Leble / Perelomova The Dynamical Projectors Method

Hydro and Electrodynamics
1. Auflage 2018
ISBN: 978-1-351-10797-6
Verlag: Taylor & Francis
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 564 Seiten

The dynamical projectors method proves to reduce a multicomponent problem to the simplest one-component problem with its solution determined by specific initial or boundary conditions. Its universality and application in many different physical problems make it particularly useful in hydrodynamics, electrodynamics, plasma physics, and boundary layer problems. A great variety of underlying mechanisms are included making this book useful for those working in wave theory, hydrodynamics, electromagnetism, and applications.

Autoren/Hrsg.

Leble, Sergey

Perelomova, Anna

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Technische Wissenschaften Sonstige Technologien | Angewandte Technik Lasertechnologie, Holographie
• Technische Wissenschaften Technik Allgemein Technische Optik, Lasertechnologie

Inhaltsverzeichnis

Introduction. General technique. General proper space - eigenvector problem for perturbations over a homogeneous ground state. Definition of projecting operators for non-orthogonal basis. General construction of the projecting operators. Weaklynonhomogeneous ground state. Iteration scheme. Projectors for the iterations. Acoustics. One-dimensional problem. Non-dissipativelinear problem. Acoustic and entropy modes. Weak nonlinearity account. Dissipative problems. Heating caused by pulses. Illustrations.Heating caused by modulated acoustic wave. Self-reflection of acoustic pulse. General proper space - eigenvector problem forperturbations over a homogeneous ground state in hermohydrodynamics. Projectors of general linear problem. Weak nonlinearitywithout dissipation. Dissipation effects. Beams. Streaming. Boundary layer problem. Acoustic and Tollmienn-Schlichting waves. Preliminary remarks. Basic equations for compressible liquid. Modes in the linear approximation. The Tollmienn-Schlichting mode. Acoustic modes. Peculiarities of non-commutative projecting in the inhomogeneous linear problem. Nonlinear flow: coupled dynamicequations. Resonance interaction of acoustic and TS modes. Hydrodynamics. Perturbations over a stratified background. Exponentialstratification of a ground state. Acoustic and internal gravity waves in 2+1 problem. Arbitrary stratification. One-dimensional wavesand an entropy mode. Acoustic-gravity waves: interaction and attenuation. Introduction to kinetic-continuous description of a mediumdisturbance dynamics. Rossby and Poincare waves. Initialization and diagnostics. Electrodynamics. 1D electrodynamics. Polarized hybrid fields. Polarization account. Kerr nonlinearity. Nonlinear 1D equations. Short pulses. Ultrashort pulses. Rectangular waveguides. Directed modes in rectangular waveguides. Polarization account. Interaction. Cylindrical waveguides. Directed modes in cylindrical waveguides. Polarization account. Dielectric waveguide modes. Optical fibers.

Über Autor(innen)

Prof. Sergey B. Leble received his Ph.D in 1974 from Leningrad State in St. Petersburg, Russia with a focus on theory of elementary particles and curvature. In 1987 he received his Dr. hab. from Leningrad State University with a focus on waveguide propagation of nonlinear waves in layered media, followed by a professor diploma in 1989. He has published 7 books, contributed many chapters in collective monographs, and published over 200 scientific journal articles in the field of theoretical and mathematical physics as well as applied mathematics. He is now a Professor of Kant Federal University in Kaliningrad, Russia.

Anna Perelomova was born in Moscow in 1965. After graduating from a high school in 1982, she began studying in the Department of Acoustics at the Physical Faculty of Moscow State University where she specialized in radiophysics and received a degree with honors in 1989. Her doctoral thesis "Acoustic-gravitational waves induced by a powerful source" was awarded in 1994 by the Institute of Physics of the Earth in Moscow. Anna Perelomova defended a habilitation thesis "Interaction of acoustic and non-acoustic modes: theoretical aspects of nonlinear acoustics" in 2006 for the Department of Physics at the university named after A. Mickiewicz in Poznan, Poland. Since 2011, she has served as a professor in the Department of Technical Physics and Applied Mathematics at the Gdansk University of Technology in Poland and is the author of approximately 90 publications in the field of nonlinear hydrodynamics and acoustics.