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Read Nonlinear Waves In Fluids Recent Advances And Modern Applications 2005
In a wholly lucid manner the work covers single-particle motions, fluid equations for plasmas, wave motions, diffusion and resistivity, Landau damping, plasma instabilities and nonlinear problems. For students, this outstanding text offers a painless introduction to this important field; for teachers, a large collection of problems; and for researchers, a concise review of the fundamentals as well as original treatments of a number of topics never before explained so clearly.
This revised edition contains new material on kinetic effects, including Bernstein waves and the plasma dispersion function, and on nonlinear wave equations and solitons. For the third edition, updates will be made throughout each existing chapter, and two new chapters will be added; Ch 9 on "Special Plasmas" and Ch 10 on Plasma Applications including Atmospheric Plasmas. See the contents list for more details. Travelling waves are observed in many natural processes, ranging from the spread of diseases to the combustion of fuels.
The book is concerned with characterizing such waves in phenomena described by a nonlinear diffusion-convection-reaction equation.
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The technique employed is new and can be briefly described as an integral or integrated approach to phase-plane analysis. It leads to results which were so far unobtainable, including the effects of degenerate diffusion and nonlinear convection, or are much sharper than those obtained previously.
Applications are taken from the evolution of biological populations, diffusion of oxygen in tissue, heat transfer, thermal convection, combustion, flow in porous media, hydrology, soil-moisture flow, boundary layer theory, foam drainage, viscous fluid flow, turbulent fluid flow, the motion of plasma particles in a magnetic field, solar prominences, crystal growth, reaction chemistry, quenching, and other fields. In this way, the book brings together and improves a large number of results which have been obtained piecemeal in many different scientific disciplines. It provides a reference work for applications of nonlinear diffusion, convection and reaction, and gives a state-of-the-art survey of the study of the occurrence of travelling waves in such applications.
This set of lectures forms a self-contained graduate-level text intended as both introduction and reference for a new generation of scientists working on rogue and shock waves phenomena across a broad range of fields in applied physics and geophysics. Quite generally, rogue and shock waves are phenomena that may occur in the propagation of waves in any nonlinear dispersive medium.
Accordingly, they have been observed in very different settings, as ocean waves, in nonlinear optics, in Bose-Einstein condensates, and in plasmas. Rogue and dispersive shock waves are both characterized by the development of extremes: for the former, the wave amplitude of becomes very large, while for the latter, gradients reach extreme values.
Both aspects strongly influence the statistical properties of the wave propagation and are thus considered together in this volume regarding their underlying theoretical treatment. This volume bridges a gap in the literature by providing the systematic link between the theoretical foundations of the subject matter and up-to-date applications in both geophysical fluid dynamics and nonlinear optics. These themes are interlocked, and this will be demonstrated throughout the text. The topics address any fluid flow application, but there is a bias towards geophysical fluid dynamics, reflecting for the most part the areas where many applications been found.
The book details a few of the novel methods developed in the last few years for studying various aspects of nonlinear wave systems. The introductory chapter provides a general overview, thematically linking the objects described in the book. The book can also be used as a basis for a one-semester lecture course in applied mathematics or mathematical physics. The contributions discuss recent major advances in the study of nonlinear hyperbolic systems, addressing general theoretical issues such as symmetrizability, singularities, low regularity or dispersive perturbations.
It also investigates several physical phenomena where such systems are relevant, such as nonlinear optics, shock theory stability, relaxation and fluid mechanics boundary layers, water waves, Euler equations, geophysical flows, etc. May Jun 1, May Jun 3, Libre de Bruxelles, Belgium. Nonlineal , Zaragoza, Spain.
Modal Analysis of Nonlinear Mechanical Systems. Hyperbolic Problems: Theory, Num. Biomat Self-organization and collective dynamics , Granada, Spain. Second Ph. Mar Apr 1, Multiscale Model. Chaos, Complexity and Transport , Marseilles, France. May 30 - Jun 3, Of Campinas, Brazil. May 31 - Jun 3, Summer School on Num. Peter, MN Jun , Mathematics, Modeling and Comp. Modern Approaches to Dynamical Integrability , Univ. Advances in Computational Wave Propagation , Univ.
College London, UK. Nonlinear Guided Waves. Cadi Ayyad Univ. Nonlinear phenomena in quantum degenerate gases. TU, Berlin.
Nonlinear Waves in Fluids: Recent Advances and Modern Applications
Algebraic Methods in Dynamical Systems. Bedlewo, Poland. Chaos and Complex Systems. Istanbul Kultur University. Dresden University of Technology. May Jun 4, Fudan University, Shanghai, China.