In the past hundred years investigators have learned the significance of complex behavior in deterministic systems. The potential applications of this discovery are as numerous as they are encouraging.This text clearly presents the mathematical foundations of chaotic dynamics, including methods and results at the forefront of current research. The book begins with a thorough introduction to dynamical systems and their applications. It goes on to develop the theory of regular and stochastic behavior in higher-degree-of-freedom Hamiltonian systems, covering topics such as homoclinic chaos, KAM theory, the Melnikov method, and Arnold diffusion. Theoretical discussions are illustrated by a study of the dynamics of small circumasteroidal grains perturbed by solar radiation pressure. With alternative derivations and proofs of established results substituted for those in the standard literature, this work serves as an important source for researchers, students and teachers.Skillfully combining in-depth mathematics and actual physical applications, this book will be of interest to the applied mathematician, the theoretical mechanical engineer and the dynamical astronomer alike.

The present book contains contributions presented at the Fourth Symposium on Hybrid RANS-LES Methods, held in Beijing, China, 28-30 September 2011, being a continuation of symposia taking place in Stockholm (Sweden, 2005), in Corfu (Greece, 2007), and Gdansk (Poland, 2009). The contributions to the last two symposia were published as NNFM, Vol. 97 and Vol. 111. At the Beijing symposium, along with seven invited keynotes, another 46 papers (plus 5 posters) were presented addressing topics on Novel turbulence-resolving simulation and modelling, Improved hybrid RANS-LES methods, Comparative studies of difference modelling methods, Modelling-related numerical issues and Industrial applications.. The present book reflects recent activities and new progress made in the development and applications of hybrid RANS-LES methods in general.

This book offers a detailed, pedagogical introduction to general relativity. It includes a review of what may lie beyond and collects up-to-date essays on the experimental tests of this theory, including the precise timing of the double pulsar J0737-3039. Coverage also details the recent results of the Gravity Probe B mission.

In these volumes, the most significant of the collected papers of the Chinese-American theoretical physicist Tsung-Dao Lee are printed. A complete list of his published papers, in order of publication, appears in the Bibliography of T.D. Lee. The papers have been arranged into ten categories, in most cases according to the subject matter. At the beginning of each of the first eight categories of papers, there is a commentary on the content and significance of all of the papers in the category. The two short final categories do not have any commentaries. The editor would like to thank Dr. Richard Friedberg for his assistance in the early stages of the editorial work on this project, as well as for writing commentaries on the papers of Categories III and IV. I would also like to thank Dr. Norman Christ for writing the commentary on the papers of Category VII. The assistance of Irene Tramm was in valuable in many aspects of preparing this collection, including locating copies of Lee's p pers. GERALD FEINBERG List of Categories of T.D. Lee's Papers Volume 1 I. Weak Interactions II. Early Papers on Astrophysics and Hydrodynamics III. Statistical Mechanics IV. Polarons and Solitons Volume 2 V. Quantum Field Theory VI. Symmetry Principles Volume 3 VII. Discrete Physics VIII. Strong Interaction Models IX. Historical Papers X. Gravity (Continuum Theory) Contents (Volume 3)* Introduction (by G. Feinberg) ............................................................ ix Bibliography of T.D. Lee ................................................................. xiii VII. Discrete Physics Commentary ................................................................ ."

This book collects invited lectures and selected contributions presented at the Enzo Levi and XVIII Annual Meeting of the Fluid Dynamic Division of the Mexican Physical Society in 2012. It is intended for fourth-year undergraduate and graduate students, and for scientists in the fields of physics, engineering and chemistry with an interest in Fluid Dynamics from experimental, theoretical and computational points of view. The invited lectures are introductory in nature and avoid the use of complicated mathematics. The other selected contributions are also suitable for fourth-year undergraduate and graduate students. The Fluid Dynamics applications include oceanography, multiphase flows, convection, diffusion, heat transfer, rheology, granular materials, viscous flows, porous media flows and astrophysics. The material presented in the book includes recent advances in experimental and computational fluid dynamics and is well-suited to both teaching and research.

Aerodynamics is a science engaged in the investigation of the motion of air and other gases and their interaction with bodies, and is one of the most important bases of the aeronautic and astronautic techniques. The continuous improvement of the configurations of the airplanes and the space vehicles aid the constant enhancement of their performances are closely related with the development of the aerodynamics. In the design of new flying vehicles the aerodynamics will play more and more important role. The undertakings of aeronautics and astronautics in our country have gained achievements of world interest, the aerodynamics community has made outstanding contributions for the development of these undertakings and the science of aerodynamics. To promote further the development of the aerodynamics, meet the challenge in the new century, summary the experience, cultivate the professional personnel and to serve better the cause of aeronautics and astronautics and the national economy, the present Series of Modern Aerodynamics is organized and published.

The 29th International Symposium on Acoustical Imaging was held in Shonan Village, Kanagawa, Japan, April 15-18, 2007. This interdisciplinary Symposium has been taking place every two years since 1968 and forms a unique forum for advanced research, covering new technologies, developments, methods and theories in all areas of acoustics. In the course of the years the volumes in the Acoustical Imaging Series have developed and become well-known and appreciated reference works.

Offering both a broad perspective on the state-of-the-art in the field as well as an in-depth look at its leading edge research, this Volume 29 in the Series contains again an excellent collection of seventy papers presented in nine major categories: (1) Strain Imaging, (2) Biological and Medical Applications, (3) Acoustic Microscopy, (4) Non-Destructive Evaluation and Industrial Applications, (5) Components and Systems, (6) Geophysics and Underwater Imaging, (7) Physics and Mathematics, (8) Medical Image Analysis, (9) FDTD method and Other Numerical Simulations.

Understanding Active Noise Control Provides a concise introduction to the fundamentals and applications of active control of vibration and sound for the non-expert. It is also a useful quick reference for the specialist engineer. The book emphasises the practical applications of technology, and complex control algorithms and structures are only discussed to the extent that they aid understanding. Extensive recommendations for further reading on the subject are provided, but the text will stand alone for those seeking an overview of the key issues: fundamentals, control systems, transducers, applications and possible future directions.

Matrix Computations on Systolic-Type Arrays provides a framework which permits a good understanding of the features and limitations of processor arrays for matrix algorithms. It describes the tradeoffs among the characteristics of these systems, such as internal storage and communication bandwidth, and the impact on overall performance and cost. A system which allows for the analysis of methods for the design/mapping of matrix algorithms is also presented. This method identifies stages in the design/mapping process and the capabilities required at each stage. Matrix Computations on Systolic-Type Arrays provides a much needed description of the area of processor arrays for matrix algorithms and of the methods used to derive those arrays. The ideas developed here reduce the space of solutions in the design/mapping process by establishing clear criteria to select among possible options as well as by a-priori rejection of alternatives which are not adequate (but which are considered in other approaches). The end result is a method which is more specific than other techniques previously available (suitable for a class of matrix algorithms) but which is more systematic, better defined and more effective in reaching the desired objectives. Matrix Computations on Systolic-Type Arrays will interest researchers and professionals who are looking for systematic mechanisms to implement matrix algorithms either as algorithm-specific structures or using specialized architectures. It provides tools that simplify the design/mapping process without introducing degradation, and that permit tradeoffs between performance/cost measures selected by the designer.

This ready reference provides electrical engineers with practical information on accurate methods for measuring signals and noise in electronic circuits as well as methods for locating and reducing high frequency noise generated by circuits or external interference. Engineers often find that measuring and mitigating high frequency noise signals in electronic circuits can be problematic when utilizing common measurement methods. Demonstrating the innovative solutions he developed as a Distinguished Member of Technical Staff at AT&T/Bell Laboratories, solutions which earned him numerous U.S. and foreign patents, Douglas Smith has written the most definitive work on this subject. Smith explains design problems related to the new high frequency electronic standards, and then systematically provides laboratory proven methods for making accurate noise measurements, while demonstrating how these results should be interpreted. The technical background needed to conduct these experiments is provided as an aid to the novice, and as a reference for the professional. Smith also discusses theoretical concepts as they relate to practical applications. Many of the techniques Smith details in this book have been previously unpublished, and have been proven to solve problems in hours rather than in the days or weeks of effort it would take conventional techniques to yield results. Comprehensive and informative, this volume provides detailed coverage of such areas as: scope probe impedance, grounding, and effective bandwidth, differential measurement techniques, noise source location and identification, current probe characteristics, operation, and applications, characteristics of sources of interferenceto measurements and the minimization of their effects, minimizing coupling of external noise into the equipment under test by measurements, estimating the effect of a measurement on equipment operation, using digital scopes for single shot noise measurements, prediction of equipment electromagnetic interference (EMI) emission and susceptibility of performance, null experiments for validating measurement data, the relationship between high frequency noise and final product reliability. With governmental regulations and MIL standards now governing the emission of high frequency electronic noise and the susceptibility to pulsed EMI, the information presented in this guide is extremely pertinent. Electrical engineers will find High Frequency Measurements and Noise in Electronic Circuits an essential desktop reference for information and solutions, and engineering students will rely on it as a virtual source book for deciphering the "mysteries" unique to high frequency electronic circuits.

Stochastic elasticity is a fast developing field that combines nonlinear elasticity and stochastic theories in order to significantly improve model predictions by accounting for uncertainties in the mechanical responses of materials. However, in contrast to the tremendous development of computational methods for large-scale problems, which have been proposed and implemented extensively in recent years, at the fundamental level, there is very little understanding of the uncertainties in the behaviour of elastic materials under large strains. Based on the idea that every large-scale problem starts as a small-scale data problem, this book combines fundamental aspects of finite (large-strain) elasticity and probability theories, which are prerequisites for the quantification of uncertainties in the elastic responses of soft materials. The problems treated in this book are drawn from the analytical continuum mechanics literature and incorporate random variables as basic concepts along with mechanical stresses and strains. Such problems are interesting in their own right but they are also meant to inspire further thinking about how stochastic extensions can be formulated before they can be applied to more complex physical systems.

Linear signal spaces are of fundamental importance in signal and system theory, communication theory, and modern signal processing. This book proposes a time-frequency analysis of linear signal spaces that is based on two novel time-frequency representations called the `Wigner distribution of a linear signal space' and the `ambiguity function of a linear signal space'. Besides being a useful display and analysis tool, the Wigner distribution of a linear signal space allows the design of high-resolution time-frequency filtering methods. This book develops such methods and applies them to the enhancement, decomposition, estimation, and detection of noisy deterministic and stochastic signals. Formulation of the filtering (estimation, detection) methods in the time-frequency plane yields a direct interpretation of the effect of adding or deleting information, changing parameters, etc. In a sense, the prior information and the signal processing tasks are brought to life in the time-frequency plane. The ambiguity function of a linear signal space, on the other hand, is closely related to a novel maximum-likelihood multipulse estimator of the range and Doppler shift of a slowly fluctuating point target - an estimation problem that is important in radar and sonar. Specifically, the ambiguity function of a linear signal space is relevant to the problem of optimally designing a set of radar pulses. The concepts and methods presented are amply illustrated by examples and pictures. Time-Frequency Analysis and Synthesis of Linear Signal Spaces: Time-Frequency Filters, Signal Detection and Estimation, and Range-Doppler Estimation is an excellent reference and may be used as a text for advanced courses covering the subject.

This unique compendium introduces the field of numerical modelling of water waves. The topics included the most widely used water wave modelling approaches, presented in increasing order of complexity and categorized into phase-averaged and phase-resolving at the highest level.A comprehensive state-of-the-art review is provided for each chapter, comprising the historical development of the method, the most relevant models and their practical applications. A full description on the method's underlying assumptions and limitations are also provided. The final chapter features coupling among different models, outlining the different types of implementations, highlighting their pros and cons, and providing numerous relevant examples for full context.The useful reference text benefits professionals, researchers, academics, graduate and undergraduate students in wave mechanics in general and coastal and ocean engineering in particular.

Digital Signal Processing for Communication Systems examines the plans for the future and the progress that has already been made, in the field of DSP and its applications to communication systems. The book pursues the progression from communication and information theory through to the implementation, evaluation and performance enhancing of practical communication systems using DSP technology. Digital Signal Processing for Communication Systems looks at various types of coding and modulation techniques, describing different applications of Turbo-Codes, BCH codes and general block codes, pulse modulations, and combined modulation and coding in order to improve the overall system performance. The book examines DSP applications in measurements performed for channel characterisation, pursues the use of DSP for design of effective channel simulators, and discusses equalization and detection of various signal formats for different channels. A number of system design issues are presented where digital signal processing is involved, reporting on the successful implementation of the system components using DSP technology, and including the problems involved with implementation of some DSP algorithms. Digital Signal Processing for Communication Systems serves as an excellent resource for professionals and researchers who deal with digital signal processing for communication systems, and may serve as a text for advanced courses on the subject.

This book reconsiders the basic approaches behind the BEM method and in particular assesses and validates the equations forming the general momentum theory. One part of the book concerns the validation, using numerical fluid mechanics (CFD), of the different terms in the equations forming the momentum theory. Other parts present new ideas for extending the theory and for enhancing the accuracy of the BEM approach. Besides a general introduction and explanation of the momentum theory, the book also deals with specialized topics, such as diffusor-augmented rotors, wind tunnel corrections, tip corrections, and combined momentum/vortex theory for design of wind turbine rotors. The book contains new as well as already published material, and the author has strived to put the material into a new and more consistent context than what usually is found in similar text books. The book is primarily intended for researchers and experienced students with a basic knowledge in fluid mechanics wishing to understand and expand their knowledge on wind turbine aerodynamics. The book is self-consistent, hence all necessary derivations are shown, and it should not be necessary to seek help in other literature to understand the contents of the book.

Dynamical processes in which many timescales coexist are called dispersive. The rate coefficients for dispersive processes depend on time. In the case of a chemical reaction, the time dependence of the rate coefficient, k(t), termed the specific reaction rate, is rationalized in the following way. Reactions by their very nature have to disturb reactivity distributions of the reactants in condensed media, as the more reactive species are the first ones to disappear from the system. The extent of this disturbance depends on the ratio of the rates of reactions to the rate of internal rearrangements (mixing) in the system restoring the initial distribution in reactivity of reactants. If the rates of chemical reactions exceed the rates of internal rearrangements, then the initial distributions in reactant reactivity are not preserved during the course of reactions and the specific reaction rates depend on time. Otherwise the extent of disturbance is negligible and classical kinetics, with a constant specific reaction rate, k, termed the reaction rate constant, may be valid as an approximation. In condensed media dispersive dynamical processes are endemic and this is the first monograph devoted to these processes.

This book presents different formulations of the equations governing incompressible viscous flows, in the form needed for developing numerical solution procedures. The conditions required to satisfy the no-slip boundary conditions in the various formulations are discussed in detail. Rather than focussing on a particular spatial discretization method, the text provides a unitary view of several methods currently in use for the numerical solution of incompressible Navier-Stokes equations, using either finite differences, finite elements or spectral approximations. For each formulation, a complete statement of the mathematical problem is provided, comprising the various boundary, possibly integral, and initial conditions, suitable for any theoretical and/or computational development of the governing equations. The text is suitable for courses in fluid mechanics and computational fluid dynamics. It covers that part of the subject matter dealing with the equations for incompressible viscous flows and their determination by means of numerical methods. A substantial portion of the book contains new results and unpublished material.

Thermal Radiation: An Introduction is a complete textbook for a one-semester introductory graduate course on radiative energy transfer. It bridges the gap between a basic introduction and comprehensive coverage of thermal radiation, focusing on insight into radiative transfer as practiced by engineers. Covering radiative transfer among surfaces, with an introduction to the effects of participating media between surfaces, the book includes surface and medium property characteristics and solutions to the radiative transfer equation in simple geometries. * Tailored and organized specifically to suit a one-semester graduate course in radiative heat transfer. * Emphasis is placed on insight into radiative transfer as practiced by engineers. * Discusses how radiation is incorporated into finite element analysis (FEA) codes. The textbook is intended for instructors and graduate students in a first-year course on radiative heat transfer or advanced heat transfer. Supplementary resources for students and instructors are available online.

The replacement of fossil-derived compounds by bio-based fuels and chemicals is crucial for the implementation of a sustainable bioeconomy. In this context, microorganisms are key players for biofuels' production from renewable sources. Biotechnological biofuel production processes require conversion microorganisms capable of both efficiently assimilating renewable low-cost carbon sources and diverting their metabolisms towards the specific biofuel. Exploring the wide diversity of microorganisms available on Earth will surely aid to make the production of green fuels a reality. This book gives a wide overview of different microbial-based processes for green fuels production. The book also includes techno-economic analysis and highlights strategic, commercial and environmental interests in promoting green fuels. All these facts make this book very valuable not only for the scientific community but also for biofuel companies and policy makers.

This book offers frameworks for the material modeling of gradient materials both for finite and small deformations within elasticity, plasticity, viscosity, and thermomechanics. The first chapter focuses on balance laws and holds for all gradient materials. The next chapters are dedicated to the material modeling of second and third-order materials under finite deformations. Afterwards the scope is limited to the geometrically linear theory, i.e., to small deformations. The next chapter offers an extension of the concept of internal constraints to gradient materials. The final chapter is dedicated to incompressible viscous gradient fluids with the intention to describe, among other applications, turbulent flows, as already suggested by Saint-Venant in the middle of the 19th century.

This monograph presents computational techniques and numerical analysis to study conservation laws under uncertainty using the stochastic Galerkin formulation. With the continual growth of computer power, these methods are becoming increasingly popular as an alternative to more classical sampling-based techniques. The text takes advantage of stochastic Galerkin projections applied to the original conservation laws to produce a large system of modified partial differential equations, the solutions to which directly provide a full statistical characterization of the effect of uncertainties. Polynomial Chaos Methods of Hyperbolic Partial Differential Equations focuses on the analysis of stochastic Galerkin systems obtained for linear and non-linear convection-diffusion equations and for a systems of conservation laws; a detailed well-posedness and accuracy analysis is presented to enable the design of robust and stable numerical methods. The exposition is restricted to one spatial dimension and one uncertain parameter as its extension is conceptually straightforward. The numerical methods designed guarantee that the solutions to the uncertainty quantification systems will converge as the mesh size goes to zero. Examples from computational fluid dynamics are presented together with numerical methods suitable for the problem at hand: stable high-order finite-difference methods based on summation-by-parts operators for smooth problems, and robust shock-capturing methods for highly nonlinear problems. Academics and graduate students interested in computational fluid dynamics and uncertainty quantification will find this book of interest. Readers are expected to be familiar with the fundamentals of numerical analysis. Some background in stochastic methods is useful but notnecessary.

This book deals with the application of spectral methods to problems of uncertainty propagation and quanti?cation in model-based computations. It speci?cally focuses on computational and algorithmic features of these methods which are most useful in dealing with models based on partial differential equations, with special att- tion to models arising in simulations of ?uid ?ows. Implementations are illustrated through applications to elementary problems, as well as more elaborate examples selected from the authors' interests in incompressible vortex-dominated ?ows and compressible ?ows at low Mach numbers. Spectral stochastic methods are probabilistic in nature, and are consequently rooted in the rich mathematical foundation associated with probability and measure spaces. Despite the authors' fascination with this foundation, the discussion only - ludes to those theoretical aspects needed to set the stage for subsequent applications. The book is authored by practitioners, and is primarily intended for researchers or graduate students in computational mathematics, physics, or ?uid dynamics. The book assumes familiarity with elementary methods for the numerical solution of time-dependent, partial differential equations; prior experience with spectral me- ods is naturally helpful though not essential. Full appreciation of elaborate examples in computational ?uid dynamics (CFD) would require familiarity with key, and in some cases delicate, features of the associated numerical methods. Besides these shortcomings, our aim is to treat algorithmic and computational aspects of spectral stochastic methods with details suf?cient to address and reconstruct all but those highly elaborate examples.

This collection on "Mechanics of Generalized Continua - from Micromechanical Basics to Engineering Applications" brings together leading scientists in this field from France, Russian Federation, and Germany. The attention in this publication is be focussed on the most recent research items, i.e., - new models, - application of well-known models to new problems, - micro-macro aspects, - computational effort, - possibilities to identify the constitutive equations, and - old problems with incorrect or non-satisfying solutions based on the classical continua assumptions.