This book aims to coherently present applications of group analysis to integro-differential equations in an accessible way. The book will be useful to both physicists and mathematicians interested in general methods to investigate nonlinear problems using symmetries.

A variety of nonlinear effects occur in a plasma. First, there are the wave­ steepening effects which can occur in any fluid in which the propagation speed depends upon the wave-amplitude. In a dispersive medium this can lead to classes of nonlinear waves which may have stationary solutions like solitons and shocks. Because the plasma also acts like an inherently nonlinear dielectric resonant interactions among waves lead to exchange of energy among them. Further, an electromagnetic wave interacting with a plasma may parametrically excite other waves in the plasma. A large-amplitude Langmuir wave undergoes a modulational instability which arises through local depressions in plasma density and the corresponding increases in the energy density of the wave electric field. Whereas a field collapse occurs in two and three dimensions, in a one-dimensional case, spatially localized stationary field structures called Langmuir solitons can result. Many other plasma waves like upper-hybrid waves, lower-hybrid waves etc.

The aim of this book is to describe an efficient procedure to model dynamical contact problems with friction. This procedure is applied to different practical problems and verified by experiments.

Contact mechanics was and is an important branch in mechanics which covers a broad field of theoretical, numerical and experimental investigations. In this carefully edited book the reader will obtain a state-of-the-art overview on formulation, mathematical analysis and numerical solution procedures of contact problems. The contributions collected in this volume summarize the lectures presented during the 4th Contact Mechanics Interantional symposium (CMIS) held in Hannover, Germany, 2005, by leading scientists in the area of contact mechanics.

Turbulence takes place in most flow situations whethertheyoccur naturally or in technological systems. Therefore, considerable effort is being expended in an attempt to understand the phenomenon of turbulence. The recent discovery ofcoherent structure in turbulent shear flows and the modem developments in computer capabilities have revolutionized research work in turbulence. There is a strong evidence that the coherent structure in turbulent shear flows is reminiscent of nonlinear stability waves. As such, the interest in nonlinear stability waves has increased not only for the understandingofthe latterstages of the laminar-turbulent transition process, but also for understanding the coherent structures in turbulent flows. Also. the advances in computers have made direct numerical simulation possible at Low-Reynolds numbers and large-eddy simulation possible at high Reynolds numbers. This made first-principles prediction of turbulence-generated noise feasible. Therefore, this book aims at presenting a graduate-level introductory study of turbulence while accounting for such recent views of concern to researchers. This book is an outgrowth oflecture notes on the subject offered to graduate students in engineering. The book should be of interest to research engineers and graduatestudents in science and engineering. The theoretical basis presented is sufficient not only for studying the specialized literature on turbulence but also for theoretical investigations on the subject.

The practical and theoretical relevance of problems to the NP-complete degree vf complexity are widely known. From the practical point of view it is sufficient to remember that in this class we find most of the combinatorial and optimization problems which b,,.·e the widest range of applications, for example scheduling problems, optimization problems on graphs, integer programming etc. As far as the theoretical relevance is concerned ;;.•e should remember that one of the most outstanding problems in Computer Science, the problem of deciding whether any NP-complete set can be recognized in polynomial time, coincides with the problem of knowing whether the computation power of a nondeterministic Turing machine which accepts a set in polynomial time is strictly stronger than the power of ordinary polynomially bounded Turing machines or not. Until recen#y the design of algorithms for finding exact approximate solutions to practical instances of hard combinatorial and optimization problems was the main concern of experts in Operations Research while the study of the complexity of these problems with respect to various computation models and the analysis of general solution techniques was the main interest of computer scientists.

Chaos: A Program Collection for the PC presents an outstanding selection of executable programs with introductory texts to chaos theory and its simulation. Students in physics, mathematics, and engineering will find a thorough introduction to fundamentals and applications in this field. Many numerical experiments and suggestions for further studies help the reader to become familiar with this fascinating topic. The second edition includes one CD-ROM, the executable programs are Windows 95 compatible.

The conference "Chaos in Astronomy" was held in Athens on 17-20 Sep 2007. International leaders in the field addressed the topics:
Chaos in large N-body systems and in galactic dynamics
Chaos in solar system dynamics
Statistical mechanics of systems with regular and chaotic orbits
Chaos in the formation of large-scale structure in the Universe
Fundamental concepts, methods and tools.
The book contains carefully edited refereed contributions. It serves as a reference to researchers and will give an overview to students and newcomers entering any field of dynamical astronomy.

This book introduces the reader the theory of nonlinear inclusions and hemivariational inequalities with emphasis on the study of contact mechanics. The work covers both abstract results in the area of nonlinear inclusions, hemivariational inequalities as well as the study of specific contact problems, including their modelling and their variational analysis. Provided results are based on original research on the existence, uniqueness, regularity and behavior of the solution for various classes of nonlinear stationary and evolutionary inclusions. In carrying out the variational analysis of various contact models, one systematically uses results of hemivariational inequalities and, in this way, illustrates the applications of nonlinear analysis in contact mechanics. New mathematical methods are introduced and applied in the study of nonlinear problems, which describe the contact between a deformable body and a foundation. Contact problems arise in industry, engineering and geophysics. Their variational analysis presented in this book lies the background for their numerical analysis. This volume will interest mathematicians, applied mathematicians, engineers, and scientists as well as advanced graduate students.

This is the fourth book from the Series "Scientific Fundamentals of Ro­ botics". The first two volumes have established abackqround for studying the dynamics and control of robots. While the first book was exclusive­ ly devoted to the dynamics of active spatial mechanisms, the second treated the problems of the dynamic control of manipulation robots. In contrast to the first two books, where recursive computer-aided me­ thods for setting robot dynamic equations where described, this mono­ graph presents a new approach to the formation of robot dynamics. The goal is to achieve the real-time model computation using up-to-date mi­ crocomputers. The presented concept could be called a numeric-symbolic, or analytic, approach to robot modelling.

The last two years have witnessed a continuation in the breakthrough shift toward pulse tube cryocoolers for long-life, high-reliability cryocooler applications. One class of pulse tubes that has reached maturity is referred to as “Stirling type” because they are based on the linear Oxford Stirling-cooler type compressor; these generally provide cooling in the 30 to 100 K temperature range and operate at frequencies from 30 to 60 Hz. The other type of pulse tube cooler making great advances is the so-called “Gifford-McMahon type. ” Pulse tube coolers of this type use a G-M type compressor and lower frequency operation to achieve temperatures in the 2 to 10 K temperature range.

Classical mechanics is the basis for any university-level study of technical-scientific disciplines. But most existing manuals use a technological and engineering approach, with basic aspects sometimes insufficiently highlighted. This book introduces the concepts and applications of classical mechanics into Newtonian formalism. Newtonian dynamics is useful for solving applied physics and engineering problems, but also a fascinating theory anchored in questions posed since the times of the Greek philosophers, regarding space, the flow of time, measurable physical quantities, the physical principles with the mathematical structure needed to describe the Universe, etc. The author aims to encourage students to think about these fundamental aspects and how they will be addressed in modern physics, including the successes and limitations of Newton's mechanics. The book is designed to mirror the progress of the students using it, with earlier chapters assuming no more than basic high school instruction and later ones geared toward subsequent enhanced understanding. The book is designed for students of undergraduate programs in physics, mathematics, chemistry, and engineering who will deal with modern physics, as they will benefit from an approach in which the aspects of classical mechanics are introduced in a propaedeutic approach towards relativistic physics and quantum mechanics.

The increasing size and complexity of new structural forces in engineering have made it necessary for designers to be aware of their dynamic behaviour. Dynamics is a subject which has traditionally been poorly taught in most engineering courses. This book was conceived as a way of providing engineers with a deeper knowledge of dynamic analysis and of indicating to them how some of the new vibrations problems can be solved. The authors start from basic principles to end up with the latest random vibration applications.

The present book deals with the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations, which are currently used in many fields of engineering mechanics with applied character, like elasticity, plasticity, thermoelastoplasticity, viscoelasticity, viscoplasticity, fracture mechanics, structural analysis, fluid mechanics, aerodynamics and elastodynamics. These types of singular integral equations form the latest high technology on the solution of very important problems of solid and fluid mechanics and therefore special attention should be given by the reader of the present book, who is interested for the new technology of the twentieth-one century.

As the Boundary Element Method develops into a tool of engineering analysis more effort is dedicated to studying new applications and solving different problems. This book contains chapters on the basic principles of the technique, time dependent problems, fluid mechanics, hydraulics, geomechanics and plate bending. The number of non-linear and time dependent problems which have become amenable to solution using boundary elements have induced many researchers to investigate in depth the basis of the method. Chapter 0 of this book presents an ap­ proach based on weighted residual and error approximations, which permits easy construction of the governing boundary integral equations.