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The concept of entropy arises in diverse branches of science, including physics, where it plays a crucial role. However, the nature of entropy as a unifying concept is not widely discussed—it is dealt with in a piecemeal manner within different contexts. The interpretation of the concept is also subtly different in each case. This book will draw these diverse threads together and present entropy as one of the crucial physical concepts. It will cover a range of different applications of entropy, from the classical theory of thermodynamics, the statistical approach, entropy in quantum theory, information theory and finally, its manifestation in black hole physics. Each will be presented in a manner suitable for undergraduates and interested laypersons with no previous knowledge. The book will take an overview of these areas and see to what extent the concept of entropy is being treated in the same way in each, and how it differs.Key Features: Provides an accessible introduction to the exciting topic of entropy, setting out its manifestations in classical thermodynamics, statistical mechanics, and information theory Covers applications in black holes, quantum theory, and Big Bang cosmology

An engaging undergraduate introduction to the statistical mechanics of phase transitionsStatistical mechanics deploys a powerful set of mathematical approaches for studying the thermodynamic properties of complex physical systems. This textbook introduces students to the statistical mechanics of systems undergoing changes of state, focusing on the basic principles for classifying distinct thermodynamic phases and the critical phenomena associated with transitions between them. Uniquely designed to promote active learning, Statistical Mechanics of Phases and Phase Transitions presents some of the most beautiful and profound concepts in physics, enabling students to obtain an essential understanding of a computationally challenging subject without getting lost in the details.Provides a self-contained, conceptually deep introduction to the statistical mechanics of phases and phase transitions from a modern perspectiveCarefully leads students from spontaneously broken symmetries to the universality of phase transitions and the renormalization groupEncourages student-centric active learning suitable for both the classroom and self-studyFeatures a wealth of guided worksheets with full solutions throughout the book that help students learn by doingIncludes informative appendixes that cover key mathematical concepts and methodsIdeal for undergraduate physics majors and beginning graduate studentsSolutions manual for all end-of-chapter problems (available only to instructors)

This book provides an accessible introduction to thermal physics with computational approaches that complement the traditional mathematical treatments of classical thermodynamics and statistical mechanics. It guides readers through visualizations and simulations in the Python programming language, helping them to develop their own technical computing skills (including numerical and symbolic calculations, optimizations, recursive operations, and visualizations). Python is a highly readable and practical programming language, making this book appropriate for students without extensive programming experience.This book may serve as a thermal physics textbook for a semester-long undergraduate thermal physics course or may be used as a tutorial on scientific computing with focused examples from thermal physics. This book will also appeal to engineering students studying intermediate-level thermodynamics as well as computer science students looking to understand how to apply their computer programming skills to science.Key features Major concepts in thermal physics are introduced cohesively through computational and mathematical treatments. Computational examples in Python programming language guide students on how to simulate and visualize thermodynamic principles and processes for themselves.

The laws of nature encompass the small, the large, the few, and the many. In this book, we are concerned with classical (i.e., not quantum) many-body systems, which refers to any microscopic or macroscopic system that contains a large number of interacting entities. The nearest-neighbor Ising model, originally developed in 1920 by Wilhelm Lenz, forms a cornerstone in our theoretical understanding of collective effects in classical many-body systems and is to date a paradigm in statistical physics. Despite its elegant and simplistic description, exact analytical results in dimensions equal and larger than two are difficult to obtain. Therefore, much work has been done to construct methods that allow for approximate, yet accurate, analytical solutions. One of these methods is the Bethe-Guggenheim approximation, originally developed independently by Hans Bethe and Edward Guggenheim in 1935. This approximation goes beyond the well-known mean field approximation and explicitly accounts for pair correlations between the spins in the Ising model. In this book, we embark on a journey to exploit the full capacity of the Bethe-Guggenheim approximation, in non-uniform and non-equilibrium settings. Throughout we unveil the non-trivial and a priori non-intuitive effects of pair correlations in the classical nearest-neighbor Ising model, which are taken into account in the Bethe-Guggenheim approximation and neglected in the mean field approximation.

This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, is devoted to the fundamentals of Perturbation Theory (PT) as well as key applications areas such as Classical and Quantum Mechanics, Celestial Mechanics, and Molecular Dynamics. Less traditional fields of application, such as Biological Evolution, are also discussed. Leading scientists in each area of the field provide a comprehensive picture of the landscape and the state of the art, with the specific goal of combining mathematical rigor, explicit computational methods, and relevance to concrete applications. New to this edition are chapters on Water Waves, Rogue Waves, Multiple Scales methods, legged locomotion, Condensed Matter among others, while all other contributions have been revised and updated. Coverage includes the theory of (Poincare'-Birkhoff) Normal Forms, aspects of PT in specific mathematical settings (Hamiltonian, KAM theory, Nekhoroshev theory, and symmetric systems), technical problems arising in PT with solutions, convergence of series expansions, diagrammatic methods, parametric resonance, systems with nilpotent real part, PT for non-smooth systems, and on PT for PDEs [write out this acronym partial differential equations]. Another group of papers is focused specifically on applications to Celestial Mechanics, Quantum Mechanics and the related semiclassical PT, Quantum Bifurcations, Molecular Dynamics, the so-called choreographies in the N-body problem, as well as Evolutionary Theory. Overall, this unique volume serves to demonstrate the wide utility of PT, while creating a foundation for innovations from a new generation of graduate students and professionals in Physics, Mathematics, Mechanics, Engineering and the Biological Sciences.

Statistical Mechanics: Fundamentals and Model Solutions, Second EditionFully 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 AuthorProfessor Teunis C. Dorlas is at the Dublin Institute for Advanced Studies, Ireland.

Rational extended thermodynamics (RET) is the theory that is applicable to nonequilibrium phenomena out of local equilibrium. It is expressed by the hyperbolic system of field equations with local constitutive equations and is strictly related to the kinetic theory with the closure method of the hierarchies of moment equations. The book intends to present, in a systematic way, new results obtained by RET of gases in both classical and relativistic cases, and it is a natural continuation of the book'Rational Extended Thermodynamics beyond the Monatomic Gas'by the same authors published in 2015. However, this book addresses much wider topics than those of the previous book. Its contents are as follows: RET of rarefied monatomic gases and of polyatomic gases; a simplified RET theory with 6 fields being valid far from equilibrium; RET where both molecular rotational and vibrational modes exist; mixture of gases with multi-temperature. The theory is applied to several typical topics (sound waves, shock waves, etc.) and is compared with experimental data. From a mathematical point of view, RET can be regarded as a theory of hyperbolic symmetric systems, of which it is possible to conduct a qualitative analysis. The book represents a valuable resource for applied mathematicians, physicists, and engineers, offering powerful models for many potential applications such as reentering satellites into the atmosphere, semiconductors, and nanoscale phenomena.

This book provides an ideal introduction to the use of Feynman path integrals in the fields of quantum mechanics and statistical physics. It is written for graduate students and researchers in physics, mathematical physics, applied mathematics as well as chemistry. The material is presented in an accessible manner for readers with little knowledge of quantum mechanics and no prior exposure to path integrals. It begins with elementary concepts and a review of quantum mechanics that gradually builds the framework for the Feynman path integrals and how they are applied to problems in quantum mechanics and statistical physics. Problem sets throughout the book allow readers to test their understanding and reinforce the explanations of the theory in real situations.Features: Comprehensive and rigorous yet, presents an easy-to-understand approach. Applicable to a wide range of disciplines. Accessible to those with little, or basic, mathematical understanding.

This book investigates two possibilities for describing classical-mechanical physical systems along with their Hamiltonian dynamics in the framework of quantum mechanics.The first possibility consists in exploiting the geometrical properties of the set of quantum pure states of'microsystems'and of the Lie groups characterizing the specific classical system. The second approach is to consider quantal systems of a large number of interacting subsystems – i.e. macrosystems, so as to study the quantum mechanics of an infinite number of degrees of freedom and to look for the behaviour of their collective variables. The final chapter contains some solvable models of “quantum measurement'describing dynamical transitions from'microsystems'to'macrosystems'.

This contributed volume provides an up-to-date overview of the mechanics of granular materials, ranging from sparse media to soils. With chapters exploring state-of-the-art theoretical, experimental, and applied trends in the study of granular matter in various states, readers will be motivated to learn about the current challenges and potential avenues of exploration in this active area of research. Including a variety of perspectives, this volume will be a valuable reference for audiences in a number of fields. Specific topics covered include:X-ray tomography techniques for analyzing sandEvaluation of effective stress in unsaturated soilsHyper-plasticityWave propagation in granular systemsPartly saturated porous mediaMulti-scale approaches to the dynamics of sparse mediaViews on Microstructures in Granular Materials is an ideal resource for PhD students and researchers in applied mathematics, solid-state physics, civil engineering, and mechanical engineering.

This book presents the basic elements of theoretical physics in a highly accessible, captivating way for university students in the third year of a degree in physics. It covers analytical mechanics, thermodynamics and statistical physics, special and general relativity and non-relativistic quantum theory, fully developing the necessary mathematical methods beyond standard calculus. The central theme is scientific curiosity and the main focus is on the experimental meaning of all quantities and equations. Several recent verifications of General Relativity are presented, with emphasis on the physical effects – why they were predicted to exist and what signals they were seen to produce. Similarly, the basic reasons why superconductors have zero resistance and are perfect diamagnets are pinpointed. Quantum Eraser Experiments and Delayed Choice Experiments are described. Many statements of Quantum Theory are a challenge to common sense and some crucial predictionshave often been considered hard to believe and have been tested experimentally. The book examines the EPR paradox, Bell states and teleportation.To show the beauty and richness of the subject, various topics from different areas of Physics are covered. These include: discrete quantum models and lattices (periodic and not), Casimir effect, Anyons, Fano Resonances, the Hanbury Brown and Twiss effect, the Aharonov-Bohm effect, the Meitner-Auger effect, Squeezed Light, the Rabi model, neutrino oscillations, aspects of Quantum Transport, Quantum Pumping, and Berry phases, black holes and cosmological problems.

What is the world beyond the Planck scale that provides the minimum unit of the universe? The goal of quantum gravity is to reveal physical laws in such a world. There, quantum fluctuations of gravity become large, and what is called a background-free world where the concept of time and distance is lost shall be realized. The renormalizable quantum gravity introduced in this book offers a theory in which such a world is described by a certain conformal field theory and a deviation from there is handled as a perturbation. This is the state-of-the-art of modern physics that will help in understanding the history of the universe, from its birth to the present.

This textbook gives a basic introduction to theoretical physics. It deals with mechanics, electrodynamics, theory of relativity, quantum mechanics and statistical physics, thus covering all the standard disciplines of theoretical physics in a single volume. The material is presented in a concise style, enabling the reader to follow the central themes. Various excursions rarely found in other textbooks are designed to give deeper insight into interesting and current topics. A chapter on the mathematical background gives easy access to the other chapters and many exercises are included to support learning. The book is an ideal resource for advanced undergraduate and graduate students seeking to consolidate their knowledge.

An introductory textbook exploring the subject of Lagrangian and Hamiltonian dynamics, with a relaxed and self-contained setting. Lagrangian and Hamiltonian dynamics is the continuation of Newton's classical physics into new formalisms, each highlighting novel aspects of mechanics that gradually build in complexity to form the basis for almost all of theoretical physics. Lagrangian and Hamiltonian dynamics also acts as a gateway to more abstract concepts routed in differential geometry and field theories and can be used to introduce these subject areas to newcomers. Journeying in a self-contained manner from the very basics, through the fundamentals and onwards to the cutting edge of the subject, along the way the reader is supported by all the necessary background mathematics, fully worked examples, thoughtful and vibrant illustrations as well as an informal narrative and numerous fresh, modern and inter-disciplinary applications. The book contains some unusual topics for a classical mechanics textbook. Most notable examples include the'classical wavefunction', Koopman-von Neumann theory, classical density functional theories, the'vakonomic'variational principle for non-holonomic constraints, the Gibbs-Appell equations, classical path integrals, Nambu brackets and the full framing of mechanics in the language of differential geometry.

Articles in this volume are based on lectures presented at the Park City summer school on “Mathematics and Materials” in July 2014. The central theme is a description of material behavior that is rooted in statistical mechanics. While many presentations of mathematical problems in materials science begin with continuum mechanics, this volume takes an alternate approach. All the lectures present unique pedagogical introductions to the rich variety of material behavior that emerges from the interplay of geometry and statistical mechanics. The topics include the order-disorder transition in many geometric models of materials including nonlinear elasticity, sphere packings, granular materials, liquid crystals, and the emerging field of synthetic self-assembly. Several lectures touch on discrete geometry (especially packing) and statistical mechanics. The problems discussed in this book have an immediate mathematical appeal and are of increasing importance in applications, but are not as widely known as they should be to mathematicians interested in materials science. The volume will be of interest to graduate students and researchers in analysis and partial differential equations, continuum mechanics, condensed matter physics, discrete geometry, and mathematical physics.

The Physical World offers a grand vision of the essential unity of physics that will enable the reader to see the world through the eyes of a physicist and understand their thinking. The text follows Einstein's dictum that'explanations should be made as simple as possible, but no simpler', to give an honest account of how modern physicists understand their subject, including the shortcomings of current theory. The result is an up-to-date and engaging portrait of physics that contains concise derivations of the important results in a style where every step in a derivation is clearly explained, so that anyone with the appropriate mathematical skills will find the text easy to digest. It is over half a century since The Feynman Lectures in Physics were published. A new authoritative account of fundamental physics covering all branches of the subject is now well overdue. The Physical World has been written to satisfy this need. The book concentrates on the conceptual principles of each branch of physics and shows how they fit together to form a coherent whole. Emphasis is placed on the use of variational principles in physics, and in particular the principle of least action, an approach that lies at the heart of modern theoretical physics, but has been neglected in most introductory accounts of the subject.

Describing non-equilibrium'cold'plasmas through a chemical physics approach, this book uses the state-to-state plasma kinetics, which considers each internal state as a new species with its own cross sections. Extended atomic and molecular master equations are coupled with Boltzmann and Monte Carlo methods to solve the electron energy distribution function. Selected examples in different applied fields, such as microelectronics, fusion, and aerospace, are presented and discussed including the self-consistent kinetics in RF parallel plate reactors, the optimization of negative ion sources and the expansion of high enthalpy flows through nozzles of different geometries.The book will cover the main aspects of the state-to-state kinetic approach for the description of nonequilibrium cold plasmas, illustrating the more recent achievements in the development of kinetic models including the self-consistent coupling of master equations and Boltzmann equation for electron dynamics.To give a complete portrayal, the book will assess fundamental concepts and theoretical formulations, based on a unified methodological approach, and explore the insight in related scientific problems still opened for the research community.

In this book, the thermodynamic observables of the classical one- and two-dimensional ferromagnetic and antiferromagnetic Ising models on a square lattice are simulated, especially at the phase transitions (if applicable) using the classical Monte Carlo algorithm of Metropolis. Finite size effects and the influence of an external magnetic field are described. The critical temperature of the 2d ferromagnetic Ising model is obtained using finite size scaling. Before presenting the Ising model, the basic concepts of statistical mechanics are recapped. Furthermore, the general principles of Monte Carlo methods are explained.

Granular systems arise in a variety of geological and industrial settings, from landslides, avalanches, and erosion to agricultural grains and pharmaceutical powders. Understanding the underlying physics that governs their behavior is the key to developing effective handling and transport mechanisms as well as appropriate environmental policies.Han

In this introductory text, physics concepts are introduced as a means of understanding experimental observations, not as a sequential list of facts to be memorized. The book is structured around the key scientific discoveries that led to much of our current understanding of the universe. Numerous exercises are provided that utilize Mathematica software to help students explore how the language of mathematics is used to describe physical phenomena. Topics requiring quantum mechanics for a more complete explanation are identified but not pursued.In a departure from the traditional methodology and subject matter used in introductory physics texts, this is organized in a manner that will facilitate a guided discovery style of instruction. Students will obtain much more detailed information about fewer topics and will also gain proficiency with Mathematica, a powerful tool with many potential uses in subsequent courses.

This book gives a survey of astrophysics at the advanced undergraduate level, providing a physics-centred analysis of a broad range of astronomical systems. It originates from a two-semester course sequence at Rutgers University that is meant to appeal not only to astrophysics students but also more broadly to physics and engineering students. The organisation is driven more by physics than by astronomy; in other words, topics are first developed in physics and then applied to astronomical systems that can be investigated, rather than the other way around. The first half of the book focuses on gravity. The theme in this part of the book, as well as throughout astrophysics, is using motion to investigate mass. The goal of Chapters 2-11 is to develop a progressively richer understanding of gravity as it applies to objects ranging from planets and moons to galaxies and the universe as a whole. The second half uses other aspects of physics to address one of the bigquestions. While “Why are we here?” lies beyond the realm of physics, a closely related question is within our reach: “How did we get here?” The goal of Chapters 12-20 is to understand the physics behind the remarkable story of how the Universe, Earth and life were formed. This book assumes familiarity with vector calculus and introductory physics (mechanics, electromagnetism, gas physics and atomic physics); however, all of the physics topics are reviewed as they come up (and vital aspects of vector calculus are reviewed in the Appendix).

Based around a series of real-life scenarios, this engaging introduction to statistical reasoning will teach you how to apply powerful statistical, qualitative and probabilistic tools in a technical context. From analysis of electricity bills, baseball statistics, and stock market fluctuations, through to profound questions about physics of fermions and bosons, decaying nuclei, and climate change, each chapter introduces relevant physical, statistical and mathematical principles step-by-step in an engaging narrative style, helping to develop practical proficiency in the use of probability and statistical reasoning. With numerous illustrations making it easy to focus on the most important information, this insightful book is perfect for students and researchers of any discipline interested in the interwoven tapestry of probability, statistics, and physics.

This book reviews the basic ideas of the Law of Large Numbers with its consequences to the deterministic world and the issue of ergodicity. Applications of Large Deviations and their outcomes to Physics are surveyed. The book covers topics encompassing ergodicity and its breaking and the modern applications of Large deviations to equilibrium and non-equilibrium statistical physics, disordered and chaotic systems, and turbulence.

The principle aim of the book is to present a self-contained, modern account of similarity and symmetry methods, which are important mathematical tools for both physicists, engineers and applied mathematicians. The idea is to provide a balanced presentation of the mathematical techniques and applications of symmetry methods in mathematics, physics and engineering.That is why it includes recent developments and many examples in finding systematically conservation laws, local and nonlocal symmetries for ordinary and partial differential equations.The role of continuous symmetries in classical and quantum field theories is exposed at a technical level accessible even for non specialists. The importance of symmetries in continuum mechanics and mechanics of materials is highlighted through recent developments, such as the construction of constitutive models for various materials combining Lie symmetries with experimental data.As a whole this book is a unique collection of contributions from experts in the field, including specialists in the mathematical treatment of symmetries, researchers using symmetries from a fundamental, applied or numerical viewpoint.The book is a fascinating overview of symmetry methods aimed for graduate students in physics, mathematics and engineering, as well as researchers either willing to enter in the field or to capture recent developments and applications of symmetry methods in different scientific fields.

Since the second half of the 20th century machine computations have played a critical role in science and engineering. Computer-based techniques have become especially important in molecular biology, since they often represent the only viable way to gain insights into the behavior of a biological system as a whole. The complexity of biological systems, which usually needs to be analyzed on different time- and size-scales and with different levels of accuracy, requires the application of different approaches, ranging from comparative analysis of sequences and structural databases, to the analysis of networks of interdependence between cell components and processes, through coarse-grained modeling to atomically detailed simulations, and finally to molecular quantum mechanics. This book provides a comprehensive overview of modern computer-based techniques for computing the structure, properties and dynamics of biomolecules and biomolecular processes. The twenty-two chapters, written by scientists from all over the world, address the theory and practice of computer simulation techniques in the study of biological phenomena. The chapters are grouped into four thematic sections dealing with the following topics: the methodology of molecular simulations; applications of molecular simulations; bioinformatics methods and use of experimental information in molecular simulations; and selected applications of molecular quantum mechanics. The book includes an introductory chapter written by Harold A. Scheraga, one of the true pioneers in simulation studies of biomacromolecules.

This book investigates a discrete theory beyond space and time of QCD-entanglement that creates space-time. Quantum entanglement is known as the most striking property of electrodynamics. It provides both a foundation for quantum information technology and a challenge for theoretical physics. Unfortunately, the equations of motion for entangled systems, quantum jumps and similar phenomena are always conceived as models in space-time. Regardless, whether we consider a quantized local oscillator, a heterodyne detection model, a Bell inequality, a CHSH-inequality, an objective pure state system, or a nonlinear steering inequality, it is always formulated in space-time, using the x, ¦ Òx and so on. This is a doubtable method, since proceeding in this way, we are constructing space-time models of those events that bring about this very space-time, the frames, wherein they are supposed to move. Those who carry out calculations in EPR quantum-steering experiments are acquainted with the Kochen-Specker theorem. But they are still deriving the estimates for expectation values of densities and inequalities from the implicit assumption of states in Hilbert-space. Though some of us have cooperatively managed to close all the major loopholes, the locality loophole, the freedom-of-choice loophole and the detection loophole, none of us has as yet realized that a closure of the locality-loophole in strong qcd-interaction is entirely impossible. A space-like separation of hadronic events cannot be achieved. The reason for our weak models is in the lack of a suitable exact theory of interaction. Such a theory is complete and phenomenologically consistent to some extent. Theoretically, both the iterant algebra of polarized entangled strings as well as the derived geometric algebra of the known space-time is incompatible with complete space-like separation. The loophole opening up on this basis is as large and as old as that universe we pretend to know. Time as a forth coordinate does not have the same relevance in quantum mechanics as position. This has deep phenomenological roots. There is no mathematics of any elementary particle in something like a global space-time. There is no reasonable proof for the existence of any time-energy uncertainty principle since t is not an operator. The commutator [t, H] does not exist. There is however a possibility to introduce iterative temporal shift- and tangle-time operators as algebraic elements in a self-reflexive domain of discrete events disclosed in presence. Starting with polarization in iterant spaces that allow for touch of events, and logic comparison, it becomes possible that these quantum-informatic events pile up to form both space-time and quantum chromodynamics in its current form. Ultimately, the self-reflexive domain that we may call the present turns out as a location-space which contains a substructure that we denote as the past. The past can be constructed as a partially ordered subset of the present. The present involves motion beyond time. Time is a locally constructed measure. Realizing this signifies the beginning of a new form of mathematical physics.

This textbook offers an advanced undergraduate or initial graduate level introduction to topics such as kinetic theory, equilibrium statistical mechanics and the theory of fluctuations from a modern perspective. The aim is to provide the reader with the necessary tools of probability theory and thermodynamics (especially the thermodynamic potentials) to enable subsequent study at advanced graduate level. At the same time, the book offers a bird's eye view on arguments that are often disregarded in the main curriculum courses. Further features include a focus on the interdisciplinary nature of the subject and in-depth discussion of alternative interpretations of the concept of entropy. While some familiarity with basic concepts of thermodynamics and probability theory is assumed, this does not extend beyond what is commonly obtained in basic undergraduate curriculum courses.

Bringing together over fifty contributions on all aspects of nonlinear and complex dynamics, this impressive topical collection is both a scientific and personal tribute, on the occasion of his 70th birthday, by many outstanding colleagues in the broad fields of research pursued by Prof. Manuel G Velarde. The topics selected reflect the research areas covered by the famous Instituto Pluridisciplinar at the Universidad Complutense of Madrid, which he co-founded over two decades ago, and include: fluid physics and related nonlinear phenomena at interfaces and in other geometries, wetting and spreading dynamics, geophysical and astrophysical flows, and novel aspects of electronic transport in anharmonic lattices, as well as topics in neurodynamics and robotics.

Mathematical Physics in One Dimension: Exactly Soluble Models of Interacting Particles covers problems of mathematical physics with one-dimensional analogs. The book discusses classical statistical mechanics and phase transitions; the disordered chain of harmonic oscillators; and electron energy bands in ordered and disordered crystals. The text also describes the many-fermion problem; the theory of the interacting boson gas; the theory of the antiferromagnetic linear chains; and the time-dependent phenomena of many-body systems (i.e., classical or quantum-mechanical dynamics). Physicists and mathematicians will find the book invaluable.

Multiply charged ions have always been in the focus of atomic physics, astrophysics, plasma physics, and theoretical physics. Within the last few years, strong progress has been achieved in the development of ion sources, ion storage rings, ion traps, and methods to cool ions. As a consequence, nowadays, experiments with ensembles of multiply charged ions of brilliant quality are performed in many laboratories. The broad spectrum of the experiments demonstrates that these ions are an extremely versatile tool for investigations in pure and applied physics. It was the aim of this ASI to bring together scientists working in different fields of research with multiply charged ions in order to get an overview of the state of the art, to sound out possibilities for fruitful cooperations, and to discuss perspectives for the future. Accordingly, the programme of the ASI reached from established areas like QED calculations, weak interactions, x-ray astronomy, x-ray lasers, multi photon excitation, heavy-ion induced fusion, and ion-surface interactions up to the very recently opened areas like bound-beta decay, laser and x-ray spectroscopy, and spectrometry of ions in rings and traps, and the interaction of highly charged ions with biological cells. Impressive progress in nearly all of the fields could be reported during the meeting which is documented by the contributions to this volume. The theoretical understand­ ing of QED and correlation effects in few-electron heavy ions is rapidly developing.

This book represents a concise summary of non-relativistic quantum mechanics on the level suitable for university students of physics. It covers, perhaps even slightly exceeds, a one-year course of about 50 lectures, requiring basic knowledge of calculus, algebra, classical mechanics and a bit of motivation for the quantum adventure. The exposition is succinct, with minimal narration, but with a maximum of explicit and hierarchically structured mathematical derivations. The text covers all essential topics of university courses of quantum mechanics – from general mathematical formalism to specific applications. The formulation of quantum theory is accompanied by illustrations of the general concepts of elementary quantum systems. Some subtleties of mathematical foundations are overviewed, but the formalism is used in an accessible, intuitive way. Besides the traditional topics of non-relativistic quantum mechanics, such as single-particle dynamics, symmetries, semiclassical and perturbative approximations, density-matrix formalism, scattering theory, theory of angular momentum, description of many-particle systems – the course also touches upon some modern issues, including quantum entanglement, decoherence, measurement, nonlocality, and quantum information. Historical context and chronology of basic achievements is outlined in brief remarks. The book is intended for beginners as a supplement to lectures, however, it may also be used by more advanced students as a compact and comprehensible overview of elementary quantum theory.

This textbook presents essential methodology for physicists of the theory and applications of fluid mechanics within a single volume. Building steadily through a syllabus, it will be relevant to almost all undergraduate physics degrees which include an option on hydrodynamics, or a course in which hydrodynamics figures prominently.

Presenting some of the most recent results of Russian research into shock compression, as well as historical overviews of the Russian research programs into shock compression, this volume will provide Western researchers with many novel ideas and points of view. The chapters in this volume are written by leading Russian specialists various fields of high-pressure physics and form accounts of the main researches on the behavior of matter under shock-wave interaction. The experimental portions contain results of studies of shock compression of metals to high and ultra-high pressure, shock initiation of polymorphic transformations, strength, fracture and fragmentation under shock compression, and detonation of condensed explosives. There are also chapters on theoretical investigations of shock-wave compression and plasma states in regimes of high-pressure and high- temperature. The topics of the book are of interest to scientists and engineers concerned with questions of material behavior under impulsive loading and to the equation of state of matter. Application is to questions of high-speed impact, inner composition of planets, verification of model representations of material behavior under extreme 1oading conditions, syntheses of new materials, development of new technologies for material processing, etc. Russian research differs from much of the Western work in that it has traditionally been wider-ranging and more directed to extremes of response than to precise characterization of specific materials and effects. Western scientists could expect to benefit from the perspective gained from close knowledge of the Russian work.

Proceedings of the NATO ARW, Shoresh, Israel, from 30 June to 4 July 2003

The book is devoted to the physical properties of nonideal plasma, in which the effects of interparticle interactions are substantial. Such a plasma is usually compressed so strongly that it is called dense plasma. Interest in plasma studies has increased over the last 10 or 15 years, owing to the development of modern technology and sophisticated facilities whose oper­ ation is based on a high energy density. As a result of a recent sharp increase in the number of experimental and theoretical investigations, much interesting and reliable data on the properties of dense plasma have been obtained. The data are distributed in a rapidly growing number of original publications and reviews. This volume is a systematic treatment of the thermodynamics (ionization equilibrium, particle composition), charge transport properties (especially electric con­ ductivity), optical properties (peculiarities of continuous and discrete spectra), and collective modes (features and manifestations) of nonideal plasma. Theoretical models are considered along with the experimental data. The book is intended for the wide range of readers, including specialists in plasma physics and various researchers who need knowledge in this field.

Intended for beginners in ergodic theory, this book addresses students as well as researchers in mathematical physics. The main novelty is the systematic treatment of characteristic problems in ergodic theory by a unified method in terms of convergent power series and renormalization group methods, in particular. Basic concepts of ergodicity, like Gibbs states, are developed and applied to, e.g., Asonov systems or KAM Theory. Many examples illustrate the ideas and, in addition, a substantial number of interesting topics are treated in the form of guided problems.

High Temperature Gas Dynamics is a class-tested primer for students, scientists and engineers who would like to have a basic understanding of the physics and the behaviour of high-temperature gases. It is a valuable tool for astrophysicists as well. The first chapters treat the basic principles of quantum and statistical mechanics and how to derive thermophysical properties from them. Special topics are included that are rarely found in other textbooks, such as the thermophysical and transport properties of multi-temperature gases and a novel method to compute radiative transfer. Furthermore, collision processes between different particles are discussed. Separate chapters deal with the production of high-temperature gases and with electrical emission in plasmas, as well as related diagnostic techniques.

Thermodynamic Diagrams for High Temperature Plasmas of Air, Air-Carbon, Carbon-Hydrogen Mixtures, and Argon provides information relating to the properties of equilibrium gas plasmas formed from hydrocarbons, from air without argon, from pure argon, and from mixtures of air and carbon at various compositions, temperatures and pressures. The data are presented in graphical rather than tabular form to provide a clearer picture of the plasma processes investigated. This book is composed of four chapters, and begins with the introduction to the characteristics of plasmas, with emphasis on their thermodynamic properties. The succeeding chapter deals with the theoretical basis of the computations of thermodynamic properties using a system of equations derived from quantized Boltzmann statistics. These topics are followed by discussions on the calculation of equilibrium compositions and the thermodynamic values for thermal plasmas. The final chapter describes proposed models on which the calculations are based. This book will prove useful to chemical technologists and researchers.

In this monograph, nonequilibrium statistical mechanics is developed by means of ensemble methods on the basis of the Boltzmann equation, the generic Boltzmann equations for classical and quantum dilute gases, and a generalised Boltzmann equation for dense simple fluids. The theories are developed in forms parallel with the equilibrium Gibbs ensemble theory in a way fully consistent with the laws of thermodynamics. The generalised hydrodynamics equations are the integral part of the theory and describe the evolution of macroscopic processes in accordance with the laws of thermodynamics of systems far removed from equilibrium. Audience: This book will be of interest to researchers in the fields of statistical mechanics, condensed matter physics, gas dynamics, fluid dynamics, rheology, irreversible thermodynamics and nonequilibrium phenomena.

The physical properties of fluids are perhaps among the most extensively investigated physical constants of any single group of materials. This is particularly true of the thermodynamic prop­ erties of pure substances since the condition of thermodynamic equilibrium provides the simplest considerations for experimental measurement as well as theoretical treatment. In the case of non­ equilibrium transport properties, the situation is significantly complicated by the necessity of measurement of gradients in the experiment and the mathematical difficulties in handling non­ equilibrium distribution functions in theoretical treatments. Hence, our knowledge of the trans­ port properties of gases and liquids is perhaps one order of magnitude lower than for equilibrium thermodynamic properties. This situation is very much apparent when examining the available nu­ merical data on the viscosity of fluids particularly at high pressures. In this work, the authors have performed an outstanding contribution to the engineering literature by their critical evaluation of the pressure dependence of the available data on the viscosity of selected substances. The recommended values reported in the tables and figures also incorporate the saturated liquid and gas states as well as the data of the dilute gas in an attempt to integrate the present work with the recently published work by CINDAS/Purdue University on the viscosity of fluids at low pressures [166]. A deliberate effort was made to treat as many of the substances in the CINDAS volume as possible for which adequate high pressure data exist.

This monograph creates a systematic interpretation of the theoretical and the most actual experimental aspects of the internal wave dynamics in the ocean. Firstly, it draws attention to the important physical effects from an oceanographical point of view which are presented in mathematical descriptions. Secondly, the book serves as an introduction to the range of modern ideas and the methods in the study of wave processes in dispersive media. The book is meant for specialists in physics of the ocean, oceanography, geophysics, hydroacoustics.

Flows with chemical reactions can occur in various fields such as combustion, process engineering, aeronautics, the atmospheric environment and aquatics.The examples of application chosen in this book mainly concern homogeneous reactive mixtures that can occur in propellers within the fields of process engineering and combustion:– propagation of sound and monodimensional flows in nozzles, which may include disequilibria of the internal modes of the energy of molecules;– ideal chemical reactors, stabilization of their steady operation points in the homogeneous case of a perfect mixture and classical instruments of experimental and theoretical analysis such as population balances, and the distribution of residence and passage times;– laminar and turbulent flames, separating those which are premixed from those which are not and which do not exhibit the same mechanisms, but which also occur in the case of triple flames.Flows and Chemical Reactions in Homogeneous Mixtures provides information on dimensional analysis, statistical thermodynamics with coupling between internal modes and chemical reactions, the apparition and damping of fluid turbulence as well as its statistical processing, bifurcations, flames in a confined medium and diffusion. Contents 1. Flows in Nozzles.2. Chemical Reactors.3. Laminar and Turbulent Flames.Appendix 1. Dimensionless Numbers, Similarity.Appendix 2. Thermodynamic Functions.Appendix 3. Concepts of Turbulence.Appendix 4. Thermodynamic functions for a mixture in disequilibrium.Appendix 5. Notion of bifurcation.Appendix 6. Confined flame.Appendix 7. Limits of Validity of the First-order Expansions for Diffusion Flames.

This 6th International Workshop in the series starting in 1969 was held at the Naval Postgraduate School in Monterey, California from 25-29 October, 1982 under the continuing directorship of Heinrich Hora. The co-directorship of the late Helmut Schwarz who helped found the series was assumed by George Miley. Fred Schwirzke served as the local organizer. Following a commemoration for Helmut Schwarz, Heinrich Hora connnented that the long title of the workshop is originally due to Nicholas Bloembergen, who prophetically envisaged that'related plasma phenomena'such as is involved in particle beam fusion is also of enormous interest to the laser connnunity. The en­ thusiastic response of the workshop advisors and the 82 participants from 11 countries supports the need for a continuation of this work­ shop-type meeting where an innnediate discussion and documentation of new results and conceptual formulations occurs, a process not possible through the usual journals. The main sponsor of this year's confer­ ence was the Fusion Studies Laboratory of the University of Illinois. Thanks are also due to the Naval Postgraduate School, Monterey, and the Department of Theoretical Physics, University of New South Wales. The conference was made feasible by the contributions of the partici­ pants, and they and their institutions deserve many thanks. Special recognition is due to the Conference Secretary, Chris Stalker (Urbana), as well as to Marie Wesson (Sydney) and to Patricia Vardaro (Monterey).

Chapter 1 - Poynting's Theorem Chapter 2 - Runge–Gross Theorem Chapter 3 - No–Communication Theorem Chapter 4 - Shell Theorem Chapter 5 - Wick's Theorem Chapter 6 - Noether's Theorem Chapter 7 - Liouville's Theorem (Hamiltonian) Chapter 8 - Mermin–Wagner Theorem Chapter 9 - Leggett–Garg Inequality & Kutta–Joukowski Theorem Chapter 10 - Laws and Theories of Optics and Acoustics Chapter 11 - Laws of Mechanics and Thermodynamics Chapter 12 - Laws and Theories of Electricity, Quantum Mechanics and Particle Physics

The past decade has seen the development of the operational understanding of fun­ damental interactions within the standard model. This has detoured our attention from the great enigmas posed by the dynamics and collective behavior of strongly interacting particles. Discovered more than 30 years ago, the thermal nature of the hadronic particle spectra has stimulated considerable theoretical effort, which so far has failed to'confirm'on the basis of microscopic interactions the origins of this phenomenon. However, a highly successful Statistical Bootstrap Model was developed by Rolf Hagedorn at CERN about 30 years ago, which has led us to consider the'boiling hadronic matter'as a transient state in the trans­ formation of hadronic particles into their melted form which we call Quark-GIuon-Plasma (QGP). Today, we return to seek detailed understanding of the thermalization processes of hadronic matter, equipped on the theoretical side with the knowledge of the fundamental strong interaction theory, the quantum chromo-dynamics (QCD), and recognizing the im­ portant role of the complex QCD-vacuum structure. On the other side, we have developed new experimental tools in the form of nuclear relativistic beams, which allow to create rather extended regions in space-time of Hot Hadronic Matter. The confluence of these new and recent developments in theory and experiment led us to gather together from June 27 to July 1, 1994, at the Grand Hotel in Divonne-Ies-Bains, France, to discuss and expose the open questions and issues in our field.

This interdisciplinary meeting has brought together a group of astrophysicists with hands-on experience in the numerical computation of astrophysical fluid dynamics, in particular nonlinear stellar pulsations, and a group of applied mathematicians who are actively engaged with the development of novel and improved numerical methods. The goal of the workshop has been for the astrophysicists to discuss in detail the numerical problems encountered in the modelling of stellar pulsations and for the mathematicians to present a survey of recent developments in numerical techniques. This astrophysical-mathematical intercourse will help the astrophysicists in the future development of more reliable and efficient codes, on the one hand, and it has introduced the mathematicians to an unfamiliar area which is a tough testing ground for their techniques. Since the difficulties encountered are common to other fluid dynamics problems, and are in fact perhaps more severe, fluid dynamicists in other research areas may fmd the results of this workshop of interest as well. Much of our theoretical understanding of the intricate and interesting behavior of variable stars rests on our ability to perform accurate numerical hydrodynamical computations of stellar models. Extensive calculations of nonlinear radial stellar pulsations with the use of increasingly powerful computers are showing more and more clearly that the numerical codes in current use have serious deficiencies.

This volume is based on courses on Statistical Mechanics which I have taught for many years at the Worcester Polytechnic Institute. My objective is to treat classical statistical mechanics and its modem applications, especially interacting particles, correlation functions, and time-dependent phenomena. My development is based primarily on Gibbs's ensemble formulation. Elementary Lectures in Statistical Mechanics is meant as a (relatively sophis­ ticated) undergraduate or (relatively straightforward) graduate text for physics students. It should also be suitable as a graduate text for physical chemistry stu­ dents. Physicists may find my treatment of algebraic manipulation to be more explicit than some other volumes. In my experience some of our colleagues are perhaps a bit over-enthusiastic about the ability or tendency of our students to complete gaps in the derivations. I emphasize a cyclic development of major themes. I could have begun with a fully detailed formal treatment of ensemble mechanics, as found in Gibbs's volume, and then given material realizations. I instead interleave formal discussions with simple concrete models. The models illustrate the formal definitions. The approach here gives students a chance to identify fundamental principles and methods before getting buried in ancillary details.

A representative cross-section of elastic biomolecules is covered in this volume, which combines seventeen contributions from leading research groups. State-of-the-art molecular mechanics experiments are described dealing with the elasticity of DNA and nucleoprotein complexes, titin and titin-like proteins in muscle, as well as proteins of the cytoskeleton and the extracellular matrix. The book speaks particularly to cell biologists, biophysicists, or bioengineers, and to senior researchers and graduate students alike, who are interested in recent advances in single-molecule technology (optical tweezers technique, atomic force microscopy), EM imaging, and computer simulation approaches to study nanobiomechanics. The findings discussed here have redefined our view of the role mechanical signals play in cellular functions and have greatly helped improve our understanding of biological elasticity in general.