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The Dynamical Projectors Method : Hydro and Electrodynamics

Author: Sergey Leble; Anna Perelomova
Publisher: Boca Raton, FL : CRC Press, 2018.
Edition/Format:   eBook : Document : English : First editionView all editions and formats
Summary:
"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  Read more...
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Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Sergey Leble; Anna Perelomova
ISBN: 9781351107990 1351107992 9781351107983 1351107984
OCLC Number: 1029242824
Description: 1 online resource : text file, PDF
Contents: Cover; Half Title; Title Page; Copyright Page; Dedication; Contents; List of Figures; Preface; Authors; Chapter 1 Introduction; Chapter 2 General Technique; 2.1 General Proper Space Definitionâ#x80;#x94;Eigenvector Problem for Perturbations over a Homogeneous Ground State; 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 Hydrodynamics3.1 On the Hydro-Thermodynamic Relations for Quasi-Isentropic Processes; 3.2 Thermoconducting Flow of an Uniform Newtonian Gas. Modes, Projectors and Dynamic Equations. Acoustic Heating; 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 Which Is Affected by Constant Mass Force; 3.4.1 Isothermal Atmosphere 1D Dynamics; 3.4.2 Examples of Projecting: Decomposition of the Total Field of Exclusively Entropy or Acoustic Parts and Energy Release with Mass Injection. 3.4.3 Dynamics of the Short-Scale WavesChapter 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 Difracting 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 Remarks on the Thermal Self-Focusing of Sound; 5.3 The Nonlinear Effects of Sound in a Liquid with Relaxation Losses. 5.4 On the Nonlinear Effects of Magnetoacoustic Perturbations in a Perfectly Conducting Viscous and Thermoconducting Gas5.4.1 On the Nonlinear Interactions in a Plasma with Finite Electrical Conductivity; Chapter 6 Boundary Layer Problem: Acoustic and Tollmienn-Schlichting Waves; 6.1 Preliminary Remarks; 6.2 Basic Equations for Compressible Fluid; 6.3 Linear Approximation; 6.4 The Tollmienn-Schlichting Mode; 6.5 Acoustic Modes; 6.6 Peculiarities of Non-Commutative Projecting in the Inhomogeneous Linear Problem; 6.7 Nonlinear Flow: Coupled Dynamic Equations. 6.8 Resonance Interaction of Acoustic and T-S ModesChapter 7 1D Electrodynamics; 7.1 Cauchy Problem for 1D Electrodynamics. Polarized Hybrid Fields; 7.1.1 The Problem Formulation Outline; 7.1.2 On Dynamical Projection Method Application: Cauchy Problem; 7.1.3 The Effect of a Cumulative Part of Interaction; 7.1.4 Dispersion Account, an Example; 7.2 General Dynamics Equations, SPE System; 7.2.1 The 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.
Responsibility: Sergey Leble, Anna Perelomova.

Abstract:

"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."--Provided by publisher.

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"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 Read more...

 
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