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.

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

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.

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".

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."

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.

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.

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.

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."

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 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.

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.

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.

Groundwater has long been one of the world's most important resources. It accounts for approximately 96% of all fresh water in the United States and supplies more than 50% of the population with potable water. Historically, this water source has generally been regarded as pristine. However, in recent years, contamination of ground water by industrial products has become a problem of growing concern. During the past four decades, the variety and quantity of organic chemicals produced in the U. S. has steadily increased. Currently, more than 40,000 different organic compounds are being manufactured, trans ported, used and eventually disposed of in the environment (Wilson, et !l (1981". Production and consumption of petroleum products has also risen in this same time period. Many of these industrial compounds are highly toxic and slightly water soluble. Thus, they pose a poten tial threat to large volumes of groundwater if they are somehow intro duced into the subsurface. Increased production of chemicals implies the increased risk of accidental spills or leakage to the soil, and indeed, the literature abounds with contamination case histories. 2 Incidences of petroleum contamination of groundwater have been documented by many authors. For example, see: Schwi11e (1967); Toms (1971); Guenther (1972); McKee, et!l (1912); Williams and Wilder (1971); Van100cke, et ~]-

The equations which we are going to study in these notes were first presented in 1963 by E. N. Lorenz. They define a three-dimensional system of ordinary differential equations that depends on three real positive parameters. As we vary the parameters, we change the behaviour of the flow determined by the equations. For some parameter values, numerically computed solutions of the equations oscillate, apparently forever, in the pseudo-random way we now call "chaotic"; this is the main reason for the immense amount of interest generated by the equations in the eighteen years since Lorenz first presented them. In addition, there are some parameter values for which we see "preturbulence," a phenomenon in which trajectories oscillate chaotically for long periods of time before finally settling down to stable stationary or stable periodic behaviour, others in which we see "intermittent chaos," where trajectories alternate be tween chaotic and apparently stable periodic behaviours, and yet others in which we see "noisy periodicity," where trajectories appear chaotic though they stay very close to a non-stable periodic orbit. Though the Lorenz equations were not much studied in the years be tween 1963 and 1975, the number of man, woman, and computer hours spent on them in recent years - since they came to the general attention of mathematicians and other researchers - must be truly immense."

The first edition of this book was greeted with broad interest from readers en gaged in various disciplines of biophysics. I received many stimulating and en couraging responses, however, some of the book's reviewers wanted to stress the fact that an extensive literature of network theory was not included or reported in the book. But the main aspect of the book is intended to be substantive rather than methodical: networks simply serve as a remedy for doing some first steps in analysing and modelling complex biological systems. For an advanced stage in the investigation of a particular system it may be appropriate to replace the pheno menological network method by more detailed techniques like statistical equations or computer simulations. According to this intention, the second edition of the book has been enlarged by further biological examples for network analysis, not by more network theory. There is a completely new section on a network model for photoreception. For this section I am obliged to J. Tiedge who did most of the detailed calculation and to my colleague Professor Stieve with whom we have had a very fruitful cooperation. Also I would like to mention that this work has been sponsored by the "Deutsche Forschungsgemei nschaft" i n the "Sonderforschungsberei ch 160." Recent results for excitable systems represented by feedback networks have also been included in the second edition, especially for limit cycle networks."