This book is an introduction to the theory, practice, and implementation of the Lattice Boltzmann (LB) method, a powerful computational fluid dynamics method that is steadily gaining attention due to its simplicity, scalability, extensibility, and simple handling of complex geometries. The book contains chapters on the method's background, fundamental theory, advanced extensions, and implementation. To aid beginners, the most essential paragraphs in each chapter are highlighted, and the introductory chapters on various LB topics are front-loaded with special "in a nutshell" sections that condense the chapter's most important practical results. Together, these sections can be used to quickly get up and running with the method. Exercises are integrated throughout the text, and frequently asked questions about the method are dealt with in a special section at the beginning. In the book itself and through its web page, readers can find example codes showing how the LB method can be implemented efficiently on a variety of hardware platforms, including multi-core processors, clusters, and graphics processing units. Students and scientists learning and using the LB method will appreciate the wealth of clearly presented and structured information in this volume.

This book offers a brief, practically complete, and relatively simple introduction to functional analysis. It also illustrates the application of functional analytic methods to the science of continuum mechanics. Abstract but powerful mathematical notions are tightly interwoven with physical ideas in the treatment of nontrivial boundary value problems for mechanical objects.

This second edition includes more extended coverage of the classical andabstract portions of functional analysis. Taken together, the first three chapters now constitute a regular text on applied functional analysis. This potential use of the book is supported by a significantly extended set of exercises with hints and solutions. A new appendix, providing a convenient listing of essential inequalities and imbedding results, has been added.

The book should appeal to graduate students and researchers in physics, engineering, and applied mathematics.

Reviews of first edition:

"This book covers functional analysis and its applications to continuum mechanics. The presentation is concise but complete, and is intended for readers in continuum mechanics who wish to understand the mathematical underpinnings of the discipline. Detailed solutions of the exercises are provided in an appendix." (L Enseignment Mathematique, Vol. 49 (1-2), 2003)

"The reader comes away with a profound appreciation both of the physics and its importance, and of the beauty of the functional analytic method, which, in skillful hands, has the power to dissolve and clarify these difficult problems as peroxide does clotted blood. Numerous exercises test the reader s comprehension at every stage. Summing Up: Recommended." (F. E. J. Linton, Choice, September, 2003)

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Single-channel hands-free teleconferencing systems are becoming popular. In order to enhance the communication quality of these systems, more and more stereophonic sound devices with two loudspeakers and two microphones are deployed. Because of the coupling between loudspeakers and microphones, there may be strong echoes, which make real-time communication very difficult. The best way we know to cancel these echoes is via a stereo acoustic echo canceller (SAEC), which can be modelled as a two-input/two-output system with real random variables. In this work, the authors recast this problem into a single-input/single-output system with complex random variables thanks to the widely linear model. From this new convenient formulation, they re-derive the most important aspects of a SAEC, including identification of the echo paths with adaptive filters, double-talk detection, and suppression.

The content of this book is multidisciplinary by nature. It uses mathematical tools from the theories of probability and stochastic processes, partial differential equations, and asymptotic analysis, combined with the physics of wave propagation and modeling of time reversal experiments. It is addressed to a wide audience of graduate students and researchers interested in the intriguing phenomena related to waves propagating in random media. At the end of each chapter there is a section of notes where the authors give references and additional comments on the various results presented in the chapter.

This volume shows how collective magnetic excitations determine most of the magnetic properties of itinerant electron magnets. Previous theories were mainly restricted to the Curie-Weiss law temperature dependence of magnetic susceptibilities. Based on the spin amplitude conservation idea including the zero-point fluctuation amplitude, this book shows that the entire temperature and magnetic field dependence of magnetization curves, even in the ground state, is determined by the effect of spin fluctuations. It also shows that the theoretical consequences are largely in agreement with many experimental observations. The readers will therefore gain a new comprehensive perspective of their unified understanding of itinerant electron magnetism.

This book applies a step-by-step treatment of the current state-of-the-art of ordinary differential equations used in modeling of engineering systems/processes and beyond. It covers systematically ordered problems, beginning with first and second order ODEs, linear and higher-order ODEs of polynomial form, theory and criteria of similarity, modeling approaches, phase plane and phase space concepts, stability optimization and ending on chaos and synchronization.

Presenting both an overview of the theory of the introductory differential equations in the context of applicability and a systematic treatment of modeling of numerous engineering and physical problems through linear and non-linear ODEs, the volume is self-contained, yet serves both scientific and engineering interests. The presentation relies on a general treatment, analytical and numerical methods, concrete examples and engineering intuition.

The scientific background used is well balanced between elementary and advanced level, making it as a unique self-contained source for both theoretically and application oriented graduate and doctoral students, university teachers, researchers and engineers of mechanical, civil and mechatronic engineering.

There is a wide field of tasks left that can only be satisfyingly attacked with the help of old-fashioned analogue technology, and one of the most important are amplifiers for analogue signals. The strongly expanded content of the second edition of "the sound of silence" leads to affordable amplifier design approaches which will end up in lowest-noise solutions not far away from the edge of physical boundaries set by room temperature and given cartridges - thus, fully compatible with very expensive so called "high-end" or "state-of-the-art" offers on today markets - and, from a noise point of view in most cases outperforming them

With easy to follow mathematical treatment it is demonstrated as well that theory is not far away from reality. Measured SNs will be found within 1dB off the calculated ones and deviations from the exact amplifier transfer won't cross the 0.1dB tolerance lines. Additionally, the book presents measurement set-ups and results. Consequently, comparisons with measurement results of test magazine will soon become easier to perform.

This new edition includes a new chapters about reference levels, Noise in Amp Input sections, Humming Problems, and much more."

The book provides a comprehensive presentation of the topic of phononic and sonic crystals, including acoustic and elastic wave propagation in homogeneous and periodic media, Bloch waves and band structures, surface phononic crystals and phononic crystal slabs, evanescent Bloch waves and complex band structures, local resonance, dispersion and negative refraction, and phononic band gap guidance. The book is accompanied with a comprehensive set of finite element model (FEM) scripts for solving basic phononic crystal problems, as supplementary material. The scripts should allow the reader to generate band structures for 2D and 3D phononic crystals, to compute Bloch waves, waveguide and cavity modes, and more. They can be accessed here: https://members.femto-st.fr/vincent-laude/freefem-scripts-numerical-simulation-phononic-crystals

This book provides a broad overview of spaciousness in music theory, from mixing and performance practice, to room acoustics, psychoacoustics and audio engineering, and presents the derivation, implementation and experimental validation of a novel type of spatial audio system. Discussing the physics of musical instruments and the nature of auditory perception, the book enables readers to precisely localize synthesized musical instruments while experiencing their timbral variance and spatial breadth. Offering interdisciplinary insights for novice music enthusiasts and experts in the field of spatial audio, this book is suitable for anyone interested in the study of music and musicology and the application of spatial audio mixing, or those seeking an overview of the state of the art in applied psychoacoustics for spatial audio.

The Stroh formalism is a powerful and elegant mathematical method developed for the analysis of the equations of anisotropic elasticity. The purpose of this exposition is to introduce the essence of this formalism and demonstrate its effectiveness in both static and dynamic elasticity. The equations of elasticity are complicated, because they constitute a system and, particularly for the anisotropic cases, inherit many parameters from the elasticity tensor. The Stroh formalism reveals simple structures hidden in the equations of anisotropic elasticity and provides a systematic approach to these equations. This work will appeal to students and researchers in applied mathematics, mechanics, and engineering science.

Contact mechanics is an active research area with deep theoretical and numerical roots. The links between nonsmooth analysis and optimization with mechanics have been investigated intensively during the last decades, especially in Europe. The study of complementarity problems, variational -, quasivariational- and hemivariational inequalities arising in contact mechanics and beyond is a hot topic for interdisciplinary research and cooperation. The needs of industry for robust solution algorithms suitable for large scale applications and the regular updates of the respective elements in major commercial computational mechanics codes, demonstrate that this interaction is not restricted to the academic environment. The contributions of this book have been selected from the participants of the CMIS 2009 international conference which took place in Crete and continued a successful series of specialized contact mechanics conferences.

"Statics and Dynamics of Rigid Bodies" presents an interdisciplinary approach to mechanical engineering through a close evaluation of the statics and dynamics of rigid bodies, presenting a concise introduction to both. This volume bridges the gap of interdisciplinary published texts linking fields like mechatronics and robotics with multi-body dynamics in order to provide readers with a clear path to understanding numerous sub-fields of mechanical engineering. Three-dimensional kinematics, rigid bodies in planar spaces and numerous vector and matrix operations are presented in order to provide a comprehensive understanding of mechanics through dynamics and rigid bodies.

This volume provides a comprehensive selection of recent studies addressing insect hearing and acoustic communication. The variety of signalling behaviours and hearing organs makes insects highly suitable animals for exploring and analysing signal generation and hearing in the context of neural processing, ecology, evolution and genetics. Across a variety of hearing species like moths, crickets, bush-crickets, grasshoppers, cicadas and flies, the leading researchers in the field cover recent scientific progress and address key points in current research, such as:

. How can we approach the evolution of hearing in insects and what is the developmental and neural origin of the auditory organs?

. How are hearing and sound production embedded in the natural lifestyle of the animals, allowing intraspecific communication but also predator avoidance and even predation?

. What are the functional properties of hearing organs and how are they achieved at the molecular, biophysical and neural levels?

. What are the neural mechanisms of central auditory processing and signal generation?

The book is intended for students and researchers both inside and outside of the fascinating field of bioacoustics and aims to foster understanding of hearing and acoustic communication in insects."

This volume contains eight state of the art contributions on mathematical aspects and applications of fast boundary element methods in engineering and industry. This covers the analysis and numerics of boundary integral equations by using differential forms, preconditioning of hp boundary element methods, the application of fast boundary element methods for solving challenging problems in magnetostatics, the simulation of micro electro mechanical systems, and for contact problems in solid mechanics. Other contributions are on recent results on boundary element methods for the solution of transient problems. This book is addressed to researchers, graduate students and practitioners working on and using boundary element methods. All contributions also show the great achievements of interdisciplinary research between mathematicians and engineers, with direct applications in engineering and industry.

This book presents a history of shock compression science, including development of experimental, material modeling, and hydrodynamics code technologies over the past six decades at Sandia National Laboratories. The book is organized into a discussion of major accomplishments by decade with over 900 references, followed by a unique collection of 45 personal recollections detailing the trials, tribulations, and successes of building a world-class organization in the field. It explains some of the challenges researchers faced and the gratification they experienced when a discovery was made. Several visionary researchers made pioneering advances that integrated these three technologies into a cohesive capability to solve complex scientific and engineering problems. What approaches worked, which ones did not, and the applications of the research are described. Notable applications include the turret explosion aboard the USS Iowa and the Shoemaker-Levy comet impact on Jupiter. The personal anecdotes and recollections make for a fascinating account of building a world-renowned capability from meager beginnings. This book will be inspiring to the expert, the non expert, and the early-career scientist. Undergraduate and graduate students in science and engineering who are contemplating different fields of study should find it especially compelling.

This Volume 5 of the successful book package "Multiphase Flow Dynamics" is devoted to nuclear thermal hydraulics which is a substantial part of nuclear reactor safety. It provides knowledge and mathematical tools for adequate description of the process of transferring the fission heat released in materials due to nuclear reactions into its environment. It step by step introduces into the heat release inside the fuel, temperature fields in the fuels, the "simple" boiling flow in a pipe described using ideas of different complexity like equilibrium, non equilibrium, homogeneity, non homogeneity. Then the "simple" three-fluid boiling flow in a pipe is described by gradually involving the mechanisms like entrainment and deposition, dynamic fragmentation, collisions, coalescence, turbulence. All heat transfer mechanisms are introduced gradually discussing their uncertainty. Different techniques are introduced like boundary layer treatments or integral methods. Comparisons with experimental data at each step demonstrate the success of the different ideas and models. After an introduction of the design of the reactor pressure vessels for pressurized and boiling water reactors the accuracy of the modern methods is demonstrated using large number of experimental data sets for steady and transient flows in heated bundles. Starting with single pipe boiling going through boiling in the rod bundles the analysis of complete vessel including the reactor is finally demonstrated. Then a powerful method for nonlinear stability analysis of flow boiling and condensation is introduced. Models are presented and their accuracies are investigated for describing critical multiphase flow at different level of complexity. Therefore the book presents a complete coverage of the modern Nuclear Thermal Hydrodynamics. This present third edition includes various updates, extensions, improvements and corrections.

The revised edition of this advanced textbook provides the reader with a solid grounding in the formalism of classical mechanics, underlying a number of powerful mathematical methods that are widely used in modern theoretical and mathematical physics. It reviews the fundamentals of Lagrangian and Hamiltonian mechanics, and goes on to cover related topics such as canonical transformations, integral invariants, potential motion in geometric setting, symmetries, the Noether theorem and systems with constraints. While in some cases the formalism is developed beyond the traditional level adopted in the standard textbooks on classical mechanics, only elementary mathematical methods are used in the exposition of the material. New material for the revised edition includes additional sections on the Euler-Lagrange equation, the Cartan two-form in Lagrangian theory, and Newtonian equations of motion in context of general relativity. Also new for this edition is the inclusion of problem sets and solutions to aid in the understanding of the material presented. The mathematical constructions involved are explicitly described and explained, so the book is a good starting point for the student new to this field. Where possible, intuitive motivations are replaced by explicit proofs and direct computations, preserving the level of rigor that makes the book useful for more advanced students intending to work in one of the branches of the vast field of theoretical physics. To illustrate how classical-mechanics formalism works in other branches of theoretical physics, examples related to electrodynamics, as well as to relativistic and quantum mechanics, are included.

This book concentrates on the properties of the stationary states in chaotic systems of particles or fluids, leaving aside the theory of the way they can be reached. The stationary states of particles or of fluids (understood as probability distributions on microscopic configurations or on the fields describing continua) have received important new ideas and data from numerical simulations and reviews are needed. The starting point is to find out which time invariant distributions come into play in physics. A special feature of this book is the historical approach. To identify the problems the author analyzes the papers of the founding fathers Boltzmann, Clausius and Maxwell including translations of the relevant (parts of) historical documents. He also establishes a close link between treatment of irreversible phenomena in statistical mechanics and the theory of chaotic systems at and beyond the onset of turbulence as developed by Sinai, Ruelle, Bowen (SRB) and others: the author gives arguments intending to support strongly the viewpoint that stationary states in or out of equilibrium can be described in a unified way. In this book it is the "chaotic hypothesis," which can be seen as an extension of the classical ergodic hypothesis to non equilibrium phenomena, that plays the central role. It is shown that SRB - often considered as a kind of mathematical playground with no impact on physical reality - has indeed a sound physical interpretation; an observation which to many might be new and a very welcome insight. Following this, many consequences of the chaotic hypothesis are analyzed in chapter 3 - 4 and in chapter 5 a few applications are proposed. Chapter 6 is historical: carefully analyzing the old literature on the subject, especially ergodic theory and its relevance for statistical mechanics; an approach which gives the book a very personal touch. The book contains an extensive coverage of current research (partly from the authors and his coauthors publications) presented in enough detail so that advanced students may get the flavor of a direction of research in a field which is still very much alive and progressing. Proofs of theorems are usually limited to heuristic sketches privileging the presentation of the ideas and providing references that the reader can follow, so that in this way an overload of this text with technical details could be avoided.

This fourth issue on "progress in turbulence" is based on the fourth ITI conference (ITI interdisciplinary turbulence initiative), which took place in Bertinoro, North Italy. Leading researchers from the engineering and physical sciences presented latest results in turbulence research. Basic as well as applied research is driven by the rather notorious difficult and essentially unsolved problem of turbulence. In this collection of contributions clear progress can be seen in different aspects, ranging from new quality of numerical simulations to new concepts of experimental investigations and new theoretical developments. The importance of turbulence is shown for a wide range of applications including: combustion, energy, flow control, urban flows, are few examples found in this volume. A motivation was to bring fundamentals of turbulence in connection with renewable energy. This lead us to add a special topic relevant to the impact of turbulence on the wind energy conversion. The structure of the present book is as such that contributions have been bundled according to covering topics i.e. I Basic Turbulence Aspects, II Particle Laden Flows, III Modeling and Simulations, IV, Experimental Methods, V Special Flows, VI Atmospheric Boundary Layer, VII Boundary Layer, VIII Wind Energy and IX Convection. This book is dedicated to the memory of Prof. Tim Nickels. Shortly after giving an invited lecture at the 4th ITI conference, the turbulence community lost a world-class scientist, a friend and devoted family man.

This book reviews the phenomenology displayed by relativistic jets as well as the most recent theoretical efforts to understand the physical mechanisms at their origin. Relativistic jets have been observed and studied in Active Galactic Nuclei (AGN) for about half a century and are believed to be fueled by accretion onto a supermassive black hole at the center of the host galaxy. Since the first discovery of relativistic jets associated with so-called "micro-quasars" much more recently, it has seemed clear that much of the physics governing the relativistic outflows in stellar X-ray binaries harboring black holes and in AGN must be common, but acting on very different spatial and temporal scales. With new observational and theoretical results piling up every day, this book attempts to synthesize a consistent, unified physical picture of the formation and disruption of jets in accreting black-hole systems. The chapters in this book offer overviews accessible not only to specialists but also to graduate students and astrophysicists working in other areas. Covered topics comprise Relativistic jets in stellar systems Launching of AGN jets Parsec-scale AGN jets Kiloparsec-scale AGN jets Black hole magnetospheres Theory of relativistic jets The structure and dynamics of the inner accretion disk The origin of the jet magnetic field X-ray observations, phenomenology, and connection with theory

This book presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general presentation of the tools of asymptotic analysis. It gives the keys to understand a boundary-layer problem and explains the methods to construct an approximation. The second part is devoted to SCEM and its applications in fluid mechanics, including external and internal flows.

The 26th International Symposium on Shock Waves in G ttingen, Germany was jointly organised by the German Aerospace Centre DLR and the French-German Research Institute of Saint Louis ISL. The year 2007 marked the 50th anniversary of the Symposium, which first took place in 1957 in Boston and has since become an internationally acclaimed series of meetings for the wider Shock Wave Community. The ISSW26 focused on the following areas: Shock Propagation and Reflection, Detonation and Combustion, Hypersonic Flow, Shock Boundary Layer Interaction, Numerical Methods, Medical, Biological and Industrial Applications, Richtmyer Meshkov Instability, Blast Waves, Chemically Reacting Flows, Diagnostics, Facilities, Flow Visualisation, Ignition, Impact and Compaction, Multiphase Flow, Nozzles Flows, Plasmas and Propulsion. The two Volumes contain the papers presented at the symposium and serve as a reference for the participants of the ISSW 26 and individuals interested in these fields.

The book is designed for advanced graduate students as well as postdoctoral researchers across several disciplines (e.g., mathematics, physics and engineering), as it provides them with tools and techniques that are essential in performing research on the flow problems of visco-plastic fluids. The following topics are treated: analysis of classical visco-plastic fluid models mathematical modeling of flows of visco-plastic fluids computing flows of visco-plastic fluids rheology of visco-plastic fluids and visco-plastic suspensions application of visco-plastic fluids in engineering sciences complex flows of visco-plastic fluids.

This volume presents state-of-the-art of reviews in the field of multiphase flow. In focusses on nonlinear aspects of multiphase flow networks as well as visualization experiments. The first chapter presents nonlinear aspects or deterministic chaos issues in the systems of multi-phase reactors.The second chapter reviews two-phase flow dynamics in combination with complex network theory. The third chapter discusses evaporation mechanism in the wick of copper heat pipes. The last chapter investigates numerically the flow dynamics and heat and mass transfer in the laminar and turbulent boundary layer on the flat vertical plate."