Nonlinear science Books
Cambridge University Press A Students Guide to the NavierStokes Equations
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£52.20
Cambridge University Press Physics of Wave Turbulence
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£59.99
Cambridge University Press Quantum Turbulence
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£89.99
Cambridge University Press An Introduction to Continuum Mechanics
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.
£72.99
Cambridge University Press Cavitation and Bubble Dynamics
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.
£52.20
Springer Nature Switzerland AG Interval Reachability Analysis: Bounding Trajectories of Uncertain Systems with Boxes for Control and Verification
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.
£999.99
Springer Nature Switzerland AG Linear and Nonlinear Programming
Book SynopsisThe 5th edition of this classic textbook covers the central concepts of practical optimization techniques, with an emphasis on methods that are both state-of-the-art and popular. One major insight is the connection between the purely analytical character of an optimization problem and the behavior of algorithms used to solve that problem. End-of-chapter exercises are provided for all chapters. The material is organized into three separate parts. Part I offers a self-contained introduction to linear programming. The presentation in this part is fairly conventional, covering the main elements of the underlying theory of linear programming, many of the most effective numerical algorithms, and many of its important special applications. Part II, which is independent of Part I, covers the theory of unconstrained optimization, including both derivations of the appropriate optimality conditions and an introduction to basic algorithms. This part of the book explores the general properties of algorithms and defines various notions of convergence. In turn, Part III extends the concepts developed in the second part to constrained optimization problems. Except for a few isolated sections, this part is also independent of Part I. As such, Parts II and III can easily be used without reading Part I and, in fact, the book has been used in this way at many universities. New to this edition are popular topics in data science and machine learning, such as the Markov Decision Process, Farkas’ lemma, convergence speed analysis, duality theories and applications, various first-order methods, stochastic gradient method, mirror-descent method, Frank-Wolf method, ALM/ADMM method, interior trust-region method for non-convex optimization, distributionally robust optimization, online linear programming, semidefinite programming for sensor-network localization, and infeasibility detection for nonlinear optimization.Table of Contents
£132.28
Springer Nature Switzerland AG Linear and Nonlinear Programming
Book SynopsisThe 5th edition of this classic textbook covers the central concepts of practical optimization techniques, with an emphasis on methods that are both state-of-the-art and popular. One major insight is the connection between the purely analytical character of an optimization problem and the behavior of algorithms used to solve that problem. End-of-chapter exercises are provided for all chapters. The material is organized into three separate parts. Part I offers a self-contained introduction to linear programming. The presentation in this part is fairly conventional, covering the main elements of the underlying theory of linear programming, many of the most effective numerical algorithms, and many of its important special applications. Part II, which is independent of Part I, covers the theory of unconstrained optimization, including both derivations of the appropriate optimality conditions and an introduction to basic algorithms. This part of the book explores the general properties of algorithms and defines various notions of convergence. In turn, Part III extends the concepts developed in the second part to constrained optimization problems. Except for a few isolated sections, this part is also independent of Part I. As such, Parts II and III can easily be used without reading Part I and, in fact, the book has been used in this way at many universities. New to this edition are popular topics in data science and machine learning, such as the Markov Decision Process, Farkas’ lemma, convergence speed analysis, duality theories and applications, various first-order methods, stochastic gradient method, mirror-descent method, Frank-Wolf method, ALM/ADMM method, interior trust-region method for non-convex optimization, distributionally robust optimization, online linear programming, semidefinite programming for sensor-network localization, and infeasibility detection for nonlinear optimization.Table of Contents
£89.99
£127.78
De Gruyter Mathematics of Deep Learning: An Introduction
Book SynopsisThe goal of this book is to provide a mathematical perspective on some key elements of the so-called deep neural networks (DNNs). Much of the interest in deep learning has focused on the implementation of DNN-based algorithms. Our hope is that this compact textbook will offer a complementary point of view that emphasizes the underlying mathematical ideas. We believe that a more foundational perspective will help to answer important questions that have only received empirical answers so far. The material is based on a one-semester course Introduction to Mathematics of Deep Learning" for senior undergraduate mathematics majors and first year graduate students in mathematics. Our goal is to introduce basic concepts from deep learning in a rigorous mathematical fashion, e.g introduce mathematical definitions of deep neural networks (DNNs), loss functions, the backpropagation algorithm, etc. We attempt to identify for each concept the simplest setting that minimizes technicalities but still contains the key mathematics.
£45.60
De Gruyter Maximal Subellipticity
Book SynopsisMaximally subelliptic partial differential equations (PDEs) are a far-reaching generalization of elliptic PDEs. Elliptic PDEs hold a special place: sharp results are known for general linear and even fully nonlinear elliptic PDEs. Over the past half-century, important results for elliptic PDEs have been generalized to maximally subelliptic PDEs. This text presents this theory and generalizes the sharp, interior regularity theory for general linear and fully nonlinear elliptic PDEs to the maximally subelliptic setting.
£138.22
World Scientific Publishing Co Pte Ltd Thermomechanics Of Nonlinear Irreversible
Book SynopsisIn this invaluable book, macroscopic irreversible thermodynamics is presented in its realm and its splendor by appealing to the notion of internal variables of state. This applies to both fluids and solids with or without microstructures of mechanical or electromagnetic origin. This unmatched richness of essentially nonlinear behaviors is the result of the use of modern mathematical techniques such as convex analysis in a clear-cut framework which allows one to put under the umbrella of “irreversible thermodynamics” behaviors which until now have been commonly considered either not easily covered, or even impossible to incorporate into such a framework.The book is intended for all students and researchers whose main concern is the rational modeling of complex and/or new materials with physical and engineering applications, such as those accounting for coupled-field, hysteresis, fracture, nonlinear-diffusion, and phase-transformation phenomena.Table of ContentsIntroduction - a post-Duhemian thermodynamics; thermostatics and thermodynamics; various thermodynamics; thermodynamics with internal variables; applications - general framework; viscosity in complex fluids; viscoplasticity and plasticity; thermodynamics of fracture; non-equilibrium thermodynamics of electromagnetic materials; waves and reaction-diffusion systems (RDS).
£85.50
World Scientific Publishing Co Pte Ltd Bioevaluation Of World Transport Networks
Book SynopsisSlime mould Physarum polycephalum is a monstrous single cell well known for its task-solving abilities — solves computational geometry and logical problems, navigates robots and generates music.The slime mould could also build motorways, highways and expressways. It is used to analyse transport networks of Africa, Australia, Belgium, Brazil, Canada, China, Germany, Iberia, Italy, Malaysia, Mexico, The Netherlands, UK and USA. The largest cities are represented by oat flakes and the slime mould is inoculated in a capital. When all oat flakes are covered by the slime mould, the structure of the protoplasmic networks formed are analyzed. In the laboratory experiments and theoretical analyses, intriguing country-specific properties of the motorway networks are uncovered and compared with the man-made and slime mould networks. They are studied as proximity graphs, leading to hierarchies of complexity and bio-rationality of the motorways.The book will inspire novel and original thoughts, paradigms and approaches for re-evaluation of historical findings on the emergence of ancient roads and will help to design future transcontinental pathways. The book is self-contained and does not require any special training or knowledge. This lavishly illustrated text will be appreciated by readers from all walks of life.Table of ContentsIntroduction (Andrew Adamatzky); Methods: How We Made Experiments and Analysed Their Results (Andrew Adamatzky); Trans-African Highways (Andrew Adamatzky and Anne Kayem); Tracing Historical Development of Australian Highways (Andrew Adamatzky and Mikhail Prokopenko); Belgian Transport Networks: Redundancy and Dissolution (Andrew Adamatzky, Bernard De Baets and Wesley Van Dessel); Brazilian Highways from Slime Mould's Point of View (Andrew Adamatzky and Pedro P B De Oliveira); Trans-Canada Slimeways: From Coast to Coast to Coast (Andrew Adamatzky and Selim G Akl); Slime Mould Imitates Highways in China (Andrew Adamatzky, Xin-She Yang and Yu-Xin Zhao); Schlauschleimer auf Autobahnen: The Case of Germany (Andrew Adamatzky and Theresa Schubert); Vie Physarale: Roman Roads With Slime Mould (Emanuele Strano, Andrew Adamatzky and Jeff Jones); Malaysian Expressways: Is There a Logic Behind? (Andrew Adamatzky, Zuwairie Ibrahim, Amar Faiz Zainal Abidin and Badaruddin Muhammad); Physarum Narcotraficum: Mexican Highways and Slime Mould (Andrew Adamatzky, Genaro J Martinez, Sergio V Chapa-Vergara, Rene Asomoza-Palacio and Christopher R Stephens); Physarum in the Netherlands: Responding to the Flood (Andrew Adamatzky, Michael Lees and Peter M A Sloot); Rebuilding Iberian Motorways with Slime Mould (Andrew Adamatzky and Ramon Alonso-Sanz); United Kingdom Road Planning with Slime Mould (Andrew Adamatzky and Jeff Jones); Slimy Interstates in the USA (Andrew Adamatzky and Andrew Ilachinski); The World's Colonisation and Trade Routes Formation (Andrew Adamatzky); Bio-Rationality of Motorways (Andrew Adamatzky, Selim Akl, Ramon Alonso-Sanz, Wesley van Dessel, Zuwairie Ibrahim, Andrew Ilachinski, Jeff Jones, Anne V D M Kayem, Genaro J Martinez, Pedro de Oliveira, Mikhail Prokopenko, Theresa Schubert, Peter Sloot, Emanuele Strano and Xin-She Yang).
£109.25
World Scientific Publishing Co Pte Ltd Nonlinear Workbook, The: Chaos, Fractals,
Book SynopsisThe Nonlinear Workbook provides a comprehensive treatment of all the techniques in nonlinear dynamics together with C++, Java and SymbolicC++ implementations. The book not only covers the theoretical aspects of the topics but also provides the practical tools. To understand the material, more than 100 worked out examples and 160 ready to run programs are included. Each chapter provides a collection of interesting problems. New topics added to the 6th edition are Swarm Intelligence, Quantum Cellular Automata, Hidden Markov Model and DNA, Birkhoff's ergodic theorem and chaotic maps, Banach fixed point theorem and applications, tau-wavelets of Haar, Boolean derivatives and applications, and Cartan forms and Lagrangian.Table of ContentsNonlinear and Chaotic Maps; Time Series Analysis; Autonomous Systems in the Plane; Nonlinear Hamilton Systems; Nonlinear Dissipative Systems; Nonlinear Driven Systems; Controlling of Chaos; Synchronization of Chaos; Fractals; Cellular Automata; Solving Differential Equations; Optimization; Neural Networks; Genetic Algorithms; Gene Expression Programming; Wavelets; Discrete Hidden Markov Processes; Fuzzy Sets and Fuzzy Logic; Swarm Intelligence; Quantum Cellular Automata; Hidden Markov Model and DNA; Birkhoff's Ergodic Theorem and Chaotic Maps; Banach Fixed Point Theorem and Applications; Tau-Wavelets of Haar; Boolean Derivatives and Applications; Cartan Forms and Lagrangian.
£86.45
Society for Industrial and Applied Mathematics Numerical Methods for Unconstrained Optimization
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.
£56.77
MP-AMM American Mathematical Topics in Nonlinear Functional Analysis
Book SynopsisIntroduces the notion of topological degree and develops its basic properties. This book uses these properties in the discussion of bifurcation theory (the possible branching of solutions as parameters vary), including the proof of Rabinowitz's global bifurcation theorem. It is suitable as a graduate level textbook and a supplementary course text.Trade Reviewextremely stimulating Zentralblatt fur MathematikTable of ContentsTopological approach: Finite dimensions Topological degree in Banach space Bifurcation theory Further topological methods Monotone operators and the min-max theorem Generalized implicit function theorems Bibliography.
£25.60
SIAM - Society for Industrial and Applied Mathematics Nonlinear Time Scale Systems in Standard and Nonstandard Forms
£90.10
Society for Industrial & Applied Mathematics,U.S. Advanced and Optimization Based Sliding Mode Control: Theory and Applications
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.
£78.20
Akademica Publishing Engineering Approach to Finite Element Analysis
Book Synopsis
£66.30
MP-AMM American Mathematical Geometric Nonlinear Functional Analysis Volume 1
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.
£77.90
MP-AMM American Mathematical Dynamics of Infinitedimensional Groups
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.
£55.80
Society for Industrial and Applied Mathematics Methods for Solving Systems of Nonlinear Equations CBMSNSF Regional Conference Series in Applied Mathematics Series Number 70
Book SynopsisThis second edition provides much-needed updates to the original volume. Like the first edition, it emphasizes the ideas behind the algorithms as well as their theoretical foundations and properties, rather than focusing strictly on computational details; at the same time, this new version is now largely self-contained and includes essential proofs. Additions have been made to almost every chapter, including an introduction to the theory of inexact Newton methods, a basic theory of continuation methods in the setting of differentiable manifolds, and an expanded discussion of minimization methods. New information on parametrized equations and continuation incorporates research since the first edition.
£58.05
Society for Industrial and Applied Mathematics Linear and Nonlinear Optimization
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.
£97.20
Nova Science Publishers Inc Nonlinearity: Problems, Solutions & Applications
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.
£195.19
SIAM - Society for Industrial and Applied Mathematics Linear and Nonlinear Inverse Problems with
Book SynopsisExplains how to identify ill-posed inverse problems arising in practice and how to design computational solution methods for them; explains computational approaches in a hands-on fashion, with related codes available on a website; and serves as a convenient entry point to practical inversion.
£65.00
Society for Industrial & Applied Mathematics,U.S. Inverse Scattering Theory and Transmission
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.
£64.60
Springer Nature Switzerland AG Physics of Nonlinear Optics
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
£47.49
Springer Nature Switzerland AG Nonlinear Dynamics: A Concise Introduction
Book SynopsisThis concise and up-to-date textbook provides an accessible introduction to the core concepts of nonlinear dynamics as well as its existing and potential applications. The book is aimed at students and researchers in all the diverse fields in which nonlinear phenomena are important. Since most tasks in nonlinear dynamics cannot be treated analytically, skills in using numerical simulations are crucial for analyzing these phenomena. The text therefore addresses in detail appropriate computational methods as well as identifying the pitfalls of numerical simulations. It includes numerous executable code snippets referring to open source Julia software packages. Each chapter includes a selection of exercises with which students can test and deepen their skills.Table of ContentsPart I Introduction.- Dynamical Systems.- Non-Chaotic Continuous Dynamics.- Part II Methods.- Defining and Measuring Chaos.- Bifurcations and Routes to Chaos.- Entropy and Dimension.- Delay Coordinates.- Information Across Timeseries.- Part III Applications.- Billiards, Conservative Systems and Ergodicity.- Forced Oscillators and Synchronisation.- Networds, Agent-Based Models and Epidemics.- Extended Systems and Spatiotemporal Chaos.- Nonlinear Dynamics of Climate & Climate Change.
£31.86
Mathematical Society of Japan Asymptotic Analysis And Singularities: Elliptic
Book SynopsisThis volume is the proceedings of the 14th MSJ International Research Institute “Asymptotic Analysis and Singularity”, which was held at Sendai, Japan in July 2005. The proceedings contain survey papers and original research papers on nonlinear partial differential equations, dynamical systems, calculus of variations and mathematical physics.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North AmericaTable of ContentsWeak KAM pairs and Monge-Kantorovich duality by P. Bernard and B. Buffoni Hydrodynamic limit and nonlinear PDEs with singularities by T. Funaki PDE and differential geometry in study of motion of elastic wires by N. Koiso Evolution of stable phases in forward-backward parabolic equations by C. Mascia, A. Terracina, and A. Tesei Analogies between superconductors and liquid crystals: Nucleation and critical fields by X.-B. Pan Method of the blowup envelope and applications by T. Suzuki Numerical study and examples on singularities of solutions to anisotropic crystalline curvature flows of nonconvex polygonal curves by C. Hirota, T. Ishiwata, and S. Yazaki On certain one-dimensional elliptic systems under different growth conditions at respective infinities by M. Iida, K. Nakashima, and E. Yanagida Stability analysis for a stripe solution in the Gierer-Meinhardt system by K. Ikeda Perturbation of structures of radial solutions to elliptic equations by Y. Kabeya On the bifurcation structure of positive stationary solutions for a competition-diffusion system by Y. Kan-on Global solutions to a one-dimensional nonlinear parabolic system modeling colonial formation by chemotactic bacteria by K. P. P. Htoo, M. Mimura, and I. Takagi Existence of standing waves for the nonlinear Schrodinger equation with double power nonlinearity and harmonic potential by H. Kikuchi The Hamiltonian formalism in reaction-diffusion systems by M. Kuwamura Speed estimate for a periodic rotating wave in an undulating zone on the sphere by B. Lou On the dynamical system of a parabolic equation with non-local term by T. Miyasita A variational approach to self-similar solutions for semilinear heat equations by Y. Naito Determination of the limit sets of trajectories of the Gierer-Meinhardt system without diffusion by W.-M. Ni, K. Suzuki, and I. Takagi Asymptotic form of solutions of the Tadjbakhsh-Odeh variational problem by S. Okabe Global existence of a reaction-diffusion-advection system by K. Osaki Blowup solutions to some systems related to biology by T. Senba On the role of the source terms in an activator-inhibitor system proposed by Gierer and Meinhardt by K. Suzuki and I. Takagi Concentration phenomena in the conformal Brezis-Nirenberg problem by F. Takahashi Interfacial analysis to a chemotaxis model equation with growth in three dimension by T. Tsujikawa.
£48.45
World Scientific Publishing Co Pte Ltd Topics In Bifurcation Theory And Applications
Book SynopsisThis textbook presents the most efficient analytical techniques in the local bifurcation theory of vector fields. It is centered on the theory of normal forms and its applications, including interaction with symmetries.The first part of the book reviews the center manifold reduction and introduces normal forms (with complete proofs). Basic bifurcations are studied together with bifurcations in the presence of symmetries. Special attention is given to examples with reversible vector fields, including the physical example given by the water waves. In this second edition, many problems with detailed solutions are added at the end of the first part (some systems being in infinite dimensions). The second part deals with the Couette-Taylor hydrodynamical stability problem, between concentric rotating cylinders. The spatial structure of various steady or unsteady solutions results directly from the analysis of the reduced system on a center manifold. In this part we also study bifurcations (simple here) from group orbits of solutions in an elementary way (avoiding heavy algebra). The third part analyzes bifurcations from time periodic solutions of autonomous vector fields. A normal form theory is developed, covering all cases, and emphasizing a partial Floquet reduction theory, which is applicable in infinite dimensions. Studies of period doubling as well as Arnold's resonance tongues are included in this part.Table of ContentsCentre manifolds normal forms, and bifurcations of vector; fields near critical points - unperturbed vector fields; perturbed vector fields; Couette-Taylor problem - formulation of the problem; Couette flow; bifurcations from Couette flow; bifurcations from Taylor vortex flow; centre manifolds, normal forms, and bifurcations of vector; fields near closed orbits - preliminaries; adaptation of Floquet thoery; unperturbed case; perturbed case.
£40.85
World Scientific Publishing Co Pte Ltd Dynamics Of Pattern, The
Book SynopsisSpirals, vortices, crystalline lattices, and other attractive patterns are prevalent in Nature. How do such beautiful patterns appear from the initial chaos? What universal dynamical rules are responsible for their formation? What is the dynamical origin of spatial disorder in nonequilibrium media? Based on the many visual experiments in physics, hydrodynamics, chemistry, and biology, this invaluable book answers those and related intriguing questions. The mathematical models presented for the dynamical theory of pattern formation are nonlinear partial differential equations. The corresponding theory is not so accessible to a wide audience. Consequently, the authors have made every attempt to synthesize long and complex mathematical calculations to exhibit the underlying physics. The book will be useful for final year undergraduates, but is primarily aimed at graduate students, postdoctoral fellows, and others interested in the puzzling phenomena of pattern formation.Table of ContentsPatterns - prelude to a dynamical description; linear stage of pattern formation; model equations; the Ginzburg-Landau equation; "crystal" formation; quasicrystals; breaking of order; localized patterns; spirals; patterns in oscillating soap films; patterns in colonies of micro-organisms; spatial disorder; patterns in chaotic media; epilogue - living matter and dynamic forms; a short guide to nonlinear dynamics; key experiments in pattern formation.
£114.00
World Scientific Publishing Co Pte Ltd Nonlinear Waves And Offshore Structures
Book SynopsisThe responses of offshore structures are significantly affected by steep nonlinear waves, currents and wind, leading to phenomena such as springing and ringing of TLPs, slow drift yaw motion of FPSOs and large oscillations of Spar platforms due to vortex shedding. Research has brought about significant progress in this field over the past few decades and introduced us to increasingly involved concepts and their diverse applicability. Thus, an in-depth understanding of steep nonlinear waves and their effects on the responses of offshore structures is essential for safe and effective designs.This book deals with analyses of nonlinear problems encountered in the design of offshore structures, as well as those that are of immediate practical interest to ocean engineers and designers. It presents conclusions drawn from recent research pertinent to nonlinear waves and their effects on the responses of offshore structures. Theories, observations and analyses of laboratory and field experiments are expounded such that the nonlinear effects can be clearly visualized.Table of ContentsGaussian Processes and Wave Spectra; Propagation of Steady and Transient Large Linear Wave Groups; Nonlinear Wave Interaction; Laboratory Nonlinear Waves; Nonlinear Wave-Body Interaction; Volterra Input-Output Model; Universal Linear System Model for Nonlinear Loading, including Wave Impact; Numerical Wave Tank; Coupled Analysis of Nonlinear Responses of TLPs, FPSOs and Spar-Platform Systems; Fatigue Due to Non-Gaussian Forces.
£63.65
World Scientific Publishing Co Pte Ltd Towards A Nonlinear Quantum Physics
Book SynopsisThe author of this book presents conceptual and experimental evidence showing that Heisenberg's uncertainty relations are not valid in all cases. Furthermore, he derives a more general set of uncertainty relations. The new relations result from the replacement of the Fourier nonlocal and nontemporal paradigm by wavelet local analysis. These results lead to a coherent and beautiful causal synthesis unifying quantum and classical physics.Table of ContentsComplementarity Principle and the Nonlocal Fourier Analysis; New Generation of Microscopes; Beyond Heisenberg's Uncertainty Relations; The Meaning of the Wave Function; Interference Without Superposition of the Wave Packets.
£65.55
World Scientific Publishing Co Pte Ltd Analysis And Control Of Complex Nonlinear
Book SynopsisNonlinear dynamics of complex processes is an active research field with large numbers of publications in basic research, and broad applications from diverse fields of science. Nonlinear dynamics as manifested by deterministic and stochastic evolution models of complex behavior has entered statistical physics, physical chemistry, biophysics, geophysics, astrophysics, theoretical ecology, semiconductor physics and -optics, etc. This field of research has induced a new terminology in science connected with new questions, problems, solutions and methods. New scenarios have emerged for spatio-temporal structures in dynamical systems far from equilibrium. Their analysis and possible control are intriguing and challenging aspects of the current research.The duality of fundamental and applied research is a focal point of its main attractivity and fascination. Basic topics and foundations are always linked to concrete and precise examples. Models and measurements of complex nonlinear processes evoke and provoke new fundamental questions that diversify and broaden the mathematical concepts and tools. In return, new mathematical approaches to modeling and analysis enlarge the scope and efficiency of applied research.Table of ContentsNoise-Induced Effects in Excitable Systems with Local and Global Coupling (X R Sailer et al.); Spiral Wave Dynamics: Reaction and Diffusion versus Kinematics (B Fiedler et al.); Pattern Formation in Semiconductors Under the Influence of Time-Delayed Feedback Control and Noise (E Scholl et al.); Trapping of Phase Fronts and Twisted Spirals in Periodically Forced Oscillatory Media (O Rudzick & A S Mikhailov); Unified Approach to Feedback-Mediated Control of Spiral Waves in Excitable Media (V S Zykov & H Engel); Building Oscillations Bottom Up: Elemental Time Scales of intracellular Calcium Dynamics (R Thul & M Falcke); Synchronization of Complex Systems: Analysis and Control (M Rosenblum & A Pikovsky); Predator-Prey Oscillations, Synchronization and Pattern Formation in Ecological Systems (B Blasius & R Tonjes); and other papers.
£154.85
World Scientific Publishing Co Pte Ltd Nonlinear Dynamics Of Piecewise Constant Systems
Book SynopsisPiecewise constant systems exist in widely expanded areas such as engineering, physics, and mathematics. Extraordinary and complex characteristics of piecewise constant systems have been reported in recent years. This book provides the methodologies for analyzing and assessing nonlinear piecewise constant systems on a theoretically and practically sound basis. Recently developed approaches for theoretically analyzing and numerically solving the nonlinear piecewise constant dynamic systems are reviewed. A new greatest integer argument with a piecewise constant function is utilized for nonlinear dynamic analyses and for establishing a novel criterion in diagnosing irregular and chaotic solutions from the regular solutions of a nonlinear dynamic system. The newly established piecewise constantization methodology and its implementation in analytically solving for nonlinear dynamic problems are also presented.Table of ContentsFundamentals of Conventional and Piecewise Constant Systems; Preliminary Theorems and Techniques for Analysis of Nonlinear Piecewise Constant Systems; Piecewise Constant Dynamical Systems and Their Behavior; Analytical and Semi-Analytical Solution Development with Piecewise Constant Arguments; Numerical and Improved Semi-Analytical Approaches Implementing Piecewise Constant Arguments; Application of P-T Method on Multi-Degree-of-Freedom Nonlinear Dynamic Systems; Periodicity-Ratio and Its Application in Diagnosing Irregularities of Nonlinear Systems.
£116.85
World Scientific Publishing Co Pte Ltd Nonlinear Workbook, The: Chaos, Fractals,
Book SynopsisNew Edition: The Nonlinear Workbook (6th Edition)The study of nonlinear dynamical systems has advanced tremendously in the last 20 years, making a big impact on science and technology. This book provides all the techniques and methods used in nonlinear dynamics. The concepts and underlying mathematics are discussed in detail.The numerical and symbolic methods are implemented in C++, SymbolicC++ and Java. Object-oriented techniques are also applied. The book contains more than 150 ready-to-run programs.The text has also been designed for a one-year course at both the junior and senior levels in nonlinear dynamics. The topics discussed in the book are part of e-learning and distance learning courses conducted by the International School for Scientific Computing, University of Johannesburg.Table of ContentsNonlinear and Chaotic Maps; Time Series Analysis; Autonomous Systems in the Plane; Nonlinear Hamilton Systems; Nonlinear Dissipative Systems; Nonlinear Driven Systems; Controlling of Chaos; Synchronization of Chaos; Fractals; Cellular Automata; Solving Differential Equations; Neural Networks; Genetic Algorithms; Gene Expression Programming; Optimization; Discrete Wavelets; Discrete Hidden Markov Processes; Fuzzy Sets and Fuzzy Logic.
£64.60
Elsevier Science Adaptive Learning Methods for Nonlinear System
Book SynopsisTrade Review"This book is a joint work of an excellent international team of scientists working in the field of nonlinear signal processing and, in particular, designing adaptive filtering algorithms utilized in system identification and nonlinear system modeling."--Mathematical Reviews ClippingsTable of Contents1. Introduction PART I – LINEAR-IN-THE-PARAMETERS NONLINEAR FILTERS 2. Orthogonal LIP Nonlinear Filters 3. Spline Adaptive Filters: Theory and Applications 4. Recent Advances on LIP Nonlinear Filters and Their Applications: Efficient Solutions and Significance Aware Filtering PART II – ADAPTIVE ALGORITHMS IN THE REPRODUCING KERNEL HILBERT SPACE 5. Maximum Correntropy Criterion Based Kernel Adaptive Filters 6. Kernel Subspace Learning for Pattern Classification 7. A Random Fourier Features Perspective of KAFs with Application to Distributed Learning over Networks 8. Kernel-based Inference of Functions over Graphs PART III – NONLINEAR MODELING WITH MULTIPLE LEARNING MACHINES 9. Online Nonlinear Modeling via Self-Organizing Trees 10. Adaptation and Learning Over Networks for Nonlinear System Modeling 11. Cooperative Filtering Architectures for Complex Nonlinear Systems PART IV – NONLINEAR MODELING BY NEURAL NETWORKS 12. Echo State Networks for Multidimensional Data: Exploiting Noncircularity and Widely Linear Models 13. Identification of Short-Term and Long-Term Functional Synaptic Plasticity from Spiking Activities 14. Adaptive H8 Tracking Control of Nonlinear Systems using Reinforcement Learning 15. Adaptive Dynamic Programming for Optimal Control of Nonlinear Distributed Parameter Systems
£999.99
Oxford University Press Nonlinear Waves Hamiltonian Systems
Book Synopsis
£999.99
Institute of Physics Publishing Introduction to the Mathematical Physics of
Book SynopsisNonlinear dynamics is a well-established discipline in physics, and this book offers a comprehensive textbook on the basic soliton theory and its applications, especially for crystalline processes. Although primarily mathematical, the author discusses the theory for nonlinear phenomena in a practical environment, paying particular attention to the presence of media where nonlinearity occurs.Written for students at upper-undergraduate and graduate levels, it is suitable for advanced physics courses on nonlinear physics. The book covers the fundamental properties of nonlinear waves, dealing with both theory and experiment. The aim is to emphasize established tools and introduce new methods underpinning important new developments in this field, especially as applied to solid-state materials. The updated edition has been extended to emphasize the importance of thermodynamics in a description of modulated crystals and contains new chapters on superconductivity that can be interpreted by the soliton mechanism. It is also updated to include new end-of-chapter problems.Key Features New updated and expanded edition of a respected and well-used book Incorporates latest developments in the field Extensive additions to applications on condensed matter and materials Includes worked examples and end of chapter exercises Extended to include applications in superconductivity
£67.50
MP-AMM American Mathematical Nonlinear Dynamics and Renormalization Group
Book SynopsisContains the proceedings from the workshop, Nonlinear Dynamics and Renormalization Group, held at the Centre de recherches mathematiques (CRM) in Montreal (Canada), as part of the year-long program devoted to mathematical physics. This volume offers the research in the rapidly developing fields of nonlinear equations and renormalization group.Table of ContentsAnalysis of some macroscopic models of high-$T_c$ superconductivity by S. Alama and L. Bronsard The effect of distribution in space in Ostwald ripening by N. D. Alikakos and G. Fusco Mathematical problems in the control of underactuated systems by D. Auckly and L. Kapitanski Axially and helically symmetric global plasma equilibria by O. I. Bogoyavlenskij On the complete ionization of a periodically perturbed quantum system by O. Costin, J. L. Lebowitz, and A. Rokhlenko The sine-Gordon model at $\beta = 4\pi$ by J. Dimock Ground states of supersymmetric matrix models by G. M. Graf Some mathematical problems in the Ginzburg-Landau theory of superconductivity by S. J. Gustafson Renormalization in radiation reaction: New developments in classical electron theory by M. K.-H. Kiessling Singular limit of the modified nonlinear Schrodinger equation by C.-K. Lin Dynamics of quantum resonances by M. Merkli Nelson diffusions and blow-up phenomena in solutions of the nonlinear Schrodinger equation with critical power by H. Nawa Embedded solitons of the DSII equation by D. E. Pelinovsky and C. Sulem On the blow up phenomenon for the critical nonlinear Schrodinger equation in 1D by G. Perelman Vorticity for the Ginzburg-Landau model of superconductors in a magnetic field by S. Serfaty Dissipation through dispersion by A. Soffer Quantum tunneling at positive temperature by B. Vasilijevic.
£999.99
MP-AMM American Mathematical Nonlinear Dynamics and Evolution Equations
Book SynopsisReflects a broad spectrum of research activities on the theory and applications of nonlinear dynamics and evolution equations. This book covers major areas of dynamical systems, ordinary, functional and partial differential equations, and applications of such equations in the mathematical modelling of various biological and physical phenomena.Table of ContentsDisease spread in metapopulations by J. Arino and P. van den Driessche On some nonlocal evolution equations arising in materials science by P. W. Bates Invariant tori for Hamiltonian PDE by W. Craig Stable and not too unstable solutions on $R^n$ for small diffusion by N. Dancer Some recent results on diffusive predator-prey models in spatially heterogeneous environment by Y. Du and J. Shi Delayed non-local diffusive systems in biological invasion and disease spread by S. A. Gourley and J. Wu Asymptotic behavior for systems comparable to quasimonotone systems by J. Jiang $C^1$-smoothness of center manifolds for differential equations with state-dependent delay by T. Krisztin Normal forms for germs of analytic families of planar vector fields unfolding a generic saddle-node or resonant saddle by C. Rousseau Generic properties of symplectic diffeomorphisms by R. Saghin and Z. Xia Mathematical aspects of modelling tumour angiogenesis by B. D. Sleeman Interpretation of the generalized asymmetric May-Leonard model of three species competition as a food web in a chemostat by G. S. K. Wolkowicz On exact Poisson structures by Y. Yi and X. Zhang.
£99.00
MP-AMM American Mathematical Systolic Geometry and Topology
Book SynopsisPresents the systolic geometry of manifolds and polyhedra, starting with the two classical inequalities. This book features Gromov's inequalities and their generalisations, as well as asymptotic phenomena for systoles of surfaces of large genus, revealing a link both to ergodic theory and to properties of congruence subgroups of arithmetic groups.Table of ContentsSystolic geometry in dimension 2: Geometry and topology of systoles Historical remarks The theorema egregium of Gauss Global geometry of surfaces Inequalities of Loewner and Pu Systolic applications of integral geometry A primer on surfaces Filling area theorem for hyperelliptic surfaces Hyperelliptic surfaces are Loewner An optimal inequality for CAT(0) metrics Volume entropy and asymptotic upper bounds Systolic geometry and topology in $n$ dimensions: Systoles and their category Gromov's optimal stable systolic inequality for $\mathbb{CP}^n$ Systolic inequalities dependent on Massey products Cup products and stable systoles Dual-critical lattices and systoles Generalized degree and Loewner-type inequalities Higher inequalities of Loewner-Gromov type Systolic inequalities for $L^p$ norms Four-manifold systole asymptotics Period map image density (by Jake Solomon) Open problems Bibliography Index.
£103.50
Society for Industrial and Applied Mathematics Extending Hinfinity Control to Nonlinear Systems
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.
£92.65
Society for Industrial and Applied Mathematics NeuroFuzzy Control of Industrial Systems with Actuator Nonlinearities Frontiers in Applied Mathematics Series Number 24
Book SynopsisNeural networks and fuzzy systems are model free control design approaches that represent an advantage over classical control when dealing with complicated nonlinear actuator dynamics. Neuro-Fuzzy Control of Industrial Systems with Actuator Nonlinearities brings neural networks and fuzzy logic together with dynamical control systems. Each chapter presents powerful control approaches for the design of intelligent controllers to compensate for actuator nonlinearities such as time delay, friction, deadzone, and backlash that can be found in all industrial motion systems, plus a thorough development, rigorous stability proofs, and simulation examples for each design. In the final chapter, the authors develop a framework to implement intelligent control schemes on actual systems. Rigorous stability proofs are further verified by computer simulations, and appendices contain the computer code needed to build intelligent controllers for real-time applications.
£999.99
Society for Industrial and Applied Mathematics Nonlinear Programming Concepts Algorithms and
Book SynopsisThis book addresses modern nonlinear programming concepts and algorithms, especially as they apply to challenging applications in chemical process engineering. It relates the material to real-world problem classes in process optimisation, thus bridging the gap between the mathematical material and the practical uses. Nonlinear Programming: Concepts, Algorithms, and Applications to Chemical Processes shows readers which methods are best suited for specific applications, how large-scale problems should be formulated and what features of these problems should be emphasised, and how existing NLP methods can be extended to exploit specific structures of large-scale optimisation models. The book serves a dual function: it will be useful to chemical engineers who wish to understand and use nonlinear programming; it will also be of interest to experts in mathematical optimisation who want to understand process engineering problems and develop better approaches to solving them.
£84.58
Cambridge University Press Latent Modes of Nonlinear Flows
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.
£999.99
Cambridge University Press Adhesive Particle Flow A DiscreteElement Approach
Book SynopsisOffering a comprehensive treatment of adhesive particle flows, this book adopts a particle-level approach oriented toward directly simulating the various fluid, electric field, collision, and adhesion forces and torques acting on the particles, within the framework of a discrete-element model. It is ideal for professionals and graduate students working in engineering and atmospheric and condensed matter physics, materials science, environmental science, and other disciplines where particulate flows have a significant role. The presentation is applicable to a wide range of flow fields, including aerosols, colloids, fluidized beds, and granular flows. It describes both physical models of the various forces and torques on the particles as well as practical aspects necessary for efficient implementation of these models in a computational framework.Table of Contents1. Introduction; 2. Modeling viewpoints and approaches; 3. Contact mechanics without adhesion; 4. Adhesion forces; 5. Fluid forces on particles; 6. Particle dispersion in turbulent flows; 7. Ellipsoidal particles; 8. Particle interactions with electric and magnetic fields; 9. Nanoscale particle dynamics; 10. Computer implementation and data analysis; 11. Applications.
£999.99
Cambridge University Press Symmetry Phase Modulation and Nonlinear Waves 31 Cambridge Monographs on Applied and Computational Mathematics Series Number 31
Book SynopsisNonlinear waves are pervasive in nature, but are often elusive when they are modelled and analysed. This book develops a natural approach to the problem based on phase modulation. It is both an elaboration of the use of phase modulation for the study of nonlinear waves and a compendium of background results in mathematics, such as Hamiltonian systems, symplectic geometry, conservation laws, Noether theory, Lagrangian field theory and analysis, all of which combine to generate the new theory of phase modulation. While the build-up of theory can be intensive, the resulting emergent partial differential equations are relatively simple. A key outcome of the theory is that the coefficients in the emergent modulation equations are universal and easy to calculate. This book gives several examples of the implications in the theory of fluid mechanics and points to a wide range of new applications.Trade Review'This book has been written by a well-established researcher in the field. His expertise is evidenced by the deft exposition of relatively challenging material. In that regard, one of the very useful functions of this book is its provision of a number of background mathematical techniques in Hamiltonians systems, symplectic geometry, Noether theory and Lagrangian field theory.' K. Alan Shore, Contemporary Physics'The book is clearly written, and only the most basic knowledge of Hamiltonian and Lagrangian theories is required.' Wen-Xiu Ma, MathSciNetTable of Contents1. Introduction; 2. Hamiltonian ODEs and relative equilibria; 3. Modulation of relative equilibria; 4. Revised modulation near a singularity; 5. Introduction to Whitham Modulation Theory – the Lagrangian viewpoint; 6. From Lagrangians to Multisymplectic PDEs; 7. Whitham Modulation Theory – the multisymplectic viewpoint; 8. Phase modulation and the KdV equation; 9. Classical view of KdV in shallow water; 10. Phase modulation of uniform flows and KdV; 11. Generic Whitham Modulation Theory in 2+1; 12. Phase modulation in 2+1 and the KP equation; 13. Shallow water hydrodynamics and KP; 14. Modulation of three-dimensional water waves; 15. Modulation and planforms; 16. Validity of Lagrangian-based modulation equations; 17. Non-conservative PDEs and modulation; 18. Phase modulation – extensions and generalizations; Appendix A. Supporting calculations – 4th and 5th order terms; Appendix B. Derivatives of a family of relative equilibria; Appendix C. Bk and the spectral problem; Appendix D. Reducing dispersive conservation laws to KdV; Appendix E. Advanced topics in multisymplecticity; References; Index.
£999.99
