The dynamical projectors hydro and electrodynamics 1st Edition by Sergey Leble, Anna Perelomova ISBN 1351107984 9781351107983

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Product details:

ISBN 10:      1351107984

ISBN 13: 978-1351107983 

Author:     Sergey Leble, Anna Perelomova

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

 

The dynamical projectors hydro and electrodynamics 1st  Table of contents:

Chapter 1: Introduction

Chapter 2: General Technique

• 2.1 General Proper Space Definition—Eigenvector Problem for Perturbations over a Homogeneous Ground
  • 2.1.1 General 1+1 D Problem: Linear Evolution in Homogeneous Case
  • 2.1.2 Transition to X-Representation
  • 2.1.3 Boundary Regime Propagation
  • 2.1.4 On Weak Nonlinearity Account Problems
  • 2.1.5 Weakly Inhomogeneous Ground State: Hyperbolic Equation
  • 2.1.6 Weak Inhomogeneity: Directed Waves
  • 2.1.7 Link to Spectral Theorem

Chapter 3: One-Dimensional Problem in Hydrodynamics

• 3.1 Hydro-Thermodynamic Relations for Quasi-Isentropic Processes
• 3.2 Thermoconducting Flow of Uniform Newtonian Gas: Modes, Projectors, and Dynamic Equations
  • 3.2.1 An Ideal Gas
  • 3.2.2 Fluids Different from Ideal Gases
• 3.3 Non-Newtonian Fluids
• 3.4 Acoustics of a Fluid Affected by Constant Mass Force
  • 3.4.1 Isothermal Atmosphere 1D Dynamics
  • 3.4.2 Decomposition of the Total Field (Exclusively Entropy or Acoustic Parts)
  • 3.4.3 Dynamics of Short-Scale Waves

Chapter 4: Coupling of Sound with Vorticity: Acoustic Streaming

• 4.1 3D Hydrodynamics and Vortex Mode
• 4.2 Five Projectors
• 4.3 Examples of Acoustic Streaming: Weakly Diffracting Beam and Stationary Waveform

Chapter 5: Projecting in Flows with Relaxation: Effects of Sound in Acoustically Active Fluids

• 5.1 Vibrationally Relaxing Gases
• 5.2 Chemically Reacting Gases
  • 5.2.1 Thermal Self-Focusing of Sound
• 5.3 Nonlinear Effects of Sound in a Liquid with Relaxation Losses
• 5.4 Nonlinear Effects of Magnetoacoustic Perturbations in Perfectly Conducting Viscous Fluids
  • 5.4.1 Nonlinear Interactions in a Plasma with Finite Electrical Conductivity

Chapter 6: Boundary Layer Problem: Acoustic and Tollmien-Schlichting Waves

• 6.1 Preliminary Remarks
• 6.2 Basic Equations for Compressible Fluid
• 6.3 Linear Approximation
• 6.4 Tollmien-Schlichting Mode
• 6.5 Acoustic Modes
• 6.6 Non-Commutative Projecting in the Inhomogeneous Linear Problem
• 6.7 Nonlinear Flow: Coupled Dynamic Equations
• 6.8 Resonance Interaction of Acoustic and T-S Modes

Chapter 7: 1D Electrodynamics

• 7.1 Cauchy Problem for 1D Electrodynamics: Polarized Hybrid Fields
  • 7.1.1 Problem Formulation
  • 7.1.2 Dynamical Projection Method Application
  • 7.1.3 Cumulative Part of Interaction
  • 7.1.4 Dispersion Account: Example
• 7.2 General Dynamics Equations (SPE System)
  • 7.2.1 Shafer-Wayne (SPE) and Generalizations
  • 7.2.2 Discussion and Conclusions
• 7.3 Boundary Regime Propagation in 1D Electrodynamics
  • 7.3.1 Statement of Problem
  • 7.3.2 Dielectric and Magnetic Permittivity Operators
  • 7.3.3 Inverse Dielectric and Magnetic Operators
  • 7.3.4 Projecting Operators in 1D Electrodynamics
  • 7.3.5 Integral Kernels Details
  • 7.3.6 Polarized Hybrid Fields: Left and Right Waves Equations
• 7.4 Polarization Account
  • 7.4.1 General Remarks
  • 7.4.2 Theory of Initial Disturbance Propagation
  • 7.4.3 Projection Method for Cauchy Problem
  • 7.4.4 Nonlinear Interactions of Polarized Waves
• 7.5 Comparison with Multiple Scale Method
• 7.6 Projection Method for Boundary Regime Propagation

Chapter 8: Metamaterials

• 8.1 Problem Statement for Metamaterials
  • 8.1.1 Introduction to Metamaterials
  • 8.1.2 Maxwell’s Equations: Dielectric and Magnetic Permittivity Operators
  • 8.1.3 Boundary Regime Problem
• 8.2 Dynamic Projecting Operators
• 8.3 Separated Equations for Hybrid Waves
• 8.4 Nonlinearity Account
• 8.5 1D Wave Propagation Equations for Lossless Drude Metamaterials
• 8.6 Kerr Nonlinearity in Lossless Drude Metamaterials
  • 8.6.1 Interaction of Left and Right Waves via Kerr Effect
  • 8.6.2 Stationary Solution
• 8.7 Waves with Two Polarizations
  • 8.7.1 Maxwell’s Equations: Boundary Regime Problem
  • 8.7.2 Separated Equations for Left and Right Waves
• 8.8 Dynamic Projecting Operators
• 8.9 Nonlinearity Account and Kerr Effect in Lossless Drude Metamaterials
  • 8.9.1 Interaction of Waves via Kerr Effect
• 8.10 Wave Packets
  • 8.10.1 Linear Wave Packets for Right Waves
  • 8.10.2 Unidirectional Wavetrain Interaction
  • 8.10.3 Coupled Nonlinear Schrödinger Equations
• 8.11 Stationary Solutions of SPE System for Unidirectional Waves

Chapter 9: Waves in Waveguides

• 9.1 Electromagnetic Waves in Metal Rectangular Waveguides
  • 9.1.1 Maxwell’s Equations and Boundary Conditions
  • 9.1.2 Evolution of Transversal Waveguide Modes
• 9.2 Projecting Operators
• 9.3 Polarizations and Directed Modes in Rectangular Waveguides
• 9.4 Cylindrical Dielectric Waveguides
  • 9.4.1 Transversal Fiber Modes
  • 9.4.2 Linear Problem Formulation: Transition to Dynamic Projecting
  • 9.4.3 Transition to Bessel Functions Basis
• 9.5 Dynamical Projecting Operators
  • 9.5.1 z-Evolution System and Transition to w-Domain
  • 9.5.2 Projection Operators in Time Domain: Dispersion Account
• 9.6 Including Nonlinearity
  • 9.6.1 Application of Projection Operators

Chapter 10: Waves in 3D Space

• 10.1 Introductory Note
• 10.2 Basic Equations and Starting Points
• 10.3 Determination of Operator Eigenvalues and Projecting Operators
  • 10.3.1 Projection with Operator P[sub(1)]
  • 10.3.2 Projection with Operator P[sub(2)]
  • 10.3.3 Results for Other Projector Operators
• 10.4 Linear Dependence of Electromagnetic Induction on the Electric Field
  • 10.4.1 Projection Operators
• 10.5 Examples with Symmetry Account
  • 10.5.1 Spherical Geometry
  • 10.5.2 Quasi-One-Dimensional Geometry
• 10.6 Concluding Remarks

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