Download or read book Nonlinear Physics of Plasmas written by Mitsuo Kono and published by Springer Science & Business Media. This book was released on 2010-10-17 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: A nonlinearity is one of the most important notions in modern physics. A plasma is rich in nonlinearities and provides a variety of behaviors inherent to instabilities, coherent wave structures and turbulence. The book covers the basic concepts and mathematical methods, necessary to comprehend nonlinear problems widely encountered in contemporary plasmas, but also in other fields of physics and current research on self-organized structures and magnetized plasma turbulence. The analyses make use of strongly nonlinear models solved by analytical techniques backed by extensive simulations and available experiments. The text is written for senior undergraduates, graduate students, lecturers and researchers in laboratory, space and fusion plasmas.
Download or read book Nonlinear Processes in Physics written by A.S. Fokas and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1979, a historical meeting took place at the Institute for Theoretical Physics in Kiev, USSR, where 48 American Scientists, specialists in nonlinear and turbulent processes, met for two weeks with their soviet counterparts. This meeting pro vided the unique opportunity for USA and USSR participants to directly interact personally and scientifically with each other. This interaction was of great impor not only for the individuals involved but also for the science of nonlinear tance phenomena in general. At the end of the meeting, it was agreed that this exchange should continue, and it was decided to have the next meeting in the USA in 1981. Unfortunately, due to the political situation at that time, the second meeting in the USA never materialized. However, in 1983, the Soviet scientists organized in Kiev a second Workshop. This second meeting was again quite successful. Similar meetings, with growing success were organized at Kiev in 1987, and 1989. It should be noted that 405 participants from 22 countries participated at the fourth Kiev workshop on Nonlinear and Turbulent Processes. The Chainnan of this workshop was V. Zakharov, who has also been a co-chainnan of all the previous workshops.
Download or read book Modeling by Nonlinear Differential Equations written by Paul Edgar Phillipson and published by World Scientific. This book was released on 2009 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to provide mathematical analyses of nonlinear differential equations, which have proved pivotal to understanding many phenomena in physics, chemistry and biology. Topics of focus are autocatalysis and dynamics of molecular evolution, relaxation oscillations, deterministic chaos, reaction diffusion driven chemical pattern formation, solitons and neuron dynamics. Included is a discussion of processes from the viewpoints of reversibility, reflected by conservative classical mechanics, and irreversibility introduced by the dissipative role of diffusion. Each chapter presents the subject matter from the point of one or a few key equations, whose properties and consequences are amplified by approximate analytic solutions that are developed to support graphical display of exact computer solutions. Sample Chapter(s). Chapter 1: Theme and Contents of this Book (85 KB). Contents: Theme and Contents of this Book; Processes in closed and Open Systems; Dynamics of Molecular Evolution; Relaxation Oscillations; Order and Chaos; Reaction Diffusion Dynamics; Solitons; Neuron Pulse Propagation; Time Reversal, Dissipation and Conservation. Readership: Advanced undergraduates, graduate students and researchers in physics, chemistry, biology or bioinformatics who are interested in mathematical modeling.
Download or read book Nonlinear Wave Processes in Acoustics written by K. Naugolnykh and published by Cambridge University Press. This book was released on 1998-05-28 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text considers models of different "acoustic" media as well as equations and behavior of finite-amplitude waves. It also considers the effects of nonlinearity, dissipation, dispersion, and for two- and three-dimensional problems, reflection and diffraction on the evolution and interaction of acoustic beams.
Download or read book The Physics of Plasmas written by T. J. M. Boyd and published by Cambridge University Press. This book was released on 2003-01-23 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Physics of Plasmas provides a comprehensive introduction to the subject, illustrating the basic theory with examples drawn from fusion, space and astrophysical plasmas. A particular strength of the book is its discussion of the various models used to describe plasma physics and the relationships between them. These include particle orbit theory, fluid equations, ideal and resistive magnetohydrodynamics, wave equations and kinetic theory. The reader will gain a firm grounding in the fundamentals, and develop this into an understanding of some of the more specialised topics. Throughout the text, there is an emphasis on the physical interpretation of plasma phenomena. Exercises are provided throughout. Advanced undergraduate and graduate students of physics, applied mathematics, astronomy and engineering will find a clear but rigorous explanation of the fundamental properties of plasmas with minimal mathematical formality. This book will also appeal to research physicists, nuclear and electrical engineers.
Download or read book Nonlinear Physics written by R. Z. Sagdeev and published by CRC Press. This book was released on 1988 with total page 726 pages. Available in PDF, EPUB and Kindle. Book excerpt: Translated from the Russian. Gathers together the basic ideas of nonlinear theory essential for all branches of physics: mechanics of continuous media, optics, radiophysics, solid state physics, plasma physics. Includes color plates. Two sets of computer software (eight scenarios of dynamic computer graphics, and an ATRS program for research workers) are available separately. Annotation copyrighted by Book News, Inc., Portland, OR
Download or read book Physics of Nonlinear Optics written by Y. V. G. S. Murti and published by Springer Nature. This book was released on 2021-07-20 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is designed to serve as a textbook for courses offered to upper-undergraduate students enrolled in physics. The first edition of this book was published in 2014. As there is a demand for the next edition, it is quite natural to take note of the several advances that have occurred in the subject over the past five years and to decide which of these are appropriate for inclusion at the textbook level, given the fundamental nature and the significance of the subject area. This is the prime motivation for bringing out a revised second edition. Among the newer mechanisms and materials, the book introduces the super-continuum generation, which arises from an excellent interplay of the various mechanisms of optical nonlinearity. The topics covered in this book are quantum mechanics of nonlinear interaction of matter and radiation, formalism and phenomenology of nonlinear wave mixing processes, optical phase conjugation and applications, self-focusing and self-phase modulation and their role in pulse modification, nonlinear absorption mechanisms, and optical limiting applications, photonic switching and bi-stability, and physical mechanisms leading to a nonlinear response in a variety of materials. This book has emerged from an attempt to address the requirement of presenting the subject at the college level. This textbook includes rigorous features such as the elucidation of relevant basic principles of physics; a clear exposition of the ideas involved at an appropriate level; coverage of the physical mechanisms of non-linearity; updates on physical mechanisms and emerging photonic materials and emphasis on the experimental study of nonlinear interactions. The detailed coverage and pedagogical tools make this an ideal textbook for students and researchers enrolled in physics and related courses.
Download or read book Advanced Photonics with Second Order Optically Nonlinear Processes written by A.D. Boardman and published by Springer. This book was released on 1998-11-30 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although it took some time to establish the word, photonics is both widely accepted and used throughout the world and a major area of activity concerns nonlinear materials. In these the nonlinearity mainly arises from second-order or third-order nonlinear optical processes. A restriction is that second-order processes only occur in media that do not possess a centre of symmetry. Optical fibres, on the other hand, being made of silica glass, created by fusing SiO molecules, are made of material with a centre of z symmetry, so the bulk of all processes are governed by third-order nonlinearity. Indeed, optical fibre nonlinearities have been extensively studied for the last thirty years and can be truly hailed as a success story of nonlinear optics. In fact, the fabrication ofsuch fibres, and the exploitation oftheir nonlinearity, is in an advanced stage - not least being their capacity to sustain envelope solitons. What then ofsecond-order nonlinearity? This is also well-known for its connection to second-harmonic generation. It is an immediate concern, however, to understand how waves can mix and conserve both energy and momentum ofthe photons involved. The problem is that the wave vectors cannot be made to match without a great deal of effort, or at least some clever arrangement has to be made - a special geometry, or crystal arrangement. The whole business is called phase matching and an inspection ofthe state-of-the-art today, reveals the subject to be in an advanced state.
Download or read book Nonlinear Dynamics and Chaos written by Steven H. Strogatz and published by CRC Press. This book was released on 2018-05-04 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
Download or read book Nonlinear Optical Waves written by A.I. Maimistov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: A non-linear wave is one of the fundamental objects of nature. They are inherent to aerodynamics and hydrodynamics, solid state physics and plasma physics, optics and field theory, chemistry reaction kinetics and population dynamics, nuclear physics and gravity. All non-linear waves can be divided into two parts: dispersive waves and dissipative ones. The history of investigation of these waves has been lasting about two centuries. In 1834 J. S. Russell discovered the extraordinary type of waves without the dispersive broadening. In 1965 N. J. Zabusky and M. D. Kruskal found that the Korteweg-de Vries equation has solutions of the solitary wave form. This solitary wave demonstrates the particle-like properties, i. e. , stability under propagation and the elastic interaction under collision of the solitary waves. These waves were named solitons. In succeeding years there has been a great deal of progress in understanding of soliton nature. Now solitons have become the primary components in many important problems of nonlinear wave dynamics. It should be noted that non-linear optics is the field, where all soliton features are exhibited to a great extent. This book had been designed as the tutorial to the theory of non-linear waves in optics. The first version was projected as the book covering all the problems in this field, both analytical and numerical methods, and results as well. However, it became evident in the process of work that this was not a real task.
Download or read book Analysis and Data Based Reconstruction of Complex Nonlinear Dynamical Systems written by M. Reza Rahimi Tabar and published by Springer. This book was released on 2019-07-04 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on a central question in the field of complex systems: Given a fluctuating (in time or space), uni- or multi-variant sequentially measured set of experimental data (even noisy data), how should one analyse non-parametrically the data, assess underlying trends, uncover characteristics of the fluctuations (including diffusion and jump contributions), and construct a stochastic evolution equation? Here, the term "non-parametrically" exemplifies that all the functions and parameters of the constructed stochastic evolution equation can be determined directly from the measured data. The book provides an overview of methods that have been developed for the analysis of fluctuating time series and of spatially disordered structures. Thanks to its feasibility and simplicity, it has been successfully applied to fluctuating time series and spatially disordered structures of complex systems studied in scientific fields such as physics, astrophysics, meteorology, earth science, engineering, finance, medicine and the neurosciences, and has led to a number of important results. The book also includes the numerical and analytical approaches to the analyses of complex time series that are most common in the physical and natural sciences. Further, it is self-contained and readily accessible to students, scientists, and researchers who are familiar with traditional methods of mathematics, such as ordinary, and partial differential equations. The codes for analysing continuous time series are available in an R package developed by the research group Turbulence, Wind energy and Stochastic (TWiSt) at the Carl von Ossietzky University of Oldenburg under the supervision of Prof. Dr. Joachim Peinke. This package makes it possible to extract the (stochastic) evolution equation underlying a set of data or measurements.
Download or read book Introduction to the Mathematical Physics of Nonlinear Waves written by Minoru Fujimoto and published by Morgan & Claypool Publishers. This book was released on 2014-03-01 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear physics is a well-established discipline in physics today, and this book offers a comprehensive account of the basic soliton theory and its applications. Although primarily mathematical, the theory for nonlinear phenomena in practical environment
Download or read book Nonlinear Magnetohydrodynamics written by D. Biskamp and published by Cambridge University Press. This book was released on 1997-07-17 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introduction to magnetohydrodynamics with emphasis on nonlinear processes.
Download or read book What Is Integrability written by Vladimir E. Zakharov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: The idea of devoting a complete book to this topic was born at one of the Workshops on Nonlinear and Turbulent Processes in Physics taking place reg ularly in Kiev. With the exception of E. D. Siggia and N. Ercolani, all authors of this volume were participants at the third of these workshops. All of them were acquainted with each other and with each other's work. Yet it seemed to be somewhat of a discovery that all of them were and are trying to understand the same problem - the problem of integrability of dynamical systems, primarily Hamiltonian ones with an infinite number of degrees of freedom. No doubt that they (or to be more exact, we) were led to this by the logical process of scientific evolution which often leads to independent, almost simultaneous discoveries. Integrable, or, more accurately, exactly solvable equations are essential to theoretical and mathematical physics. One could say that they constitute the "mathematical nucleus" of theoretical physics whose goal is to describe real clas sical or quantum systems. For example, the kinetic gas theory may be considered to be a theory of a system which is trivially integrable: the system of classical noninteracting particles. One of the main tasks of quantum electrodynamics is the development of a theory of an integrable perturbed quantum system, namely, noninteracting electromagnetic and electron-positron fields.
Download or read book Self Organized Criticality in Astrophysics written by Markus Aschwanden and published by Springer Science & Business Media. This book was released on 2011-01-11 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Markus Aschwanden introduces the concept of self-organized criticality (SOC) and shows that due to its universality and ubiquity it is a law of nature for which he derives the theoretical framework and specific physical models in this book. He begins by providing an overview of the many diverse phenomena in nature which may be attributed to SOC behaviour. The author then introduces the classic lattice-based SOC models that may be explored using numerical computer simulations. These simulations require an in-depth knowledge of a wide range of mathematical techniques which the author introduces and describes in subsequent chapters. These include the statistics of random processes, time series analysis, time scale distributions, and waiting time distributions. Such mathematical techniques are needed to model and understand the power-law-like occurrence frequency distributions of SOC phenomena. Finally, the author discusses fractal geometry and scaling laws before looking at a range of physical SOC models which may be applicable in various aspects of astrophysics. Problems, solutions and a glossary will enhance the pedagogical usefulness of the book. SOC has been receiving growing attention in the astrophysical and solar physics community. This book will be welcomed by students and researchers studying complex critical phenomena.
Download or read book Applied Nonlinear Time Series Analysis Applications In Physics Physiology And Finance written by Michael Small and published by World Scientific. This book was released on 2005-03-28 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear time series methods have developed rapidly over a quarter of a century and have reached an advanced state of maturity during the last decade. Implementations of these methods for experimental data are now widely accepted and fairly routine; however, genuinely useful applications remain rare. This book focuses on the practice of applying these methods to solve real problems.To illustrate the usefulness of these methods, a wide variety of physical and physiological systems are considered. The technical tools utilized in this book fall into three distinct, but interconnected areas: quantitative measures of nonlinear dynamics, Monte-Carlo statistical hypothesis testing, and nonlinear modeling. Ten highly detailed applications serve as case studies of fruitful applications and illustrate the mathematical techniques described in the text.
Download or read book Quantum Theory from a Nonlinear Perspective written by Dieter Schuch and published by Springer. This book was released on 2018-01-20 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal, conserving energy and, in contrast to classical theories, essentially based on the use of complex quantities. However, on a macroscopic level, processes apparently obey nonlinear irreversible evolution equations and dissipate energy. The Riccati equation, a nonlinear equation that can be linearized, has the potential to link these two worlds when applied to complex quantities. The nonlinearity can provide information about the phase-amplitude correlations of the complex quantities that cannot be obtained from the linearized form. As revealed in this wide ranging treatment, Riccati equations can also be found in many diverse fields of physics from Bose-Einstein-condensates to cosmology. The book will appeal to graduate students and theoretical physicists interested in a consistent mathematical description of physical laws.
