This is the first monograph in the theory of p-adic (and more general non-Archimedean) dynamical systems. The theory of such systems is a new intensively developing discipline on the boundary between the theory of dynamical systems, theoretical physics, number theory, algebraic geometry and non-Archimedean analysis. Investigations on p-adic dynamical systems are motivated by physical applications (p-adic string theory, p-adic quantum mechanics and field theory, spin glasses) as well as natural inclination of mathematicians to generalize any theory as much as possible (e.g., to consider dynamics not only in the fields of real and complex numbers, but also in the fields of p-adic numbers). The main part of the book is devoted to discrete dynamical systems: cyclic behavior (especially when p goes to infinity), ergodicity, fuzzy cycles, dynamics in algebraic extensions, conjugate maps, and small denominators. There are also studied p-adic random dynamical system, especially Markovian behavior (depending on p). In 1997 one of the authors proposed to apply p-adic dynamical systems for modeling of cognitive processes. algebraic structure of fields of p-adic numbers, but by their tree-like hierarchical structures. In this book, there is presented a model of probabilistic thinking on p-adic mental space based on ultrametric diffusion. There are also studied p-adic neural network and their applications to cognitive sciences: learning algorithms, memory recalling. Finally, there are considered wavelets on general ultrametric spaces, developed corresponding calculus of pseudo-differential operators and considered cognitive applications. This book will be of interest to mathematicians working in the theory of dynamical systems, number theory, algebraic geometry, non-Archimedean analysis as well as general functional analysis, theory of pseudo-differential operators; physicists working in string theory, quantum mechanics, field theory, spin glasses; psychologists and other scientists working in cognitive sciences and even mathematically oriented philosophers.

FolJowing the formulation of the laws of mechanics by Newton, Lagrange sought to clarify and emphasize their geometrical character. Poincare and Liapunov successfuIJy developed analytical mechanics further along these lines. In this approach, one represents the evolution of all possible states (positions and momenta) by the flow in phase space, or more efficiently, by mappings on manifolds with a symplectic geometry, and tries to understand qualitative features of this problem, rather than solving it explicitly. One important outcome of this line of inquiry is the discovery that vastly different physical systems can actually be abstracted to a few universal forms, like Mandelbrot's fractal and Smale's horse-shoe map, even though the underlying processes are not completely understood. This, of course, implies that much of the observed diversity is only apparent and arises from different ways of looking at the same system. Thus, modern nonlinear dynamics 1 is very much akin to classical thermodynamics in that the ideas and results appear to be applicable to vastly different physical systems. Chaos theory, which occupies a central place in modem nonlinear dynamics, refers to a deterministic development with chaotic outcome. Computers have contributed considerably to progress in chaos theory via impressive complex graphics. However, this approach lacks organization and therefore does not afford complete insight into the underlying complex dynamical behavior. This dynamical behavior mandates concepts and methods from such areas of mathematics and physics as nonlinear differential equations, bifurcation theory, Hamiltonian dynamics, number theory, topology, fractals, and others.

Presenting a comprehensive account of the physical concepts and theoretical approaches developed for the study of the dynamical properties of liquids (or, more generally, of high-density fluids), at a microscopic level, this book first discusses the basic dynamical phenomena to be interpreted, as well as the various experimental probes. It then proceeds to an exposition of the sophisticated theoretical techniques needed for a satisfactory account of both single particle and collective motions. The complications are faced in a stepwise fashion, with special attention to the physical content of the results. Based on the results of the progress achieved in the last decade the book provides a satisfactory understanding of most of the phenomena characterising this fascinating field.

Modern airborne and spaceborne imaging radars, known as synthetic aperture radars (SARs), are capable of producing high-quality pictures of the earth's surface while avoiding some of the shortcomings of certain other forms of remote imaging systems. Primarily, radar overcomes the nighttime limitations of optical cameras, and the cloud- cover limitations of both optical and infrared imagers. In addition, because imaging radars use a form of coherent illumination, they can be used in certain special modes such as interferometry, to produce some unique derivative image products that incoherent systems cannot. One such product is a highly accurate digital terrain elevation map (DTEM). The most recent (ca. 1980) version of imaging radar, known as spotlight-mode SAR, can produce imagery with spatial resolution that begins to approach that of remote optical imagers. For all of these reasons, synthetic aperture radar imaging is rapidly becoming a key technology in the world of modern remote sensing. Much of the basic workings' of synthetic aperture radars is rooted in the concepts of signal processing. Starting with that premise, this book explores in depth the fundamental principles upon which the spotlight mode of SAR imaging is constructed, using almost exclusively the language, concepts, and major building blocks of signal processing. Spotlight-Mode Synthetic Aperture Radar: A Signal Processing Approach is intended for a variety of audiences. Engineers and scientists working in the field of remote sensing but who do not have experience with SAR imaging will find an easy entrance into what can seem at times a very complicated subject. Experienced radar engineers will find that the book describes several modern areas of SAR processing that they might not have explored previously, e.g. interferometric SAR for change detection and terrain elevation mapping, or modern non-parametric approaches to SAR autofocus. Senior undergraduates (primarily in electrical engineering) who have had courses in digital signal and image processing, but who have had no exposure to SAR could find the book useful in a one-semester course as a reference.

This book is intended as a historical and critical study on the origin of the equations of motion as established in Newton's Principia. The central question that it aims to answer is whether it is indeed correct to ascribe to Galileo the inertia principle and the law of falling bodies. In order to accomplish this task, the study begins by considering theories on the motion of bodies from classical antiquity, and especially those of Aristotle. The theories developed during the Middle Ages and the Renaissance are then reviewed, with careful analysis of the contributions of, for example, the Merton and Parisian Schools and Galileo's immediate predecessors, Tartaglia and Benedetti. Finally, Galileo's work is examined in detail, starting from the early writings. Excerpts from individual works are presented, to allow the texts to speak for themselves, and then commented upon. The book provides historical evidence both for Galileo's dependence on his forerunners and for the major breakthroughs that he achieved. It will satisfy the curiosity of all who wish to know when and why certain laws have been credited to Galileo.

This book describes in detail the current, state-of-the-art numerical treatment and simulation of multiphase flows in porous media. The porous media considered range from ordinary to fractured and deformable media, the models treated from single-phase compressible flow to multiphase multicomponent flow with mass interchange, while the computational algorithms encompass everything from classical iterative solvers to modern multigrid and domain decomposition approaches. Addressing many problems originating from the applied geosciences, the book focuses on their common mathematical and computational aspects. It will serve as an excellent research reference for all geoscientists, mathematicians, physicists, and engineers who work in the mathematical modeling and numerical simulation of multiphase flows in porous media.

POLYMER MODELS AND EQUILIBRIUM PROPERTIES.

Mechanical Models for Polymer Molecules.

Equilibrium Configurations of Polymer Molecules.

ELEMENTARY APPROACH TO KINETIC THEORY.

Elastic Dumbbell Models.

The Rigid Dumbbell and Multibead-Rod Models.

The Bead-Spring Chain Models.

General Bead-Rod-Spring Models.

A GENERAL PHASE-SPACE KINETIC THEORY.

Phase-Space Theory of Polymeric Liquids.

Phase-Space Theory for Dilute Solutions.

Phase-Space Theory for Concentrated Solutions and Melts.

ELEMENTARY KINETIC THEORY FOR NETWORK MODELS.

Network Theories for Polymer Melts and Concentrated Solutions.

APPENDICES.

Summary of Continuum Mechanics Notation and Results.

Useful Mathematical Formulas.

Author Index.

Subject Index.

Con?gurational mechanics has attracted quite a bit of attention from various - search ?elds over the recent years/decades. Having been regarded in its infancy of the early years as a somewhat obscureand almost mystic ?eld of researchthat could only be understood by a happy few of insiders with a pronounced theoretical inc- nation, con?gurational mechanics has developed by now into a versatile tool that can be applied to a variety of problems. Since the seminal works of Eshelby a general notion of con?gurational - chanics has been developed and has successfully been applied to many pr- lems involving various types of defects in continuous media. The most pro- nent application is certainly the use of con?gurational forces in fracture - chanics. However, as con?gurational mechanics is related to arbitrary mat- ial inhomogeneities it has also very successfully been applied to many ma- rials science and engineering problems such as phase transitions and inelastic deformations. Also the modeling of materials with micro-structure evolution is an important ?eld, in which con?gurational mechanics can provide a better understanding of processes going on within the material. Besides these mechanically, physically, and chemically motivated applications, ideas from con?gurational mechanics are now increasingly applied within computational mechanics.

The Integrated Services Digital Network (ISDN) represents the current position in about a hundred years of evolutionary growth of the worldwide telecommunications infrastructure. This evolution is by no means complete and the next few years will see the emergence of a "Broad-band" ISDN as the next stage of evolutionary development. It is important to appreciate the evolutionary nature of the telecommunications infrastructure if one is to properly understand much of the thinking that lies behind the current ISDN proposals. This book therefore begins with a number of chapters devoted to a study of the various developments which have eventually led to the concept of an integrated digital network. These include the development of digital transmission of speech using PCM and the development of digital switching techniques based on stored program control. The book then turns to a consideration of those features of the existing telecommunications network which need to be modified in order to make ISDN a realizable practicality. Of particular importance is the digitization of transmission over the links between the user and the local exchange. Next we look at the current practice and proposals for ISDN based on the technology presently in use in the telephone network. Finally, we look at the proposals for a broadband ISDN likely to become widely available by the turn of the century.

At the opening of the "Third Meeting on Celestial Mechanics - CELMEC III", strong sensations hit our minds. The conference (18-22 June 2001) was being held in Villa Mondragone, a beautiful complex of buildings and gardens located within the township of Monte Porzio Catone, on the hills surrounding Rome. A former papal residence, the building has been recently restored by the University of Rome "Tor Vergata" to host academic activities and events. The conference room is called "Salone degli Svizzeri": here, Gregory XIII, on February 24, 1582, gave its sanction to the reform of the Julian calendar and declared officially in use the calendar still adopted nowadays. The magnificent high walls and tall ceiling strongly resounded, giving to our voice a peculiar Vatican sound, which took us by surprise. May be - we thought - a distant echo of the very words of Gregory XIII proclaiming the modem calendar was still haunting the room. Around us, in the audience, many countries were represented, thus indicating that the idea of putting together the three "souls" of modem Celestial Mechanics - perturbation theories, solar and stellar system studies, spaceflight dynamic- had been successful. CELMEC III is in fact the latest of a series of meetings (the first two editions took place in 1993 and 1997 in L' Aquila, Italy) whose aim is to establish a common ground among people working in Celestial Mechanics, yet belonging to different institutions such as universities, astronomical observatories, research institutes, space agencies and industries.

This symposium was devoted to a new celestial mechanics whose aim has become the study of such objects' as the planetary system, planetary rings, the asteroidal belt, meteor swarms, satellite systems, comet families, the zodiacal cloud, the preplanetary nebula, etc. When the three-body problem is considered instead of individual orbits we are, now, looking for the topology of extended regions of its phase space. This Symposium was one step in the effort to close the ties between two scientific families: the observationally-oriented scientists and the theoretically-oriented scientists.

This book is about the pattern formation and the evolution of crack propagation in engineering materials and structures, bridging mathematical analyses of cracks based on singular integral equations, to computational simulation of engineering design. The first two parts of this book focus on elasticity and fracture and provide the basis for discussions on fracture morphology and its numerical simulation, which may lead to a simulation-based fracture control in engineering structures. Several design concepts are discussed for the prevention of fatigue and fracture in engineering structures, including safe-life design, fail-safe design, damage tolerant design.

After starting with basic elasticity and fracture theories in parts one and two, this book focuses on the fracture morphology that develops due to the propagation of brittle cracks or fatigue cracks.

In part three, the mathematical analysis of a curved crack is precisely described, based on the perturbation method. The stability theory of interactive cracks propagating in brittle solids may help readers to understand the formation of a fractal-like cracking patterns in brittle solids, while the stability theory of crack paths helps to identify the straight versus sharply curved or sometimes wavy crack paths observed in brittle solids.

In part four, the numerical simulation method of a system of multiple cracks is introduced by means of the finite element method, which may be used for the better implementation of fracture control in engineering structures.

This book is part of a series on Mathematics for Industry and will appeal to structural engineers seeking to understand the basic backgrounds of analyses, but also to mathematicians with an interest in how such mathematical solutions are evaluated in industrial applications."

This treatise is a compendium of refereed papers based on invited talks presented at the American Chemical Society Symposium on Electrorheological (ER) Materials and Fluids. ER fluids were first investigated 50+ years ago. These fluids, which change rheology when placed in an electric field, were recognized, from the beginning, for allowing an extremely efficient interface between electrical control and mechanical devices. Critical problems, however, existed with the initial fluids, which prevented them from serious consideration for large-scale applications. While over time some of the critical problems have been solved and activity in ER technology has increased, commercial success has remained elusive. A recent Department of Energy report concluded that a primary reason for the failure to commercialize this promising technology is due to a lack in understanding the physics and chemistry of how the materials work. The goal of the symposium was to address the issue of understanding how ER materials work and how they can be used. One of the outcomes of the symposium, which we hope is conveyed in this book, is a feeling that if the mechanism of ER is to be fully understood and improved, expertise from diverse fields must be applied to the problem.

This text provides an introduction, at the level of an advanced student in engineering or physics, to the field of nanomechanics and nanomechanical devices. It provides a unified discussion of solid mechanics, transducer applications, and sources of noise and nonlinearity in such devices. Demonstrated applications of these devices, as well as an introduction to fabrication techniques, are also discussed. The text concludes with an overview of future technologies, including the potential use of carbon nanotubes and other molecular assemblies.

This thesis presents significant new results on the problem of understanding the origin of dark energy in cosmology. The work develops an original approach based on modifications of General Relativity at cosmological scales, introducing non -local effective terms that can in principle emerge from fundamental local theories. Both the phenomenological consequences and theoretical aspects of the proposal are developed in depth. The thesis also contains significant new material compared to that published by the author in scientific journals.

Theory of vibrations belongs to principal subjects needed for training mechani cal engineers in technological universities. Therefore, the basic goal of the mono graph "Advanced Theory of Vibrations 1" is to help students studying vibration theory for gaining experience in application of this theory for solving particular problems. Thus, while choosing the problems and methods to solve them, the close attention was paid to the applied content of vibration theory. The monograph is devoted to systems with a single degree of freedom and sys tems with a finite number of degrees of freedom. In particular, problems are for mulated associated with determination of frequencies and forms of vibrations, study of forced vibrations, analysis of both stable and unstable vibrations (includ ing those caused by periodic but anharmonic forces). The problems of nonlinear vibrations and of vibration stability, and those related to seeking probabilistic characteristics for solutions to these problems in the case of random forces are also considered. Problems related to parametric vibrations and statistical dynamics of mechanical systems, as well as to determination of critical parameters and of dy namic stability are also analyzed. As a rule, problems presented in the monograph are associated with particular mechanical systems and can be applied for current studies in vibration theory. Al lowing for interests of students independently studying theory of vibrations, the majority of problems are supplied with either detailed solutions or algorithms of the solutions."

This book introduces readers to the fundamentals of simulating and analyzing built and natural environments using the Computational Fluid Dynamics (CFD) method. CFD offers a powerful tool for dealing with various scientific and engineering problems and is widely used in diverse industries. This book focuses on the most important aspects of applying CFD to the study of urban, buildings, and indoor and outdoor environments. Following the logical procedure used to prepare a CFD simulation, the book covers e.g. the governing equations, boundary conditions, numerical methods, modeling of different fluid flows, and various turbulence models. Furthermore, it demonstrates how CFD can be applied to solve a range of engineering problems, providing detailed hands-on exercises on air and water flow, heat transfer, and pollution dispersion problems that typically arise in the study of buildings and environments. The book also includes practical guidance on analyzing and reporting CFD results, as well as writing CFD reports/papers.

This book introduces readers to the lattice Boltzmann method (LBM) for solving transport phenomena - flow, heat and mass transfer - in a systematic way. Providing explanatory computer codes throughout the book, the author guides readers through many practical examples, such as: * flow in isothermal and non-isothermal lid-driven cavities; * flow over obstacles; * forced flow through a heated channel; * conjugate forced convection; and * natural convection. Diffusion and advection-diffusion equations are discussed, together with applications and examples, and complete computer codes accompany the sections on single and multi-relaxation-time methods. The codes are written in MatLab. However, the codes are written in a way that can be easily converted to other languages, such as FORTRANm Python, Julia, etc. The codes can also be extended with little effort to multi-phase and multi-physics, provided the physics of the respective problem are known. The second edition of this book adds new chapters, and includes new theory and applications. It discusses a wealth of practical examples, and explains LBM in connection with various engineering topics, especially the transport of mass, momentum, energy and molecular species. This book offers a useful and easy-to-follow guide for readers with some prior experience with advanced mathematics and physics, and will be of interest to all researchers and other readers who wish to learn how to apply LBM to engineering and industrial problems. It can also be used as a textbook for advanced undergraduate or graduate courses on computational transport phenomena

The present volume offers a state-of-the-art report on the various recent scientific developments in the Theory of Porous Media (TPM) comprehending the basic theoretical concepts in continuum mechanics on porous and multiphasic materials as well as the wide range of experimental and numerical applications. Following this, the volume does not only address the sophisticated reader but also the interested beginner in the area of Porous Media by presenting a collection of articles. These articles written by experts in the field concern the fundamental approaches to multiphasic and porous materials as well as various applications to engineering problems.

The book presents a unified and well-developed approach to the dynamics of angular motions of rigid bodies subjected to perturbation torques of different physical nature. It contains both the basic foundations of the rigid body dynamics and of the asymptotic method of averaging. The rigorous approach based on the averaging procedure is applicable to bodies with arbitrary ellipsoids of inertia. Action of various perturbation torques, both external (gravitational, aerodynamical, solar pressure) and internal (due to viscous fluid in tanks, elastic and visco-elastic properties of a body) is considered in detail. The book can be used by researchers, engineers and students working in attitude dynamics of spacecraft.

This is the second volume of three books devoted to Mechanics. In this book, dynamical and advanced mechanics problems are stated, illustrated, and discussed, including a few novel concepts in comparison to standard text books and monographs. Apart from being addressed to a wide spectrum of graduate students, postgraduate students, researchers, and teachers from the fields of mechanical and civil engineering, this volume is also intended to be used as a self-contained material for applied mathematicians and physical scientists and researchers.

The free electron laser (FEL) will be an outstanding tool for research and industrial application. This book describes the physical fundamentals on the basis of classical mechanics, electrodynamics, and the kinetic theory of charged particle beams, and will be suitable for graduate students and scientists alike.After a short introduction, the book discusses the theory of the FEL amplifier and oscillator and diffraction effects in the amplifier. Waveguide FEL and shot noise are also treated.

This textbook offers a clear and comprehensive introduction to analytical mechanics, one of the core components of undergraduate physics courses. The book starts with a thorough introduction into Lagrangian mechanics, detailing the d'Alembert principle, Hamilton's principle and conservation laws. It continues with an in-depth explanation of Hamiltonian mechanics, illustrated by canonical and Legendre transformation, the generalization to quantum mechanics through Poisson brackets and all relevant variational principles. Finally, the Hamilton-Jacobi theory and the transition to wave mechanics are presented in detail. Ideally suited to undergraduate students with some grounding in classical mechanics, the book is enhanced throughout with learning features such as boxed inserts and chapter summaries, with key mathematical derivations highlighted to aid understanding. The text is supported by numerous worked examples and end of chapter problem sets. About the Theoretical Physics series Translated from the renowned and highly successful German editions, the eight volumes of this series cover the complete core curriculum of theoretical physics at undergraduate level. Each volume is self-contained and provides all the material necessary for the individual course topic. Numerous problems with detailed solutions support a deeper understanding. Wolfgang Nolting is famous for his refined didactical style and has been referred to as the "German Feynman" in reviews.