This book, the first English-language translation of Acoustique des instruments de musique, Second Edition, presents the necessary foundations for understanding the complex physical phenomena involved in musical instruments. What is the function of the labium in a flute? Which features of an instrument allow us to make a clear audible distinction between a clarinet and a trumpet? With the help of numerous examples, these questions are addressed in detail. The authors focus in particular on the significant results obtained in the field during the last fifteen years. Their goal is to show that elementary physical models can be used with benefit for various applications in sound synthesis, instrument making, and sound recording. The book is primarily addressed to graduate students and researchers; however it could also be of interest for engineers, musicians, craftsmen, and music lovers who wish to learn about the basics of musical acoustics.

This book focuses on the basic control and filtering synthesis problems for discrete-time switched linear systems under time-dependent switching signals. Chapter 1, as an introduction of the book, gives the backgrounds and motivations of switched systems, the definitions of the typical time-dependent switching signals, the differences and links to other types of systems with hybrid characteristics and a literature review mainly on the control and filtering for the underlying systems. By summarizing the multiple Lyapunov-like functions (MLFs) approach in which different requirements on comparisons of Lyapunov function values at switching instants, a series of methodologies are developed for the issues on stability and stabilization, and l2-gain performance or tube-based robustness for l disturbance, respectively, in Chapters 2 and 3. Chapters 4 and 5 are devoted to the control and filtering problems for the time-dependent switched linear systems with either polytopic uncertainties or measurable time-varying parameters in different sense of disturbances. The asynchronous switching problem, where there is time lag between the switching of the currently activated system mode and the controller/filter to be designed, is investigated in Chapter 6. The systems with various time delays under typical time-dependent switching signals are addressed in Chapter 7.

The book addresses the control issues such as stability analysis, control synthesis and filter design of Markov jump systems with the above three types of TPs, and thus is mainly divided into three parts. Part I studies the Markov jump systems with partially unknown TPs. Different methodologies with different conservatism for the basic stability and stabilization problems are developed and compared. Then the problems of state estimation, the control of systems with time-varying delays, the case involved with both partially unknown TPs and uncertain TPs in a composite way are also tackled. Part II deals with the Markov jump systems with piecewise homogeneous TPs. Methodologies that can effectively handle control problems in the scenario are developed, including the one coping with the asynchronous switching phenomenon between the currently activated system mode and the controller/filter to be designed. Part III focuses on the Markov jump systems with memory TPs. The concept of -mean square stability is proposed such that the stability problem can be solved via a finite number of conditions. The systems involved with nonlinear dynamics (described via the Takagi-Sugeno fuzzy model) are also investigated. Numerical and practical examples are given to verify the effectiveness of the obtained theoretical results. Finally, some perspectives and future works are presented to conclude the book.

This fascinating, colourful book offers in-depth insights and first-hand working experiences in the production of art works, using simple computational models with rich morphological behaviour, at the edge of mathematics, computer science, physics and biology. It organically combines ground breaking scientific discoveries in the theory of computation and complex systems with artistic representations of the research results. In this appealing book mathematicians, computer scientists, physicists, and engineers brought together marvelous and esoteric patterns generated by cellular automata, which are arrays of simple machines with complex behavior. Configurations produced by cellular automata uncover mechanics of dynamic patterns formation, their propagation and interaction in natural systems: heart pacemaker, bacterial membrane proteins, chemical rectors, water permeation in soil, compressed gas, cell division, population dynamics, reaction-diffusion media and self-organisation. The book inspires artists to take on cellular automata as a tool of creativity and it persuades scientists to convert their research results into the works of art. The book is lavishly illustrated with visually attractive examples, presented in a lively and easily accessible manner.

This book is devoted to Slime mould Physarum polycephalum, which is a large single cell capable for distributed sensing, concurrent information processing, parallel computation and decentralized actuation. The ease of culturing and experimenting with Physarum makes this slime mould an ideal substrate for real-world implementations of unconventional sensing and computing devices The book is a treatise of theoretical and experimental laboratory studies on sensing and computing properties of slime mould, and on the development of mathematical and logical theories of Physarum behavior. It is shown how to make logical gates and circuits, electronic devices (memristors, diodes, transistors, wires, chemical and tactile sensors) with the slime mould. The book demonstrates how to modify properties of Physarum computing circuits with functional nano-particles and polymers, to interface the slime mould with field-programmable arrays, and to use Physarum as a controller of microbial fuel cells. A unique multi-agent model of slime is shown to serve well as a software slime mould capable for solving problems of computational geometry and graph optimization. The multiagent model is complemented by cellular automata models with parallel accelerations. Presented mathematical models inspired by Physarum include non-quantum implementation of Shor's factorization, structural learning, computation of shortest path tree on dynamic graphs, supply chain network design, p-adic computing and syllogistic reasoning. The book is a unique composition of vibrant and lavishly illustrated essays which will inspire scientists, engineers and artists to exploit natural phenomena in designs of future and emergent computing and sensing devices. It is a 'bible' of experimental computing with spatially extended living substrates, it spanstopics from biology of slime mould, to bio-sensing, to unconventional computing devices and robotics, non-classical logics and music and arts.

The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems.

This self-contained text develops a Markov chain approach that makes the rigorous analysis of a class of microscopic models that specify the dynamics of complex systems at the individual level possible. It presents a general framework of aggregation in agent-based and related computational models, one which makes use of lumpability and information theory in order to link the micro and macro levels of observation. The starting point is a microscopic Markov chain description of the dynamical process in complete correspondence with the dynamical behavior of the agent-based model (ABM), which is obtained by considering the set of all possible agent configurations as the state space of a huge Markov chain. An explicit formal representation of a resulting "micro-chain" including microscopic transition rates is derived for a class of models by using the random mapping representation of a Markov process. The type of probability distribution used to implement the stochastic part of the model, which defines the updating rule and governs the dynamics at a Markovian level, plays a crucial part in the analysis of "voter-like" models used in population genetics, evolutionary game theory and social dynamics. The book demonstrates that the problem of aggregation in ABMs - and the lumpability conditions in particular - can be embedded into a more general framework that employs information theory in order to identify different levels and relevant scales in complex dynamical systems

This proceedings contains articles submitted to the fifth International Conference on Cognitive Neurodynamics (ICCN2015). In ICCN2015, twelve invited plenary lectures were presented by the leading scientists in their respective research fields. More than 15 mini-symposiums are organized by specialists with topics covering: motor control and learning, dynamic coding in distributed neural circuits, dynamics of firing patterns and synchronization in neuronal systems, information and signal processing techniques in neurotechnology, neural oscillations and synaptic plasticity in the hippocampus, new perspective on model-based vs. model-free brain process, neural mechanisms of internal switching, neuroinformation computation, neural model and dynamics, imaging human cognitive networks, neuroinformatics, neuroergonomics & neuroengineering, dynamic brain for communication, visual information processing and functional imaging and neural mechanisms of language processing. All articles are peer-reviewed. The ICCN is a series conference held every two years since 2007.

This book deals with methods to evaluate scientific productivity. In the book statistical methods, deterministic and stochastic models and numerous indexes are discussed that will help the reader to understand the nonlinear science dynamics and to be able to develop or construct systems for appropriate evaluation of research productivity and management of research groups and organizations. The dynamics of science structures and systems is complex, and the evaluation of research productivity requires a combination of qualitative and quantitative methods and measures. The book has three parts. The first part is devoted to mathematical models describing the importance of science for economic growth and systems for the evaluation of research organizations of different size. The second part contains descriptions and discussions of numerous indexes for the evaluation of the productivity of researchers and groups of researchers of different size (up to the comparison of research productivities of research communities of nations). Part three contains discussions of non-Gaussian laws connected to scientific productivity and presents various deterministic and stochastic models of science dynamics and research productivity. The book shows that many famous fat tail distributions as well as many deterministic and stochastic models and processes, which are well known from physics, theory of extreme events or population dynamics, occur also in the description of dynamics of scientific systems and in the description of the characteristics of research productivity. This is not a surprise as scientific systems are nonlinear, open and dissipative.

In this monograph, the authors present their recently developed theory of electromagnetic interactions. This neoclassical approach extends the classical electromagnetic theory down to atomic scales and allows the explanation of various non-classical phenomena in the same framework. While the classical Maxwell-Lorentz electromagnetism theory succeeds in describing the physical reality at macroscopic scales, it struggles at atomic scales. Here, quantum mechanics traditionally takes over to describe non-classical phenomena such as the hydrogen spectrum and de Broglie waves. By means of modifying the classical theory, the approach presented here is able to consistently explain quantum-mechanical effects, and while similar to quantum mechanics in some respects, this neoclassical theory also differs markedly from it. In particular, the newly developed framework omits probabilistic interpretations of the wave function and features a new fundamental spatial scale which, at the size of the free electron, is much larger than the classical electron radius and is relevant to plasmonics and emission physics. This book will appeal to researchers interested in advanced aspects of electromagnetic theory. Treating the classical approach in detail, including non-relativistic aspects and the Lagrangian framework, and comparing the neoclassical theory with quantum mechanics and the de Broglie-Bohm theory, this work is completely self-contained.

This book presents recent research results relating to applications of nonlinear dynamics, focusing specifically on four topics of wide interest: heart dynamics, DNA/RNA, cell mobility, and proteins. The book derives from the First BCAM Workshop on Nonlinear Dynamics in Biological Systems, held in June 2014 at the Basque Center of Applied Mathematics (BCAM). At this international meeting, researchers from different but complementary backgrounds, including molecular dynamics, physical chemistry, bio-informatics and biophysics, presented their most recent results and discussed the future direction of their studies using theoretical, mathematical modeling and experimental approaches. Such was the level of interest stimulated that the decision was taken to produce this publication, with the organizers of the event acting as editors. All of the contributing authors are researchers working on diverse biological problems that can be approached using nonlinear dynamics. The book will appeal especially to applied mathematicians, biophysicists, and computational biologists.

For the past two decades, 'complexity' has informed a range of work across the social sciences. There are diverse schools of complexity thinking, and authors have used these ideas in a multiplicity of ways, from health inequalities to the organization of large scale firms. Some understand complexity as emergence from the rule-based interactions of simple agents and explore it through agent-based modelling. Others argue against such 'restricted complexity' and for the development of case-based narratives deploying a much wider set of approaches and techniques. Major social theorists have been reinterpreted through a complexity lens and the whole methodological programme of the social sciences has been recast in complexity terms. In four parts, this book seeks to establish 'the state of the art' of complexity-informed social science as it stands now, examining: the key issues in complexity theory the implications of complexity theory for social theory the methodology and methods of complexity theory complexity within disciplines and fields. It also points ways forward towards a complexity-informed social science for the twenty-first century, investigating the argument for a post-disciplinary, 'open' social science. Byrne and Callaghan consider how this might be developed as a programme of teaching and research within social science. This book will be particularly relevant for, and interesting to, students and scholars of social research methods, social theory, business and organization studies, health, education, urban studies and development studies.

This book, which presents the peer-reviewed post-proceedings of CSNDD 2012 and CSNDD 2014, addresses the important role that relevant concepts and tools from nonlinear and complex dynamics could play in present and future engineering applications. It includes 22 chapters contributed by outstanding researchers and covering various aspects of applications, including: structural health monitoring, diagnosis and damage detection, experimental methodologies, active vibration control and smart structures, passive control of structures using nonlinear energy sinks, vibro-impact dynamic MEMS/NEMS/AFM, energy-harvesting materials and structures, and time-delayed feedback control, as well as aspects of deterministic versus stochastic dynamics and control of nonlinear phenomena in physics. Researchers and engineers interested in the challenges posed and opportunities offered by nonlinearities in the development of passive and active control strategies, energy harvesting, novel design criteria, modeling and characterization will find the book to be an outstanding introduction.

This volume sets out the basic applied mathematical and numerical methods of chaotic dynamics and illustrates the wide range of phenomena, inside and outside the laboratory, that can be treated as chaotic processes. Originally published in 1986. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Part of the Princeton Aeronautical Paperback series designed to bring to students and research engineers outstanding portions of the twelve-volume High Speed Aerodynamics and Jet Propulsion series. These books have been prepared by direct reproduction of the text from the original series and no attempt has been made to provide introductory material or to eliminate cross reference to other portions of the original volumes. Originally published in 1960. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

This book brings together different work in the new field of physics called the chaos theory, an extension of classical mechanics, in which simple and complex causes are seen to interact. Mathematics may only be able to solve simple linear equations which experiment has pushed nature into obeying in a limited way, but now that computers can map the whole plane of solutions of non-linear equations a new vision of nature is revealed. The implications are staggeringly universal in all areas of scientific work and philosophical thought.

Covering a broad range of topics, this text provides a comprehensive survey of the modelling of chaotic dynamics and complexity in the natural and social sciences. Its attention to models in both the physical and social sciences and the detailed philosophical approach make this an unique text in the midst of many current books on chaos and complexity. Part 1 deals with the mathematical model as an instrument of investigation. The general meaning of modelling and, more specifically, questions concerning linear modelling are discussed. Part 2 deals with the theme of chaos and the origin of chaotic dynamics. Part 3 deals with the theme of complexity: a property of the systems and of their models which is intermediate between stability and chaos. Including an extensive index and bibliography along with numerous examples and simplified models, this is an ideal course text.

An introduction to developments in chaos and related topics in nonlinear dynamics, including the detection and quantification of chaos in experimental data, fractals, and complex systems. Most of the important elementary concepts in nonlinear dynamics are discussed, with emphasis on the physical concepts and useful results rather than mathematical proofs and derivations. While many books on chaos are purely qualitative and many others are highly mathematical, this book fills the middle ground by giving the essential equations, but in the simplest possible form. It assumes only an elementary knowledge of calculus. Complex numbers, differential equations, and vector calculus are used in places, but those tools are described as required. The book is aimed at the student, scientist, or engineer who wants to learn how to use the ideas in a practical setting. It is written at a level suitable for advanced undergraduate and beginning graduate students in all fields of science and engineering.

Designed for those wishing to study mathematics beyond linear algebra but unready for abstract material, this "invitation" to the excitement of dynamical systems appeals to readers from a wide range of backgrounds. Rather than taking a theorem-proof-corollary-remark approach, it stresses geometry and intuition. Topics include both the classical theory of linear systems and the modern theory of nonlinear and chaotic systems as well as bifurcation, symbolic dynamics, fractals, and complex systems.
In addition to offering a unified presentation of continuous and discrete time systems, this treatment integrates computing comfortably into the text. Appendixes feature important background material, including a gentle introduction to differential equations and explanations of how to write MATLAB, Mathematica, and C programs to compute dynamical systems. Prerequisites for advanced undergraduates and graduate students include two semesters of calculus and one semester of linear algebra.

The analysis of time series data has for many years been a central component of statistical research and practice. Although the theory of linear time series is now well established, that of non-linear time series is still a rapidly developing subject. This book, now available in paperback, is an introduction to some of these developments and the present state of research. This book is intended for statistical theoreticians applied statisticians dynamicists, engineers, and scientists.

While many books have discussed methodological advances in nonlinear dynamical systems theory (NDS), this volume is unique in its focus on NDS's role in the development of psychological theory. After an introductory chapter covering the fundamentals of chaos, complexity and other nonlinear dynamics, subsequent chapters provide in-depth coverage of each of the specific topic areas in psychology. A concluding chapter takes stock of the field as a whole, evaluating important challenges for the immediate future. The chapters are written by experts in the use of NDS in each of their respective areas, including biological, cognitive, developmental, social, organizational and clinical psychology. Each chapter provides an in-depth examination of theoretical foundations and specific applications and a review of relevant methods. This edited collection represents the state of the art in NDS science across the disciplines of psychology.

Covering one of the fastest growing areas of applied mathematics, Nonlinear Dynamics and Chaos: Second Edition, is a fully updated edition of this highly respected text. Covering a breadth of topics, ranging from the basic concepts to applications in the physical sciences, the book is highly illustrated and written in a clear and comprehensible style.

• Provides a self-contained introduction to the theory and applications of nonlinear dynamics and chaos.

• Introduces the concepts of instabilities, bifurcations, and catastrophes.

• Each idea is carefully explained and supported by examples.

• Features many applications to a wide variety of scientific fields.

• Includes an illustrated glossary of geometrical dynamics.

• Features a supplementary bibliography of further reading.

• Assumes minimal background knowledge.

In this volume are collected notes of lectures delivered at the First In ternational Research Institute of the Mathematical Society of Japan. This conference, held at Tohoku University in July 1993, was devoted to geometry and global analysis. Subsequent to the conference, in answer to popular de mand from the participants, it was decided to publish the notes of the survey lectures. Written by the lecturers themselves, all experts in their respective fields, these notes are here presented in a single volume. It is hoped that they will provide a vivid account of the current research, from the introduc tory level up to and including the most recent results, and will indicate the direction to be taken by future researeh. This compilation begins with Jean-Pierre Bourguignon's notes entitled "An Introduction to Geometric Variational Problems," illustrating the gen eral framework of the field with many examples and providing the reader with a broad view of the current research. Following this, Kenji Fukaya's notes on "Geometry of Gauge Fields" are concerned with gauge theory and its applications to low-dimensional topology, without delving too deeply into technical detail. Special emphasis is placed on explaining the ideas of infi nite dimensional geometry that, in the literature, are often hidden behind rigorous formulations or technical arguments."

What is time? The Janus Point offers a ground-breaking solution to one of the greatest mysteries in physics. For over a century, the greatest minds have sought to understand why time seems to flow in one direction, ever forward. In The Janus Point, Julian Barbour offers a radically new answer: it doesn't. At the heart of this book, Barbour provides a new vision of the Big Bang - the Janus Point - from which time flows in two directions, its currents driven by the expansion of the universe and the growth of order in the galaxies, planets and life itself. What emerges is not just a revolutionary new theory of time, but a hopeful argument about the destiny of our universe. 'Both a work of literature and a masterpiece of scientific thought' Lee Smolin, author of The Trouble with Physics 'Profound...original...accessible to anyone who has pondered the mysteries of space and time' Martin Rees, Astronomer Royal 'Takes on fundamental questions, offering a new perspective on how the Universe started and where it may be headed' Science Magazine

This book provides the reader with an elementary introduction to chaos and fractals, suitable for students with a background in elementary algebra, without assuming prior coursework in calculus or physics. It introduces the key phenomena of chaos - aperiodicity, sensitive dependence on initial conditions, bifurcations - via simple iterated functions. Fractals are introduced as self-similar geometric objects and analyzed with the self-similarity and box-counting dimensions. After a brief discussion of power laws, subsequent chapters explore Julia Sets and the Mandelbrot Set. The last part of the book examines two-dimensional dynamical systems, strange attractors, cellular automata, and chaotic differential equations.
The book is richly illustrated and includes over 200 end-of-chapter exercises. A flexible format and a clear and succinct writing style make it a good choice for introductory courses in chaos and fractals.
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