Nonlinear Physics of Plasmas

Nonlinear Physics of Plasmas

Author: Mitsuo Kono

Publisher: Springer Science & Business Media

Published: 2010-10-17

Total Pages: 540

ISBN-13: 3642146945

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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.


Nonlinear Processes in Physics

Nonlinear Processes in Physics

Author: A.S. Fokas

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 343

ISBN-13: 3642777694

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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.


Nonlinear Wave Processes in Acoustics

Nonlinear Wave Processes in Acoustics

Author: K. Naugolnykh

Publisher: Cambridge University Press

Published: 1998-05-28

Total Pages: 316

ISBN-13: 9780521399845

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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.


Modeling by Nonlinear Differential Equations

Modeling by Nonlinear Differential Equations

Author: Paul Edgar Phillipson

Publisher: World Scientific

Published: 2009

Total Pages: 238

ISBN-13: 9814271608

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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.


Nonlinear Dynamics and Chaos

Nonlinear Dynamics and Chaos

Author: Steven H. Strogatz

Publisher: CRC Press

Published: 2018-05-04

Total Pages: 532

ISBN-13: 0429961111

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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.


Nonlinear Physics

Nonlinear Physics

Author: R. Z. Sagdeev

Publisher: CRC Press

Published: 1988

Total Pages: 726

ISBN-13: 9783718648283

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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


Advanced Photonics with Second-Order Optically Nonlinear Processes

Advanced Photonics with Second-Order Optically Nonlinear Processes

Author: A.D. Boardman

Publisher: Springer

Published: 1998-11-30

Total Pages: 0

ISBN-13: 9780792353164

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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.


Physics of Nonlinear Optics

Physics of Nonlinear Optics

Author: Y. V. G. S. Murti

Publisher: Springer Nature

Published: 2021-07-20

Total Pages: 188

ISBN-13: 3030739791

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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.


The Physics of Plasmas

The Physics of Plasmas

Author: T. J. M. Boyd

Publisher: Cambridge University Press

Published: 2003-01-23

Total Pages: 548

ISBN-13: 9780521459129

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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.


Quantum Theory from a Nonlinear Perspective

Quantum Theory from a Nonlinear Perspective

Author: Dieter Schuch

Publisher: Springer

Published: 2018-01-20

Total Pages: 261

ISBN-13: 3319655949

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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.