Nonlinear science Books

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Book SynopsisThe importance of complexity is well-captured by Hawking''s comment: Complexity is the science of the 21st century. From the movement of flocks of birds to the Internet, environmental sustainability, and market regulation, the study and understanding of complex non-linear systems has become highly influential over the last 30 years.In this Very Short Introduction, one of the leading figures in the field, John Holland, introduces the key elements and conceptual framework of complexity. From complex physical systems such as fluid flow and the difficulties of predicting weather, to complex adaptive systems such as the highly diverse and interdependent ecosystems of rainforests, he combines simple, well-known examples -- Adam Smith''s pin factory, Darwin''s comet orchid, and Simon''s ''watchmaker'' -- with an account of the approaches, involving agents and urn models, taken by complexity theory. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.Table of Contents1. Complex systems ; 2. Complex physical systems ; 3. Complex adaptive systems ; 4. Agents, networks, degree, and recirculation ; 5. Specialization and diversity ; 6. Emergence ; 7. Co-evolution and the formation of niches ; 8. Putting it all together ; Further reading ; Index

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Book SynopsisNonlinear dynamics and chaos involves the study of apparently random happenings within a system or process. The subject has wide applications within mathematics, engineering, physics and other physical sciences.This second edition covers the latest research conducted in this area.Trade Review"... much more extensive than before." (The Mathematical Review, March 2004) "The fully updated second edition provides a self-contained introduction to the theory and applications of nonlinear dynamics and chaos." (International Journal of Environmental Analytical Chemistry, Vol.84, No.14 – 15, 10 – 20 December 2004)Table of ContentsPreface. Preface to the First Edition. Acknowledgements from the First Edition. Introduction PART I: BASIC CONCEPTS OF NONLINEAR DYNAMICS An overview of nonlinear phenomena Point attractors in autonomous systems Limit cycles in autonomous systems Periodic attractors in driven oscillators Chaotic attractors in forced oscillators Stability and bifurcations of equilibria and cycles PART II ITERATED MAPS AS DYNAMICAL SYSTEMS Stability and bifurcation of maps Chaotic behaviour of one-and two-dimensional maps PART III FLOWS, OUTSTRUCTURES AND CHAOS The Geometry of Recurrence The Lorenz system Rosslers band Geometry of bifurcations PART IV APPLICATIONS IN THE PHYSICAL SCIENCES Subharmonic resonances of an offshore structure Chaotic motions of an impacting system Escape from a potential well Appendix. Illustrated Glossary. Bibliography. Online Resource. Index.

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Book SynopsisSince the bestselling first edition was published, there has been a lot of new research conducted in the area of nonlinear dynamics and chaos. This revised edition provides new material, including a glossary and bibliography, as well as a generous supplement of new figures and illustrations.Trade Review"... much more extensive than before." (The Mathematical Review, March 2004) "The fully updated second edition provides a self-contained introduction to the theory and applications of nonlinear dynamics and chaos." (International Journal of Environmental Analytical Chemistry, Vol.84, No.14 – 15, 10 – 20 December 2004)Table of ContentsPreface vi Preface to the First Edition xv Acknowledgements from the First Edition xxi 1 Introduction 1 1.1 Historical background 1 1.2 Chaotic dynamics in Duffing's oscillator 3 1.3 Attractors and bifurcations 8 Part I Basic Concepts of Nonlinear Dynamics 2 An overview of nonlinear phenomena 15 2.1 Undamped, unforced linear oscillator 15 2.2 Undamped, unforced nonlinear oscillator 17 2.3 Damped, unforced linear oscillator 18 2.4 Damped, unforced nonlinear oscillator 20 2.5 Forced linear oscillator 21 2.6 Forced nonlinear oscillator: periodic attractors 22 2.7 Forced nonlinear oscillator: chaotic attractor 24 3 Point attractors in autonomous systems 26 3.1 The linear oscillator 26 3.2 Nonlinear pendulum oscillations 34 3.3 Evolving ecological systems 41 3.4 Competing point attractors 45 3.5 Attractors of a spinning satellite 47 4 Limit cycles in autonomous systems 50 4.1 The single attractor 50 4.2 Limit cycle in a neural system 51 4.3 Bifurcations of a chemical oscillator 55 4.4 Multiple limit cycles in aeroelastic galloping 58 4.5 Topology of two-dimensional phase space 61 5 Periodic attractors in driven oscillators 62 5.1 The Poincare map 62 5.2 Linear resonance 64 5.3 Nonlinear resonance 66 5.4 The smoothed variational equation 71 5.5 Variational equation for subharmonics 72 5.6 Basins ofattraction by mapping techniques 73 5.7 Resonance ofa self-exciting system 76 5.8 The ABC ofnonlinear dynamics 79 6 Chaotic attractors in forced oscillators 80 6.1 Relaxation oscillations and heartbeat 80 6.2 The Birkhoff±Shaw chaotic attractor 82 6.3 Systems with nonlinear restoring force 93 7 Stability and bifurcations of equilibria and cycles 106 7.1 Liapunov stability and structural stability 106 7.2 Centre manifold theorem 109 7.3 Local bifurcations of equilibrium paths 111 7.4 Local bifurcations of cycles 123 7.5 Basin changes at local bifurcations 126 7.6 Prediction ofincipient instability 128 Part II Iterated Maps as Dynamical Systems 8 Stability and bifurcation of maps 135 8.1 Introduction 135 8.2 Stability of one-dimensional maps 138 8.3 Bifurcations of one-dimensional maps 139 8.4 Stability of two-dimensional maps 149 8.5 Bifurcations of two-dimensional maps 156 8.6 Basin changes at local bifurcations of limit cycles 158 9 Chaotic behaviour of one- and two-dimensional maps 161 9.1 General outline 161 9.2 Theory for one-dimensional maps 164 9.3 Bifurcations to chaos 167 9.4 Bifurcation diagram of one-dimensional maps 170 9.5 He non map 174 Part III Flows, Outstructures, and Chaos 10 The geometry of recurrence 183 10.1 Finite-dimensional dynamical systems 183 10.2 Types ofrecurrent behaviour 187 10.3 Hyperbolic stability types for equilibria 195 10.4 Hyperbolic stability types for limit cycles 200 10.5 Implications ofhyperbolic structure 205 11 The Lorenz system 207 11.1 A model ofthermal convection 207 11.2 First convective instability 209 11.3 The chaotic attractor ofLorenz 214 11.4 Geometry ofa transition to chaos 222 1 2 RoÈssler's band 229 12.1 The simply folded band in an autonomous system 229 12.2 Return map and bifurcations 233 12.3 Smale's horseshoe map 238 12.4 Transverse homoclinic trajectories 243 12.5 Spatial chaos and localized buckling 246 13 Geometry of bifurcations 249 13.1 Local bifurcations 249 13.2 Global bifurcations in the phase plane 258 13.3 Bifurcations of chaotic attractors 266 Part IV Applications in the Physical Sciences 14 Subharmonic resonances of an offshore structure 285 14.1 Basic equation and non-dimensional form 286 14.2 Analytical solution for each domain 288 14.3 Digital computer program 289 14.4 Resonance response curves 290 14.5 Effect of damping 294 14.6 Computed phase projections 296 14.7 Multiple solutions and domains ofattraction 298 15 Chaotic motions of an impacting system 302 15.1 Resonance response curve 302 15.2 Application to moored vessels 306 15.3 Period-doubling and chaotic solutions 306 16 Escape from a potential well 313 16.1 Introduction 313 16.2 Analytical formulation 314 16.3 Overview ofthe steady-state response 319 16.4 The two-band chaotic attractor 324 16.5 Resonance ofthe steady states 328 16.6 Transients and basins ofattraction 333 16.7 Homoclinic phenomena 340 16.8 Heteroclinic phenomena 346 16.9 Indeterminate bifurcations 352 Appendix 359 Illustrated Glossary 369 Bibliography 402 Online Resources 428 Index 429

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Book SynopsisThis book concerns the use of concepts from statistical physics in the description of financial systems. The authors illustrate the scaling concepts used in probability theory, critical phenomena, and fully developed turbulent fluids. These concepts are then applied to financial time series. The authors also present a stochastic model that displays several of the statistical properties observed in empirical data. Statistical physics concepts such as stochastic dynamics, short- and long-range correlations, self-similarity and scaling permit an understanding of the global behaviour of economic systems without first having to work out a detailed microscopic description of the system. Physicists will find the application of statistical physics concepts to economic systems interesting. Economists and workers in the financial world will find useful the presentation of empirical analysis methods and well-formulated theoretical tools that might help describe systems composed of a huge number oTrade Review'… they have been remarkably successful in presenting a clear and concise introductory summary of a large body of work on the statistical properties of stock prices.' Burton Malkiel, Journal of Economic Literature'Clearly and concisely written, this book provides an excellent introduction to the problem of understanding the empirical statistical properties of prices.' Doyne Farmer, Prediction Company, Santa Fe and the Santa Fe Institute'I feel the book is a useful introduction to the empirical aspects of econophysics.' Blake LeBaron, Nature'The authors are leading researchers in the field, and were well-regarded statistical physicists before that … the book seems aimed the other way, at physicists interested in economics, and for them it would make a good introduction to finance. The writing is clear and friendly, the production values high and the guides to further reading excellent. They will find it well worth their time and money.' Cosma Shalizi, Institute of PhysicsTable of ContentsPreface; 1. Introduction; 2. Efficient market hypothesis; 3. Random walk; 4. Lévy stochastic processes and limit theorems; 5. Scales in financial data; 6. Stationarity and time correlation; 7. Time correlation in financial time series; 8. Stochastic models of price dynamics; 9. Scaling and its breakdown; 10. ARCH and GARCH processes; 11. Financial markets and turbulence; 12. Correlation and anti-correlation between stocks; 13. Taxonomy of a stock portfolio; 14. Options in idealized markets; 15. Options in real markets; Appendix A: notation guide; Appendix B: martingales; References; Index.

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Book SynopsisSolitons are waves with exceptional stability properties which appear in many areas of physics. The basic properties of solitons are introduced here using examples from macroscopic physics (e.g. blood pressure pulses and fibre optical communications). The book then presents the main theoretical methods before discussing applications from solid state or atomic physics such as dislocations, excitations in spin chains, conducting polymers, ferroelectrics and BoseâEinstein condensates. Examples are also taken from biological physics and include energy transfer in proteins and DNA fluctuations. Throughout the book the authors emphasise a fresh approach to modelling nonlinearities in physics. Instead of a perturbative approach, nonlinearities are treated intrinsically and the analysis based on the soliton equations introduced in this book. Based on the authors' graduate course, this textbook gives an instructive view of the physics of solitons for students with a basic knowledge of general pTable of ContentsList of Portraits; Preface; Part I. Different Classes of Solitons: Introduction; 1. Nontopological solitons: the Korteweg-de Vries equation; 2. Topological soltitons: sine-Gordon equation; 3. Envelope solitons and nonlinear localisation: the nonlinear Schrödinger equation; 4. The modelling process: ion acoustic waves in a plasma; Part II. Mathematical Methods for the Study of Solitons: Introduction; 5. Linearisation around the soliton solution; 6. Collective coordinate method; 7. The inverse-scattering transform; Part III. Examples in Solid State and Atomic Physics: Introduction; 8. The Ferm–Pasta–Ulam problem; 9. A simple model for dislocations in crystals; 10. Ferroelectric domain walls; 11. Incommensurate phases; 12. Solitons in magnetic systems; 13. Solitons in Conducting polymers; 14. Solitons in Bose–Einstein condensates; Part IV. Nonlinear Excitations in Biological Molecules: Introduction; 15. Energy localisation and transfer in proteins; 16. Nonlinear dynamics and statistical physics of DNA; Conclusion: Physical solitons: do they exist?; Part V. Appendices: A. Derivation of the KdV equation for surface hydrodynamic waves; B. Mechanics of a continuous medium; C. Coherent states of an harmonic oscillator; References; Index.

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Book SynopsisUnderstanding the behaviour of particles suspended in a fluid has many important applications across a range of fields, including engineering and geophysics. Comprising two main parts, this book begins with the well-developed theory of particles in viscous fluids, i.e. microhydrodynamics, particularly for single- and pair-body dynamics. Part II considers many-body dynamics, covering shear flows and sedimentation, bulk flow properties and collective phenomena. An interlude between the two parts provides the basic statistical techniques needed to employ the results of the first (microscopic) in the second (macroscopic). The authors introduce theoretical, mathematical concepts through concrete examples, making the material accessible to non-mathematicians. They also include some of the many open questions in the field to encourage further study. Consequently, this is an ideal introduction for students and researchers from other disciplines who are approaching suspension dynamics for the fTrade Review'The authors introduce theoretical, mathematical concepts through concrete examples, making the material accessible to non-mathematicians … this is an ideal introduction for students and researchers from other disciplines who are approaching suspension dynamics for the first time.' Sylvie Pic, zbMATHTable of ContentsPreface; Prologue; Part I. Microhydrodynamics: 1. Basic concepts in viscous flow; 2. One sphere in Stokes flow; 3. Sophisticated techniques; 4. Particle pair interactions; Interlude: from the microscopic to the macroscopic; 5. Statistical and stochastic concepts; Part II. Toward a Description of Macroscopic Phenomena in Suspensions: 6. Sedimentation; 7. Shear flow; 8. Beyond Stokes flow: finite inertia; Epilogue; References; Index.

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Book SynopsisThe techniques used to solve non-linear problems differ greatly from those dealing with linear features. Deriving all the necessary theorems from first principles, this 2005 textbook should give upper undergraduates and graduate students a thorough understanding using as little background material as possible.Trade ReviewReview of the hardback: '… presents an introduction to critical point theory addressed to students with a modest background in Lebesgue integration and linear functional analysis. Many important methods from nonlinear analysis are introduced in a problem oriented way … well written … should be present in the library of any researcher interested in Lévy processes and Lie groups.' Zentralblatt MATHTable of Contents1. Extrema; 2. Critical points; 3. Boundary value problems; 4. Saddle points; 5. Calculus of variations; 6. Degree theory; 7. Conditional extrema; 8. Minimax methods; 9. Jumping nonlinearities; 10. Higher dimensions.

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Book SynopsisProviding engineers with the tools to solve real-world heat transfer problems, this textbook includes advanced topics not covered in other books on the subject. Examples are complex and timely problems that are inherently interesting. It integrates Maple, MATLAB®, FEHT and Engineering Equation Solver (EES) directly with the heat transfer material.Trade ReviewReview of the hardback: '… this book significantly raises the bar for heat transfer text books. Further, the integration of theory with computational tools makes the book of high interest at the professional level. Readers are encouraged to go to the website and explore this book and the supporting materials in depth … a major contribution to education in the field of heat transfer.' Journal of Heat Transfer EngineeringTable of Contents1. One-dimensional, steady-state conduction; 2. Two-dimensional, steady-state conduction; 3. Transient conduction; 4. External forced convection; 5. Internal forced convection; 6. Natural convection; 7. Boiling and condensation; 8. Heat exchangers; 9. Mass transfer; 10. Radiation.

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Book SynopsisStudents learning the subject from scratch will value this comprehensive text, which presents three major types of dynamics, from the basics to some of the latest results: measure preserving transformations; continuous maps on compact spaces; and operators on function spaces. It will also be a valuable reference for experienced researchers.Trade Review"Overall the writing is clear and the author has included motivational and expository material, as well as some examples and exercises. The presentation is nicely unified, and the different parts of the book interact well." Michael Hochman, Mathematical ReviewsTable of ContentsIntroduction; Part I. Entropy in Ergodic Theory: 1. Shannon information and entropy; 2. Dynamical entropy of a process; 3. Entropy theorems in processes; 4. Kolmogorov–Sinai entropy; 5. The ergodic law of series; Part II. Entropy in Topological Dynamics: 6. Topological entropy; 7. Dynamics in dimension zero; 8. The entropy structure; 9. Symbolic extensions; 10. A touch of smooth dynamics; Part III. Entropy Theory for Operators: 11. Measure theoretic entropy of stochastic operators; 12. Topological entropy of a Markov operator; 13. Open problems in operator entropy; Appendix A. Toolbox; Appendix B. Conditional S-M-B; List of symbols; References; Index.

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Book SynopsisThis text covers key mathematical principles and algorithms for nonlinear filters used in image processing. It offers insight into the underlying mathematical and filter design methodologies needed to construct and use nonlinear filters in a variety of applications.Table of ContentsPreface. Logical Image Operators (E. Dougherty & J. Barrera). Computational Gray-Scale Operators (E. Dougherty & J. Barrera). Translation-Invariant Set Operators (E. Dougherty). Granulometric Filters (E. Dougherty & Y. Chen) Easy Recipes for Morphological Filters (H. Heijmans). Introduction to Connected Operators (H. Heijmans). Representation and Optimization of Stack Filters (J. Astola & P. Kuosmanen). Invariant Signals of Median and Stack Filters (J. Astola & P. Kuosmanen). Binary Polynomial Transforms and Logical Correlation (K. Egiazarian, et al.). Applications of Binary Polynomial Transforms (K. Egiazarian, et al.). Random Sets in View of Image Filtering Applications (I. Molchanov). Index.

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Book SynopsisPresents a systematic and unified study of geometric nonlinear functional analysis. This book presents a study of uniformly continuous and Lipschitz functions between Banach spaces, which leads naturally also to the classification of Banach spaces and of their important subsets (mainly spheres) in the uniform and Lipschitz categories.Table of ContentsIntroduction Retractions, extensions and selections Retractions, extensions and selections (special topics) Fixed points Differentiation of convex functions The Radon-Nikodym property Negligible sets and Gateaux differentiability Lipschitz classification of Banach spaces Uniform embeddings into Hilbert space Uniform classification of spheres Uniform classification of Banach spaces Nonlinear quotient maps Oscillation of uniformly continuous functions on unit spheres of finite-dimensional subspaces Oscillation of uniformly continuous functions on unit spheres of infinite-dimensional subspaces Perturbations of local isometries Perturbations of global isometries Twisted sums Group structure on Banach spaces Appendices Bibliography Index.

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Book SynopsisRefers to unitary groups of Hilbert spaces, the infinite symmetric group, groups of homeomorphisms of manifolds, and groups of transformations of measure spaces. This book presents an approach to the study of such groups based on ideas from geometric functional analysis and from exploring the interplay between dynamical properties of those groups.Table of ContentsIntroduction The Ramsey-Dvoretzky-Milman phenomenon The fixed point on compacta property The concentration property Levy groups Urysohn metric space and its group of isometries Minimal flows Further aspects of concentration Oscillation stability and distortion Bibliography Index.

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Book SynopsisA need for a deeper understanding of the convergence properties of augmented Lagrangian algorithms and of their relationship to operator-splitting methods such as alternating-methods direction and the development of more efficient algorithms prompted the authors to write this book. The volume is oriented to applications in continuum mechanics. This volume deals with the numerical simulation of the behavior of continuous media by augmented Lagrangian and operator-splitting methods (coupled to finite-element approximations). It begins with a description of the mechanical and mathematical frameworks of the considered applications as well as a general analysis of the basic numerical methods additionally used to study them. These ideas are then applied to specific classes of mechanical problems.

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Book SynopsisThis book has become the standard for a complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations. Originally published in 1983, it provides information needed to understand both the theory and the practice of these methods and provides pseudocode for the problems. The algorithms covered are all based on Newton's method or 'quasi-Newton' methods, and the heart of the book is the material on computational methods for multidimensional unconstrained optimization and nonlinear equation problems. The republication of this book by SIAM is driven by a continuing demand for specific and sound advice on how to solve real problems.

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Book SynopsisH-infinity control originated from an effort to codify classical control methods, where one shapes frequency response functions for linear systems to meet certain objectives. H-infinity control underwent tremendous development in the 1980s and made considerable strides toward systematizing classical control. This book addresses the next major issue of how this extends to nonlinear systems. At the core of nonlinear control theory lie two partial differential equations (PDEs). One is a first-order evolution equation called the information state equation, which constitutes the dynamics of the controller. One can view this equation as a nonlinear dynamical system. Much of this volume is concerned with basic properties of this system, such as the nature of trajectories, stability, and, most important, how it leads to a general solution of the nonlinear H-infinity control problem.

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Book SynopsisProvides an introduction to the applications, theory, and algorithms of linear and nonlinear optimization. The emphasis is on practical aspects - discussing modern algorithms, as well as the influence of theory on the interpretation of solutions or on the design of software. The book includes several examples of realistic optimization models that address important applications. The succinct style of this second edition is punctuated with numerous real-life examples and exercises, and the authors include accessible explanations of topics that are not often mentioned in textbooks, such as duality in nonlinear optimization, primal-dual methods for nonlinear optimization, filter methods, and applications such as support-vector machines. The book is designed to be flexible. It has a modular structure, and uses consistent notation and terminology throughout. It can be used in many different ways, in many different courses, and at many different levels of sophistication.

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Book SynopsisExtracting the latent underlying structures of complex nonlinear local and nonlocal flows is essential for their analysis and modeling. In this Element the authors attempt to provide a consistent framework through Koopman theory and its related popular discrete approximation - dynamic mode decomposition (DMD).Table of Contents1. Introduction; 2. Preliminaries; 3. Motivation for This Work; 4. Koopman Eigenfunctions and Modes; 5. Koopman Theory for Partial Differential Equation; 6. Mode Decomposition Based on Time State-Space Mapping; 7. Examples; 8. Conclusion; List of Symbols; List of Abbreviations; Appendix A Extended Dynamic Mode Decomposition Induced from Inverse Mapping; Appendix B Sparse Representation; References.

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Book SynopsisThe second edition of this best-selling textbook presents the concepts of continuum mechanics for advanced undergraduates and graduates. It features derivations of the basic equations of mechanics in invariant (vector and tensor) form and specification of governing equations to various co-ordinate systems, and numerous illustrative examples, chapter summaries and exercises.Table of Contents1. Introduction; 2. Vectors and tensors; 3. Kinematics of continua; 4. Stress measures; 5. Conservation and balance laws; 6. Constitutive equations; 7. Linearized elasticity; 8. Fluid mechanics and heat transfer; 9. Linearized viscoelasticity.

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Book SynopsisCavitation and Bubble Dynamics deals with the fundamental physical processes of bubble dynamics and the phenomenon of cavitation. It is ideal for graduate students and research engineers and scientists, and a basic knowledge of fluid flow and heat transfer is assumed. The analytical methods presented are developed from basic principles.Table of Contents1. Phase change, nucleation, and cavitation; 2. Spherical bubble dynamics; 3. Cavitation bubble collapse; 4. Dynamics of oscillating bubbles; 5. Translation of bubbles; 6. Homogeneous bubbly flows; 7. Cavitating flows; 8. Free streamline flows; Index.

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Book SynopsisThis book provides new research on the advances in non-linear dynamics. Chapter One studies compactions in carbon nanotube arrays. Chapter Two reviews the elastic and plastic type behaviours in the Fractal Theory of Motion at nanoscale. Chapter Three analyses a particular model of tumour progression, assuming that the invasive cells, the connective tissue and the proteases are moving through a non-differential medium governed by the Non-Standard Scale Relativity Theory (NSRT) (Scale Relativity Theory with arbitrary constant fractal dimension). Chapter Four studies the process of drug release from a polymer matrix. Chapter Five examines the implications of drug release from a polymeric matrix process. Chapter Six reviews behaviours of travelling waves and Shapiro step types in a tumour-growth model. Chapter Seven discusses the astonishing evolutionary dynamics of a class of nonlinear discrete 2D pattern formations and growth models.

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Book SynopsisThis book provides research summaries from a number of different focuses in Mathematics, and compiles biographical sketches of top professionals in this important field.

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Book SynopsisNon-linear, or chaotic behaviour in real world systems has been reported in electronic circuits and communications systems, chemical reactions, biological behaviour. Applications include solitons, integrable systems, cellular automata, pattern formation, qualitative structure and bifurcation theory, onset of chaos and turbulence, analytic dynamics, and transport phenomena. This book presents important new research in this dynamic field.

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Book SynopsisThis book focuses on recent and significant research on non-linear, or chaotic behaviour which in real world systems has been reported in electronic circuits and communications systems, chemical reactions, biological behaviour. Applications include solitons, integrable systems, cellular automata, pattern formation, qualitative structure and bifurcation theory, onset of chaos and turbulence, analytic dynamics, and transport phenomena.

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Book SynopsisProvides the foundations of the theory of nonlinear optimization as well as some related algorithms and presents a variety of applications from diverse areas of applied sciences. The author combines three pillars of optimization and rigorously and gradually builds the connection between theory, algorithms, applications, and implementation.

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Book SynopsisA compendium of the authors’ recently published results, this book discusses sliding mode control of uncertain nonlinear systems, with a particular emphasis on advanced and optimization based algorithms. The authors survey classical sliding mode control theory and introduce four new methods of advanced sliding mode control. They analyze classical theory and advanced algorithms, with numerical results complementing the theoretical treatment. Case studies examine applications of the algorithms to complex robotics and power grid problems. Advanced and Optimization Based Sliding Mode Control: Theory and Applications is the first book to systematize the theory of optimization based higher order sliding mode control and illustrate advanced algorithms and their applications to real problems. It presents systematic treatment of event-triggered and model based event-triggered sliding mode control schemes, including schemes in combination with model predictive control, and presents adaptive algorithms as well as algorithms capable of dealing with state and input constraints. Additionally, the book includes simulations and experimental results obtained by applying the presented control strategies to real complex systems.

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Book SynopsisInverse scattering theory is a major theme in applied mathematics, with applications to such diverse areas as medical imaging, geophysical exploration, and nondestructive testing. The inverse scattering problem is both nonlinear and ill-posed, thus presenting challenges in the development of efficient inversion algorithms. A further complication is that anisotropic materials cannot be uniquely determined from given scattering data. In the first edition of Inverse Scattering Theory and Transmission Eigenvalues, the authors discussed methods for determining the support of inhomogeneous media from measured far field data and the role of transmission eigenvalue problems in the mathematical development of these methods. In this second edition, three new chapters describe recent developments in inverse scattering theory. In particular, the authors explore the use of modified background media in the nondestructive testing of materials and methods for determining the modified transmission eigenvalues that arise in such applications from measured far field data. They also examine nonscattering wave numbers—a subset of transmission eigenvalues—using techniques taken from the theory of free boundary value problems for elliptic partial differential equations and discuss the dualism of scattering poles and transmission eigenvalues that has led to new methods for the numerical computation of scattering poles.This book will be of interest to research mathematicians and engineers and physicists working on problems in target identification. It will also be useful to advanced graduate students in many areas of applied mathematics.

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Book SynopsisAtomically scaled “smart” devices, artificial intelligence, neuromorphic functions, alternative logic operations and computing, new memory storage paradigms, ultra-fast/bio-inspired/flexible/transparent/energy-efficient nanoelectronics – these contemporary concepts are driving forces for the progressive development of science and technology, mirroring societal expectations and solving its problems. Inspired by the concept of the memristor (memory + resistor), Redox-based resistive switching Random Access Memories (ReRAM) and Phase Change Memories (PCM) are thought capable of all these operations and functionalities. In addition, researchers aim to use these memristive systems to enable the fundamental properties of life, including order, plasticity, response to stimuli, metabolism, homeostasis, growth, and heredity or reproduction, based on the functionalities of biological systems. This volume, which brings together experts from industry and academia, will cover the fundamentals as well as specific demands and limitations in e.g. materials selection, processing, suitable model systems, technical requirements and the potential device applications, providing a bridge for terminologies, theories, models, and applications. The topics covered in this volume include: Electrochemical metallization ReRAMs (ECM) Valence change ReRAMs (VCM) Phase-change memories (PCM) Synaptic and neuromorphic functionsTable of ContentsElectrochemical metallization ReRAMs (ECM); Valence change ReRAMs (VCM); Phase-change memories (PCM); Synaptic and neuromorphic functions

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Book SynopsisThis book provides a challenging and stimulating introduction to the contemporary topics of complexity and criticality, and explores their common basis of scale invariance, a central unifying theme of the book.Criticality refers to the behaviour of extended systems at a phase transition where scale invariance prevails. The many constituent microscopic parts bring about macroscopic phenomena that cannot be understood by considering a single part alone. The phenomenology of phase transitions is introduced by considering percolation, a simple model with a purely geometrical phase transition, thus enabling the reader to become intuitively familiar with concepts such as scale invariance and renormalisation. The Ising model is then introduced, which captures a thermodynamic phase transition from a disordered to an ordered system as the temperature is lowered in zero external field. By emphasising analogies between percolation and the Ising model, the reader's intuition of phase transitions is developed so that the underlying theoretical formalism may be appreciated fully. These equilibrium systems undergo a phase transition only if an external agent finely tunes certain external parameters to particular values.Besides fractals and phase transitions, there are many examples in Nature of the emergence of such complex behaviour in slowly driven non-equilibrium systems: earthquakes in seismic systems, avalanches in granular media and rainfall in the atmosphere. A class of non-equilibrium systems, not constrained by having to tune external parameters to obtain critical behaviour, is addressed in the framework of simple models, revealing that the repeated application of simple rules may spontaneously give rise to emergent complex behaviour not encoded in the rules themselves. The common basis of complexity and criticality is identified and applied to a range of non-equilibrium systems. Finally, the reader is invited to speculate whether self-organisation in non-equilibrium systems might be a unifying concept for disparate fields such as statistical mechanics, geophysics and atmospheric physics.Visit for animations for the models in the book (available for Windows and Linux), solutions to exercises, as well as a list with corrections.Trade Review"Personally, I enjoyed reading this book very much. The arguments are clear and draw attention to a number of useful insights ... Students will find the presentation on self-organized criticality fun to read, particularly because it deals with real phenomena, such as earthquakes, rice-pile avalanches and rainfall ... I strongly agree with these authors that undergraduates need to be exposed to issues related to complexity and criticality. Their textbook is the first that I have seen that makes developing such courses feasible."Mathematical ReviewsTable of ContentsPercolation: Percolating Phase Transition; In One and Two Dimensions, and in the Bethe Lattice; Geometric Properties of Clusters; Scaling Ansatz, Scaling Functions and Scaling Relations; Universality; Real-Space Renormalisation Group; Ising Model: Review of Thermodynamics and Statistical Mechanics; Symmetry Breaking; Ferromagnetic Phase Transition; In One and Two Dimensions, and in the Mean-Field; Landau Theory of Continuous Phase Transitions; Scaling Ansatz, Scaling Functions and Scaling Relations; Universality; Real-Space Renormalisation Group; Self-Organised Criticality: BTW Model in One and Two Dimensions, and in the Mean-Field; A Rice Pile Experiment and the Oslo Model; Earthquakes and the OFC Model; Rainfall; Self-Organised Criticality as a Unifying Principle.

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Book SynopsisNonlinear Structures & Systems, Volume 1: Proceedings of the 37th IMAC, A Conference and Exposition on Structural Dynamics, 2019, the first volume of eight from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Nonlinear Dynamics, including papers on: Nonlinear Reduced-order Modeling Jointed Structures: Identification, Mechanics, Dynamics Experimental Nonlinear Dynamics Nonlinear Model & Modal Interactions Nonlinear Damping Nonlinear Modeling & Simulation Nonlinearity & System Identification

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Book SynopsisThis brief presents a suite of computationally efficient methods for bounding trajectories of dynamical systems with multi-dimensional intervals, or ‘boxes’. It explains the importance of bounding trajectories for evaluating the robustness of systems in the face of parametric uncertainty, and for verification or control synthesis problems with respect to safety and reachability properties. The methods presented make use of: interval analysis; monotonicity theory; contraction theory; and data-driven techniques that sample trajectories. The methods are implemented in an accompanying open-source Toolbox for Interval Reachability Analysis. This brief provides a tutorial description of each method, focusing on the requirements and trade-offs relevant to the user, requiring only basic background on dynamical systems. The second part of the brief describes applications of interval reachability analysis. This makes the brief of interest to a wide range of academic researchers, graduate students, and practising engineers in the field of control and verification. Trade Review“The motivation of this book is to provide to the readers tutorial presentations of several approaches for interval reachability analysis, without requiring any previous knowledge and experience of reachability analysis. Two parts, Part I and Part II, are used for this purpose. Part I describes six main methods for interval reachability analysis and in Part II several applications are presented.” (Takashi Amemiya, Mathematical Reviews, October, 2022)Table of ContentsChapter 1. Introduction.- Part 1: Reachability Methods.- Chapter 2. Interval Analysis.- Chapter 3. Monotonicity.- Chapter 4. Mixed-Monotonicity.- Chapter 5. Sampled-Data Mixed-Monotonicity.- Chapter 6. Growth Bounds.- Chapter 7. Sampling-Based Methods.- Part 2: Applications.- Chapter 8. Safety and Reachability Verification.- Chapter 9. Interval Volume as a Robustness Measure.- Chapter 10. Abstraction-Based Control Synthesis.

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Book SynopsisThe book is designed to serve as a textbook for courses offered to upper-undergraduate students enrolled in physics. The first edition of this book was published in 2014. As there is a demand for the next edition, it is quite natural to take note of the several advances that have occurred in the subject over the past five years and to decide which of these are appropriate for inclusion at the textbook level, given the fundamental nature and the significance of the subject area. This is the prime motivation for bringing out a revised second edition. Among the newer mechanisms and materials, the book introduces the super-continuum generation, which arises from an excellent interplay of the various mechanisms of optical nonlinearity. The topics covered in this book are quantum mechanics of nonlinear interaction of matter and radiation, formalism and phenomenology of nonlinear wave mixing processes, optical phase conjugation and applications, self-focusing and self-phase modulation and their role in pulse modification, nonlinear absorption mechanisms, and optical limiting applications, photonic switching and bi-stability, and physical mechanisms leading to a nonlinear response in a variety of materials. This book has emerged from an attempt to address the requirement of presenting the subject at the college level. This textbook includes rigorous features such as the elucidation of relevant basic principles of physics; a clear exposition of the ideas involved at an appropriate level; coverage of the physical mechanisms of non-linearity; updates on physical mechanisms and emerging photonic materials and emphasis on the experimental study of nonlinear interactions. The detailed coverage and pedagogical tools make this an ideal textbook for students and researchers enrolled in physics and related courses.Table of Contents1 From Optics to Photonics 1.1 The Charm and Challenge of Modern Optics 1.2 The Nature of Optical Non-linearity 1.3 Overcoming the Materials Bottleneck 1.4 The Expanding Frontiers 1.5 Problems and Prospects 1.6 Explorations 2 A Phenomenological View of Nonlinear Optics 2.1 Optics in the Nonlinear World 2.1.1 Introduction 2.1.2 First Order Susceptibility 2.1.3 Second Order Susceptibility 2.1.4 Third Order Susceptibility 2.2 Time Domain Response 2.2.1 First Order Polarization- Time Domain Response 2.2.2 Second Order Polarization - Time Domain Response 2.3 Frequency Domain Response 2.3.1 First Order Susceptibility 2.3.2 Second Order Susceptibility 2.3.3 General Order (n) Susceptibility 2.4 The nth order polarization 2.5 Monochromatic Waves 2.6 Calculation of the Factor K 2.6.1 Optical Rectification 2.6.2 Second Harmonic Generation 2.6.3 Pockels Effect 2.6.4 Frequency Mixing : Sum and Difference Frequency generation 2.6.5 Third Harmonic Generation 2.6.6 Nondegenerate Four Wave Mixing 2.7 Explorations 3. Symmetry and Susceptibility 3.1 Introduction 3.2 Crystal Symmetry and Susceptibility Tensors 3.2.1 Neumann Principle 3.2.2 Symmetry of Second Order Susceptibility 3.2.3 Second Harmonic Generation 3.2.4 Kleinmann Symmetry 3.2.5 Symmetry of Third Order Susceptibility 3.3 The Dielectric Permittivity Tensor 3.4 The Refractive Index Ellipsoid 3.5 Explorations 4 Calculation of Non-linear Susceptibilities 4.1 Introduction 4.1.1 Physical Quantities in Quantum Physics 4.1.2 The Projection Operator 4.2 The Equation of Motion 4.3 Ensembles of Particles 4.4 Time-dependent Perturbation 4.5 Dipolar Interaction 4.6 First Order Density Matrix 4.7 Second Order Density Matrix 4.8 Third order Density Matrix 4.9 Double Integrals in the Expressions for the Density Matrix 4.10 Second Harmonic Susceptibility 4.11 Relaxation Effects 4.12 Applications to Color Centers 4.12.1 Third Order Susceptibility 4.12.3 Second Order Susceptibility 4.13. Explorations 5 Nonlinear Wave Mixing Processes 5.1 Introduction 5.2 Elements of Electromagnetism 5.3 Travelling Electromagnetic Waves in Free Space 5.3.1 Energy Density in the Travelling Wave 5.4 Propagation of Electromagnetic Waves in Linear Materials 5.5 Propagation of Electromagnetic Waves in Nonlinear Materials 5.5.1 The Wave Equation 5.5.2 Energy Transfer Rate 5.6 Three Wave Mixing 5.6.1 An Approximation 5.7 Second Harmonic Generation 5.7.1 Phase Matching Schemes 5.7.2 Accurate Treatment of Second Harmonic Generation 5.8 Explorations 6 Optical Phase Conjugation and Bi-stability 6.1 Optical Phase Conjugation 6.1.1 Phase Conjugation as Time reversal 6.1.2 Phase Conjugation through Four-wave-mixing 6.1.3 Practical Realization 6.1.4 The Peculiar Properties of the Phase Conjugate Beam 6.1.5 The Grating Picture 6.1.6 Applications of Phase Conjugation 6.2 Optical Bi-stability and Photonic Switching 6.2.1 Refractive Index at High Intensities : An Overview 6.2.2. Fabry-Perot Etalon 6.2.2 Photonic Switching in a Nonlinear Fabry-Perot Etalon 6.3 Explorations 7 Self Focusing, Phase Modulation and Pulse Shaping 7.1 Self Focusing of Light 7.1.1 The Concept of Self Focusing 7.1.2 Self Trapping and Spatial Solitons 7.1.3 The z-Scan Experiment 7.1.4 Analysis of the z-scan trace 7.1.5 Measurement of Nonlinear Optical Absorption 7.1.6 Mechanisms of Nonlinear Absorption 7.2 Self Phase Modulation 7.3 Pulse Shaping and Optical Soliton Propagation 7.3.1 Solitary Waves and Optical Solitons 7.4 Explorations 8 Materials and Mechanisms 8.1 Introduction 8.2 Mechanisms of Non-linearity 8.2.1 Anharmonicity of Potential 8.2.2 Thermal Mechanism 8.2.3 Orientational Mechanism 8.2.4 Inelastic Photon Scattering 8.2.5 Photorefractivity 8.2.6 Saturable Absorption 8.2.7 Band Gap Distortion (Franz-Keldysh Effect) 8.2.8 Band filling Mechanism 8.2.9 Non-parabolicity of Bands 8.2.10 Delocalization of Electrons 8.3 A Perspective on Newer Materials and Mechanisms 8.3.1 Low Dimensional Materials 8.3.2 Photonic Bandgap Materials 8.3.3 Slowing of light and the effect on non-linearity 8.3.4 Super-continuum Generation 8.4 Explorations 9. Basics of Multi-photon Microscopy 9.1 Introduction 9.2. Techniques for Bio-imaging with High resolution 9.2.1 Fluorescence Microscopy 9.2.2 Confocal Scanning Microscopy 9.3. Multi-photon Microscopy with IR Laser Sources 9.3.1 Principles and Experimental Techniques 9.3.2 Fluorescent Labels in Microscopy 9.4 Use of Multiphoton Absorption in Quantum Dots 9.5 Outlook 9.6 Explorations

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