الصفحة 1
الصفحة 1
Wavelets, Multiscale Systems and Hypercomplex Analysis
This volume contains a selection of papers on the topics of Clifford analysis and wavelets and multiscale analysis, the latter being understood in a very wide sense. The theory of wavelets is mathematically rich and has many practical applications.
Vortex Dominated Flows : Analysis and Computation for Multiple Scale Phenomena
Addressed to both graduate students and researchers this monograph provides in-depth analyses of vortex dominated flows via matched and multiscale asymptotics, and it demonstrates how insight gained through these analyses can be exploited in the construction of robust, efficient, and accurate numerical techniques.
Tsunami and Nonlinear Waves
The need for tsunami research and analysis has grown dramatically following the devastating tsunami of December 2004, which affected Southern Asia. This book pursues a detailed theoretical and mathematical analysis of the fundamentals of tsunamis, especially the evolution and dynamics of tsunamis and other great waves. Of course, it includes specific measurement results from the 2004 tsunami, but the emphasis centres on the nature of the waves themselves and their links to nonlinear phenomena. Throughout, methods of nonlinear dynamics and integrable systems are employed to develop novel concep.
Time and Space in Economics
In August 2005, a small but important conference took place at Chuo University in Tokyo, Japan. This international conference, the Chuo Meeting on Economics of Time and Space 2005 (Chuo METS 05), aimed to enrich the respective disciplines of the economics of time (dynamic economics) and the economics of space (spatial economics) and to expand their applicability in the real world. The chapters contained herein are based on the papers presented at that conference. Part I of the book deals with Keynesian macrodynamics, which allows for the existence of involuntary unemployment; Part II focuses on nonlinear dynamics, with an emphasis on the complexity that is generated as a result of the nonlinearity of the system; Part III consists of an empirical analysis of spatial economics through geographical relationships with economic activity; and Part IV analyzes the effects of spatial competition between economic organizations or agents on economic performance in a region.
Thinking in Complexity : The Computational Dynamics of Matter, Mind, and Mankind
The theory of nonlinear, complex systems has become by now a proven problem-solving approach in the natural sciences. In this book, Klaus Mainzer discusses, the common framework behind these ideas and challenges. Emphasis is given to the evolution of new structures in natural and cultural systems.
Thin Films of Soft Matter
A detailed overview and comprehensive analysis of the main theoretical and experimental advances on free surface thin film and jet flows of soft matter is given. At the theoretical front the book outlines the basic equations and boundary conditions and the derivation of low-dimensional models for the evolution of the free surface. Such models include long-wave expansions and equations of the boundary layer type and are analyzed via linear stability analysis, weakly nonlinear theories and strongly nonlinear analysis including construction of stationary periodic and solitary wave and similarity solutions. At the experimental front a variety of very recent experimental developments is outlined and the link between theory and experiments is illustrated. Such experiments include spreading drops and bubbles, imbibitions, singularity formation at interfaces and experimental characterization of thin films using atomic force microscopy, ellipsometry and contact angle measurements and analysis of patterns using Minkowski functionals.
Thermo-Dynamics of Plates and Shells
This monograph is devoted to the investigation of nonlinear dynamics of plates and shells embedded in a temperature field. Numerical approaches and rigorous mathematical proofs of solution existence in certain classes of differential equations with various dimensions are applied. Both closed shell-type constructions and sectorial shells are studied. The considered problems are approximated by 2D and 3D constructions taking into account various types of nonlinearities (geometrical and/or physical with coupled deformation and temperature fields), and are subjected to an action of stationary and non-stationary thermal loads.
The Logistic Map and the Route to Chaos : From the Beginnings to Modern Applications
Pierre-Francois Verhulst, with his seminal work using the logistic map to describe population growth and saturation, paved the way for the many applications of this tool in modern mathematics, physics, chemistry, biology, economics and sociology. Indeed nowadays the logistic map is considered a useful and paradigmatic showcase for the route leading to chaos. This volume gathers contributions from some of the leading specialists in the field to present a state-of-the art view of the many ramifications of the developments initiated by Verhulst over a century ago.
Semiconductor Lasers : Stability, Instability and Chaos
This monograph describes fascinating recent progress in the field of chaos, stability and instability of semiconductor lasers. Applications and future prospects are discussed in detail. The book emphasizes the various dynamics induced in semiconductor lasers by optical and electronic feedback, optical injection, and injection current modulation. Recent results of both theoretical and experimental investigations are presented. Demonstrating applications of semiconductor laser chaos, control and noise, Semiconductor Lasers describes suppression and chaotic secure communications. For those who are interested in optics but not familiar with nonlinear systems, a brief introduction to chaos analysis is presented.
Self-Organizing Natural Intelligence : Issues of Knowing, Meaning, and Complexity
This book proposes, utilizes, and demonstrates the research superiority of a highly developed multidisciplinary theory models approach to intelligence. With conceptual tools, concepts and mathematical methods more suited to continuous, dynamic phenomena of living things, the entire scope of natural intelligence based upon empirical studies of actual human and animal experience is addressed. Results show that human and animal intelligence is largely self-organizing and emergent across a spectrum of major categories of kinds of natural intelligence, not limited to a single "top down" capacity as current proponents of the single-capacity g-theory and IQ approach support.
Self-Organized Morphology in Nanostructured Materials
In this volume, concepts of nonlinear dynamics and self-organization are applied to topics in materials sciences with emphasis on semiconductors, soft matter, and biomaterials.
Self-Assembly, Pattern Formation and Growth Phenomena in Nano-Systems ; Proceedings of the NATO Advanced Study Institute, held in St. Etienne de Tinee, France, August 28 - September 11, 2004
Contains lecture notes written by the lecturers of the NATO Advanced Study Institute. This book gives examples of self-organization phenomena on micro- and nano-scale as well as examples of the interplay between phenomena on nano- and macro-scales leading to complex behavior in various physical, chemical and biological systems.
Photonic neural networks with spatiotemporal dynamics: paradigms of computing and implementation
Offers novel multidisciplinary viewpoints on photonic neuralnetworks, illustrating recent advances in three types of computing methodologies:fluorescence energy transfer computing, spatial-photonic spin system, and photonic reservoir computing. The book consists of four parts: The first part introduces the backgrounds ofoptical computing and neural network dynamics; the second part presents fluorescenceenergy transfer computing, a novel computing technology based on nanoscalenetworks of fluorescent particles; the third and fourth parts review the models andimplementation of spatial photonic spin systems and photonic reservoir computing,respectively.
Optimization in Medicine
This volume presents a wide range of medical applications that can utilize mathematical computing. Examples include using an algorithm for considering the seed reconstruction problem in brachytherapy and using optimization-classification models to assist in the early prediction, diagnosis and detection of diseases. Discrete optimization techniques and measures derived from the theory of nonlinear dynamics, with analysis of multi-electrode electroencephalographic (EEG) data, assist in predicting impending epileptic seizures. Mathematics in medicine can also be found in recent cancer research. Sophisticated mathematical models and optimization algorithms have been used to generate treatment plans for radionuclide implant and external beam radiation therapy. Optimization techniques have also been used to automate the planning process in Gamma Knife treatment, as well as to address a variety of medical image registration problems.
Nonlinear Partial Differential Equations for Scientists and Engineers
This expanded and revised second edition is a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied applications. Building upon the successful material of the first book, this edition contains updated modern examples and applications from areas of fluid dynamics, gas dynamics, plasma physics, nonlinear dynamics, quantum mechanics, nonlinear optics, acoustics, and wave propagation. Methods and properties of solutions are presented, along with their physical significance, making the book more useful for a diverse readership.
Nonlinear Dynamics of Structures Under Extreme Transient Loads
Covers model building for different engineering structures and provides detailed presentations of extreme loading conditions. A number of illustrations are given quantifying; a plane crash or explosion induced impact loading, the effects of strong earthquake motion, and the impact and long-duration effects of strong stormy winds—along with a relevant framework for using modern computational tools. The book considers the levels of reserve in existing structures, and ways of reducing the negative impact of high-risk situations by employing sounder design procedures.
Nonlinear Dynamics of Chaotic and Stochastic Systems : Tutorial and Modern Developments
This book is a complete treatise on the theory of nonlinear dynamics of chaotic and stochastic systems. It contains both an exhaustive introduction to the subject as well as a detailed discussion of fundamental problems and research results in a field to which the authors have made important contributions themselves.
Nonlinear dynamics of a wheeled vehicle
This book provides an overview of the theory of stability analysis and its applications. It is focused on various methods devoted to analyzing wheeled vehicle behavior. The authors provide both basic and advanced knowledge of the subject.
Nonlinear Dynamics in Geosciences
Nonlinear Dynamics in Geosciences is comprised of the proceedings of "20 Years of Nonlinear Dynamics in Geosciences", held June 11-16, 2006 in Rhodes, Greece as part of the Aegean Conferences. The volume brings together the most up-to-date research from the atmospheric sciences, hydrology, geology, and other areas of geosciences, and discusses the advances made in the last two decades and the future directions of nonlinear dynamics. Topics covered include predictability, ensemble prediction, nonlinear prediction, nonlinear time series analysis, low-dimensional chaos, nonlinear modeling, fractals and multifractals, bifurcation, complex networks, self-organized criticality, extreme events, and other aspects of nonlinear science.
Nonlinear dynamics in complex systems via fractals and fractional calculus
Current advances in the knowledge of nonlinear dynamical networks, systems and processes, as well as their unified repercussions, allow us to include some typical complex natural phenomena, from the nanoscale to an extra-galactic scale, in an unitarian comprehensive manner. In other words, the physical, biological and financial data, as well as technological ones (mechanical or electronic devices), of complex systems available today can be managed by the same unique conceptual approach, both analytically and through a computer simulation, using effective nonlinear dynamics procedures. This volume collected some important advances in the fields of fractal curves, fractal analysis and fractional calculus, as well as new solutions of fractal differential equations.
