events being capable of causing losses comparable to the total losses of all smaller disasters of the same type. Audience: This SpringerBrief will be a valuable resource for those working in the fields of natural disaster research, risk assessment and loss mitigation at regional and federal governing bodies and in the insurance business, as well as for a broad range of readers interested in problems concerning natural disasters and their effects on human life.
Statistical and Condensed Matter Physics
by Serguei N. BurmistrovThe book outlines the fundamentals of statistical and condensed matter physics. The statistical physics is the basis of condensed matter physics and the tool for studying a variety of condensed media in the thermodynamic (heat) conditions. The statistical physics is presented within the framework of canonical Gibbs distribution entailing the relations known from the classical (heat) thermodynamics. The application of the statistical theory embraces such topics as ideal classical and quantum gases, Bose-type excitations, phase transitions and critical phenomena, normal Fermi liquid, superconductivity, weakly non-ideal Bose gases, superfluidity, and magnetism. Each section ends with one or several problems with the solutions clarifying the paragraph content and delivering some additional physical examples. The problems give an opportunity for a reader to check the own real knowledge of the material studied.
Statistical and Nonlinear Physics (Encyclopedia of Complexity and Systems Science Series)
by Bulbul ChakrabortyThis volume of the Encyclopedia of Complexity and Systems Science, Second Edition, focuses on current challenges in the field from materials and mechanics to applications of statistical and nonlinear physics in the life sciences. Challenges today are mostly in the realm of non-equilibrium systems, although certain equilibrium systems also present serious hurdles. Where possible, pairwise articles focus on a single topic, one from a theoretical perspective and the other from an experimental one, providing valuable insights. In other cases, theorists and experimentalists have collaborated on a single article. Coverage includes both quantum and classical systems, and emphasizes 1) mature fields that are not covered in the current specialist literature, (2) topics that fall through the cracks in disciplinary journals/books, or (3) developing areas where the knowledge base is large and robust and upon which future developments will depend. The result is an invaluable resource for condensed matter physicists, material scientists, engineers and life scientists.
Statistical and Thermal Physics: An Introduction
by Michael J.R. HochThermal and statistical physics has established the principles and procedures needed to understand and explain the properties of systems consisting of macroscopically large numbers of particles. By developing microscopic statistical physics and macroscopic classical thermodynamic descriptions in tandem, Statistical and Thermal Physics: An Introduction provides insight into basic concepts and relationships at an advanced undergraduate level. This second edition is updated throughout, providing a highly detailed, profoundly thorough, and comprehensive introduction to the subject and features exercises within the text as well as end-of-chapter problems. Part I of this book consists of nine chapters, the first three of which deal with the basics of equilibrium thermodynamics, including the fundamental relation. The following three chapters introduce microstates and lead to the Boltzmann definition of the entropy using the microcanonical ensemble approach. In developing the subject, the ideal gas and the ideal spin system are introduced as models for discussion. The laws of thermodynamics are compactly stated. The final three chapters in Part I introduce the thermodynamic potentials and the Maxwell relations. Applications of thermodynamics to gases, condensed matter, and phase transitions and critical phenomena are dealt with in detail. Initial chapters in Part II present the elements of probability theory and establish the thermodynamic equivalence of the three statistical ensembles that are used in determining probabilities. The canonical and the grand canonical distributions are obtained and discussed. Chapters 12-15 are concerned with quantum distributions. By making use of the grand canonical distribution, the Fermi–Dirac and Bose–Einstein quantum distribution functions are derived and then used to explain the properties of ideal Fermi and Bose gases. The Planck distribution is introduced and applied to photons in radiation and to phonons on solids. The last five chapters cover a variety of topics: the ideal gas revisited, nonideal systems, the density matrix, reactions, and irreversible thermodynamics. A flowchart is provided to assist instructors on planning a course. Key Features: Fully updated throughout, with new content on exciting topics, including black hole thermodynamics, Heisenberg antiferromagnetic chains, entropy and information theory, renewable and nonrenewable energy sources, and the mean field theory of antiferromagnetic systems Additional problem exercises with solutions provide further learning opportunities Suitable for advanced undergraduate students in physics or applied physics. Michael J.R. Hoch spent many years as a visiting scientist at the National High Magnetic Field Laboratory at Florida State University, USA. Prior to this, he was a professor of physics and the director of the Condensed Matter Physics Research Unit at the University of the Witwatersrand, Johannesburg, where he is currently professor emeritus in the School of Physics.
Statistical and Thermal Physics: Fundamentals and Applications
by M.D. SturgeThis book is based on many years of teaching statistical and thermal physics. It assumes no previous knowledge of thermodynamics, kinetic theory, or probability---the only prerequisites are an elementary knowledge of classical and modern physics, and of multivariable calculus. The first half of the book introduces the subject inductively but rigorously, proceeding from the concrete and specific to the abstract and general. In clear physical language the book explains the key concepts, such as temperature, heat, entropy, free energy, chemical potential, and distributions, both classical and quantum. The second half of the book applies these concepts to a wide variety of phenomena, including perfect gases, heat engines, and transport processes. Each chapter contains fully worked examples and real-world problems drawn from physics, astronomy, biology, chemistry, electronics, and mechanical engineering.
Statistical Applications for Environmental Analysis and Risk Assessment
by Joseph OfungwuStatistical Applications for Environmental Analysis and Risk Assessment guides readers through real-world situations and the best statistical methods used to determine the nature and extent of the problem, evaluate the potential human health and ecological risks, and design and implement remedial systems as necessary. Featuring numerous worked examples using actual data and "ready-made" software scripts, Statistical Applications for Environmental Analysis and Risk Assessment also includes:* Descriptions of basic statistical concepts and principles in an informal style that does not presume prior familiarity with the subject* Detailed illustrations of statistical applications in the environmental and related water resources fields using real-world data in the contexts that would typically be encountered by practitioners* Software scripts using the high-powered statistical software system, R, and supplemented by USEPA's ProUCL and USDOE's VSP software packages, which are all freely available* Coverage of frequent data sample issues such as non-detects, outliers, skewness, sustained and cyclical trend that habitually plague environmental data samples* Clear demonstrations of the crucial, but often overlooked, role of statistics in environmental sampling design and subsequent exposure risk assessment.
Statistical Approach to Quantum Field Theory
by Andreas WipfOver the past few decades the powerful methods of statistical physics and Euclidean quantum field theory have moved closer together, with common tools based on the use of path integrals. The interpretation of Euclidean field theories as particular systems of statistical physics has opened up new avenues for understanding strongly coupled quantum systems or quantum field theories at zero or finite temperatures. Accordingly, 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. This text is based on course-tested notes for graduate students and, as such, its style is essentially pedagogical, requiring only some basics of mathematics, statistical physics, and quantum field theory. Yet it also contains some more sophisticated concepts which may be useful to researchers in the field. Each chapter ends with a number of problems - guiding the reader to a deeper understanding of some of the material presented in the main text - and, in most cases, also features some listings of short, useful computer programs.
Statistical Approach to Quantum Field Theory: An Introduction (Lecture Notes in Physics #992)
by Andreas WipfThis new expanded second edition has been totally revised and corrected. The reader finds two complete new chapters. One covers the exact solution of the finite temperature Schwinger model with periodic boundary conditions. This simple model supports instanton solutions – similarly as QCD – and allows for a detailed discussion of topological sectors in gauge theories, the anomaly-induced breaking of chiral symmetry and the intriguing role of fermionic zero modes. The other new chapter is devoted to interacting fermions at finite fermion density and finite temperature. Such low-dimensional models are used to describe long-energy properties of Dirac-type materials in condensed matter physics. The large-N solutions of the Gross-Neveu, Nambu-Jona-Lasinio and Thirring models are presented in great detail, where N denotes the number of fermion flavors. Towards the end of the book corrections to the large-N solution and simulation results of a finite number of fermion flavors are presented. Further problems are added at the end of each chapter in order to guide the reader to a deeper understanding of the presented topics. This book is meant for advanced students and young researchers who want to acquire the necessary tools and experience to produce research results in the statistical approach to Quantum Field Theory.
Statistical Approaches for Landslide Susceptibility Assessment and Prediction
by Subrata Mondal Sujit MandalThis book focuses on the spatial distribution of landslide hazards of the Darjeeling Himalayas. Knowledge driven methods and statistical techniques such as frequency ratio model (FRM), information value model (IVM), logistic regression model (LRM), index overlay model (IOM), certainty factor model (CFM), analytical hierarchy process (AHP), artificial neural network model (ANN), and fuzzy logic have been adopted to identify landslide susceptibility. In addition, a comparison between various statistical models were made using success rate cure (SRC) and it was found that artificial neural network model (ANN), certainty factor model (CFM) and frequency ratio based fuzzy logic approach are the most reliable statistical techniques in the assessment and prediction of landslide susceptibility in the Darjeeling Himalayas. The study identified very high, high, moderate, low and very low landslide susceptibility locations to take site-specific management options as well as to ensure developmental activities in theDarjeeling Himalayas.Particular attention is given to the assessment of various geomorphic, geotectonic and geohydrologic attributes that help to understand the role of different factors and corresponding classes in landslides, to apply different models, and to monitor and predict landslides. The use of various statistical and physical models to estimate landslide susceptibility is also discussed. The causes, mechanisms and types of landslides and their destructive character are elaborated in the book. Researchers interested in applying statistical tools for hazard zonation purposes will find the book appealing.
Statistical Benchmarks for Quantum Transport in Complex Systems: From Characterisation To Design (Springer Theses)
by Mattia WalschaersThis book introduces a variety of statistical tools for characterising and designing the dynamical features of complex quantum systems. These tools are applied in the contexts of energy transfer in photosynthesis, and boson sampling. In dynamical quantum systems, complexity typically manifests itself via the interference of a rapidly growing number of paths that connect the initial and final states. The book presents the language of graphs and networks, providing a useful framework to discuss such scenarios and explore the rich phenomenology of transport phenomena. As the complexity increases, deterministic approaches rapidly become intractable, which leaves statistics as a viable alternative.
Statistical Data Analysis for the Physical Sciences
by Adrian BevanData analysis lies at the heart of every experimental science. Providing a modern introduction to statistics, this book is ideal for undergraduates in physics. It introduces the necessary tools required to analyse data from experiments across a range of areas, making it a valuable resource for students. In addition to covering the basic topics, the book also takes in advanced and modern subjects, such as neural networks, decision trees, fitting techniques, and issues concerning limit or interval setting. Worked examples and case studies illustrate the techniques presented, and end-of-chapter exercises help test the reader's understanding of the material.
Statistical Downscaling and Bias Correction for Climate Research
by Douglas Maraun Martin WidmannStatistical downscaling and bias correction are becoming standard tools in climate impact studies. This book provides a comprehensive reference to widely-used approaches, and additionally covers the relevant user context and technical background, as well as a synthesis and guidelines for practitioners. It presents the main approaches including statistical downscaling, bias correction and weather generators, along with their underlying assumptions, skill and limitations. Relevant background information on user needs and observational and climate model uncertainties is complemented by concise introductions to the most important concepts in statistical and dynamical modelling. A substantial part is dedicated to the evaluation of regional climate projections and their value in different user contexts. Detailed guidelines for the application of downscaling and the use of downscaled information in practice complete the volume. Its modular approach makes the book accessible for developers and practitioners, graduate students and experienced researchers, as well as impact modellers and decision makers.
Statistical Geoinformatics for Human Environment Interface (Chapman & Hall/CRC Applied Environmental Statistics)
by Wayne L. Myers Ganapati P. PatilStatistical Geoinformatics for Human Environment Interface presents two paradigms for studying both space and interface with regard to human/environment: localization and multiple indicators. The first approach localizes thematic targets by treating space as a pattern of vicinities, with the pattern being a square grid and the placement of viciniti
A Statistical Mechanical Interpretation of Algorithmic Information Theory (SpringerBriefs in Mathematical Physics #36)
by Kohtaro TadakiThis book is the first one that provides a solid bridge between algorithmic information theory and statistical mechanics. Algorithmic information theory (AIT) is a theory of program size and recently is also known as algorithmic randomness. AIT provides a framework for characterizing the notion of randomness for an individual object and for studying it closely and comprehensively. In this book, a statistical mechanical interpretation of AIT is introduced while explaining the basic notions and results of AIT to the reader who has an acquaintance with an elementary theory of computation.A simplification of the setting of AIT is the noiseless source coding in information theory. First, in the book, a statistical mechanical interpretation of the noiseless source coding scheme is introduced. It can be seen that the notions in statistical mechanics such as entropy, temperature, and thermal equilibrium are translated into the context of noiseless source coding in a natural manner. Then, the framework of AIT is introduced. On this basis, the introduction of a statistical mechanical interpretation of AIT is begun. Namely, the notion of thermodynamic quantities, such as free energy, energy, and entropy, is introduced into AIT. In the interpretation, the temperature is shown to be equal to the partial randomness of the values of all these thermodynamic quantities, where the notion of partial randomness is a stronger representation of the compression rate measured by means of program-size complexity. Additionally, it is demonstrated that this situation holds for the temperature itself as a thermodynamic quantity. That is, for each of all the thermodynamic quantities above, the computability of its value at temperature T gives a sufficient condition for T to be a fixed point on partial randomness.In this groundbreaking book, the current status of the interpretation from both mathematical and physical points of view is reported. For example, a total statistical mechanical interpretation of AIT that actualizes a perfect correspondence to normal statistical mechanics can be developed by identifying a microcanonical ensemble in the framework of AIT. As a result, the statistical mechanical meaning of the thermodynamic quantities of AIT is clarified. In the book, the close relationship of the interpretation to Landauer's principle is pointed out.
Statistical Mechanics: An Introductory Graduate Course (Graduate Texts in Physics)
by A. J. Berlinsky A. B. HarrisIn a comprehensive treatment of Statistical Mechanics from thermodynamics through the renormalization group, this book serves as the core text for a full-year graduate course in statistical mechanics at either the Masters or Ph.D. level. Each chapter contains numerous exercises, and several chapters treat special topics which can be used as the basis for student projects. The concept of scaling is introduced early and used extensively throughout the text. At the heart of the book is an extensive treatment of mean field theory, from the simplest decoupling approach, through the density matrix formalism, to self-consistent classical and quantum field theory as well as exact solutions on the Cayley tree. Proceeding beyond mean field theory, the book discusses exact mappings involving Potts models, percolation, self-avoiding walks and quenched randomness, connecting various athermal and thermal models. Computational methods such as series expansions and Monte Carlo simulations are discussed, along with exact solutions to the 1D quantum and 2D classical Ising models. The renormalization group formalism is developed, starting from real-space RG and proceeding through a detailed treatment of Wilson’s epsilon expansion. Finally the subject of Kosterlitz-Thouless systems is introduced from a historical perspective and then treated by methods due to Anderson, Kosterlitz, Thouless and Young. Altogether, this comprehensive, up-to-date, and engaging text offers an ideal package for advanced undergraduate or graduate courses or for use in self study.
Statistical Mechanics: A Concise Advanced Textbook (UNITEXT for Physics)
by Sergio CecottiThis textbook is based on lecture notes that the author delivered at Qiuzhen College (Tsinghua University), a Chinese institution known for its exceptionally talented mathematics students. The book's intended audience shapes its character. It introduces Statistical Mechanics from the ground up, offering a fully self-contained presentation that aims for mathematical precision. It distinguishes rigorous results from controlled approximations and provides physical insights into phenomena. Despite its concise nature (suited for a one-semester basic course), this book covers several topics typically not found in introductory texts. These include Shannon's information-theoretic interpretation of entropy, the gauge approach to order-disorder duality in the Ising model, the Yang-Lee theory, and the quantum dissipation-fluctuation theorem. Additionally, it explores frustrated and quenched systems, including an introduction to the celebrated Parisi solution of the Sherrington-Kirkpatrick model of spin glasses. The path integral formalism is extensively discussed from various perspectives to suit different applications. Chapter 2 approaches path integrals through the Feynman-Kac formula and second quantization. In Chapter 5, they are examined within the context of effective field theories like Landau-Ginzburg theory, while Chapter 6 delves into their connection with Brownian motion, Langevin stochastic differential equations, and Fokker-Planck diffusion PDEs. The book also explores the relationship between stochastic processes and supersymmetry. Various techniques for computing path integrals, especially functional determinants, are introduced throughout the relevant chapters, offering the most suitable computational tools for each application.
Statistical Mechanics: Fundamentals and Model Solutions
by Teunis C DorlasStatistical Mechanics: Fundamentals and Model Solutions, Second Edition Fully updated throughout and with new chapters on the Mayer expansion for classical gases and on cluster expansion for lattice models, this new edition of Statistical Mechanics: Fundamentals and Model Solutions provides a comprehensive introduction to equilibrium statistical mechanics for advanced undergraduate and graduate students of mathematics and physics. The author presents a fresh approach to the subject, setting out the basic assumptions clearly and emphasizing the importance of the thermodynamic limit and the role of convexity. With problems and solutions, the book clearly explains the role of models for physical systems, and discusses and solves various models. An understanding of these models is of increasing importance as they have proved to have applications in many areas of mathematics and physics. Features Updated throughout with new content from the field An established and well-loved textbook Contains new problems and solutions for further learning opportunity Author Professor Teunis C. Dorlas is at the Dublin Institute for Advanced Studies, Ireland.
Statistical Mechanics of Classical and Disordered Systems: Luminy, France, August 2018 (Springer Proceedings in Mathematics & Statistics #293)
by Véronique Gayrard Louis-Pierre Arguin Nicola Kistler Irina KourkovaThese proceedings of the conference Advances in Statistical Mechanics, held in Marseille, France, August 2018, focus on fundamental issues of equilibrium and non-equilibrium dynamics for classical mechanical systems, as well as on open problems in statistical mechanics related to probability, mathematical physics, computer science, and biology. Statistical mechanics, as envisioned more than a century ago by Boltzmann, Maxwell and Gibbs, has recently undergone stunning twists and developments which have turned this old discipline into one of the most active areas of truly interdisciplinary and cutting-edge research. The contributions to this volume, with their rather unique blend of rigorous mathematics and applications, outline the state-of-the-art of this success story in key subject areas of equilibrium and non-equilibrium classical and quantum statistical mechanics of both disordered and non-disordered systems. Aimed at researchers in the broad field of applied modern probability theory, this book, and in particular the review articles, will also be of interest to graduate students looking for a gentle introduction to active topics of current research.