This volume contains the texts of the four series of lectures presented by B.Cockburn, C.Johnson, C.W. Shu and E.Tadmor at a C.I.M.E. Summer School. It is aimed at providing a comprehensive and up-to-date presentation of numerical methods which are nowadays used to solve nonlinear partial differential equations of hyperbolic type, developing shock discontinuities. The most effective methodologies in the framework of finite elements, finite differences, finite volumes spectral methods and kinetic methods, are addressed, in particular high-order shock capturing techniques, discontinuous Galerkin methods, adaptive techniques based upon a-posteriori error analysis.

This book contributes to the mathematical theory of systems of differential equations consisting of the partial differential equations resulting from conservation of mass and momentum, and of constitutive equations with internal variables. The investigations are guided by the objective of proving existence and uniqueness, and are based on the idea of transforming the internal variables and the constitutive equations. A larger number of constitutive equations from the engineering sciences are presented. The book is therefore suitable not only for specialists, but also for mathematicians seeking for an introduction in the field, and for engineers with a sound mathematical background.

Physics on Your Feet (2nd Edition) is a significantly expanded collection of physics problems covering the broad range of topics in classical and modern physics that were, or could have been, asked at oral PhD exams at University of California at Berkeley. The questions are easy to formulate, but some of them can only be answered using an outside-of-the box approach. Detailed solutions are provided, from which the reader is guaranteed to learn a lot about the physicists' way of thinking. The book is also packed full of cartoons and dry humor to help take the edge off the stress and anxiety surrounding exams. This is a helpful guide for students preparing for their exams, as well as a resource for university lecturers looking for good instructive problems. No exams are necessary to enjoy the book!

This manual contains detailed solutions of slightly more than half of the end of chapter problems in The Dynamics of Heat. The numbers of the problems includ ed here are listed on the following page. A friend who knows me well noticed that I have included only those problems which I could actually solve myself. Also, to make things more interesting, I have built random errors into the solutions. If you find any of them, please let me know. Also, if you have different ways of solving a problem, I would be happy to hear from you. Any feedback, also on the book in general, would be greatly appreciated. There is an Errata sheet for the first printing of The Dynamics of Heat. By the time you read this, it should be available on the Internet for you to download. A reference to the URL of the sheet can be found in the announcement of my book on Springer's WWWpages (www.springer-ny.com). Winterthur, 1996 Hans Fuchs vi Numbers of Problems Solved Prologue 1,2,4,5,6,8, 12, 13, 17, 19,23,25,27,30,32,33,34,38,39,40,42,44,47, 49,50,53,55,60,61,62 Chapter 1 2,4,5,8,9,11,13,15, 16, 17, 18,20,21,24,26,27,29,31,33,34,37,39,41, 42,44,45,47,49,51,53,55,57,58,60,62 Chapter 2 1,3,5,6,7,9,10,12,14,15,16,17,19,20,22,23,24,26,27, 29, 30, 32, 33, 36,37,38,41,42,46,47,49 Interlude 2,3,4,5,6,8,10,11,12,13, 18, 19,20,21,23,24,28 Chapter 3 2,4,6,8,10,12,15,16,17,18,22,24,25,28,30,31,35,36 Chapter 4 1,2,4,6,8,9, 11, 12, 13, 15, 18,20,21,22,25,27,28,29,30,31,33,34,35, 39,40,43,44,46 Epilogue 1, 2, 11 PROLOGUE Solutions of Selected Problems 2 PROLOGUE: Problem 1 Calculate the hydraulic capacitance of a glass tube used in a mercury pressure gauge. The inner diameter of the tube is 8.0 mm.

This book provides a comprehensive framework for workers in materials science, physics, chemistry, metrology and non-destructive testing, entering the field of photothermal and thermal wave techniques and can be used by those making use of these methods for a wide range of applications. The essential physics is covered from basic principles, using thermal wave analysis to gain physical insight. Each of the commonly used measurement systems is described and assessed, and the major application areas: spectroscopy; non-destructive evaluation; thermal properties measurement and semiconductor material evaluation are each reviewed.

This monograph gives a systematic presentation of ideas, methods and results of the modern statistical theory of open systems -- systems capable of exchanging matter, energy and information with the surrounding world. The resulting self-organization can lead to more sophisticated and advanced structures. Central to this work are the statistical criteria of self-organization. The feasibility of a unified description of kinetic, hydrodynamic and diffusion processes in passive and active macroscopic systems without resorting to the methods of perturbation theory is demonstrated. On this basis, a general definition of thermal flux is given in terms of the entropy gradient. Moreover, a consistent method for calculating both kinetic and hydrodynamic fluctuations is proposed. This approach is then used to construct a theory of classical and anomalous Brownian motion in nonlinear media. This theory makes it possible to treat in an original way the phenomenon of turbulence, and to propose a unified kinetic description of laminar and turbulent motion. The proposed methods are also applied to the statistical description of quantum macroscopic open systems. This provides answers as to whether or not the quantum mechanical description is complete, and whether or not there are hidden parameters in quantum mechanics. The book has no analogy in the existing literature. It is both a monograph and a textbook, and is based largely on the author's original research. The book will be useful to postgraduate students and researchers in chemistry, physics, mathematics, economics, sociology, and engineering.

The book is designed for students taking introduction and intermediate thermodynamics courses in degrees and HNDs in Mechanical Engineering, Chemical Engineering and Process Engineering. The text provides a progressive development of ideas together with progress questions placed at regular intervals throughout the material. In the main, these questions are designed to be worked through before the student moves on through the text. This allows the assimilation of material at a rate which suits the individual.

A completely revised edition that combines a comprehensive coverage of statistical and thermal physics with enhanced computational tools, accessibility, and active learning activities to meet the needs of today's students and educators This revised and expanded edition of Statistical and Thermal Physics introduces students to the essential ideas and techniques used in many areas of contemporary physics. Ready-to-run programs help make the many abstract concepts concrete. The text requires only a background in introductory mechanics and some basic ideas of quantum theory, discussing material typically found in undergraduate texts as well as topics such as fluids, critical phenomena, and computational techniques, which serve as a natural bridge to graduate study. Completely revised to be more accessible to students Encourages active reading with guided problems tied to the text Updated open source programs available in Java, Python, and JavaScript Integrates Monte Carlo and molecular dynamics simulations and other numerical techniques Self-contained introductions to thermodynamics and probability, including Bayes' theorem A fuller discussion of magnetism and the Ising model than other undergraduate texts Treats ideal classical and quantum gases within a uniform framework Features a new chapter on transport coefficients and linear response theory Draws on findings from contemporary research Solutions manual (available only to instructors)

This book puts emphasis on developing the basic ideas behind the different approaches to non-equilibrium thermodynamics and on applying them to solids. After a survey about different approaches an introduction to their common fundamentals is given in the first part. In the second part the mechanical behavior of special materials such as viscoelasticity, viscoplasticity, viscoelastoplasticity, and thermoplasticity are discussed. The third part is devoted to extended thermodynamics. The basic ideas, phenomenological as well as microscopical, are reviewed and applied to thermo- and viscoelastic materials. Electromagnetic solids showing dielectric relaxation, such as ceramics, showing electromagneto-mechanical hysteresis and superconductivity are treated in the fourth part. In the last part stability with regard to constitutive equations is investigated. Especially stability of quasi-static processes and of elastic-plastic systems are discussed.

The application of thermal analysis is outlined by 18 contributions, writtenby experts in the various fields of geosciences. Emphasis was laid on the determination of minerals and technical products, kinetic parameters and calorific values in glass and ceramics technology, characterization of raw materials (e.g. clays, industrial minerals), in quality control and performance assessment, but also in environment protection from soil and water pollution, using re-evaluated existing and new data and improved combined modern methods. This book is addressed to practitioners, scientistsand students in mineralogy/crystallography, applied geology, material sciences, and environmental sciences.

Concise yet thorough, accessible, authoritative, and affordable. These are the hallmarks of books in the remarkable Physics and its Applications series. Thermodynamics is an essential part of any physical sciences education, but it is so full of pitfalls and subtleties, that many students fail to appreciate its elegance and power. In Thermal Physics, the author emphasizes understanding the basic ideas and shows how the important thermodynamics results can be simply obtained from the fundamental relations without getting lost in a maze of partial differentials. In this second edition, the author incorporated new sections on scales of temperature, availability, the degradation of energy, and lattice defects. The text contains ample illustrations and examples of applications of thermodynamics in physics, engineering, and chemistry.

by Noll, then scantly known, at the Carnegie Institute of Technology. An invita- tional meeting on visco-elasticity in the following April at Lancaster, Pennsyl- vania, brought Coleman and Noll together. In those days a person went to a meet- ing so as to learn from a few competent lectures without having to be himself one more "invited speaker" or to listen to many multiples of ten minutes of trivial trash. Ericksen lectured on "laminar shear flows" of incompressible, Rivlin-Erick- sen fluids. That class of flows contains all those for which Rivlin and others had obtained exact solutions. Ericksen's paper, with Criminale & Filbey as co-authors, was to appear soon in Volume 1 of the Archive. At the meeting, Coleman and Noll found that they had similar views on thermodynamics. The rheologists there, like those we had encountered elsewhere, told us that classical thermodynamics was a complete, closed, perfect science, all in Gibbs's paper, and they laughed at us. We laughed at them, but silently, for we had read fundamental parts of Gibbs's work, especially that on the isothermal and isentropic theories of three-dimensional elasticity, which, surely, the rheologists could not understand. We knew also the basic inequality for increase of entropy asserted by Duhem (1901) and in "The Mechanical Foundations" (1952) called "the Clausius-Duhem inequality" (Eq. (28. 5", from which Eckart (1940) had drawn consequences by guessing the signs oftwo terms ("Mechanical Foundations", text following Eq. (31. 1".

Proceedings of the NATO Advanced Study Institute on Propagation of Correlations in Constrained Systems, Cargese, Corsica, France, July 2-14, 1990

The book is meant to be primarily a textbook. Therefore most of the examples of special thermodynamic systems are standards in different fields. The number of the examples, however, is restricted. For more applications we refer the reader to the rich literature on thermodynamics. The author hopes that the book, which is concerned above all with basic connections, will be interesting not only for students but also for academic teachers and other scientists who like the structural analysis of fundamentals in physics. According to the character of a textbook, this book is not intended to demonstrate new results. Nevertheless, the way of the logical deductions, and of the presentations used in this book, as well as the choice of illustrating examples are not only influenced by literature but also by discussions with colleagues and friends. In this respect I should like to mention the Professors A. Stahl, J. Meixner, R. Bausch, H.-K. Janssen, R. Bessenrodt, Dr. E. Scholl, and Dr. C. Escher in Germany, as well as Professor C. A. Mead in Minneapolis, and Professor R. St. Berry in Chicago. Particular thank is directed to Professor V. Dohm for critically reading certain parts of the manuscript and making valuable proposals for improvements.

Das Buch bietet eine kompakte Zusammenstellung der wichtigsten Ph nomene in der Tieftemperaturphysik, die sowohl Studenten (mit dieser Vertiefungsrichtung im Hauptstudium), als auch Doktoranden, Wissenschaftlern und Ingenieuren, die auf diesem Gebiet t tig sind, als Lehrbuch dienen kann. Es eignet sich als Grundlage f r entsprechende Vorlesungen.

The 25th Anniversary Meeting of the Society of Engineering Science was held as a joint conference with the Applied Mechanics Division of the American Society of Mechanical Engineers at the University of California, Berkeley from June 20-22, 1988. With the encouragement and support of the SES, we decided to organize a symposium in honor of A. C. Eringen: the founding president of the Society of Engineering Science who provided pioneering leadership during the critical first decade of the Society's existence. We felt that there was no better way to do this than with a Symposium on Engineering Science -- the field that A. C. Eringen has devoted his life to. Professor Eringen had the foresight, even in his own early work, to see the need for an intimate amalgamation of engineering and science (transcending the bounds of the traditional engineering disciplines) to address unsolved problems of technological importance. Sustained by the belief that there was the need to provide a forum for researchers who had embraced this broader interdisciplinary approach, Professor Eringen founded the Society of Engineering Science and the International Journal of Engineering Science in 1963. Since that time, he has made countless contributions to the advancement of engineering science through his research, educational and organizational activities. The participants in the Symposium were former students and colleagues of Professor Eringen who have been strongly influenced by his professional activities and research in engineering science.

From the preface: "The book is written for scientists, practicing engineers and students interested in the analysis of system dynamics. Experience has shown that the volume is of special value to analysts and designers of control systems in many disciplines of engineering. The first two chapters can be of great use as a textbook for subjects from the field of dynamics and control systems in university undergraduate courses, while the third chapter is intended for more detailed graduate study. Having this in mind, every section of the book ends in many solved numerical examples. This can be of great use in the continuing education and home-study of all those who are concerned with this fast-developing field."

It was when I saw the countless number of icebergs floating in the North Atlantic Ocean in August 1964 that I decided to commence research into the solidification mechanism of metals, and already I have been continu- ing this research for two decades. In 1970 my former professor Susumu Miyata received a letter from Pre- sident Jiro Komatsu of the Tokyo Keigokin Seisaskusho Co., Ltd. The letter enclosed a copy of an article written by Mr. Imao Sasaki, chief of the casting research section at Daihatsu Motor Co., Ltd., entitled "Aruminyumu gyoko riron no shimpo" (Progress in aluminum solidi- fication theory) from a journal called "Kinzoku Zairyo" (Metals in En- gineering). This article introduced my research in considerable detail and well-written style. After stating that I "rebuffed conventional theories and enlightened casting engineers", Sasaki wrote that "These research results deserve great attention from casting engineers for the progress they have brought about in basic theories on improved soundness in casting quality." The letter from President Komatsu was a request to arrange a meeting with me. Saying that "I've heard you mention your theory occasionally, but I'd like to hear a full discussion of it for once", Professor Miyata accompanied me to the Tokyo Keigokin Seisakusho Co., Ltd. at Gyoda in Saitama Pre- fecture.

This volume collects papers dedicated toWalterNoll on his sixtieth birthday, January 7, 1985. They first appeared in Volumes 86-97 (1984-1987) of the Archive for Rational Mechanics and Analysis. At the request ofthe Editors the list of authors to be invited was drawn up by B.D. Coleman, M. Feinberg, and J. Serrin. WalterNoll's influence upon research into the foundations of mechanics and thermodynamics is plain, everywhere acknowledged. Less obvious is the wide effect his writings have exerted upon those who apply mechanics to special problems, but it is witnessed by the now frequent use of terms, concepts, and styles of argument he introduced, use sometimes by young engineers who have learnt them in some recent textbook and hence take them for granted, oftenwith no idea whence they come. Examples are "objectivity", "material frame- indifference", "constitutive equation", "reduced form" of the last-named, "sim- plematerial", "simplesolid", "simplefluid", "isotropygroup",andtheassociated notations and lines of reasoning.

The present simulation method has been developed at the Institute for Power Technology and Steam Generation (IVD) of the University of Stuttgart. It is being successfully employed in the analysis of processes involving large state changes such as start-ups, shut downs, malfunctions and failures in steam power generating unit, which is a large scale system consisting of several subsystems with distributed parameters, to which the steam generator also belongs. This research resulted from the increasing use of the once-through boiler, while simultaneously raising the steam parameters into the region of the supercritical state, using sliding pressure operation, combined processes with gas and steam turbines etc. The objective of this system simulation is to reduce losses of heat and condensate and to minimise unavoidable thermal stresses. The project was financed between 1979 and 1983 by the German Research Society (DFG) as part of the special research section Nr. 157 'Thermal power plants'. The Westfalen Power Company Inc. (VEW) sponsored the start-up code 'DYSTAR'. We would like to express our thanks for this support. The following members of the IVD were involved in this research project: Dr.-Ing. J. Kley Dipl.-Ing. G. Riemenschneider Dr.-Ing. A. Rolf Dipl.-Ing. U. Mayer Dipl.-lng. E. Dr.-lng. M. Klug Pfleger Dr.-Ing. G. Berndt Presently it is intended to use this non-linear, time-variant model of a power generating unit with a variable process and system struc ture as the basis for simple code versions, which one can employ e.g."

Written to introduce readers to molecular descriptions of thermodynamics, chemical systems, and biomolecules, Statistical Thermodynamics discusses the aspects of statistical thermodynamics of most use and interest to chemistry students. Topics include: probability; energy and interactions; statistical mechanics; harmonic oscillators; ideal gas; imperfect gas; heat capacities of gas; rubber elasticity; conformation of polymers; surface adsorption; law of mass action; Ising model; and more. Rich with illustrations and tables to illuminate rather difficult concepts, the text equips students with the ability to apply the method to their own systems.

The material included in this book was first presented in a series of lectures de livered at the University of Minnesota in June 1983 in connection with the con ference "Thermodynamics and Phase Transitions." This conference was one of the principal events in the first year of operation of the Institute for Mathematics and its Applications (lMA) at the University of Minnesota. The Institute was founded under the auspices of the National Science Foun dation of the United States and the University of Minnesota and is devoted to strengthening and fostering the relation of mathematics with its various applica tions to problems of the real world. The present volume constitutes an important element in the continuing pub lication program of the Ipstitute. Previous publications in this program have ap peared as lecture notes in the well-known Springer series, and future ones will be part of a new series "IMA Volumes in Applied Mathematics." Preface Until recently it was believed that thermodynamics could be given a rigorous foundation only in certain restricted circumstances, particularly those involving reversible and quasi-static processes. More general situations, commonly arising in continuum theories, have therefore been treated on the assumption that inter nal energy, entropy and absolute temperature are a priori given quantities, or have been dealt with on a more or less ad hoc basis, with emphasis for example on various types of variational formulations and maximization rules."

Computational fluid flow is not an easy subject. Not only is the mathematical representation of physico-chemical hydrodynamics complex, but the accurate numerical solution of the resulting equations has challenged many numerate scientists and engineers over the past two decades. The modelling of physical phenomena and testing of new numerical schemes has been aided in the last 10 years or so by a number of basic fluid flow programs (MAC, TEACH, 2-E-FIX, GENMIX, etc). However, in 1981 a program (perhaps more precisely, a software product) called PHOENICS was released that was then (and still remains) arguably, the most powerful computational tool in the whole area of endeavour surrounding fluid dynamics. The aim of PHOENICS is to provide a framework for the modelling of complex processes involving fluid flow, heat transfer and chemical reactions. PHOENICS has now been is use for four years by a wide range of users across the world. It was thus perceived as useful to provide a forum for PHOENICS users to share their experiences in trying to address a wide range of problems. So it was that the First International PHOENICS Users Conference was conceived and planned for September 1985. The location, at the Dartford Campus of Thames Polytechnic, in the event, proved to be an ideal site, encouraging substantial interaction between the participants.

In the seven years since this volume first appeared. there has been an enormous expansion of the range of problems to which Monte Carlo computer simulation methods have been applied. This fact has already led to the addition of a companion volume ("Applications of the Monte Carlo Method in Statistical Physics", Topics in Current Physics. Vol . 36), edited in 1984, to this book. But the field continues to develop further; rapid progress is being made with respect to the implementation of Monte Carlo algorithms, the construction of special-purpose computers dedicated to exe cute Monte Carlo programs, and new methods to analyze the "data" generated by these programs. Brief descriptions of these and other developments, together with numerous addi tional references, are included in a new chapter , "Recent Trends in Monte Carlo Simulations" , which has been written for this second edition. Typographical correc tions have been made and fuller references given where appropriate, but otherwise the layout and contents of the other chapters are left unchanged. Thus this book, together with its companion volume mentioned above, gives a fairly complete and up to-date review of the field. It is hoped that the reduced price of this paperback edition will make it accessible to a wide range of scientists and students in the fields to which it is relevant: theoretical phYSics and physical chemistry , con densed-matter physics and materials science, computational physics and applied mathematics, etc.