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Weak Dependence : With Examples and Applications
This monograph is aimed at developing Doukhan/Louhichi's (1999) idea to measure asymptotic independence of a random process. The authors propose various examples of models fitting such conditions such as stable Markov chains, dynamical systems or more complicated models, nonlinear, non-Markovian, and heteroskedastic models with infinite memory. Most of the commonly used stationary models fit their conditions. The simplicity of the conditions is also their strength.
Vibrations and Stability : Advanced Theory, Analysis, and Tools
Ties together classical and modern topics of advanced vibration analysis in an interesting and lucid manner. It is intended for advanced students, university teachers, and researchers in mechanical/structural engineering dynamics, and professional engineers aiming at strengthening their theoretical foundation. Assuming background knowledge in elementary vibrations, it provides a set of useful tools for understanding and analyzing the more complex dynamical phenomena that can be met in engineering and scientific practice. Summarizing first basic linear vibration theory, it progresses over various types of nonlinearity and nonlinear interaction to bifurcation analysis, chaotic vibrations, and special high-frequency effects. It trains the student to analyze simple models, recognize nonlinear phenomena, and work with advanced tools such as perturbation analysis and bifurcation analysis
Unifying Themes in Complex Systems IV ; Proceedings of the Fourth International Conference on Complex Systems
In June of 2002, over 500 professors, students and researchers met in Boston, Massachusetts for the Fourth International Conference on Complex Systems. The attendees represented a remarkably diverse collection of fields: biology, ecology, physics, engineering, computer science, economics, psychology and sociology, The goal of the conference was to encourage cross-fertilization between the many disciplines represented and to deepen understanding of the properties common to all complex systems. This volume contains 43 papers selected from the more than 200 presented at the conference. Topics include: cellular automata, neurology, evolution, computer science, network dynamics, and urban planning.
Understanding Non-equilibrium Thermodynamics : Foundations, Applications, Frontiers
Our time is characterized by an explosion of information and by an accel- ation of knowledge. A book cannot compete with the huge amount of data available on the Web. However, to assimilate all this information, it is n- essary to structure our knowledge in a useful conceptual framework. The purpose of the present work is to provide such a structure for students and researchers interested by the current state of the art of non-equilibrium th- modynamics. The main features of the book are a concise and critical pres- tation of the basic ideas, illustrated by a series of examples, selected not only for their pedagogical value but also for the perspectives o?ered by recent technological advances. This book is aimed at students and researchers in physics, chemistry, engineering, material sciences, and biology. We have been guided by two apparently antagonistic objectives: gener- ity and simplicity. To make the book accessible to a large audience of n- specialists, we have decided about a simpli?ed but rigorous presentation. Emphasis is put on the underlying physical background without sacri?cing mathematical rigour, the several formalisms being illustrated by a list of - amplesandproblems.
Unconventional Computing ; 7th International Conference, UC 2008 Vienna, Austria, August 25-28, 2008. Proceedings
The book is devoted to all aspects of unconventional computation ranging from theoretical and experimental aspects to various applications. Typical topics are: natural computing including quantum, cellular, molecular, neural and evolutionary computing, chaos and dynamical system-based computing, and various proposals for computations that go beyond the Turing model.
Unconventional Computation ; 6th International Conference, UC 2007, Kingston, Canada, August 13-17, 2007, Proceedings
This book constitutes the refereed proceedings of the Sixth International Conference on Unconventional Computation, UC 2007,organized under the auspices of the EATCS by the Centre for Discrete Math.
Ultrasonic Processes and Machines : Dynamics, Control and Applications
Presents the foundations of dynamics and control for ultrasonic processing systems. The intention is to bridge the gap between theory and the practical application of ultrasonic technology. This book considers ultrasonic systems as special vibratory machines that function by exploiting nonlinear dynamic processes. Recommendations are given for designing and tuning ultrasonic machines. The ultrasonic machines analysed are predominantly concerned with the processing of solids. Applications include: ultrasonic erosion, ultrasonic hardening, ultrasonic welding, ultrasonically assisted plastic deformation, ultrasonically assisted turning, and ultrasonically assisted drilling.
Twin-Control : A Digital Twin Approach to Improve Machine Tools Lifecycle
Summarizes the results of the European research project “Twin-model based virtual manufacturing for machine tool-process simulation and control” (Twin-Control). The first part reviews the applications of ICTs in machine tools and manufacturing, from a scientific and industrial point of view, and introduces the Twin-Control approach, while Part 2 discusses the development of a digital twin of machine tools. The third part addresses the monitoring and data management infrastructure of machines and manufacturing processes and numerous applications of energy monitoring. Part 4 then highlights various features developed in the project by combining the developments covered in Parts 3 and 4 to control the manufacturing processes applying the so-called CPSs. Lastly, Part 5 presents a complete validation of Twin-Control features in two key industrial sectors: aerospace and automotive. The book offers a representative overview of the latest trends in the manufacturing industry, with a focus on machine tools.
Tutorials in Mathematical Biosciences I : Mathematical Neuroscience
Introduces some basic theories on computational neuroscience. Chapter 1 is a brief introduction to neurons, tailored to the subsequent chapters. Chapter 2 is a self-contained introduction to dynamical systems and bifurcation theory, oriented towards neuronal dynamics. The theory is illustrated with a model of Parkinson's disease. Chapter 3 reviews the theory of coupled neural oscillators observed throughout the nervous systems at all levels; it describes how oscillations arise, what pattern they take, and how they depend on excitory or inhibitory synaptic connections. Chapter 4 specializes to one particular neuronal system, namely, the auditory system. It includes a self-contained introduction, from the anatomy and physiology of the inner ear to the neuronal network that connects the hair cells to the cortex, and describes various models of subsystems.
Turbulence and Diffusion : Scaling Versus Equations
This book is an introduction to the multidisciplinary field of anomalous diffusion in complex systems, with emphasis on the scaling approach as opposed to techniques based on the quantitative analysis of underlying transport equations. Typical examples of such systems are turbulent plasmas, convective rolls, zonal flow systems and stochastic magnetic fields. From the more methodological point of view, the approach relies on the general use of correlations estimates, quasilinear equations and continuous time random walk techniques. Yet, the mathematical descriptions are not meant to become a fixed set of recipes but rather develop and strengthen the reader's physical intuition and understanding on the underlying mechanisms involved.
Trend and Applications of Mathematics to Mechanics ; STAMM 2002
The book collects a selection of papers most of which are revised and enriched versions of the contributions presented at the 12th Symposium on Trends of Applications of Mathematics to Mechanics (STAMM) which was sponsored by the International Society for the Interaction between Mathematics and Mechanics (ISIMM) and held in Maiori (Salerno), Italy from September 29th to October 4th, 2002. The Symposium attracted many leading researchers from around the world who are working at the interface between Mathematics and Mechanics. The importance of a close link between these two disciplines have long been recognized and each of them get benefits and stimuli by open problems, methods and results emerging from the other one. The book collects 22 papers which contribute special investigations and more wide presentations of linear and nonlinear problems.
Topological Fixed Point Theory of Multivalued Mappings
This book is devoted to the topological fixed point theory of multivalued mappings including applications to differential inclusions and mathematical economy. It is the first monograph dealing with the fixed point theory of multivalued mappings in metric ANR spaces. Although the theoretical material was tendentiously selected with respect to applications, the text is self-contained. Current results are presented." "This book will be especially useful for post-graduate students and researchers interested in fixed point theory, and in particular, topological methods in nonlinear analysis, differential equations and dynamical systems.
Topological Degree Approach to Bifurcation Problems
Topological bifurcation theory is one of the most essential topics in mathematics. This book contains original bifurcation results for the existence of oscillations and chaotic behaviour of differential equations and discrete dynamical systems under variation of involved parameters. Using topological degree theory and a perturbation approach in dynamical systems, a broad variety of nonlinear problems are studied, including: non-smooth mechanical systems with dry frictions; weakly coupled oscillators; systems with relay hysteresis; differential equations on infinite lattices of Frenkel-Kontorova and discretized Klein-Gordon types; blue sky catastrophes for reversible dynamical systems; buckling of beams; and discontinuous wave equations.
Topics in Gravitational Dynamics : Solar, Extra-Solar and Galactic Systems
This set of lectures collects surveys of open problems in celestial dynamics and dynamical astronomy applied to solar, extra-solar and galactic systems. Emphasis is on questions of stability of planetary systems.
Topics in Almost Automorphy
The range of applications include at present linear and nonlinear evolution equations, integro-differential and functional-differential equations, dynamical systems, etc...It has become imperative to take a bearing of the main steps of the the ory. That is the main purpose of this monograph. It is intended to inform the reader and pave the road to more research in the field. It is not a self contained book.
The Physics of Coronary Blood Flow
This book is devoted specifically to the dynamics and physics of coronary blood flow. While relevance to the clinical and pathophysiological issues is clearly maintained, the book approaches the subject from a biomedical engineering point of view. With this perspective, the Physics of Coronary Blood Flow complements other treatments of the subject that focus largely on the clinical and pathophysiological issues.
The Painlevé Handbook
This book introduces the reader to methods allowing one to build explicit solutions to these equations. A prerequisite task is to investigate whether the chances of success are high or low, and this can be achieved without any a priori knowledge of the solutions, with a powerful algorithm presented in detail called the Painlevé test. If the equation under study passes the Painlevé test, the equation is presumed integrable. If on the contrary the test fails, the system is nonintegrable or even chaotic, but it may still be possible to find solutions.
The Monodromy Group
In singularity theory and algebraic geometry, the monodromy group is embodied in the Picard-Lefschetz formula and the Picard-Fuchs equations. There is a deep connection of monodromy theory with Galois theory of differential equations and algebraic functions.
The Fermi-Pasta-Ulam Problem : A Status Report
This volume reviews the current understanding of this paradox without trying to force coherence on differing perspectives on the same problem by various groups or approaches. The contributions comprise studies of one-dimensional chains, descriptions of numerical methods, heuristic theories, addressing the "long standing and controversial problem of distinguishing chaos from noise in signal analysis," metastability, the relation of the FPU motions with the integrable equations, approaches using methods of perturbation theory and the proof of the applicability of KAM theory in FPU chains with energy very close to a minimum. For the convenience of the reader the original work of FPU is reprinted in an appendix.
Tensor Network Contractions : Methods and Applications to Quantum Many-Body Systems
This book is intended for graduated students, but can also be used as a professional book for researchers in the related fields. To understand most of the contents in the book, only basic knowledge of quantum mechanics and linear algebra is required. In order to fully understand some advanced parts, the reader will need to be familiar with notion of condensed matter physics and quantum information, that however are not necessary to understand the main parts of the book. This book is a good source for non-specialists on quantum physics to understand tensor network algorithms and the related mathematics.
