Principles of Statistical Radiophysics is concerned with the theory of random func tions (processes and fields) treated in close association with a number of applications in physics. Primarily, the book deals with radiophysics in its broadest sense, i.e., l viewed as a general theory of oscillations and waves of any physical nature * This translation is based on the second (two-volume) Russian edition. It appears in four volumes: 1. Elements of Random Process Theory 2. Correlation Theory of Random Processes 3. Elements of Random Fields 4. Wave Propagation Through Random Media. The four volumes are, naturally, to a large extent conceptually interconnected (being linked, for instance, by cross-references); yet for the advanced reader each of them might be of interest on its own. This motivated the division of the Principles into four separate volumes. The text is designed for graduate and postgraduate students majoring in radio physics, radio engineering, or other branches of physics and technology dealing with oscillations and waves (e.g., acoustics and optics). As a rule, early in their career these students face problems involving the use of random functions. The book pro vides a sound basis from which to understand and solve problems at this level. In addition, it paves the way for a more profound study of the mathematical theory, should it be necessary2. The reader is assumed to be familiar with probability theory.

An international workshop on Elementary Excitations and Fluctuations in Magnetic Systems was held in San Miniato, Italy, for five days beginning 28 May, 1984. The workshop comprised eight working sessions that contai- ned a total of 43 invited talks, and 58 scientists were in attendance from 14 countries. Our aim was to review some topics of current interest in the statistical physics of magnetic materials and models, with an emphasis on theoretical studies and confrontations between these and experimental and computer simulation data. book contains summary papers written by the invited speakers, and This the material will be of immediate interest to graduate students and resear- chers engaged in studies of magnetic properties. There is, perhaps, no ef- fective way to record and convey the benefit of the numerous discussions between the participants that are a significant integral feature of a work- shop. The magnificent .venue of the workshop, I Cappuccini, was made availa- ble to us by the.Cassa di Risparmio San Miniato. Financial support for the workshop was received from Consiglio Nazionale delle Ricerche, Universita degli Studi di Firenze and the Gruppo Nazionale Struttura,della Materia. Our administrative load and the burden of preparing the proceedings for publication was made light by the talents of Carla Pardini (CNR, Florence), and Caroline Monypenny and Jane Warren (Rutherford Appleton Laboratory). Fina 11y, we wish to thank all the participants for their attendance and individual contributions to the success of the workshop.

This volume consists of edited papers presented at the International Symposion Gas Phase Chemical Reaction Systems: Experiments and Models 100 Years After Max Bodenslein, held at the Internationales Wissenschaftsforum Heidelberg (IWH) in Heidelberg during July 25-28, 1995. The intention of this symposion was to bring together leading researchers from the fields of reaction dynamics, kinetics, catalysis and reactive flow model ling to discuss and review the advances in the understanding of chemical kinetics about 100 years after Max Bodenstein's pioneering work on the "hydrogen iodine reaction", which he carried out at the Chemistry Institute of the University of Heidelberg. The idea to focus in his doctoral thesis [1] on this reaction was brought up by his supervisor Victor Meyer (successor of Robert Bunsen at the Chemistry Institute of the University of Heidelberg) and originated from the non reproducible behaviour found by Bunsen and Roscoe in their early photochemical investigations of the H2/Cl2 system [2] and by van't Hoff [3], and V. Meyer and co-workers [4] in their experiments on the slow combustion of H2/02 mixtures.

The Second European Turbulence Conference was held at the Technische Univer sitat Berlin, Federal Republic of Germany, from August 30th to September 2nd 1988 under the auspices of the European Mechanics Committee. It was primar ily devoted to fundamental aspects of turbulence, and aimed at bringing together engineers, physicists, and mathematicians. The scientific committee - serving also as Sub-committee of the European Turbulence Conference - consisted of the following members: G. Comte-Bellot (Lyon), H.-H. Fernholz and H.E. Fiedler (both from Berlin) as co-chairmen of the conference, U. Frisch (Nice), J.C.R. Hunt (Cambridge), E. Krause (Aachen), M. Landahl (Stockholm), A.M. Obukhov (Moscow), and G. Ooms (Amsterdam). The conference programme comprised 6 invited lectures and 94 contributions, presented either orally or at poster sessions. There were 165 participants from 18 countries. All papers published in these conference proceedings were, with the exception of the invited ones, again refereed by the members of the scientific committee. The main research topics discussed at this meeting were stability and gener ation of turbulence, effects of rotation, stratification and buoyancy forces, novel instrumentation, manipulation and control, boundary layers with separation and reattachment, computer simulation, turbulent diffusion, image analysis and flow visualization, vorticity dynamics and turbulence, and large-scale structures. We have taken the liberty of regrouping some papers following the submitted final versions for this volume. Authors may therefore find their paper under a different heading from that in the conference programme."

In the tradition of its predecessors, this volume comprises a selection of the best papers presented at the Ninth International Symposium on Applications of Laser Techniques to Fluid Mechanics, held in Lisbon in July 2000.
The papers reflect the state-of-the-art in laser applications of laser techniques in fluid mechanics describing novel ideas for instrumentation, instrumentation developments, results of measurements of wall-bounded flows, free flows and flames and flow and combustion in engines. The papers demonstrate the continuing interest in the development of an understanding of new methodologies and implementation in terms of new instrumentation.

Cellular automata are fully discrete dynamical systems with dynamical variables defined at the nodes of a lattice and taking values in a finite set. Application of a local transition rule at each lattice site generates the dynamics. The interpretation of systems with a large number of degrees of freedom in terms of lattice gases has received considerable attention recently due to the many applications of this approach, e.g. for simulating fluid flows under nearly realistic conditions, for modeling complex microscopic natural phenomena such as diffusion-reaction or catalysis, and for analysis of pattern-forming systems. The discussion in this book covers aspects of cellular automata theory related to general problems of information theory and statistical physics, lattice gas theory, direct applications, problems arising in the modeling of microscopic physical processes, complex macroscopic behavior (mostly in connection with turbulence), and the design of special-purpose computers.

Rhythms are a basic phenomenon in all physiological systems. They cover an enormous range of frequencies with periods from the order of milliseconds up to some years. They are described by many disciplines and are investigated usually in the context of the physiology of the respective function or organ. The importance given to the research on rhythmicity is quite different in different systems. In some cases where the functional significance is obvious rhythms are at the center of interest, as in the case of respiration or locomotion. In other fields they are considered more or less as interesting epiphenomena or at best as indicators without essential functional significance, as in the case of cardiovascular or EEG rhythms. Recently the study of physiological rhythms has attracted growing interest in several fields, especially with respect to rhythm research in humans and its rapidly spreading applications in basic behavioral research, and as a diagnostic tool in clinical medicine. This development was favored by two methodological and conceptual ad vances: on the one hand, the availability of non-invasive methods of continu ous recording of physiological parameters and their computer-assisted evaluation, and on the other, the rapid development of theoretical analyses, for example, the understanding of dynamic systems, the generation of coordinated macroscopic pro cesses in systems comprising many single elements, and the mathematical tools for treating nonlinear oscillators and their mutual coupling.

A special survey of the extensive field of Constitutive Laws is given in 11 lectures, divided into three parts: Thermodynamics of Materials, Stochastic Processes and Material Behaviour, Constitutive Relations for Simple Fluids and Microphysics of Solids. The collection of lectures comprehends a novel survey of thermodynamical constitutive theories, and contributions to material theories with after-effects including experiments, stochastic constitutive laws, molecular dynamics for simulating material properties, electrodynamical constitutive properties, and thermodynamic and microphysical modelling of polymers. The selected lectures emphasize the microstructural aspect of constitutive laws, and this collection presents a new facet of constitutive laws.

This volume contains the lectures presented at the mini-symposium on "Micromechanics" held in conjunction with the CSME Mechanical Engineer ing Forum 1990 between the 3rd and 8th June, 1990 at the University of Toronto, Canada. The expressed purpose of this symposium was to discuss some recent developments in the Micromechanics of Materials and how ad vances in this field now relate to the solution of practical engineer ing problems. Due to the time limit set for this section of the Engineer ing Forum as well as the restriction on the number of papers to be pre sented, it was not possible to cover a much wider range of topics. How ever, an attempt was made to include the most important advances asso ciated with the progress made in micromechanics in its application to material science and engineering over the past decade. Thus, the topics are concerned with: the fundamental aspects of the thermodynamics of structured solids (part I), - the micromechanical behaviour of alloys (part II), - the modelling of the material behaviour on the basis of continuum theory (part III), and finally the important new approach to the characterization of various mate rials and their responses to external agencies by the use of proba bilistic micromechanics (part IV). We would like to take this opportunity to thank the Chairman of the Organizing Committee, Prof. F. P. J. Rimrott, and the President of the CSME, Prof. T. S."

Our aim in this book is to present and enlarge upon those aspects of parallel computing that are needed by practitioners of computational science. Today al most all classical sciences, such as mathematics, physics, chemistry and biology, employ numerical methods to help gain insight into nature. In addition to the traditional numerical methods, such as matrix inversions and the like, a whole new field of computational techniques has come to assume central importance, namely the numerical simulation methods. These methods are much less fully developed than those which are usually taught in a standard numerical math ematics course. However, they form a whole new set of tools for research in the physical sciences and are applicable to a very wide range of problems. At the same time there have been not only enormous strides forward in the speed and capability of computers but also dramatic new developments in computer architecture, and particularly in parallel computers. These improvements offer exciting prospects for computer studies of physical systems, and it is the new techniques and methods connected with such computer simulations that we seek to present in this book, particularly in the light of the possibilities opened up by parallel computers. It is clearly not possible at this early stage to write a definitive book on simulation methods and parallel computing."

The Sixth International Symposium on Gas Flow and Chemical Lasers (GCL) was held in Jerusalem, Israel, on September 8-12, 1986. The charm and beauty of Jerusalem and the unique blending of ancient and modern made this Symposium an enjoyable experience for the 165 participants and the accompanying persons. Yet, it seems that the invited and contributed papers presented at the Symposium were equally attractive so that most of the participants attended most sessions, resisting the temptations outside the session hall. Indeed, many speakers presented up-to-date results that were obtained, or cleared, just a few days before the Symposium. This volume is a compi lation of 19 invited and 61 contributed papers and of a panel discussion on the prospects for short wavelength chemical lasers held at the closing session of the Symposium. This discussion is presented as recorded in order to re tain the flavour of spontaneous presentation at the risk - or advantage - of presenting some venturous ideas, and the danger of misquoting. In editing the book, a deductive approach has been attempted. The book starts with some fundamental issues, namely fluid dynamics and optics, and then deals with the design, diagnostics, propagation and applications of various gas laser systems, covering the wavelength spectrum from XUV to infrared. Then follow recent developments of general interest to the laser community and the book concludes with an eye to the future, i.e., with a section on short wavelength chemical lasers."

Lectures on Non-linear Plasma Kinetics is an introduction to modern non-linear plasma physics showing how many of the techniques of modern non-linear physics find applications in plasma physics and how, in turn, the results of this research find applications in astrophysics. Emphasis is given to explaining the physics of nonlinear processes and the radical change of cross-sections by collective effects. The author discusses new nonlinear phenomena involving the excitation of coherent nonlinear structures and the dynamics of their random motions in relation to new self-organization processes. He also gives a detailed description of applications of the general theory to various research fields, including the interaction of powerful radiation with matter, controlled thermonuclear research, etc.

Mon but n'a jamais be de m'occuper des ces matieres comme physicien, mais seulement comme /ogicien ... F. REECH, 1856 I do not think it possible to write the history of a science until that science itself shall have been understood, thanks to a clear, explicit, and decent logical structure. The exuberance of dim, involute, and undisciplined his torical essays upon classical thermodynamics reflects the confusion of the theory itself. Thermodynamics, despite its long history, has never had the benefit of a magisterial synthesis like that which EULER gave to hydro dynamics in 1757 or that which MAXWELL gave to electromagnetism in 1873; the expositions in the works of discovery in thermodynamics stand a pole apart from the pellucid directness of the notes in which CAUCHY presented his creation and development of the theory of elasticity from 1822 to 1845. Thermodynamics was born in obscurity and disorder, not to say confusion, and there the common presentations of it have remained. With this tractate I aim to provide a simple logical structure for the classical thermodynamics of homogeneous fluid bodies. Like any logical structure, it is only one of many possible ones. I think it is as simple and pretty as can be."

The 3rd edition is thoroughly revised, applications are substantially enriched, it includes a new account of the early history of the subject (from 1800 to 1957) and a new chapter recounting the recent solution of open problems of long standing in classical aerodynamics. The bibliography comprises now over fifteen hundred titles.

From the reviews:

"The author is known as one of the leading experts in the field. His masterly written book is, surely, the most complete exposition in the subject of conservations laws." --Zentralblatt MATH

A IUTAM symposium on "Measuring Techniques in Gas-Liquid Two Phase Flows" was held on July 5-8, 1983 in Nancy, France. This topic in cluded instrumentation for steam-water and liquid-vapor flows but strictly excluded measuring techniques for gas or liquid flows with solid particles. The top priority in the paper selection was given to presentations of new methods which had been substantiated by theoretical modeling, calibration tests and comparison tests with other techniques. Examples of experimental resul ts obtained with the proposed instrumentation had to be displayed. However the interpretation of these results in terms of two-phase flow or heat transfer modeling did not fall wi thin the scope of the meeting. Thirty four papers were presented during the Symposium and 79 participants coming from Canada, European countries, Japan and the United States attended the sessions. They represented not only Universities but also state agencies and private companies. After the meeting each paper was peer-reviewed by at least three referees. The Editors of this Procee dings Volume are pleased to extend their deep gratitude to the following reviewers: J.L. Achard, R.J. Adrian, B. Azzopardi, J.A. Boure, G. Costigan, M. Courtaud, A.E. Dukler, F. Durst, J.R. Fincke, G. Gouesbet, P. Griffith, T.J. Hanratty, A. Hawighorst, T.R. Heidrick, G. Hetsroni, Y.Y. Hsu, M."

Physicists firmly believe that the differential equations of nature should be hyperbolic so as to exclude action at a distance; yet the equations of irreversible thermodynamics - those of Navier-Stokes and Fourier - are parabolic. This incompatibility between the expectation of physicists and the classical laws of thermodynamics has prompted the formulation of extended thermodynamics. After describing the motifs and early evolution of this new branch of irreversible thermodynamics, the authors apply the theory to mon-atomic gases, mixtures of gases, relativistic gases, and "gases" of phonons and photons. The discussion brings into perspective the various phenomena called second sound, such as heat propagation, propagation of shear stress and concentration, and the second sound in liquid helium. The formal mathematical structure of extended thermodynamics is exposed and the theory is shown to be fully compatible with the kinetic theory of gases. The study closes with the testing of extended thermodynamics through the exploitation of its predictions for measurements of light scattering and sound propagation.

J-B. J. FOURIER'S immensely influential treatise Theorie Analytique de la Chaleur [21J, and the subsequent developments and refinements of FOURIER's ideas and methods at the hands of many authors, provide a highly successful theory of heat conduction. According to that theory, the growth or decay of the temperature e in a conducting body is governed by the heat equation, that is, by the parabolic partial differential equation Such has been the influence of FOURIER'S theory, which must forever remain the classical theory in that it sets the standard against which all other theories are to be measured, that the mathematical investigation of heat conduction has come to be regarded as being almost identicalt with the study of the heat equation, and the reader will not need to be reminded that intensive analytical study has t But not entirely; witness, for example, those theories which would replace the heat equation by an equation which implies a finite speed of propagation for the temperature. The reader is referred to the article [9] of COLEMAN, FABRIZIO, and OWEN for the derivation of such an equation from modern Continuum Thermody namics and for references to earlier work in this direction. viii Introduction amply demonstrated that the heat equation enjoys many properties of great interest and elegance.

Technical progress has for a very long time been directly dependent on progress in metallurgy, which is itself connected with improvements in the technology of alloys. Metals are most frequently used in the form of alloys for several reasons: the quantity of pure metal in its native state in the earth's crust is very limited; pure metals must be extracted from ores which are themselves impure. Finally, the methods of treatment used lead more easily to alloys than to pure metals. The most typical case is that of iron, where a pure ore may be found, but which is the starting point for cast iron or steel, alloys of iron and carbon. In addition, the properties of alloys are in general superior to those of pure metals and modem metallurgy consists of controlling these properties so as to make them conform to the requirements of the design office. Whilst the engineer was formerly compelled to adapt his designs and constructions to the materials available, such as wood, stone, bronze, iron, cast iron and ordinary steels, he can now expect, due to metallurgical research, the creation of special alloys meeting specific requirements. These requirements must of course be reasonable, but VIII INTRODUCTION must be sufficiently imperative for them to become the motive for progress.

This research monograph presents a systematic treatment of the theory of the propagation of transient electromagnetic fields (such as optical pulses) through dielectric media which exhibit both dispersion a.nd absorption. The work divides naturally into two parts. Part I presents a summary of the fundamental theory of the radiation and propagation of rather general electromagnetic waves in causal, linear media which are homogeneous and isotropic but which otherwise have rather general dispersive and absorbing properties. In Part II, we specialize to the propagation of a plane, transient electromagnetic field in a homogeneous dielectric. Although we have made some contributions to the fundamental theory given in Part I, most of the results of our own research appear in Part II. The purpose of the theory presented in Part II is to predict and to explain in explicit detail the dynamics of the field after it has propagated far enough through the medium to be in the mature-dispersion regime. It is the subject of a classic theory, based on the research conducted by A. Sommerfeld and L.

"Principles of Statistical Radiophysics" is a four-volume series that introduces the newcomer to the theory of random functions. It aims at providing the background necessary to understand papers and monographs on the subject and to carry out independent research in the fields where fluctuations are of importance, e.g. radiophysics, optics, astronomy, and acoustics. Volume 3, "Elements of Random Fields," gives the basic mathematical definitions, general properties and specific forms of random fields, the generalization from correlation theory to random fields. It deals with stochastic partial differential equations, wave scattering at a chaotic screen, single scattering in random media and thermal fluctuations and radiation of electromagnetic fields.

th This volume contains the proceedings of the X Congress of the Interna- tional Association of Mathematical Physics, held at the University of Leipzig from 30 July until 9 August 1991. There were more than 400 participants, from 29 countries, making it a truly international gathering. The congress had the support of the Deutsche Forschungsgemeinschaft, the European Economic Community, the International Association of Math- ematical Physics, the International Mathematical Union and the Interna- tional Union of Pure and Applied Physics. There were also sponsors from in- dustry and commerce: ATC Mann, Deutsche Bank AG, Miele & Cie GmbH, NEC Deutschland GmbH, Rank Xerox, Siemens AG and Stiftungsfonds IBM Deutschland. On behalf of the congress participants and the members of the International Association of Mathematical Physics, I would like to thank all these organisations for their very generous support. The congress took place under the auspices of the Ministerp6isident des Freistaates Sachsen, K. Biedenkopf. The conference began with an address by A. Uhlmann, Chairman of the Local Organizing Committee. This was followed by speeches of welcome from F. Magirius, City President of Leipzig; C. Weiss, Rector of the Uni- versity of Leipzig; and A. Jaffe, President of the International Association of Mathematical Physics.

This Tract gives an account of certain recent attempts to construct a satisfactory theory of thermodynamics for materials which have a memory for the past. Naturally it draws heavily on the writings of those who have made significant contributions to the field. I am particularly grateful to Professor C. A. Truesdell of The lohns Hopkins University for his invitation to write the Tract and to Professor A. E. Green of Oxford for his comments on various parts of the manuscript. Hertford College, Oxford December 1971 W. A. Day Contents Introduction 1 Chapter 1 Preliminaries 5 1. 1 Vector and Tensor Analysis. 5 1. 2 Paths and Line Integrals . 7 1. 3 Kinematics and the Balance Laws 11 1. 4 Simple Materials with Memory 15 21 Chapter 2 A Theory of Thermodynamics . 2. 1 Processes. 21 2. 2 The Thermodynamic Inequality . 23 2. 3 Heat Conduction Inequalities . 24 2. 4 The Conversion of Heat into Mechanical Work 27 31 The Construction of the Entropy Chapter 3 The Clausius Inequality 31 3. 1 3. 2 Fading Memory . 34 3. 3 The Entropy in Equilibrium. Thermostatics. 38 3. 4 The Entropy away from Equilibrium. The Clausius- Planck Inequality 45 Chapter 4 Applications . . 55 4. 1 Thermoelasticity and Materials of Differential Type 55 4. 2 A Class of Viscoelastic Materials . . . . . . 60 Chapter 5 Thermodynamics based on the Clausius-Duhem Inequality . . . . . . . . . . 77 5. 1 The Clausius-Duhem Inequality. 78 5.

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chif1ese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Substances possessing heterogeneous microstructure on the nanometer and micron scales are scientifically fascinating and technologically useful. Examples of such substances include liquid crystals, microemulsions, biological matter, polymer mixtures and composites, vycor glasses, and zeolites. In this volume, an interdisciplinary group of researchers report their developments in this field. Topics include statistical mechanical free energy theories which predict the appearance of various microstructures, the topological and geometrical methods needed for a mathematical description of the subparts and dividing surfaces of heterogeneous materials, and modern computer-aided mathematical models and graphics for effective exposition of the salient features of microstructured materials.