Nonlinear problems are of interest to engineers, physicists and mathematicians and many other scientists because most systems are inherently nonlinear in nature. As nonlinear equations are difficult to solve, nonlinear systems are commonly approximated by linear equations. This works well up to some accuracy and some range for the input values, but some interesting phenomena such as chaos and singularities are hidden by linearization and perturbation analysis. It follows that some aspects of the behavior of a nonlinear system appear commonly to be chaotic, unpredictable or counterintuitive. Although such a chaotic behavior may resemble a random behavior, it is absolutely deterministic. Analytical Routes to Chaos in Nonlinear Engineering discusses analytical solutions of periodic motions to chaos or quasi-periodic motions in nonlinear dynamical systems in engineering and considers engineering applications, design, and control. It systematically discusses complex nonlinear phenomena in engineering nonlinear systems, including the periodically forced Duffing oscillator, nonlinear self-excited systems, nonlinear parametric systems and nonlinear rotor systems. Nonlinear models used in engineering are also presented and a brief history of the topic is provided. Key features: Considers engineering applications, design and control Presents analytical techniques to show how to find the periodic motions to chaos in nonlinear dynamical systems Systematically discusses complex nonlinear phenomena in engineering nonlinear systems Presents extensively used nonlinear models in engineering Analytical Routes to Chaos in Nonlinear Engineering is a practical reference for researchers and practitioners across engineering, mathematics and physics disciplines, and is also a useful source of information for graduate and senior undergraduate students in these areas.
This book covers the principles of modeling and simulation of nonlinear distortion in wireless communication systems with MATLAB simulations and techniques In this book, the author describes the principles of modeling and simulation of nonlinear distortion in single and multichannel wireless communication systems using both deterministic and stochastic signals. Models and simulation methods of nonlinear amplifiers explain in detail how to analyze and evaluate the performance of data communication links under nonlinear amplification. The book addresses the analysis of nonlinear systems with stochastic inputs and establishes the performance metrics of communication systems with regard to nonlinearity. In addition, the author also discusses the problem of how to embed models of distortion in system-level simulators such as MATLAB and MATLAB Simulink and provides practical techniques that professionals can use on their own projects. Finally, the book explores simulation and programming issues and provides a comprehensive reference of simulation tools for nonlinearity in wireless communication systems. Key Features: Covers the theory, models and simulation tools needed for understanding nonlinearity and nonlinear distortion in wireless systems Presents simulation and modeling techniques for nonlinear distortion in wireless channels using MATLAB Uses random process theory to develop simulation tools for predicting nonlinear system performance with real-world wireless communication signals Focuses on simulation examples of real-world communication systems under nonlinearity Includes an accompanying website containing MATLAB code This book will be an invaluable reference for researchers, RF engineers, and communication system engineers working in the field. Graduate students and professors undertaking related courses will also find the book of interest.
The present monography is dedicated to a fashionable trend in nonlinear analysis - the theories of blow-up of solutions for final time. In this book nonlinear Sobolev type equations are systematically studied. The book will be interesting both to experts in the field of nonlinear analysis and to students and post-graduate students of the corresponding specialties.
Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains describes a comprehensive framework for the identification and analysis of nonlinear dynamic systems in the time, frequency, and spatio-temporal domains. This book is written with an emphasis on making the algorithms accessible so that they can be applied and used in practice. Includes coverage of: The NARMAX (nonlinear autoregressive moving average with exogenous inputs) model The orthogonal least squares algorithm that allows models to be built term by term where the error reduction ratio reveals the percentage contribution of each model term Statistical and qualitative model validation methods that can be applied to any model class Generalised frequency response functions which provide significant insight into nonlinear behaviours A completely new class of filters that can move, split, spread, and focus energy The response spectrum map and the study of sub harmonic and severely nonlinear systems Algorithms that can track rapid time variation in both linear and nonlinear systems The important class of spatio-temporal systems that evolve over both space and time Many case study examples from modelling space weather, through identification of a model of the visual processing system of fruit flies, to tracking causality in EEG data are all included to demonstrate how easily the methods can be applied in practice and to show the insight that the algorithms reveal even for complex systems NARMAX algorithms provide a fundamentally different approach to nonlinear system identification and signal processing for nonlinear systems. NARMAX methods provide models that are transparent, which can easily be analysed, and which can be used to solve real problems. This book is intended for graduates, postgraduates and researchers in the sciences and engineering, and also for users from other fields who have collected data and who wish to identify models to help to understand the dynamics of their systems.
The technology of hydrodynamic modeling and marine craft motion control systems has progressed greatly in recent years. This timely survey includes the latest tools for analysis and design of advanced guidance, navigation and control systems and presents new material on underwater vehicles and surface vessels. Each section presents numerous case studies and applications, providing a practical understanding of how model-based motion control systems are designed. Key features include: a three-part structure covering Modeling of Marine Craft; Guidance, Navigation and Control Systems; and Appendices, providing all the supporting theory in a single resource kinematics, kinetics, hydrostatics, seakeeping and maneuvering theory, and simulation models for marine craft and environmental forces guidance systems, sensor fusion and integrated navigation systems, inertial measurement units, Kalman filtering and nonlinear observer design for marine craft state-of-the-art methods for feedback control more advanced methods using nonlinear theory, enabling the user to compare linear design techniques before a final implementation is made. linear and nonlinear stability theory, and numerical methods companion website that hosts links to lecture notes and download information for the Marine Systems Simulator (MSS) which is an open source Matlab/Simulink® toolbox for marine systems. The MSS toolbox includes hydrodynamic models and motion control systems for ships, underwater vehicles and floating structures With an appropriate balance between mathematical theory and practical applications, academic and industrial researchers working in marine and control engineering aspects of manned and unmanned maritime vehicles will benefit from this comprehensive handbook. It is also suitable for final year undergraduates and postgraduates, lecturers, development officers, and practitioners in the areas of rigid-body modeling, hydrodynamics, simulation of marine craft, control and estimation theory, decision-support systems and sensor fusion. www.wiley.com/go/fossen_marine
A unified and coherent treatment of analytical, computational and experimental techniques of nonlinear dynamics with numerous illustrative applications. Features a discourse on geometric concepts such as Poincare maps. Discusses chaos, stability and bifurcation analysis for systems of differential and algebraic equations. Includes scores of examples to facilitate understanding.
The building blocks of MEMS design through closed-form solutions Microelectromechanical Systems, or MEMS, is the technology of very small systems; it is found in everything from inkjet printers and cars to cell phones, digital cameras, and medical equipment. This book describes the principles of MEMS via a unified approach and closed-form solutions to micromechanical problems, which have been recently developed by the author and go beyond what is available in other texts. The closed-form solutions allow the reader to easily understand the linear and nonlinear behaviors of MEMS and their design applications. Beginning with an overview of MEMS, the opening chapter also presents dimensional analysis that provides basic dimensionless parameters existing in large- and small-scale worlds. The book then explains microfabrication, which presents knowledge on the common fabrication process to design realistic MEMS. From there, coverage includes: Statics/force and moment acting on mechanical structures in static equilibrium Static behaviors of structures consisting of mechanical elements Dynamic responses of the mechanical structures by the solving of linear as well as nonlinear governing equations Fluid flow in MEMS and the evaluation of damping force acting on the moving structures Basic equations of electromagnetics that govern the electrical behavior of MEMS Combining the MEMS building blocks to form actuators and sensors for a specific purpose All chapters from first to last use a unified approach in which equations in previous chapters are used in the derivations of closed-form solutions in later chapters. This helps readers to easily understand the problems to be solved and the derived solutions. In addition, theoretical models for the elements and systems in the later chapters are provided, and solutions for the static and dynamic responses are obtained in closed-forms. This book is designed for senior or graduate students in electrical and mechanical engineering, researchers in MEMS, and engineers from industry. It is ideal for radio frequency/electronics/sensor specialists who, for design purposes, would like to forego numerical nonlinear mechanical simulations. The closed-form solution approach will also appeal to device designers interested in performing large-scale parametric analysis.
The book provides a comprehensive compilation of fundamentals, technical solutions and applications for medical imaging systems. It is intended as a handbook for students in biomedical engineering, for medical physicists, and for engineers working on medical technologies, as well as for lecturers at universities and engineering schools. For qualified personnel at hospitals, and physicians working with these instruments it serves as a basic source of information. This also applies for service engineers and marketing specialists. The book starts with the representation of the physical basics of image processing, implying some knowledge of Fourier transforms. After that, experienced authors describe technical solutions and applications for imaging systems in medical diagnostics. The applications comprise the fields of X-ray diagnostics, computed tomography, nuclear medical diagnostics, magnetic resonance imaging, sonography, molecular imaging and hybrid systems. Considering the increasing importance of software based solutions, emphasis is also laid on the imaging software platform and hospital information systems.
A distinctive discussion of the nonlinear dynamical phenomena of semiconductor lasers. The book combines recent results of quantum dot laser modeling with mathematical details and an analytic understanding of nonlinear phenomena in semiconductor lasers and points out possible applications of lasers in cryptography and chaos control. This interdisciplinary approach makes it a unique and powerful source of knowledge for anyone intending to contribute to this field of research. By presenting both experimental and theoretical results, the distinguished authors consider solitary lasers with nano-structured material, as well as integrated devices with complex feedback sections. In so doing, they address such topics as the bifurcation theory of systems with time delay, analysis of chaotic dynamics, and the modeling of quantum transport. They also address chaos-based cryptography as an example of the technical application of highly nonlinear laser systems.
The Duffing Equation: Nonlinear Oscillators and their Behaviour brings together the results of a wealth of disseminated research literature on the Duffing equation, a key engineering model with a vast number of applications in science and engineering, summarizing the findings of this research. Each chapter is written by an expert contributor in the field of nonlinear dynamics and addresses a different form of the equation, relating it to various oscillatory problems and clearly linking the problem with the mathematics that describe it. The editors and the contributors explain the mathematical techniques required to study nonlinear dynamics, helping the reader with little mathematical background to understand the text. The Duffing Equation provides a reference text for postgraduate and students and researchers of mechanical engineering and vibration / nonlinear dynamics as well as a useful tool for practising mechanical engineers. Includes a chapter devoted to historical background on Georg Duffing and the equation that was named after him. Includes a chapter solely devoted to practical examples of systems whose dynamic behaviour is described by the Duffing equation. Contains a comprehensive treatment of the various forms of the Duffing equation. Uses experimental, analytical and numerical methods as well as concepts of nonlinear dynamics to treat the physical systems in a unified way.
The first comprehensive book to uniquely combine the three fields of systems engineering, operations/production systems, and multiple criteria decision making/optimization Systems engineering is the art and science of designing, engineering, and building complex systems—combining art, science, management, and engineering disciplines. Operations and Production Systems with Multiple Objectives covers all classical topics of operations and production systems as well as new topics not seen in any similiar textbooks before: small-scale design of cellular systems, large-scale design of complex systems, clustering, productivity and efficiency measurements, and energy systems. Filled with completely new perspectives, paradigms, and robust methods of solving classic and modern problems, the book includes numerous examples and sample spreadsheets for solving each problem, a solutions manual, and a book companion site complete with worked examples and supplemental articles. Operations and Production Systems with Multiple Objectives will teach readers: How operations and production systems are designed and planned How operations and production systems are engineered and optimized How to formulate and solve manufacturing systems problems How to model and solve interdisciplinary and systems engineering problems How to solve decision problems with multiple and conflicting objectives This book is ideal for senior undergraduate, MS, and PhD graduate students in all fields of engineering, business, and management as well as practitioners and researchers in systems engineering, operations, production, and manufacturing.
This book provides researchers and engineers in the imaging field with the skills they need to effectively deal with nonlinear inverse problems associated with different imaging modalities, including impedance imaging, optical tomography, elastography, and electrical source imaging. Focusing on numerically implementable methods, the book bridges the gap between theory and applications, helping readers tackle problems in applied mathematics and engineering. Complete, self-contained coverage includes basic concepts, models, computational methods, numerical simulations, examples, and case studies. Provides a step-by-step progressive treatment of topics for ease of understanding. Discusses the underlying physical phenomena as well as implementation details of image reconstruction algorithms as prerequisites for finding solutions to non linear inverse problems with practical significance and value. Includes end of chapter problems, case studies and examples with solutions throughout the book. Companion website will provide further examples and solutions, experimental data sets, open problems, teaching material such as PowerPoint slides and software including MATLAB m files. Essential reading for Graduate students and researchers in imaging science working across the areas of applied mathematics, biomedical engineering, and electrical engineering and specifically those involved in nonlinear imaging techniques, impedance imaging, optical tomography, elastography, and electrical source imaging
Systems biology is a relatively new biological study field that focuses on the systematic study of complex interactions in biological systems, thus using a new perspective (integration instead of reduction) to study them. Particularly from year 2000 onwards, the term is used widely in the biosciences, and in a variety of contexts. Systems biology is the study of the interconnected aspect of molecular, cellular, tissue, whole animal and ecological processes, and comprises mathematical and mechanistic studies of dynamical, mesoscopic, open, spatiotemporally defined, nonlinear, complex systems that are far from thermodynamic equilibrium.
The capability to predict the nonlinear response of beams, plates and shells when subjected to thermal and mechanical loads is of prime interest to structural analysis. In fact, many structures are subjected to high load levels that may result in nonlinear load-deflection relationships due to large deformations. One of the important problems deserving special attention is the study of their nonlinear response to large deflection, postbuckling and nonlinear vibration. A two-step perturbation method is firstly proposed by Shen and Zhang (1988) for postbuckling analysis of isotropic plates. This approach gives parametrical analytical expressions of the variables in the postbuckling range and has been generalized to other plate postbuckling situations. This approach is then successfully used in solving many nonlinear bending, postbuckling, and nonlinear vibration problems of composite laminated plates and shells, in particular for some difficult tasks, for example, shear deformable plates with four free edges resting on elastic foundations, contact postbuckling of laminated plates and shells, nonlinear vibration of anisotropic cylindrical shells. This approach may be found its more extensive applications in nonlinear analysis of nano-scale structures. Concentrates on three types of nonlinear analyses: vibration, bending and postbuckling Presents not only the theoretical aspect of the techniques, but also engineering applications of the method A Two-Step Perturbation Method in Nonlinear Analysis of Beams, Plates and Shells is an original and unique technique devoted entirely to solve geometrically nonlinear problems of beams, plates and shells. It is ideal for academics, researchers and postgraduates in mechanical engineering, civil engineering and aeronautical engineering.
This Student Solutions Manual contains detailed Solutions for the odd-numbered problems in the text Radiation Detection and Measurement. These Solutions are intended for student use and study while using the textbook. The even-numbered Solutions are excluded from this Student Solutions Manual, so that that they will not be available to students, and instructors may use them for student assessment.