Probabilistic models are widely used for description and an analysis of various processes in system reliability, risk, queuing, data communication, logistic and storage systems. The book contains various applications of the theory of continuous-time Markov-modulated processes in operation research. All analytical results are illustrated by numerical computations. Used algorithms allow overcoming computation difficulties successfully. For example, a calculation of transient probabilities of states for a continuous-time finite Markov chain uses eigenvalues and eigenvectors of the corresponding matrix (generator). In a more complex case of differential or integral equations, such a simple explicit form of a solution is missing. The explicit form of solution is presented by means of infinity sums of functions. For example, often we have to deal with the so-called renewal equation. Its solution is presented as an infinite sum of the renewal function. In this case, an approximation of functions of interest and iterative computation procedures are used.
Probabilistic models are widely used for description and an analysis of various processes in system reliability, risk, queuing, data communication, logistic and storage systems. The book contains various applications of the theory of continuous-time Markov-modulated processes in operation research. All analytical results are illustrated by numerical computations. Used algorithms allow overcoming computation difficulties successfully. For example, a calculation of transient probabilities of states for a continuous-time finite Markov chain uses eigenvalues and eigenvectors of the corresponding matrix (generator). In a more complex case of differential or integral equations, such a simple explicit form of a solution is missing. The explicit form of solution is presented by means of infinity sums of functions. For example, often we have to deal with the so-called renewal equation. Its solution is presented as an infinite sum of the renewal function. In this case, an approximation of functions of interest and iterative computation procedures are used.
This book contains a systematic study of ecological communities of two or three interacting populations. Starting from the Lotka-Volterra system, various regulating factors are considered, such as rates of birth and death, predation and competition. The different factors can have a stabilizing or a destabilizing effect on the community, and their interplay leads to increasingly complicated behavior. Studying and understanding this path to greater dynamical complexity of ecological systems constitutes the backbone of this book. On the mathematical side, the tool of choice is the qualitative theory of dynamical systems — most importantly bifurcation theory, which describes the dependence of a system on the parameters. This approach allows one to find general patterns of behavior that are expected to be observed in ecological models. Of special interest is the reaction of a given model to disturbances of its present state, as well as to changes in the external conditions. This leads to the general idea of “dangerous boundaries” in the state and parameter space of an ecological system. The study of these boundaries allows one to analyze and predict qualitative and often sudden changes of the dynamics — a much-needed tool, given the increasing antropogenic load on the biosphere.As a spin-off from this approach, the book can be used as a guided tour of bifurcation theory from the viewpoint of application. The interested reader will find a wealth of intriguing examples of how known bifurcations occur in applications. The book can in fact be seen as bridging the gap between mathematical biology and bifurcation theory.
This biography of the famous Soviet physicist Leonid Isaakovich Mandelstam (1889-1944), who became a Professor at Moscow State University in 1925, describes his contributions to both physics and technology, as well as discussing the scientific community which formed around him, usually called the Mandelstam school. Mandelstam’s life story is thereby placed in its proper cultural context. The following more general issues are taken under consideration: the impact of German scientific culture on Russian science; the problems and fates of Russian intellectuals during the revolutionary and post-revolutionary years; the formation of the Soviet Academy of Sciences; and transformation of the system of higher education in the USSR during the 1920's and 1930's.The author shows that Mandelstam’s fundamental writings and his lectures notes allow to reconstruct his philosophy of science and his approach to the social and ethical functions of science and science education. That reconstruction is enhanced through extensive use of hitherto unpublished archival material as well as the transcripts of personal interviews conducted by the author.
This biography of the famous Soviet physicist Leonid Isaakovich Mandelstam (1889–1944), who became a Professor at Moscow State University in 1925 and an Academician (the highest scientific title in the USSR) in 1929, describes his contributions to both physics and technology. It also discusses the scientific community that formed around him, commonly known as the Mandelstam School. By doing so, it places Mandelstam’s life story in its cultural context: the context of German University (until 1914), the First World War, the Civil War, and the development of the Socialist Revolution (until 1925) and the young socialist country. The book considers various general issues, such as the impact of German scientific culture on Russian science; the problems and fates of Russian intellectuals during the revolutionary and post-revolutionary years; the formation of the Soviet Academy of Science, the State Academy; and the transformation of the system of higher education in the USSR during the 1920s and 1930s. Further, it reconstructs Mandelstam’s philosophy of science and his approach to the social and ethical function of science and science education based on his fundamental writings and lecture notes. This reconstruction is enhanced by extensive use of previously unpublished archive material as well as the transcripts of personal interviews conducted by the author. The book also discusses the biographies of Mandelstam’s friends and collaborators: German mathematician and philosopher Richard von Mises, Soviet Communist Party official and philosopher B.M.Hessen, Russian specialist in radio engineering N.D.Papalexy, the specialists in non-linear dynamics A.A.Andronov, S.E. Chaikin, A.A.Vitt and the plasma physicist M.A.Leontovich. This second, extended edition reconstructs the social and economic backgrounds of Mandelstam and his colleagues, describing their positions at the universities and the institutes belonging to the Academy of Science. Additionally, Mandelstam’s philosophy of science is investigated in connection with the ideological attacks that occurred after Mandelstam’s death, particularly the great mathematician A.D.Alexandrov’s criticism of Mandelstam’s operationalism.
Contains both an exhaustive introduction to the subject as well as a detailed discussion of fundamental problems and research results. Despite the unified presentation of the subject, care has been taken to present the material in largely self-contained chapters.
This textbook is based on a lecture course in synergetics given at the University of Moscow. In this second of two volumes, we discuss the emergence and properties of complex chaotic patterns in distributed active systems. Such patterns can be produced autonomously by a system, or can result from selective amplification of fluctuations caused by external weak noise. Although the material in this book is often described by refined mathematical theories, we have tried to avoid a formal mathematical style. Instead of rigorous proofs, the reader will usually be offered only "demonstrations" (the term used by Prof. V. I. Arnold) to encourage intuitive understanding of a problem and to explain why a particular statement seems plausible. We also refrained from detailing concrete applications in physics or in other scientific fields, so that the book can be used by students of different disciplines. While preparing the lecture course and producing this book, we had intensive discussions with and asked the advice of Prof. V. I. Arnold, Prof. S. Grossmann, Prof. H. Haken, Prof. Yu. L. Klimontovich, Prof. R. L. Stratonovich and Prof. Ya.
This book offers a survey of the historic development of selected areas of chemistry and chemical physics, discussing in detail the European, American and Russian approaches to the development of chemistry. Other key topics include the kinetics and non-linear thermodynamics of chemical reactions and mathematical modeling, which have found new applications in the theory of dynamical systems. The first observations of the periodicity of chemical reactions were lost in the mist of time. In the second half of the 19th century, the phenomenon of chemical periodicity was studied in relation to electrochemistry, solutions and colloids. Discovered in the late 19th century, Liesegang rings are still enigmatic and remain attractive for researchers. However, the discovery of the Belousov–Zhabotinsky reaction marked the successful culmination of the efforts to find a true chemical oscillatory reaction. The book investigates chemical phenomena that were neglected in the past, but have been rediscovered, placing them into a new conceptual framework. For example, it notes that William Bray, who discovered the first oscillatory homogeneous reaction in 1921, was influenced by the first bio-mathematicians who predicted chemical oscillations in homogeneous systems.
This book starts with an introduction to the basic concepts of multistability, then illustrates how multistability arises in different systems and explains the main mechanisms of multistability emergence. A special attention is given to noise which can convert a multistable deterministic system to a monostable stochastic one. Furthermore, the most important applications of multistability in different areas of science, engineering and technology are given attention throughout the book, including electronic circuits, lasers, secure communication, and human perception. The book aims to provide a first approach to multistability for readers, who are interested in understanding its fundamental concepts and applications in several fields. This book will be useful not only to researchers and engineers focusing on interdisciplinary studies, but also to graduate students and technicians. Both theoreticians and experimentalists will rely on it, in fields ranging from mathematics and laser physics to neuroscience and astronomy. The book is intended to fill a gap in the literature, to stimulate new discussions and bring some fundamental issues to a deeper level of understanding of the mechanisms underlying self-organization of matter and world complexity.
Volume I, entitled Russian Mathematics Education: History and World Significance, consists of several chapters written by distinguished authorities from Russia, the United States and other nations. It Examines the hostory of mathematics education in Russia and its relevance to mathematics education throughout the world. The second volume, entitled Russian Mathematics education is highly respected for its achievements and was once very influential internationally, it has never been explored in depth. This publication does just that. --Book Jacket.
This book gives an exposition of the exciting field of control of oscillatory and chaotic systems, which has numerous potential applications in mechanics, laser and chemical technologies, communications, biology and medicine, economics, ecology, etc.A novelty of the book is its systematic application of modern nonlinear and adaptive control theory to the new class of problems. The proposed control design methods are based on the concepts of Lyapunov functions, Poincare maps, speed-gradient and gradient algorithms. The conditions which ensure such control goals as an excitation or suppression of oscillations, synchronization and transformation from chaotic mode to the periodic one or vice versa, are established. The performance and robustness of control systems under disturbances and uncertainties are evaluated.The described methods and algorithms are illustrated by a number of examples, including classical models of oscillatory and chaotic systems: coupled pendula, brusselator, Lorenz, Van der Pol, Duffing, Henon and Chua systems. Practical examples from different fields of science and technology such as communications, growth of thin films, synchronization of chaotic generators based on tunnel diods, stabilization of swings in power systems, increasing predictability of business-cycles are also presented.The book includes many results on nonlinear and adaptive control published previously in Russian and therefore were not known to the West.Researchers, teachers and graduate students in the fields of electrical and mechanical engineering, physics, chemistry, biology, economics will find this book most useful. Applied mathematicians and control engineers from various fields of technology dealing with complex oscillatory systems will also benefit from it.
This fascinating work is devoted to the fundamental phenomenon in physics – synchronization that occurs in coupled non-linear dissipative oscillators. Examples of such systems range from mechanical clocks to population dynamics, from the human heart to neural networks. The main purpose of this book is to demonstrate that the complexity of synchronous patterns of real oscillating systems can be described in the framework of the general approach, and the authors study this phenomenon as applied to oscillations of different types, such as those with periodic, chaotic, noisy and noise-induced nature.
The book provides a concise and rigor introduction to the fundamentals of methods for solving the principal problems of modern non-linear dynamics. This monograph covers the basic issues of the theory of integrable systems and the theory of dynamical chaos both in nonintegrable conservative and in dissipative systems. A distinguishing feature of the material exposition is to add some comments, historical information, brief biographies and portraits of the researchers who made the most significant contribution to science. This allows one to present the material as accessible and attractive to students to acquire indepth scientific knowledge of nonlinear mechanics, feel the atmosphere where those or other important discoveries were made. The book can be used as a textbook for advanced undergraduate and graduate students majoring in high-tech industries and high technology (the science based on high technology) to help them to develop lateral thinking in early stages of training. Contents: Nonlinear Oscillations Integrable Systems Stability of Motion and Structural Stability Chaos in Conservative Systems Chaos and Fractal Attractors in Dissipative Systems Conclusion References Index
This book provides an outline of theoretical concepts and their experimental verification in studies of self-organization phenomena in chemical systems, as they emerged in the mid-20th century and have evolved since. Presenting essays on selected topics, it was prepared by authors who have made profound contributions to the field. Traditionally, physical chemistry has been concerned with interactions between atoms and molecules that produce a variety of equilibrium structures - or the 'dead' order - in a stationary state. But biological cells exhibit a different 'living' kind of order, prompting E. Schrödinger to pose his famous question “What is life?” in 1943. Through an unprecedented theoretical and experimental development, it was later revealed that biological self-organization phenomena are in complete agreement with the laws of physics, once they are applied to a special class of thermodynamically open systems and non-equilibrium states. This knowledge has in turn led to the design and synthesis of simple inorganic systems capable of self-organization effects. These artificial 'living organisms' are able to operate on macroscopic to microscopic scales, even down to single-molecule machines. In the future, such research could provide a basis for a technological breakthrough, comparable in its impact with the invention of lasers and semiconductors. Its results can be used to control natural chemical processes, and to design artificial complex chemical processes with various functionalities. The book offers an extensive discussion of the history of research on complex chemical systems and its future prospects.
A modern introduction to synchronization phenomena, combining the development of deep mathematical concepts with illustrative examples and practical applications.
The book is devoted to the foundations of the theory of boundary-value problems for various classes of systems of differential-operator equations whose linear part is represented by Fredholm operators of the general form. A common point of view on numerous classes of problems that were traditionally studied independently of each other enables us to study, in a natural way, the theory of these problems, to supplement and improve the existing results, and in certain cases, study some of these problems for the first time. With the help of the technique of generalized inverse operators, the Vishik– Lyusternik method, and iterative methods, we perform a detailed investigation of the problems of existence, bifurcations, and branching of the solutions of linear and nonlinear boundary-value problems for various classes of differential-operator systems and propose new procedures for their construction. For more than 11 years that have passed since the appearance of the first edition of the monograph, numerous new publications of the authors in this direction have appeared. In this connection, it became necessary to make some additions and corrections to the previous extensively cited edition, which is still of signifi cant interest for the researchers. For researchers, teachers, post-graduate students, and students of physical and mathematical departments of universities. Contents: Preliminary Information Generalized Inverse Operators in Banach Spaces Pseudoinverse Operators in Hilbert Spaces Boundary-Value Problems for Operator Equations Boundary-Value Problems for Systems of Ordinary Differential Equations Impulsive Boundary-Value Problems for Systems of Ordinary Differential Equations Solutions of Differential and Difference Systems Bounded on the Entire Real Axis
Systems with mechanical degrees of freedom containing unstable objects are analysed in this monograph and algorithms for their control are developed, discussed, and numerically tested. This is achieved by identifying unstable modes of motion and using all available resources to suppress them. By using this approach the region of states from which a stable regime can be reached is maximised. The systems discussed in this book are models for pendula and vehicles and find applications in mechatronics, robotics as well as in mechanical and automotive engineering.
Spirals, 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.
Modern air and space craft demand a huge variety of sensing elements for detecting and controlling their behavior and operation. These sensors often differ significantly from those designed for applications in automobile, ship, railway, and other forms of transportation, and those used in industrial, chemical, medical, and other areas. This book offers insight into an appropriate selection of these sensors and describes their principles of operation, design, and achievable performance along with particulars of their construction. Drawn from the activities of the International Federation of Automatic Control (IFAC), especially its Aerospace Technical Committee, the book provides details on the majority of sensors for aircraft and many for spacecraft, satellites, and space probes. It is written by an international team of twelve authors representing four countries from Eastern and Western Europe and North America, all with considerable experience in aerospace sensor and systems design. Highlights include: • coverage of aerospace vehicle classification, specific design criteria, and the requirements of onboard systems and sensors; • reviews of airborne flight parameter sensors, weather sensors and collision avoidance devices; • discussions on the important role of inertial navigation systems (INS) and separate gyroscopic sensors for aerospace vehicle navigation and motion control; • descriptions of engine parameter information collection systems, including fuel quantity and consumption sensors, pressure pick-ups, tachometers, vibration control, and temperature sensors; and • descriptions and examples of sensor integration.
Especially designed as self-sustaining oscillating systems, resonant robotic systems use the natural modes of oscillation of electromechanical modules for their movements. In fact, manipulator systems built on these principles demonstrate record-breaking characteristics in performance. The authors summarize the results and experience of research on, and development of, resonant robotic systems. For the readers convenience, a presentation of design concepts is followed by solutions to new dynamical and control problems. The book is intended for designers, researchers and graduate students.
A treatment of various kinds of limit theorems for stochastic processes defined as a result of random perturbations of dynamical systems. Apart from the long-time behaviour of the perturbed system, exit problems, metastable states, optimal stabilisation, and asymptotics of stationary distributions are considered in detail. The authors'main tools are the large deviation theory, the central limit theorem for stochastic processes, and the averaging principle. The results allow for explicit calculations of the asymptotics of many interesting characteristics of the perturbed system, and most of these results are closely connected with PDEs. This new edition contains expansions on the averaging principle, a new chapter on random perturbations of Hamiltonian systems, along with new results on fast oscillating perturbations of systems with conservation laws. New sections on wave front propagation in semilinear PDEs and on random perturbations of certain infinite-dimensional dynamical systems have been incorporated into the chapter on sharpenings and generalisations.
Offering alternative models based on such concepts as satisficing (acceptance of viable choices that may not be the undiscoverable optimum) and bouded rationality (the limited extent to which rational calculation can direct human behaviour), Simon shows why more empirical research based on experiments and direct observation, rather than just statistical analysis of economic aggregates, is needed.
This Reference eBook deals with an existing classification of a nanosized structure and an analysis of its properties. It summarizes an information about how a grain size affects physical, mechanical, thermal, and other properties of a nanostructured material. A basic method, which is employed for a fabrication of an isolated nanoparticle, an ultradisperse powder, a compact nanocystalline, nanoporous, and amorphous material, a fullerene, a nanotube, and a nanostuctured coating, is considered. Investigation methods, which are applied to study the nanostructured material, are briefly described. A modern understanding of a formation of the nanostructured and nanocomposite coating, which are fabricated using a ion-plasma deposition method, is reposted. A potential application of the nanostructured material and coating in a field of engineering is demonstrated. Readership: Graduate, Postgraduate, Ph.D. Students, Researchers and Industry Professionals. The eBook contains 9 Chapters, 87 Figures, 14 Tables, 411 References-totally, 155 Pages. It was approved by two Scientific Boards from National Kharkov University and Sumy State University. A main content of this eBook is a basis for lectures presented for students at Sumy State University (the Physical-Technical Faculty), Kharkov National University (the Physical Faculty), Omsk State University (the Physical Faculty, the Department of Material Science), East-Kazakhstan State Technical University (Ust-Kamenogorsk, Kazakhstan), and Moscow State University (the Physical Faculty, Moscow, Russia). A source of this eBook is original papers of leading world-known scientists, who ware involved in a field of new nano composite material fabrication, nanotechnologies, and researches. This version had not been published elsewhere. It is interesting for a wide circle of specialists, Masters, aspirants, scientific researchers, and a technical staff of Higher Education System, Research Institutes and Laboratories. It covers recent data since 2008 to 2010 year.
The papers in this edited volume aim to provide a better understanding of the dynamics and control of a large class of hybrid dynamical systems that are described by different models in different state space domains. They not only cover important aspects and tools for hybrid systems analysis and control, but also a number of experimental realizations. Special attention is given to synchronization a universal phenomenon in nonlinear science that gained tremendous significance since its discovery by Huygens in the 17th century. Possible applications of the results introduced in the book include control of mobile robots, control of CD/DVD players, flexible manufacturing lines, and complex networks of interacting agents. The book is based on the material presented at a similarly entitled minisymposium at the 6th European Nonlinear Dynamics Conference held in St Petersburg in 2008. It is unique in that it contains results of several international and interdisciplinary collaborations in the field, and reflects state-of-the-art technological development in the area of hybrid mechanical systems at the forefront of the 21st century.
This book deals with fundamental problems, concepts, and methods of multiparameter stability theory with applications in mechanics. It presents recent achievements and knowledge of bifurcation theory, sensitivity analysis of stability characteristics, general aspects of nonconservative stability problems, analysis of singularities of boundaries for the stability domains, stability analysis of multiparameter linear periodic systems, and optimization of structures under stability constraints. Systems with finite degrees of freedom and with continuous models are both considered. The book combines mathematical foundation with interesting classical and modern mechanical problems.A number of mechanical problems illustrating how bifurcations and singularities change the behavior of systems and lead to new physical phenomena are discussed. Among these problems, the authors consider systems of rotating bodies, tubes conveying fluid, elastic columns under the action of periodic and follower forces, optimization problems for conservative systems, etc. The methods presented are constructive and easy to implement in computer programs.This book is addressed to graduate students, academics, researchers, and practitioners in aerospace, naval, civil, and mechanical engineering. No special background is needed; just a basic knowledge of mathematics and mechanics.
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