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Singular Perturbations and Hysteresis by Michael P. Mortell,Robert E. O'Malley,Alexei Pokrovskii,Vladimir Sobolev Pdf
This book unifies many important recent developments in the analysis of singular perturbation and hysteresis phenomena in an accessible and comprehensive fashion. In April 2002 at University College Cork in Ireland, the editors conducted a workshop to provide a forum for experts to share their interests and knowledge. For this book, the editors have compiled research from those practitioners in areas such as reacting systems, semiconductor lasers, shock phenomena in economic modeling, and fluid mechanics, all with an emphasis on hysteresis and singular perturbations. A basic introduction to hysteresis and singular perturbation theory is included, with simple examples from both physics and mathematics. Later chapters address: applications of hysteresis to economics; various aspects of the asymptotic theory of singularly perturbed systems; typical problems of the asymptotic theory of contrast structures; and the geometrical approach to an investigation of models with singular perturbations and hysteresis.
Singular Perturbations by Elena Shchepakina,Vladimir Sobolev,Michael P. Mortell Pdf
These lecture notes provide a fresh approach to investigating singularly perturbed systems using asymptotic and geometrical techniques. It gives many examples and step-by-step techniques, which will help beginners move to a more advanced level. Singularly perturbed systems appear naturally in the modelling of many processes that are characterized by slow and fast motions simultaneously, for example, in fluid dynamics and nonlinear mechanics. This book’s approach consists in separating out the slow motions of the system under investigation. The result is a reduced differential system of lesser order. However, it inherits the essential elements of the qualitative behaviour of the original system. Singular Perturbations differs from other literature on the subject due to its methods and wide range of applications. It is a valuable reference for specialists in the areas of applied mathematics, engineering, physics, biology, as well as advanced undergraduates for the earlier parts of the book, and graduate students for the later chapters.
Extended Abstracts Spring 2018 by Andrei Korobeinikov,Magdalena Caubergh,Tomás Lázaro,Josep Sardanyés Pdf
This volume contains extended abstracts outlining selected presentations delivered by participants of the joint international multidisciplinary workshop MURPHYS-HSFS-2018 (MUltiRate Processes and HYSteresis; Hysteresis and Slow-Fast Systems), dedicated to the mathematical theory and applications of the multiple scale systems, the systems with hysteresis and general trends in the dynamical systems theory. The workshop was jointly organized by the Centre de Recerca Matemàtica (CRM), Barcelona, and the Collaborative Research Center 910, Berlin, and held at the Centre de Recerca Matemàtica in Bellaterra, Barcelona, from May 28th to June 1st, 2018. This was the ninth workshop continuing a series of biennial meetings started in Ireland in 2002, and the second workshop of this series held at the CRM. Earlier editions of the workshops in this series were held in Cork, Pechs, Suceava, Lutherstadt and Berlin. The collection includes brief research articles reporting new results, descriptions of preliminary work, open problems, and the outcome of work in groups initiated during the workshop. Topics include analysis of hysteresis phenomena, multiple scale systems, self-organizing nonlinear systems, singular perturbations and critical phenomena, as well as applications of the hysteresis and the theory of singularly perturbed systems to fluid dynamics, chemical kinetics, cancer modeling, population modeling, mathematical economics, and control. The book is intended for established researchers, as well as for PhD and postdoctoral students who want to learn more about the latest advances in these highly active research areas.
Historical Developments in Singular Perturbations by Robert E. O'Malley Pdf
This engaging text describes the development of singular perturbations, including its history, accumulating literature, and its current status. While the approach of the text is sophisticated, the literature is accessible to a broad audience. A particularly valuable bonus are the historical remarks. These remarks are found throughout the manuscript. They demonstrate the growth of mathematical thinking on this topic by engineers and mathematicians. The book focuses on detailing how the various methods are to be applied. These are illustrated by a number and variety of examples. Readers are expected to have a working knowledge of elementary ordinary differential equations, including some familiarity with power series techniques, and of some advanced calculus. Dr. O'Malley has written a number of books on singular perturbations. This book has developed from many of his works in the field of perturbation theory.
Extended Abstracts Summer 2016 by Andrei Korobeinikov Pdf
This volume contains extended abstracts outlining selected presentations given by participants of the joint international multidisciplinary workshop MURPHYS-HSFS-2016 (MUltiRate Processes and HYSteresis; Hysteresis and Slow-Fast Systems), which was dedicated to the mathematical theory and applications of multiple scale systems and systems with hysteresis, and held at the Centre de Recerca Matemàtica (CRM) in Barcelona from June 13th to 17th, 2016. The collection includes brief research articles on new results, preliminary work, open problems, and the outcomes of group work initiated during the workshop. The book addresses multiple scale phenomena, singular perturbations, phase transitions, and hysteresis phenomena occurring in mathematical, physical, economic, engineering and information systems. Its scope includes both new results in the theory of hysteresis, singularly perturbed systems and dynamical systems in general; and applications to the physical, chemical, biological, microbiological, economic, and engineering sciences, such as: elasto-plasticity and mechanical structures, damage processes, magnetic materials, photonics and optoelectronics, energy storage systems, hydrology, biology, semiconductor lasers, and shock phenomena in economic modeling. Given its breadth of coverage, the book offers a valuable resource for established researchers, as well as for PhD and postdoctoral students who want to learn more about the latest advances in these highly active research areas.
Multiple Time Scale Dynamics by Christian Kuehn Pdf
This book provides an introduction to dynamical systems with multiple time scales. The approach it takes is to provide an overview of key areas, particularly topics that are less available in the introductory form. The broad range of topics included makes it accessible for students and researchers new to the field to gain a quick and thorough overview. The first of its kind, this book merges a wide variety of different mathematical techniques into a more unified framework. The book is highly illustrated with many examples and exercises and an extensive bibliography. The target audience of this book are senior undergraduates, graduate students as well as researchers interested in using the multiple time scale dynamics theory in nonlinear science, either from a theoretical or a mathematical modeling perspective.
Geometric Singular Perturbation Theory Beyond the Standard Form by Martin Wechselberger Pdf
This volume provides a comprehensive review of multiple-scale dynamical systems. Mathematical models of such multiple-scale systems are considered singular perturbation problems, and this volume focuses on the geometric approach known as Geometric Singular Perturbation Theory (GSPT). It is the first of its kind that introduces the GSPT in a coordinate-independent manner. This is motivated by specific examples of biochemical reaction networks, electronic circuit and mechanic oscillator models and advection-reaction-diffusion models, all with an inherent non-uniform scale splitting, which identifies these examples as singular perturbation problems beyond the standard form. The contents cover a general framework for this GSPT beyond the standard form including canard theory, concrete applications, and instructive qualitative models. It contains many illustrations and key pointers to the existing literature. The target audience are senior undergraduates, graduate students and researchers interested in using the GSPT toolbox in nonlinear science, either from a theoretical or an application point of view. Martin Wechselberger is Professor at the School of Mathematics & Statistics, University of Sydney, Australia. He received the J.D. Crawford Prize in 2017 by the Society for Industrial and Applied Mathematics (SIAM) for achievements in the field of dynamical systems with multiple time-scales.
Assistive Robotics by Hongye Su,Tianmiao Wang,Mohammad O Tokhi,Gurvinder S Virk Pdf
This book provides state-of-the-art scientific and engineering research findings and developments in the area of mobile robotics and associated support technologies around the theme of assistive robotics. The book contains peer reviewed articles presented at the CLAWAR 2015 conference. The book contains a comprehensive collection of papers on legged locomotion with numbers of legs from two upward to multi-legs, which includes robots cable of climbing walls, poles, or more complex structures such as continuing the distinctive CLAWAR themes. There are also a strong showing of articles covering human assist devices, notably exoskeletal and prosthetic devices, as well as social robots designed to meet the growing challenges of global ageing population. Contents: Plenary Presentations:Infrastructure Robotics: Opportunities and Challengesÿ(Gamini Dissanayake)Understanding Animal Locomotion Using Bio-Inspired Robotics and Soft Roboticsÿ(Tianmiao Wang)Assistive Robots:A Behavior Adaptation Method Based on Hierarchical POMDPsÿ(Y Tao, Y Chen, D Xu and J Zheng)Design and Control of Exoskeleton for Elderly Mobilityÿ(G Al Rezage, M O Tokhi and S K Ali)Assessing Human Robot Interaction: The Role of Long-Run Experimentsÿ(I Ferreira and J S Sequeira)Autonomous Robots:Wall Climbing Robot Motion Simulation in Non-Deterministic Area with Existing Moving Objectsÿ(V G Gradetsky, M M Knyazkov, A M Nunuparov, E A Semyonov and A N Sukhanov)Design and Implementation of a Scansorial Robotÿ(M A H Hassan and M O Tokhi)Biologically-Inspired Systems and Solutions:A Bio-Inspired Behavior Based Bipedal Locomotion Control ? B4LC Method for Bipedal Upslope Walkingÿ(J Zhao, Q Liu, S Schuetz and K Berns)Design and Implementation of a Smart Robotic Shark with Multi-Sensorsÿ(S Chen, J Yu, X Li and J Yuan)Control Algorithm for Walking Robot with Mosaic Bodyÿ(A V Panchenko, I A Orlov and V E Pavlovsky)Innovative Design of Clawar:A Novel Inspection Robot Moving on High-Voltage Power Transmission Lineÿ(T Guanghong and F Lijin)Rise-Rover: A Wall-Climbing Robot with High Reliability and Load-Carrying Capacityÿ(J Xiao, B Li, K Ushiroda and Q Song)Inspection and Innovative Sensing:An Innovative Torque Sensor Design for the Lightest Hydraulic Quadruped Robotÿ(H Khan, F Cannella, D Caldwell and C Semini)Mapping Repetitive Structural Tunnel Environments for a Biologically Inspired Climbing Robotÿ(G Paul, S Mao, L Liu and R Xiong)Locomotion:Application of Local Slopes in the Study of Metastable Walkingÿ(A T Safa, M Naraghi and A Alasty)A Mechanism of Particle Swarm Optimization on Motor Patterns in the B4LC Systemÿ(Q Liu, J Zhao, S Schuetz and K Berns)Dynamical Analysis of Large Deflection Compliant Leg During Terrestrial Locomotionÿ(T Fang, X Wang, Z Chen, M Xu and S Zhang)Manipulation, Intelligence and Learning for CLAWAR:Radiation Dosing Software Control of a Robot System for the Atlas Scanning Facilityÿ(H Marin-Reyes and R French)Acquisition Slope Surface Walking for Humanoids via Transfer Learningÿ(Y Wang, X Han, Z Liu, D Luo and X Wu)Medical and Rehabilitation Robotics:A Real-Time Gait Phase Detection Method for Prosthesis Controlÿ(J Li, X Zhou, C Li, W Li, H Zhang and H Gu)Powered Knee Orthosis for Performance of Assistance and Rehabilitation Purposesÿ(M Shysh, A Safonov, A Telesh and U Schmucker)Modelling and Simulation of CLAWAR:Wall Climbing Robot Motion with Adaptive Vacuum Contact Devicesÿ(V G Gradetsky, M M Knyazkov, A A Kryukova, E A Semyonov and A N Sukhanov)Combination of Affine Deformation and Dynamic Movement Primitive in Learning Human Motion for Redundant Manipulatorÿ(J Hu and R Xiong)Perception, Localization and Rescue Operations:Multi-Session Slam Over Low Dynamic Workspace Using RGBD Sensorÿ(Y Wang, R Xiong, S Huang and J Wu)Mechanism and Anti-Explosion Design of an Omnitread Serpentine Robot for Searching in Coal Minesÿ(G Liu, J Yan, C Li, Z Han, L Zhu, J Zhao and L Li)Planning and Control:Lidar-Based Navigation-Level Path Planning for Field-Capable Legged Robotsÿ(I Havoutis, D G Caldwell and C Semini)A Simple Modeling Method and Trajectory Planning for a Car-Like Climbing Robot Used to Strip Coating from the Outer Surface of Pipes Underwaterÿ(H Wang, C Yang, X Deng and J Fan)Underwater and Sea Robotics:Towards Deep-Sea Monitoring with SMIS ? Experimental Trials of Deep-Sea Acoustic Localizationÿ(S Neumann, D Oertel, H Wrn, M Kurowski, D Dewitz, J J Waniek, D Kaiser and R Mars)Mechanical Design of a Two-Joint Robotic Fishÿ(C Zhang, J Yu and M Tan)A Novel Hydraulic Mechanism for Bio-Inspired Undulating Robot: Modeling and Morphological Analysisÿ(H Xu, T Hu, X Zhang and L Zhang)and other papers Readership:ÿSystems and control engineers, electrical engineers, mechanical engineers in academic, research and industrial settings; engineers and practitioners in the public services sectors in health care, manufacturing, supply and delivery services.
Introduction to Singular Perturbations by Robert E. Jr. O'Malley Pdf
Introduction to Singular Perturbations provides an overview of the fundamental techniques for obtaining asymptomatic solutions to boundary value problems. This text explores singular perturbation techniques, which are among the basic tools of several applied scientists. This book is organized into eight chapters, wherein Chapter 1 discusses the method of matched asymptomatic expansions, which has been frequently applied to several physical problems involving singular perturbations. Chapter 2 considers the nonlinear initial value problem to illustrate the regular perturbation method, and Chapter 3 explains how to construct asymptotic solutions for general linear equations. Chapter 4 discusses scalar equations and nonlinear system, whereas Chapters 5 and 6 explain the contrasts for initial value problems where the outer expansion cannot be determined without obtaining the initial values of the boundary layer correction. Chapters 7 and 8 deal with boundary value problem that arises in the study of adiabatic tubular chemical flow reactors with axial diffusion. This monograph is a valuable resource for applied mathematicians, engineers, researchers, students, and readers whose interests span a variety of fields.
Multiplicity of Time Scales in Complex Systems by Bernhelm Booss,Jens Hesselbjerg Christensen,Katherine Richardson,Oriol Vallès Codina Pdf
This highly interdisciplinary volume brings together a carefully curated set of case studies examining complex systems with multiple time scales (MTS) across a variety of fields: materials science, epidemiology, cell physiology, mathematics, climatology, energy transition planning, ecology, economics, sociology, history, and cultural studies. The book addresses the vast diversity of interacting processes underlying the behaviour of different complex systems, highlighting the multiplicity of characteristic time scales that are a common feature of many and showcases a rich variety of methodologies across disciplinary boundaries. Self-organizing, out-of-equilibrium, ever-evolving systems are ubiquitous in the natural and social world. Examples include the climate, ecosystems, living cells, epidemics, the human brain, and many socio-economic systems across history. Their dynamical behaviour poses great challenges in the pressing context of the climate crisis, since they may involve nonlinearities, feedback loops, and the emergence of spatial-temporal patterns, portrayed by resilience or instability, plasticity or rigidity; bifurcations, thresholds and tipping points; burst-in excitation or slow relaxation, and worlds of other asymptotic behaviour, hysteresis, and resistance to change. Chapters can be read individually by the reader with special interest in such behaviours of particular complex systems or in specific disciplinary perspectives. Read together, however, the case studies, opinion pieces, and meta-studies on MTS systems presented and analysed here combine to give the reader insights that are more than the sum of the book's individual chapters, as surprising similarities become apparent in seemingly disparate and unconnected systems. MTS systems call into question naïve perceptions of time and complexity, moving beyond conventional ways of description, analysis, understanding, modelling, numerical prediction, and prescription of the world around us. This edited collection presents new ways of forecasting, introduces new means of control, and -- perhaps as the most demanding task -- it singles out a sustainable description of an MTS system under observation, offering a more nuanced interpretation of the floods of quantitative data and images made available by high- and low-frequency measurement tools in our unprecedented era of information flows.
Multiple Scale and Singular Perturbation Methods by J.K. Kevorkian,J.D. Cole Pdf
This book is a revised and updated version, including a substantial portion of new material, of our text Perturbation Methods in Applied Mathematics (Springer Verlag, 1981). We present the material at a level that assumes some familiarity with the basics of ordinary and partial differential equations. Some of the more advanced ideas are reviewed as needed; therefore this book can serve as a text in either an advanced undergraduate course or a graduate-level course on the subject. Perturbation methods, first used by astronomers to predict the effects of small disturbances on the nominal motions of celestial bodies, have now become widely used analytical tools in virtually all branches of science. A problem lends itself to perturbation analysis if it is "close" to a simpler problem that can be solved exactly. Typically, this closeness is measured by the occurrence of a small dimensionless parameter, E, in the governing system (consisting of differential equations and boundary conditions) so that for E = 0 the resulting system is exactly solvable. The main mathematical tool used is asymptotic expansion with respect to a suitable asymptotic sequence of functions of E. In a regular perturbation problem, a straightforward procedure leads to a system of differential equations and boundary conditions for each term in the asymptotic expansion. This system can be solved recursively, and the accuracy of the result improves as E gets smaller, for all values of the independent variables throughout the domain of interest. We discuss regular perturbation problems in the first chapter.