Nonlinear Phenomena in Plasma Physics and Hydrodynamics PDF Download

Author: R. Z. Sagdeev
Publisher:
ISBN: 9780714725031
Category : Hydrodynamics
Languages : en
Pages : 223

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Author: V.N Oraevsky
Publisher: Routledge
ISBN: 1351428209
Category : Science
Languages : en
Pages : 182

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Book Description
For the first time in a single book, Non-Linear Instabilities in Plasmas and Hydrodynamics presents the underlying physics of fast secondary instabilities. This exceptionally well-written, introductory book discusses the basic ideas of the physics of secondary or induced, nonlinear instabilities in wave-sustaining media. The authors, world-renowned experts in the field, have brought together the results of papers scattered throughout the literature to explain subjects as diverse as fluctuation chaos, wave-turbulent instabilities, vortex dynamos, beam-plasma interactions, plasma confinement, and the origins of typhoons in the Earth's atmosphere and magnetic fields in galaxies. Paving the way for new and exciting research in the future, this broad, interdisciplinary book enables a wide range of physicists to apply the concepts discussed to obtain new results in plasma physics, space physics, hydrodynamics, and geophysics.

Author: Anatoli Tur
Publisher: Springer
ISBN: 3319527339
Category : Science
Languages : en
Pages : 313

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Book Description
This monograph introduces readers to the hydrodynamics of vortex formation, and reviews the last decade of active research in the field, offering a unique focus on research topics at the crossroads of traditional fluids and plasmas. Vortices are responsible for the process of macroscopic transport of momentum, energy and mass, and are formed as the result of spontaneous self-organization. Playing an important role in nature and technology, localized, coherent vortices are regularly observed in shear flows, submerged jets, afterbody flows and in atmospheric boundary layers, sometimes taking on the form of vortex streets. In addition, the book addresses a number of open issues, including but not limited to: which singularities are permitted in a 2D Euler equation besides point vortices? Which other, even more complex, localized vortices could be contained in the Euler equation? How do point vortices interact with potential waves?

Author: Carles Simó
Publisher: Springer Science & Business Media
ISBN: 940114673X
Category : Mathematics
Languages : en
Pages : 681

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Book Description
A survey of current knowledge about Hamiltonian systems with three or more degrees of freedom and related topics. The Hamiltonian systems appearing in most of the applications are non-integrable. Hence methods to prove non-integrability results are presented and the different meaning attributed to non-integrability are discussed. For systems near an integrable one, it can be shown that, under suitable conditions, some parts of the integrable structure, most of the invariant tori, survive. Many of the papers discuss near-integrable systems. From a topological point of view, some singularities must appear in different problems, either caustics, geodesics, moving wavefronts, etc. This is also related to singularities in the projections of invariant objects, and can be used as a signature of these objects. Hyperbolic dynamics appear as a source on unpredictable behaviour and several mechanisms of hyperbolicity are presented. The destruction of tori leads to Aubrey-Mather objects, and this is touched on for a related class of systems. Examples without periodic orbits are constructed, against a classical conjecture. Other topics concern higher dimensional systems, either finite (networks and localised vibrations on them) or infinite, like the quasiperiodic Schrödinger operator or nonlinear hyperbolic PDE displaying quasiperiodic solutions. Most of the applications presented concern celestial mechanics problems, like the asteroid problem, the design of spacecraft orbits, and methods to compute periodic solutions.

Author: Gary Webb
Publisher: Springer
ISBN: 3319725114
Category : Science
Languages : en
Pages : 306

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Book Description
This text focuses on conservation laws in magnetohydrodynamics, gasdynamics and hydrodynamics. A grasp of new conservation laws is essential in fusion and space plasmas, as well as in geophysical fluid dynamics; they can be used to test numerical codes, or to reveal new aspects of the underlying physics, e.g., by identifying the time history of the fluid elements as an important key to understanding fluid vorticity or in investigating the stability of steady flows. The ten Galilean Lie point symmetries of the fundamental action discussed in this book give rise to the conservation of energy, momentum, angular momentum and center of mass conservation laws via Noether’s first theorem. The advected invariants are related to fluid relabeling symmetries – so-called diffeomorphisms associated with the Lagrangian map – and are obtained by applying the Euler-Poincare approach to Noether’s second theorem. The book discusses several variants of helicity including kinetic helicity, cross helicity, magnetic helicity, Ertels’ theorem and potential vorticity, the Hollman invariant, and the Godbillon Vey invariant. The book develops the non-canonical Hamiltonian approach to MHD using the non-canonical Poisson bracket, while also refining the multisymplectic approach to ideal MHD and obtaining novel nonlocal conservation laws. It also briefly discusses Anco and Bluman’s direct method for deriving conservation laws. A range of examples is used to illustrate topological invariants in MHD and fluid dynamics, including the Hopf invariant, the Calugareanu invariant, the Taylor magnetic helicity reconnection hypothesis for magnetic fields in highly conducting plasmas, and the magnetic helicity of Alfvén simple waves, MHD topological solitons, and the Parker Archimedean spiral magnetic field. The Lagrangian map is used to obtain a class of solutions for incompressible MHD. The Aharonov-Bohm interpretation of magnetic helicity and cross helicity is discussed. In closing, examples of magnetosonic N-waves are used to illustrate the role of the wave number and group velocity concepts for MHD waves. This self-contained and pedagogical guide to the fundamentals will benefit postgraduate-level newcomers and seasoned researchers alike.

Author: Heinrich Hora
Publisher: SPIE Press
ISBN: 9780819435095
Category : Mathematics
Languages : en
Pages : 240

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Book Description
This acts as a reference work for the field of high intensity and/or high plasma density laser-plasma interactions for years to come. It covers everything from single particles to dense fluids, from computational physics to the practical results in fusion. In addition, it contains treatments of the theory of electrodynamics, laser-driven hydrodynamics, the Lorentz force, complex refractive index and relativistic effects in plasmas. Although ""the swamp of plasma physics"" is mostly a classical place, the author indicates where quantum and classical calculations converge.

Author: Vladimir I. Arnold
Publisher: Springer Science & Business Media
ISBN: 3540489266
Category : Mathematics
Languages : en
Pages : 505

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Book Description
The main purpose of the book is to acquaint mathematicians, physicists and engineers with classical mechanics as a whole, in both its traditional and its contemporary aspects. As such, it describes the fundamental principles, problems, and methods of classical mechanics, with the emphasis firmly laid on the working apparatus, rather than the physical foundations or applications. Chapters cover the n-body problem, symmetry groups of mechanical systems and the corresponding conservation laws, the problem of the integrability of the equations of motion, the theory of oscillations and perturbation theory.

Author: A.I. Maimistov
Publisher: Springer Science & Business Media
ISBN: 9401724482
Category : Science
Languages : en
Pages : 668

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Book Description
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.

Author: Vladimir I. Arnold
Publisher: Springer Science & Business Media
ISBN: 9783540206149
Category : Mathematics
Languages : en
Pages : 664

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Book Description
Vladimir Arnold is one of the most outstanding mathematicians of our time Many of these problems are at the front line of current research

Author: Albert C. J. Luo
Publisher: Springer Science & Business Media
ISBN: 3642123430
Category : Science
Languages : en
Pages : 327

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Book Description
In memory of Dr. George Zaslavsky, "Long-range Interactions, Stochasticity and Fractional Dynamics" covers the recent developments of long-range interaction, fractional dynamics, brain dynamics and stochastic theory of turbulence, each chapter was written by established scientists in the field. The book is dedicated to Dr. George Zaslavsky, who was one of three founders of the theory of Hamiltonian chaos. The book discusses self-similarity and stochasticity and fractionality for discrete and continuous dynamical systems, as well as long-range interactions and diluted networks. A comprehensive theory for brain dynamics is also presented. In addition, the complexity and stochasticity for soliton chains and turbulence are addressed. The book is intended for researchers in the field of nonlinear dynamics in mathematics, physics and engineering. Dr. Albert C.J. Luo is a Professor at Southern Illinois University Edwardsville, USA. Dr. Valentin Afraimovich is a Professor at San Luis Potosi University, Mexico.