One of the most important routes to chaos is the chaotic intermittency. However, there are many cases that do not agree with the classical theoretical predictions. In this book, an extended theory for intermittency in one-dimensional maps is presented. A new general methodology to evaluate the reinjection probability density function (RPD) is developed in Chapters 5 to 8. The key of this formulation is the introduction of a new function, called M(x), which is used to calculate the RPD function. The function M(x) depends on two integrals. This characteristic reduces the influence on the statistical fluctuations in the data series. Also, the function M(x) is easy to evaluate from the data series, even for a small number of numerical or experimental data. As a result, a more general form for the RPD is found; where the classical theory based on uniform reinjection is recovered as a particular case. The characteristic exponent traditionally used to characterize the intermittency type, is now a function depending on the whole map, not just on the local map. Also, a new analytical approach to obtain the RPD from the mathematical expression of the map is presented. In this way all cases of non standard intermittencies are included in the same frame work. This methodology is extended to evaluate the noisy reinjection probability density function (NRPD), the noisy probability of the laminar length and the noisy characteristic relation. This is an important difference with respect to the classical approach based on the Fokker-Plank equation or Renormalization Group theory, where the noise effect was usually considered just on the local Poincare map. Finally, in Chapter 9, a new scheme to evaluate the RPD function using the Perron-Frobenius operator is developed. Along the book examples of applications are described, which have shown very good agreement with numerical computations.

This is the first book to treat two areas of speech synthesis: natural language processing and the inherent problems it presents for speech synthesis; and digital signal processing, with an emphasis on the concatenative approach. The text guides the reader through the material in a step-by-step easy-to-follow way. The book will be of interest to researchers and students in phonetics and speech communication, in both academia and industry.

This book presents research advances in the field of Continuous Media with Microstructure and considers the three complementary pillars of mechanical sciences: theory, research and computational simulation. It focuses on the following problems: thermodynamic and mathematical modeling of materials with extensions of classical constitutive laws, single and multicomponent media including modern multifunctional materials, wave propagation, multiscale and multiphysics processes, phase transformations, and porous, granular and composite materials. The book presents the proceedings of the 2nd Conference on Continuous Media with Microstructure, which was held in 2015 in Lagow, Poland, in memory of Prof. Krzysztof Wilmanski.

* New chapter specifically on electric vehicles * Increased international focus, with more examples from outside the USA * Pedagogical features including learning objectives at the start of each chapter, in-chapter questions and end-of-chapter suggested online activities * Student companion website material: multiple choice questions and homework exercises * Instructor companion website material: lecture slides, solution files for instructors; suggested questions for discussion forums to increase engagement; and activities to achieve the chapter learning objectives, including quizzes with answers, that instructors can use to assess student attainment

Why writing a book about a specialized task of the large topic of complex systems? And who will read it? The answer is simple: The fascination for a didactically valuable point of view, the elegance of a closed concept and the lack of a comprehensive disquisition.

The fascinating part is that field equations can have localized solutions exhibiting the typical characteristics of particles. Regarding the field equations this book focuses on, the field phenomenon of localized solutions can be described in the context of a particle formalism, which leads to a set of ordinary differential equations covering the time evolution of the position and the velocity of each particle. Moreover, starting from these particle dynamics and making the transition to many body systems, one considers typical phenomena of many body systems as shock waves and phase transitions, which themselves can be described as field phenomena. Such transitions between different level of modelling are well known from conservative systems, where localized solutions of quantum field theory lead to the mechanisms of elementary particle interaction and from this to field equations describing the properties of matter. However, in dissipative systems such transitions have not been considered yet, which is adjusted by the presented book. The elegance of a closed concept starts with the observation of self-organized current filaments in a semiconductor gas discharge system. These filaments move on random paths and exhibit certain particle features like scattering or the formation of bound states. Neither the reasons for the propagation of the filaments nor the laws of the interaction between the filaments can be registered by direct observations. Therefore a model is established, which is phenomenological in the first instance due to the complexity of the experimental system. This model allows to understand the existence of localized structures, their mechanisms of movement, and their interaction, at least, on a qualitative level. But this model is also the starting point for developing a data analysis method that enables the detection of movement and interaction mechanisms of the investigated localized solutions. The topic is rounded of by applying the data analysis to real experimental data and comparing the experimental observations to the predictions of the model.

A comprehensive publication covering the interesting topic of localized solutions in reaction diffusion systems in its width and its relation to the well known phenomena of spirals and patterns does not yet exist, and this is the third reason for writing this book. Although the book focuses on a specific experimental system the model equations are as simple as possible so that the discussed methods should be adaptable to a large class of systems showing particle-like structures.

Therefore, this book should attract not only the experienced scientist, who is interested in self-organization phenomena, but also the student, who would like to understand the investigation of a complex system on the basis of a continuous description.

Non-Linear Field Theories of Mechanics has become a classic treatise in the field of continuum mechanics. Originally published nearly forty years ago, it probably has influenced practically all subsequent monographs on the subject. Its main parts are: - The General Theory of Material Behavior - Elasticity - Fluidity This third edition includes the corrections made by the late C. Truesdell in his personal copy. It is annotated by S. Antman who describes the monograph’s genesis and the impact it has made on the modern development of mechanics. Originally published as Volume III/3 of the famous Encyclopedia of Physics in 1965, this book describes and summarizes "everything that was both known and worth knowing in the field at the time." It also greatly contributed to the unification and standardization of the concepts, terms and notations in the field.

This volume contains fourteen papers on mathematical problems of flow and transport through porous media presented at the conference held at Oberwolfach, June 21-27, 1992. Among the topics covered are miscible and immiscible displacement, groundwater contamination, reaction-diffusion instabilities and moving boundaries, random and fractal media, microstructure models, homogenization, spatial heterogeneties, inverse problems, degenerate equations. The papers deal with aspects of modelling, mathematical theory, numerical methods and applications in the engineering sciences.

This work systematically investigates a large number of oscillatory network configurations that are able to describe many real systems such as electric power grids, lasers or even the heart muscle, to name but a few. The book is conceived as an introduction to the field for graduate students in physics and applied mathematics as well as being a compendium for researchers from any field of application interested in quantitative models.

This book reports on the latest developments in computational fluid dynamics and turbulence modeling, with a special emphasis on hybrid RANS-LES methods and their industrial applications. It gathers the proceedings of the Sixth Symposium on Hybrid RANS-LES Methods, held on September 26-28 in Strasbourg, France. The different chapters covers a wealth of topics such as flow control, aero-acoustics, aero-elasticity and CFD-based multidisciplinary optimization. Further topics include wall-modelled Large Eddy Simulation (WMLES), embedded LES, Lattice-Bolzman methods, turbulence-resolving applications and comparisons between LES, hybrid RANS-LES and URANS methods. The book addresses academic researchers, graduate students, industrial engineers, as well as industrial R&D managers and consultants dealing with turbulence modelling, simulation and measurement, and with multidisciplinary applications of computational fluid dynamics.

Acoustics of Layered Media II presents the theory of sound propagation and reflection of spherical waves and bounded beams in layered media. It is mathematically rigorous but at the same time care is taken that the physical usefulness in applications and the logic of the theory are not hidden. Both moving and stationary media, discretely and continuously layered, including a range-dependent environment, are treated for various types of acoustic wave sources. Detailed appendices provide further background on the mathematical methods.This second edition reflects the notable recent progress in the field of acoustic wave propagation in inhomogeneous media.

This monograph is planned to provide the application of the soliton theory to solve certain practical problems selected from the fields of solid mechanics, fluid mechanics and biomechanics. The work is based mainly on the authors' research carried out at their home institutes, and on some specified, significant results existing in the published literature. The methodology to study a given evolution equation is to seek the waves of permanent form, to test whether it possesses any symmetry properties, and whether it is stable and solitonic in nature. Students of physics, applied mathematics, and engineering are usually exposed to various branches of nonlinear mechanics, especially to the soliton theory. The soliton is regarded as an entity, a quasi-particle, which conserves its character and interacts with the surroundings and other solitons as a particle. It is related to a strange phenomenon, which consists in the propagation of certain waves without attenuation in dissipative media. This phenomenon has been known for about 200 years (it was described, for example, by the Joule Verne's novel Les histoires de Jean Marie Cabidoulin, Ed. Hetzel), but its detailed quantitative description became possible only in the last 30 years due to the exceptional development of computers. The discovery of the physical soliton is attributed to John Scott Russell. In 1834, Russell was observing a boat being drawn along a narrow channel by a pair of horses."

This volume collects the edited and reviewed contribution presented in the 7th iTi Conference in Bertinoro, covering fundamental and applied aspects in turbulence. In the spirit of the iTi conference, the volume is produced after the conference so that the authors had the opportunity to incorporate comments and discussions raised during the meeting. In the present book, the contributions have been structured according to the topics: I Theory II Wall bounded flows III Pipe flow IV Modelling V Experiments VII Miscellaneous topics

Nonsmoothness and nonconvexity arise in numerous applications of mechan- ics and modeling due to the need for studying more and more complicated phe- nomena and real life applications. Mathematicians have started to provide the necessary tools and theoretical results underpinning these applications. Ap- plied mathematicians and engineers have begun to realize the benefits of this new area and are adopting, increasingly, these new tools in their work. New computational tools facilitate numerical applications and enable the theory to be tested, and the resulting feedback poses new theoretical questions. Because of the upsurge in activity in the area of nonsmooth and noncon- vex mechanics, Professors Gao and Ogden, together with the late Professor P.D. Panagiotopoulos, had planned to organize a Minisymposium with the title Nonsmooth and Nonconvex Mechanics within the ASME 1999 Mechanics & Materials Conference, June 27-30 1999, Blacksburg, Virginia. After the unex- pected death of Professor Panagiotopoulos the first two editors invited the third editor (Professor Stavroulakis) to join them. A large number of mathematical and engineering colleagues supported our efforts by presenting lectures at the Minisymposium in which the available mathematical methods were described and many problems of nonsmooth and nonconvex mechanics were discussed. The interest of the many participants encourages us all to continue our research efforts.

Introduction to Dynamical Systems and Geometric Mechanics provides a comprehensive tour of two fields that are intimately entwined: dynamical systems is the study of the behavior of physical systems that may be described by a set of nonlinear first-order ordinary differential equations in Euclidean space, whereas geometric mechanics explore similar systems that instead evolve on differentiable manifolds. The first part discusses the linearization and stability of trajectories and fixed points, invariant manifold theory, periodic orbits, Poincare maps, Floquet theory, the Poincare-Bendixson theorem, bifurcations, and chaos. The second part of the book begins with a self-contained chapter on differential geometry that introduces notions of manifolds, mappings, vector fields, the Jacobi-Lie bracket, and differential forms.

Humans have always been fascinated by marine life, from extremely small diatoms to the largest mammal that inhabits our planet, the blue whale. However, studying marine life in the ocean is an extremely difficult propo- tion because an ocean environment is not only vast but also opaque to most instruments and can be a hostile environment in which to perform expe- ments and research. The use of acoustics is one way to effectively study animal life in the ocean. Acoustic energy propagates in water more efficiently than almost any form of energy and can be utilized by animals for a variety of purposes and also by scientists interested in studying their behavior and natural history. However, underwater acoustics have traditionally been in the domain of physicists, engineers and mathematicians. Studying the natural history of animals is in the domain of biologists and physiologists. Und- standing behavior of animals has traditionally involved psychologists and zoologists. In short, marine bioacoustics is and will continue to be a diverse discipline involving investigators from a variety of backgrounds, with very different knowledge and skill sets. The inherent inter-disciplinary nature of marine bioacoustics presents a large challenge in writing a single text that would be meaningful to various investigators and students interested in this field. Yet we have embarked on this challenge to produce a volume that would be helpful to not only beginning investigators but to seasoned researchers.

Modern experiments and numerical simulations show that the long-known coherent structures in turbulence take the form of elongated vortex tubes and vortex sheets. The evolution of vortex tubes may result in spiral structures which can be associated with the spectral power laws of turbulence. The mutual stretching of skewed vortex tubes, when they are close to each other, causes rapid growth of vorticity. Whether this process may or may not lead to a finite-time singularity is one of the famous open problems of fluid dynamics.

This book contains the proceedings of the NATO ARW and IUTAM Symposium held in Zakopane, Poland, 2-7 September 2001. The papers presented, carefully reviewed by the International Scientific Committee, cover various aspects of the dynamics of vortex tubes and sheets and of their analogues in magnetohydrodynamics and in quantum turbulence. The book should be a useful reference for all researchers and students of modern fluid dynamics.

Unlike other books on this subject, which tend to concentrate on 2-D dynamics, this text focuses on the application of Newton-Euler methods to complex, real-life 3-D dynamics problems. It is thus ideal for elective courses in intermediate dynamics.

This book provides the first comprehensive overview of the fascinating topic of audio source separation based on non-negative matrix factorization, deep neural networks, and sparse component analysis. The first section of the book covers single channel source separation based on non-negative matrix factorization (NMF). After an introduction to the technique, two further chapters describe separation of known sources using non-negative spectrogram factorization, and temporal NMF models. In section two, NMF methods are extended to multi-channel source separation. Section three introduces deep neural network (DNN) techniques, with chapters on multichannel and single channel separation, and a further chapter on DNN based mask estimation for monaural speech separation. In section four, sparse component analysis (SCA) is discussed, with chapters on source separation using audio directional statistics modelling, multi-microphone MMSE-based techniques and diffusion map methods. The book brings together leading researchers to provide tutorial-like and in-depth treatments on major audio source separation topics, with the objective of becoming the definitive source for a comprehensive, authoritative, and accessible treatment. This book is written for graduate students and researchers who are interested in audio source separation techniques based on NMF, DNN and SCA.

Adaptive Signal Models: Theory, Algorithms and Audio Applications presents methods for deriving mathematical models of natural signals. The introduction covers the fundamentals of analysis-synthesis systems and signal representations. Some of the topics in the introduction include perfect and near-perfect reconstruction, the distinction between parametric and nonparametric methods, the role of compaction in signal modeling, basic and overcomplete signal expansions, and time-frequency resolution issues. These topics arise throughout the book as do a number of other topics such as filter banks and multiresolution. The second chapter gives a detailed development of the sinusoidal model as a parametric extension of the short-time Fourier transform. This leads to multiresolution sinusoidal modeling techniques in Chapter Three, where wavelet-like approaches are merged with the sinusoidal model to yield improved models. In Chapter Four, the analysis-synthesis residual is considered; for realistic synthesis, the residual must be separately modeled after coherent components (such as sinusoids) are removed. The residual modeling approach is based on psychoacoustically motivated nonuniform filter banks. Chapter Five deals with pitch-synchronous versions of both the wavelet and the Fourier transform; these allow for compact models of pseudo-periodic signals. Chapter Six discusses recent algorithms for deriving signal representations based on time-frequency atoms; primarily, the matching pursuit algorithm is reviewed and extended. The signal models discussed in the book are compact, adaptive, parametric, time-frequency representations that are useful for analysis, coding, modification, and synthesis of natural signals such as audio. The models are all interpreted as methods for decomposing a signal in terms of fundamental time-frequency atoms; these interpretations, as well as the adaptive and parametric natures of the models, serve to link the various methods dealt with in the text. Adaptive Signal Models: Theory, Algorithms and Audio Applications serves as an excellent reference for researchers of signal processing and may be used as a text for advanced courses on the topic.

This book is dedicated to the recent developments in RET with the aim to explore polyatomic gas, dense gas and mixture of gases in non-equilibrium. In particular we present the theory of dense gases with 14 fields, which reduces to the Navier-Stokes Fourier classical theory in the parabolic limit. Molecular RET with an arbitrary number of field-variables for polyatomic gases is also discussed and the theory is proved to be perfectly compatible with the kinetic theory in which the distribution function depends on an extra variable that takes into account a molecule's internal degrees of freedom. Recent results on mixtures of gases with multi-temperature are presented together with a natural definition of the average temperature. The qualitative analysis and in particular, the existence of the global smooth solution and the convergence to equilibrium are also studied by taking into account the fact that the differential systems are symmetric hyperbolic. Applications to shock and sound waves are analyzed together with light scattering and heat conduction and the results are compared with experimental data. Rational extended thermodynamics (RET) is a thermodynamic theory that is applicable to non-equilibrium phenomena. It is described by differential hyperbolic systems of balance laws with local constitutive equations. As RET has been strictly related to the kinetic theory through the closure method of moment hierarchy associated to the Boltzmann equation, the applicability range of the theory has been restricted within rarefied monatomic gases. The book represents a valuable resource for applied mathematicians, physicists and engineers, offering powerful models for potential applications like satellites reentering the atmosphere, semiconductors and nano-scale phenomena.

Automatic modulation recognition is a rapidly evolving area of signal analysis. In recent years, interest from the academic and military research institutes has focused around the research and development of modulation recognition algorithms. Any communication intelligence (COMINT) system comprises three main blocks: receiver front-end, modulation recogniser and output stage. Considerable work has been done in the area of receiver front-ends. The work at the output stage is concerned with information extraction, recording and exploitation and begins with signal demodulation, that requires accurate knowledge about the signal modulation type. There are, however, two main reasons for knowing the current modulation type of a signal; to preserve the signal information content and to decide upon the suitable counter action, such as jamming. Automatic Modulation Recognition of Communications Signals describes in depth this modulation recognition process. Drawing on several years of research, the authors provide a critical review of automatic modulation recognition. This includes techniques for recognising digitally modulated signals. The book also gives comprehensive treatment of using artificial neural networks for recognising modulation types. Automatic Modulation Recognition of Communications Signals is the first comprehensive book on automatic modulation recognition. It is essential reading for researchers and practising engineers in the field. It is also a valuable text for an advanced course on the subject.

The "Turbulence and Interactions 2006" (TI2006) conference was held on the island of Porquerolles, France, May 29-June 2, 2006. The scientific sponsors of the conference were * Association Francaise de Mecanique, * CD-adapco, * DGA * Ecole Polytechnique Federale de Lausanne (EPFL), * ERCOFTAC : European Research Community on Flow, Turbulence and Combustion, * FLUENT, * The French Ministery of Foreign Affairs, * Laboratoire de Modelisation en Mecanique, Paris 6, * ONERA. The conference was a unique event. Never before have so many organisations concerned with turbulence works come together in one conference. As the title "Turbulence and Interactions" anticipated, the workshop was not run with parallel sessions but instead of one united gathering where people had strong interactions and discussions. Many of the 85 or so attendants were veterans of previous ERCOFTAC conferences. Some young researchers attended their very first int- national meeting. The organisers were fortunate in obtaining the presence of the following - vited speakers: N. Adams (TUM, Germany), C. Cambon (ECL, France), J.-P. Dussauge (Polytech Marseille, France), D.A. Gosman (Imperial College, UK), Y. Kaneda (Nagoya University, Japan), O. Simonin (IMFT, France), G. Tryggvason (WPI, USA), D. Veynante (ECP, France), F. Waleffe (University of Wisconsin, USA), Y.K. Zhou (University of California, USA). The topics covered by the 59 papers ranged from experimental results through theory to computations. The papers of the conference went through the usual - viewing process for two special issues of international journals : Computers and Fluids, and Flow, Turbulence and Combustion.

Our everyday life is in?uenced by many unexpected (dif?cult to predict) events usually referred as a chance. Probably, we all are as we are due to the accumulation point of a multitude of chance events. Gambling games that have been known to human beings nearly from the beginning of our civilization are based on chance events. These chance events have created the dream that everybody can easily become rich. This pursuit made gambling so popular. This book is devoted to the dynamics of the mechanical randomizers and we try to solve the problem why mechanical device (roulette) or a rigid body (a coin or a die) operating in the way described by the laws of classical mechanics can behave in such a way and produce a pseudorandom outcome. During mathematical lessons in primary school we are taught that the outcome of the coin tossing experiment is random and that the probability that the tossed coin lands heads (tails) up is equal to 1/2. Approximately, at the same time during physics lessons we are told that the motion of the rigid body (coin is an example of suchabody)isfullydeterministic. Typically,studentsarenotgiventheanswertothe question Why this duality in the interpretation of the simple mechanical experiment is possible? Trying to answer this question we describe the dynamics of the gambling games based on the coin toss, the throw of the die, and the roulette run.

Applications of some selected soft computing methods to acoustics and sound engineering are presented in this book. The aim of this research study is the implementation of soft computing methods to musical signal analysis and to the recognition of musical sounds and phrases. Accordingly, some methods based on such learning algorithms as neural networks, rough sets and fuzzy-logic were conceived, implemented and tested. Additionally, the above-mentioned methods were applied to the analysis and verification of subjective testing results. The last problem discussed within the framework of this book was the problem of fuzzy control of the classical pipe organ instrument.
The obtained results show that computational intelligence and soft computing may be used for solving some vital problems in both musical and architectural acoustics.

This volume is devoted to the exciting topic of dissipative solitons, i.e. pulses or spatially localised waves in systems exhibiting gain and loss. Examples are laser systems, nonlinear resonators and optical transmission lines. The physical principles and mathematical concepts are explained in a clear and concise way, suitable for students and young researchers. The similarities and differences in the notion of a soliton between dissipative systems and Hamiltonian and integrable systems are discussed, and many examples are given. The contributions are written by the world's leading experts in the field, making it a unique exposition of this emerging topic.