Non-linear stochastic systems are at the center of many engineering disciplines and progress in theoretical research had led to a better understanding of non-linear phenomena. This book provides information on new fundamental results and their applications which are beginning to appear across the entire spectrum of mechanics. The outstanding points of these proceedings are Coherent compendium of the current state of modelling and analysis of non-linear stochastic systems from engineering, applied mathematics and physics point of view. Subject areas include: Multiscale phenomena, stability and bifurcations, control and estimation, computational methods and modelling. For the Engineering and Physics communities, this book will provide first-hand information on recent mathematical developments. The applied mathematics community will benefit from the modelling and information on various possible applications.

The Second Monte Verita Colloquium Fundamental Problematic Issues in Turbu lence was held in Monte Verita, Switzerland, on March 23-27, 1998. The main goal of the Colloquium was to bring together in the relaxed atmo sphere of Monte Verita a group of leading scientists (consisting of representatives of different generations) and to discuss informally and free of the influence of funding agencies and/or other "politics" of nonscientific nature the basic issues of turbulence. The intention was to put major emphasis on the exposition of the problematic aspects and discussion(s) - not mere reporting of results, i. e. not hav ing just one more meeting. For this purpose it was originally thought to leave all the afternoons free of formal presentations at all. However, this intention became unrealistic due to a number of reasons, and, in the first place, due to strong pres sure from various parts of the scientific community and non-scientific constraints to broaden the scope and to increase the number of participants as compared to the First Colloquium held in 1991. This resulted in a considerable reduction of time for discussions. Nevertheless, the remaining time for discussions was much larger than usually allocated at scientific conferences. On the scientific side the main idea was to bring together scientists work ing in turbulence from different fields, such as mathematics, physics, engineering and others. In this respect the Colloquium was definitely very successful and re sulted in a number of interesting interactions and contacts."

This book gathers contributions to the 20th biannual symposium of the German Aerospace Aerodynamics Association (STAB) and the German Society for Aeronautics and Astronautics (DGLR). The individual chapters reflect ongoing research conducted by the STAB members in the field of numerical and experimental fluid mechanics and aerodynamics, mainly for (but not limited to) aerospace applications, and cover both nationally and EC-funded projects. Special emphasis is given to collaborative research projects conducted by German scientists and engineers from universities, research-establishments and industries. By addressing a number of cutting-edge applications, together with the relevant physical and mathematics fundamentals, the book provides readers with a comprehensive overview of the current research work in the field. Though the book's primary emphasis is on the aerospace context, it also addresses further important applications, e.g. in ground transportation and energy.

The book focuses on the main physical ideas and mathematical methods of the microscopic theory of fluids, starting with the basic principles of statistical mechanics. The detailed derivation of results is accompanied by explanation of their physical meaning. The same approach refers to several specialized topics of the liquid state, most of which are recent developments, such as: a perturbation approach to the surface tension, an algebraic perturbation theory of polar nonpolarizable fluids and ferrocolloids, a semi-phenomenological theory of the Tolman length and some others. The book addresses researchers as well as graduate students in physics and chemistry with research interests in the statistical physics of fluids.

Nonlinear Dynamics of Complex Systems describes chaos, fractal and stochasticities within celestial mechanics, financial systems and biochemical systems. Part I discusses methods and applications in celestial systems and new results in such areas as low energy impact dynamics, low-thrust planar trajectories to the moon and earth-to-halo transfers in the sun, earth and moon. Part II presents the dynamics of complex systems including bio-systems, neural systems, chemical systems and hydro-dynamical systems. Finally, Part III covers economic and financial systems including market uncertainty, inflation, economic activity and foreign competition and the role of nonlinear dynamics in each.

Feedback-Based Orthogonal Digital Filters: Theory, Applications, and Implementation develops the theory of a feedback-based orthogonal digital filter and examines several applications where the filter topology leads to a simple and efficient solution. The development of the filter structure is linked to concepts in observer theory. Several signal processing problems can be represented as estimation problems, where a parametric representation of the input is used, to try and replicate it locally. This estimation problem can be solved using an identity observer, and the filter topology falls in this framework. Hence the filter topology represents a universal building block that can find application in several problems, such as spectral estimation, time-recursive computation of transforms, etc. Further, because of the orthogonality constraints satisfied by the structure, it also represents a robust solution under finite precision conditions. The book also presents the observer-based viewpoint of several signal processing problems, and shows that problems that are typically treated independently in the literature are in fact linked and can be cast in a single unified framework. In addition to examining the theoretical issues, the book describes practical issues related to a hardware implementation of the building block, in both the digital and analog domain. On the digital side, issues relating to implementation using semi-custom chips (FPGA's), and ASIC design are examined. On the analog side, the design and testing of a fabricated chip, that functions as a multi-sinusoidal phase-locked-loop, are described. Feedback-Based Orthogonal Digital Filters serves as an excellent reference. May be used as a text for advanced courses on the subject.

Adaptive structural systems in conjunction with multifunctional materials facilitate technical solutions with a wide spectrum of applications and a high degree of integration. By virtue of combining the actuation and sensing capabilities of piezoelectric materials with the advantages of fiber composites, the anisotropic constitutive properties may be tailored according to requirements and the failure behavior can be improved. Such adaptive fiber composites are very well-suited for the task of noise and vibration reduction. In this respect the helicopter rotor system represents a very interesting and widely perceptible field of application. The occurring oscillations can be reduced with aid of aerodynamic couplings via fast manipulation of the angle of attack, being induced by twist actuation of the rotor blade. On the one hand the sensing properties may be used to determine the current state of deformation, while on the other hand the actuation properties may be used to attain the required state of deformation. The implementation of such concepts requires comprehensive knowledge of the theoretical context, which shall be illuminated in the work at hand from the examination of the material behavior to the simulation of the rotating structure.

This book provides analytical solutions to a number of classical problems in transport processes, i.e. in fluid mechanics, heat and mass transfer. Expanding computing power and more efficient numerical methods have increased the importance of computational tools. However, the interpretation of these results is often difficult and the computational results need to be tested against the analytical results, making analytical solutions a valuable commodity. Furthermore, analytical solutions for transport processes provide a much deeper understanding of the physical phenomena involved in a given process than do corresponding numerical solutions. Though this book primarily addresses the needs of researchers and practitioners, it may also be beneficial for graduate students just entering the field.

This work investigates the theoretical and cosmological implications of modifying Einstein's theory of general relativity. It explores two classes of modifications to gravity: those in which the graviton is given a small mass, and those in which Lorentz invariance is spontaneously broken. It elucidates the nature of cosmological perturbations in theories of massive bimetric gravity, including a potentially deadly instability. Theories of gravity beyond general relativity could explain why the expansion of the Universe is accelerating, obviating the need for a dark energy, and can also affect the evolution of the early Universe. Next, it investigates the nature of spacetime in massive gravity theories that contain two different spacetime metrics. Lastly, the strongest constraints to date are placed on the size of Lorentz-violating effects in the gravity sector during inflation.

This collection of over 200 detailed worked exercises adds to and complements the textbook "Fluid Mechanics" by the same author, and, at the same time, illustrates the teaching material via examples. The exercises revolve around applying the fundamental concepts of "Fluid Mechanics" to obtain solutions to diverse concrete problems, and, in so doing, the students' skill in the mathematical modelling of practical problems is developed. In addition, 30 challenging questions WITHOUT detailed solutions have been included. While lecturers will find these questions suitable for examinations and tests, students themselves can use them to check their understanding of the subject.

Two complete new chapters have been introduced. The first one, Chapter 16, amplifies the many rich interactions between Geographie Information Systems (GIS) and the Navstar CPS. The words and pietures in this new chapter foeus on the powerful eleetronie mapmaking techniques that rely on Navstar navigation together with the many benefits stemming from the full-eolored "layered" maps now being produeed. Chapter 17, which is also new, deals with Intelligent Vehicle Highway Systems (lVHS). Navstar navigation techniques form the hidden backbone of most of the new electronic teehnologies that are helping to make America's traffic f10w more smoothly. Chapter 17 c10ses with narrative descriptions of three interesting IVHS projects: emergency tow-truck dispatching, optimum ambulance-routing, and the in-car traffie reports now being beamed into family cars cruising along Ameriea's major traffic arteries. Many helpful individuals contributed toward the successful completion of Under- standing the Navstar. My lovely wife, Cyndy, was unquestionably the most beneficial contributor. Her affectionate comments and her broad-ranging support were greatly appreciated. So was her diligent and uncomplaining work in word-process- ing the many drafts of the final manuseript. The artists, Lloyd and lInka Wing and Anthony and Dianne Vega, were also enormously helpful in providing quality figures and tables on schedule. They have become true masters of the Macintosh computer with its many beils and whistles. Preparing a book for publication is a time-consuming, invigorating task. I hope you enjoy reading it as much as I enjoyed putting it together for your use.

This reader-friendly resource covers the broad spectrum of satellite principles and their associated technologies. While other books limit their coverage to specialized services or to satellite payloads such as communication satellites, Satellite Systems focuses upon the methodology of launching satellites, keeping them there, the environments under which they operate, and other facets particular to their operation. Pattan's detailed, elaborate approach does not assume that the reader is versed in esoteric mathematics. Satellite Systems is specific enough to be a valuable working-tool to scientists and engineers in related fields, yet general enough to be accessible to students and interested lay people. Pattan throughly explores the concepts and technologies of satellite systems in simple, direct terms. Satellite Systems includes precise coverage of: *various orbits and the services they provide *international launch of vehicles and launch sites *phased array antennas for satellite network applications *mobile satellite services from land vehicles, aircraft, and ships *low orbit satellites for telecommunication and position determination applications *international frequency allocations for satellite control, payload management, and status *geometric relationships between satellite and Earth stations used in interference analysis, orbit determination, and location *the hostile environments in which satellites operate and cope *and much more Satellite Systems is a self-contained, extensive introduction that offers professionals and advanced undergraduate and graduate students of satellite systems the tools they need for in-depth understanding of the complexities of the subject. It is ideal as both a reference and a training text for engineers, technicians, communication lawyers, weather professionals, telecommunications experts, students, and anyone interested insatellites and satellite technology.

The origins of turbulent flow and the transition from laminar to turbulent flow are among the most important unsolved problems of fluid mechanics and aerodynamics. Besides being a fundamental question of fluid mechanics, there are many practical applications for information regarding transition location and the details of the subsequent turbulent flow. This proceedings volume contains the papers of two keynote lectures as well as of 104 technical presentations and posters that were presented at the IUTAM Symposium on Laminar-Turbulent Transition in Sedona, Arizona, September 13-17, 1999. The papers published in the present volume document the state of the art in transition research, and therefore, increased emphasis on the various topics covered in this meeting can be expected in the future.

This monograph, entirely devoted to Convection in Fluids, presents a unified rational approach of various convective phenomena in fluids (mainly considered as a thermally perfect gas or an expansible liquid), where the main driving mechanism is the buoyancy force (Archimedean thrust) or temperature-dependent surface tension in homogeneities (Marangoni effect). Also, the general mathematical formulation (for instance, in the Benard problem - heated from below) and the effect of free surface deformation are taken into account. In the case of atmospheric thermal convection, the Coriolis force and stratification effects are also considered.

This volume gives a rational and analytical analysis of the above mentioned physical effects on the basis of the full unsteady Navier-Stokes and Fourier (NS-F) equations - for a Newtonian compressible viscous and heat-conducting fluid - coupled with the associated initials (at initial time), boundary (lower-at the solid plane) and free surface (upper-in contact with ambiant air) conditions. This, obviously, is not an easy but a necessary task if we have in mind a rational modelling process, and work within a numerically coherent simulation on a high speed computer."

The objective of this book is to present the main theoretical approaches and models in shallow water acoustics as well as different experimental results. The focus is primarily concentrated on physical results describing the sound field in wave length. The authors show dynamic phenomena (tides, internal waves) from the perspective of acoustic influence as well as the scattering of sound over the macroscopic body in shallow water waveguide. The method of acoustic probing can be used by physicists, geophysicists, geologists and oceanographers.

The Earth's atmosphere is often portrayed as a thin and finite blanket covering our planet, separate from the emptiness of outer space. In reality, the transition is gradual and a tiny fraction of the atmophere gases is still present at the altitude of low orbiting satellites. The very high velocities of these satellites ensure that their orbital motion can still be considerably affected by air density and wind. This influence can be measured using accelerometers and satellite tracking techniques. The opening chapters of this thesis provide an excellent introduction to the various disciplines that are involved in the interpretation of these observations: orbital mechanics, satellite aerodynamics and upper atmospheric physics. A subsequent chapter, at the heart of this work, covers advances in the algorithms used for processing satellite accelerometry and Two-Line Element (TLE) orbit data. The closing chapters provide an elaborate analysis of the resulting density and wind products, which are generating many opportunities for further research, to improve the modelling and understanding of the thermosphere system and its interactions with the lower atmosphere, the ionosphere-magnetosphere system and the Sun.

This book presents a general classical field theory, incorporating continuum mechanics, electrodynamics, and thermodynamics. The continuum equations of material behavior are derived from the principles of Onsager's non-equilibrium thermodynamics supplemented with dynamic degrees of freedom. The book contains the basic principles and methods of modern continuum mechanics and of rheology. Non-equilibrium thermodynamics is discussed in detail. Applications include elasticity, thermoelasticity, viscoelasticity, plasticity, rheooptics, etc. The models of rheology are developed within a consistent thermodynamic framework. Viscoelastic and plastic response, Ostwald's curve of generalized Newtonian fluids, creep, elasticity preceding plastic flow, the rules of rheooptics, etc., are discussed, and the empirical Cox-Merz rule is proved. The thermodynamic results are compared to the results of microscopic theories. Several kinds of colloids, polymers, and liquid crystals are studied. The technical level of the book is high. It is designed for engineers, physicists, natural scientists and applied mathematicians.

A strong reference on the problem of signal and speech enhancement, describing the newest developments in this exciting field. The general emphasis is on noise reduction, because of the large number of applications that can benefit from this technology.

The heh~vior of matter anrl waves in a rlynamical setting nffer~ many challenging prohlems to the mathematician anrl the m~terials scientist alike. Unrler review in this volume are a variety of nonlioear phenomena whose con- sirleration entails new perspectives, oot commooly fouorl in the literatllre. Of particular note is the experimental aspect of many of the papers. In arlrlition, attention has been given ta the interaction of electromagnetic anrl mechanical pro- perties of materials. Ouestions arise which cannat naw he answererl. Attempts are marle to rlescrihe anrl to unrlerstand phenomena which are far from equilihrium ar which suffer ahrupt changes in behavior. Some of this requires tentative physical or aoalytical assumptions. The hases for these hypotheses lie in the quest for a rational theory which agrees with experiment. This Volume anr! Volume 2, ~scUJation theory, compution, an'!. methorls ~ com- pensated ~~mpact~ess, offer oi fferent vi ewpoi nts of some of the rlynami cal stllrli es considereo during the 19f14-19R5 IMA program, Continullm Physics and Partial Differenti al Equati ons. Contents of the other volumes, fOllnrl at the enrl of the hook, contain other relevant titles.

This text provides an overview of important theory, principles, and concepts in the field of thermodynamics, making this abstract and complex subject easy to comprehend while building practical skills in the process. It enhances understanding of heat transfer, steam tables, energy concepts, power generation, psychrometry, refrigeration cycles, and more. Practical, easily accessible case studies illustrate various thermodynamics principles. Each chapter concludes with a list of questions or problems, with answers at the back of the book.

1. 1 A paradigm About one hundred years ago, Maurice Couette, a French physicist, de signed an apparatus consisting of two coaxial cylinders, the space between the cylinders being filled with a viscous fluid and the outer cylinder being rotated at angular velocity O2. The purpose of this experiment was, follow ing an idea of the Austrian physicist Max Margules, to deduce the viscosity of the fluid from measurements of the torque exerted by the fluid on the inner cylinder (the fluid is assumed to adhere to the walls of the cylinders). At least when O is not too large, the fluid flow is nearly laminar and 2 the method of Couette is valuable because the torque is then proportional to 110, where II is the kinematic viscosity of the fluid. If, however, O is 2 2 increased to a very large value, the flow becomes eventually turbulent. A few years later, Arnulph Mallock designed a similar apparatus but allowed the inner cylinder to rotate with angular velocity 01, while O2 = o. The surprise was that the laminar flow, now known as the Couette flow, was not observable when 0 exceeded a certain "low" critical value Ole, even 1 though, as we shall see in Chapter II, it is a solution of the model equations for any values of 0 and O ."

This book leads directly to the most modern numerical techniques for compressible fluid flow, with special consideration given to astrophysical applications. Emphasis is put on high-resolution shock-capturing finite-volume schemes based on Riemann solvers. The applications of such schemes, in particular the PPM method, are given and include large-scale simulations of supernova explosions by core collapse and thermonuclear burning and astrophysical jets. Parts two and three treat radiation hydrodynamics. The power of adaptive (moving) grids is demonstrated with a number of stellar-physical simulations showing very crispy shock-front structures.