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Dynamical Projectors Method: Hydro and Electrodynamics [Kõva köide]

, (Gdansk University of Technology)
  • Formaat: Hardback, 302 pages, kõrgus x laius: 234x156 mm, kaal: 566 g, 100 Illustrations, black and white
  • Ilmumisaeg: 27-Mar-2018
  • Kirjastus: CRC Press
  • ISBN-10: 1138035602
  • ISBN-13: 9781138035607
Teised raamatud teemal:
Dynamical Projectors Method: Hydro and ElectrodynamicsSuurem pilt
  • Formaat: Hardback, 302 pages, kõrgus x laius: 234x156 mm, kaal: 566 g, 100 Illustrations, black and white
  • Ilmumisaeg: 27-Mar-2018
  • Kirjastus: CRC Press
  • ISBN-10: 1138035602
  • ISBN-13: 9781138035607
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781138035607.html
Märksõnad:
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.

"The authors developed a universal and elegant tool dynamical projector method. Using this method for very complicated hydro-thermodynamic and electrodynamics problem settings, they were able to get a lot of interesting analytical results in areas where before often just numerical methods were applicable."

L. A. Bordag, University of Applied Sciences Zittau/Görlitz, Zittau, Germany

"The book is intended for professionals working in various fields of linear and nonlinear mathematical physics, partial differential equations and theoretical physics. The book is written clearly, and in my opinion, its material will be useful and easy to understand for professionals and for students familiar with ordinary and partial differential equations."

Sergey Dobrokhotov, Russian Academy of Sciences, Moscow, Russia

Arvustused

"The authors developed a universal and elegant tool dynamical projector method. Using this method for very complicated hydro-thermodynamic and electrodynamics problem settings, they were able to get a lot of interesting analytical results in areas where before often just numerical methods were applicable." L. A. Bordag, University of Applied Sciences Zittau/Görlitz, Zittau, Germany

"The book is intended for professionals working in various fields of linear and nonlinear mathematical physics, partial differential equations and theoretical physics. The book is written clearly, and in my opinion, its material will be useful and easy to understand for professionals and for students familiar with ordinary and partial differential equations." Sergey Yu. Dobrokhotov, Russian Academy of Sciences, Moscow, Russia

List of Figures xv
Preface xvii
Authors xix
Chapter 1 Introduction 1(26)
Chapter 2 General Technique 27(24)
2.1 General Proper Space Definition-Eigenvector Problem for Perturbations over a Homogeneous Ground State
27(24)
2.1.1 General 1+1 D Problem. Linear Evolution in Homogeneous Case
27(3)
2.1.2 Transition to X-Representation
30(2)
2.1.3 Boundary Regime Propagation
32(5)
2.1.4 On Weak Nonlinearity Account Problems
37(3)
2.1.5 Weakly Inhomogeneous Ground State. Hyperbolic Equation
40(1)
2.1.6 Weak Inhomogeneity. Directed Waves
41(2)
2.1.7 Link to Spectral Theorem
43(8)
Chapter 3 One-Dimensional Problem in Hydrodynamics 51(24)
3.1 On the Hydro-Thermodynamic Relations for Quasi-Isentropic Processes
51(5)
3.2 Thermoconducting Flow of an Uniform Newtonian Gas. Modes, Projectors and Dynamic Equations. Acoustic Heating
56(6)
3.2.1 An Ideal Gas
56(3)
3.2.2 Fluids Different from Ideal Gases
59(3)
3.3 Non-Newtonian Fluids.
62(2)
3.4 Acoustics of a Fluid Which Is Affected by Constant Mass Force
64(11)
3.4.1 Isothermal Atmosphere 1D Dynamics
64(3)
3.4.2 Examples of Projecting: Decomposition of the Total Field of Exclusively Entropy or Acoustic Parts and Energy Release with Mass Injection
67(2)
3.4.3 Dynamics of the Short-Scale Waves
69(6)
Chapter 4 Coupling of Sound with Vorticity: Acoustic Streaming 75(8)
4.1 3D Hydrodynamics and Vortex Mode
75(2)
4.2 Five Projectors
77(3)
4.3 Examples of Acoustic Streaming: Weakly Difracting Beam and Stationary Waveform
80(3)
Chapter 5 Projecting in Flows with Relaxation: Effects of Sound in Acoustically Active Fluids 83(48)
5.1 Vibrationally Relaxing Gases
83(17)
5.2 Chemically Reacting Gases
100(8)
5.2.1 Remarks on the Thermal Self-Focusing of Sound
106(2)
5.3 The Nonlinear Effects of Sound in a Liquid with Relaxation Losses
108(6)
5.4 On the Nonlinear Effects of Magnetoacoustic Perturbations in a Perfectly Conducting Viscous and Thermoconducting Gas
114(17)
5.4.1 On the Nonlinear Interactions in a Plasma with Finite Electrical Conductivity
123(8)
Chapter 6 Boundary Layer Problem: Acoustic and Tollmienn-Schlichting Waves 131(16)
6.1 Preliminary Remarks
131(2)
6.2 Basic Equations for Compressible Fluid
133(1)
6.3 Linear Approximation
134(1)
6.4 The Tollmienn-Schlichting Mode
135(1)
6.5 Acoustic Modes
136(1)
6.6 Peculiarities of Non-Commutative Projecting in the Inhomogeneous Linear Problem
137(2)
6.7 Nonlinear Flow: Coupled Dynamic Equations
139(2)
6.8 Resonance Interaction of Acoustic and T-S Modes
141(6)
Chapter 7 1D Electrodynamics 147(36)
7.1 Cauchy Problem for 1D Electrodynamics. Polarized Hybrid Fields
147(6)
7.1.1 The Problem Formulation Outline
147(1)
7.1.2 On Dynamical Projection Method Application: Cauchy Problem
148(2)
7.1.3 The Effect of a Cumulative Part of Interaction
150(1)
7.1.4 Dispersion Account, an Example
151(2)
7.2 General Dynamics Equations, SPE System
153(2)
7.2.1 The Shafer-Wayne (SPE) and Generalizations
154(1)
7.2.2 Discussion and Conclusions
154(1)
7.3 Boundary Regime Propagation in 1D Electrodynamics
155(12)
7.3.1 Statement of Problem
155(2)
7.3.2 Operators of Dielectric Permittivity and Magnetic Permeability
157(2)
7.3.3 Inverse Dielectric and Magnetic Operators
159(1)
7.3.4 Projecting Operators in 1D Electrodynamics with Unique Polarization: Boundary Regime Propagation
160(3)
7.3.5 On Integral Kernels Details
163(2)
7.3.6 Polarized Hybrid Fields. Equations for Left and Right Waves
165(2)
7.4 Polarization Account
167(7)
7.4.1 General Remarks
167(1)
7.4.2 Theory of Initial Disturbance Propagation, Cauchy Problem Formulation
168(1)
7.4.3 The Projection Method for the Cauchy Problem
169(3)
7.4.4 Nonlinearity Account, Interaction of Polarized Waves: General Relations
172(2)
7.5 Comparison of Results Obtained with the Multiple Scale Method
174(2)
7.6 Projection Method for Boundary Regime Propagation
176(7)
Chapter 8 Metamaterials 183(42)
8.1 Statement of Problem for Metamaterials
183(4)
8.1.1 Two Words on Metamaterials
183(1)
8.1.2 Maxwell's Equations. Operators of Dielectric Permittivity and Magnetic Permeability
183(3)
8.1.3 Boundary Regime Problem
186(1)
8.2 Dynamic Projecting Operators
187(2)
8.3 Separated Equations and Definitions for Hybrid Waves
189(2)
8.4 Nonlinearity Account
191(1)
8.5 General Equations of 1D Wave Propagation in a Metamaterial That Is Described by the Lossless Drude Model
192(2)
8.6 Kerr Nonlinearity Account for Lossless Drude Metamaterials
194(6)
8.6.1 Equations of Interaction of Left and Right Waves with Kerr Effect
194(1)
8.6.2 Stationary Solution
195(5)
8.7 Statement of Problem for Waves with Two Polarizations
200(3)
8.7.1 Maxwell's Equations. Boundary Regime Problem
200(3)
8.8 Dynamic Projecting Operators
203(4)
8.9 Separated Equations and Definition for Left and Right Waves
207(2)
8.10 General Nonlinearity Account
209(2)
8.11 Kerr Nonlinearity Account for Lossless Drude Metamaterials
211(2)
8.11.1 Equations of Interaction of the Waves via Kerr Effect
211(2)
8.12 Wave Packets
213(7)
8.12.1 Linear Wave Packets for the Right Waves
213(1)
8.12.2 Unidirectional Wavetrains Interaction
214(4)
8.12.3 Coupled Nonlinear Schrodinger Equations
218(2)
8.13 Stationary Solutions of SPE System for Unidirectional Waves
220(5)
Chapter 9 Waves in Waveguides 225(36)
9.1 Electromagnetic Waves in Metal Rectangular Waveguide Filled with a Material: Projecting Operators Method
225(8)
9.1.1 Maxwell's Equations for a Waveguide. Boundary Conditions
225(1)
9.1.2 The Transversal Waveguide Modes Evolution
226(7)
9.2 Projecting Operators
233(1)
9.3 Polarizations and Directed Modes in Rectangular Waveguides
233(1)
9.4 Cylindrical Dielectric Waveguides
233(7)
9.4.1 On Transversal Fiber Modes
233(1)
9.4.2 A Formulation and Solution of Linear Problem, a Step to Dynamic Projecting Procedure
234(1)
9.4.3 Transition to Bessel Functions Basis
235(5)
9.5 Dynamical Projecting Operators
240(6)
9.5.1 z-Evolution System and Transition to w-Domain
240(5)
9.5.2 Projection Operators in Time Domain. Dispersion Account
245(1)
9.6 Including Nonlinearity
246(10)
9.6.1 Application of Projection Operators
254(2)
9.7 Appendix
256(5)
Chapter 10 Waves in 3D Space 261(14)
10.1 Introductory Note
261(1)
10.2 Basic Equations and Starting Points
262(2)
10.3 Determination of Operator Eigenvalues, Eigenvectors and Projecting Operators for a Full System of Maxwell's Equations
264(5)
10.3.1 Projection by Operator P1 Application
266(1)
10.3.2 Projection with Operator P2
267(1)
10.3.3 Results for Other Projector Operator
267(2)
10.4 The Case of the Linear Dependence of Electromagnetic Induction on the Electric Field and the Magnetic Induction on the Magnetic Field
269(3)
10.4.1 Projection Operators
270(2)
10.5 Examples with a Symmetry Account
272(1)
10.5.1 Spherical Geometry
272(1)
10.5.2 Quasi-One-Dimensional Geometry
272(1)
10.6 Concluding Remarks
273(2)
Index 275
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.



Prof. 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.