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Unified Non-Local Theory of Transport Processes
Generalized Boltzmann Physical Kinetics
2nd Edition - February 5, 2015
Author: Boris V. Alexeev
Language: English
Hardback ISBN:9780444634788
9 7 8 - 0 - 4 4 4 - 6 3 4 7 8 - 8
eBook ISBN:9780444634870
9 7 8 - 0 - 4 4 4 - 6 3 4 8 7 - 0
Unified Non-Local Theory of Transport Processess, 2nd Edition provides a new theory of transport processes in gases, plasmas and liquids. It is shown that the well-known Boltzmann…Read more
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Unified Non-Local Theory of Transport Processess, 2nd Edition provides a new theory of transport processes in gases, plasmas and liquids. It is shown that the well-known Boltzmann equation, which is the basis of the classical kinetic theory, is incorrect in the definite sense. Additional terms need to be added leading to a dramatic change in transport theory. The result is a strict theory of turbulence and the possibility to calculate turbulent flows from the first principles of physics.
Fully revised and expanded edition, providing applications in quantum non-local hydrodynamics, quantum solitons in solid matter, and plasmas
Uses generalized Boltzmann kinetic theory as an highly effective tool for solving many physical problems beyond classical physics
Addresses dark matter and energy
Presents non-local physics in many related problems of hydrodynamics, gravity, black holes, nonlinear optics, and applied mathematics
Theoretical and applied physicists, astrophysicists, astronomers, cosmologists, engineers
Preface
Historical Introduction and the Problem Formulation
Chapter 1: Generalized Boltzmann Equation
Abstract
1.1 Mathematical Introduction—Method of Many Scales
1.2 Hierarchy of Bogolubov Kinetic Equations
1.3 Derivation of the Generalized Boltzmann Equation
1.4 Generalized Boltzmann H-Theorem and the Problem of Irreversibility of Time
1.5 Generalized Boltzmann Equation and Iterative Construction of Higher-Order Equations in the Boltzmann Kinetic Theory
1.6 Generalized Boltzmann Equation and the Theory of Non-Local Kinetic Equations with Time Delay
Chapter 2: Theory of Generalized Hydrodynamic Equations
Abstract
2.1 Transport of Molecular Characteristics
2.2 Hydrodynamic Enskog Equations
2.3 Transformations of the Generalized Boltzmann Equation
2.4 Generalized Continuity Equation
2.5 Generalized Momentum Equation for Component
2.6 Generalized Energy Equation for Component
2.7 Summary of the Generalized Enskog Equations and Derivation of the Generalized Hydrodynamic Euler Equations
Chapter 3: Quantum Non-Local Hydrodynamics
Abstract
3.1 Generalized Hydrodynamic Equations and Quantum Mechanics
3.2 GHEs, Quantum Hydrodynamics. SE as the Consequence of GHE
3.3 SE and its Derivation from Liouville Equation
3.4 Direct Experimental Confirmations of the Non-Local Effects
Chapter 4: Application of Unified Non-Local Theory to the Calculation of the Electron and Proton Inner Structures
Abstract
4.1 Generalized Quantum Hydrodynamic Equations
4.2 The Charge Internal Structure of Electron
4.3 The Derivation of the Angle Relaxation Equation
4.4 The Mathematical Modeling of the Charge Distribution in Electron and Proton
4.5 To the Theory of Proton and Electron as Ball-like Charged Objects
Chapter 5: Non-Local Quantum Hydrodynamics in the Theory of Plasmoids and the Atom Structure
Abstract
5.1 The Stationary Single Spherical Plasmoid
5.2 Results of the Mathematical Modeling of the Rest Solitons
5.3 Nonstationary 1D Generalized Hydrodynamic Equations in the Self-Consistent Electrical Field. Quantization in the Generalized Quantum Hydrodynamics
5.4 Moving Quantum Solitons in Self-Consistent Electric Field
5.5 Mathematical Modeling of Moving Solitons
5.6 Some Remarks Concerning CPT (Charge-Parity-Time) Principle
5.7 About Some Mysterious Events of the Last Hundred Years
Chapter 6: Quantum Solitons in Solid Matter
Abstract
6.1 Quantum Oscillators in the Unified Non-local Theory
6.2 Application of Non-Local Quantum Hydrodynamics to the Description of the Charged Density Waves in the Graphene Crystal Lattice
6.3 Generalized Quantum Hydrodynamic Equations Describing the Soliton Movement in the Crystal Lattice
6.4 Results of the Mathematical Modeling Without the External Electric Field
6.5 Results of the Mathematical Modeling With the External Electric Field
6.6 Spin Effects in the Generalized Quantum Hydrodynamic Equations
6.7 To the Theory of the SC
Chapter 7: Generalized Boltzmann Physical Kinetics in Physics of Plasma
Abstract
7.1 Extension of Generalized Boltzmann Physical Kinetics for the Transport Processes Description in Plasma
7.2 Dispersion Equations of Plasma in Generalized Boltzmann Theory
7.3 The Generalized Theory of Landau Damping
7.4 Evaluation of Landau Integral
7.5 Estimation of the Accuracy of Landau Approximation
7.6 Alternative Analytical Solutions of the Vlasov-Landau Dispersion Equation
7.7 The Generalized Theory of Landau Damping in Collisional Media
Chapter 8: Physics of a Weakly Ionized Gas
Abstract
8.1 Charged Particles Relaxation in “Maxwellian” Gas and the Hydrodynamic Aspects of the Theory
8.2 Distribution Function (DF) of the Charged Particles in the “Lorentz” Gas
8.3 Charged Particles in Alternating Electric Field
8.4 Conductivity of a Weakly Ionized Gas in the Crossed Electric and Magnetic Fields
8.5 Investigation of the GBE for Electron Energy Distribution in a Constant Electric Field with due Regard for Inelastic Collisions
Chapter 9: Generalized Boltzmann Equation in the Theory of the Rarefied Gases and Liquids
Abstract
9.1 Kinetic Coefficients in the Theory of the Generalized Kinetic Equations. Linearization of the Generalized Boltzmann Equation
9.2 Approximate Modified Chapman-Enskog Method
9.3 Kinetic Coefficient Calculation with Taking into Account the Statistical Fluctuations
9.4 Sound Propagation Studied with the Generalized Equations of Fluid Dynamics
9.5 Shock Wave Structure Examined with the Generalized Equations of Fluid Dynamics
9.6 Boundary Conditions in the Theory of the Generalized Hydrodynamic Equations
9.7 To the Kinetic and Hydrodynamic Theory of Liquids
Chapter 10: Strict Theory of Turbulence and Some Applications of the Generalized Hydrodynamic Theory
Abstract
10.1 About Principles of Classical Theory of Turbulent Flows
10.2 Theory of Turbulence and Generalized Euler Equations
10.3 Theory of Turbulence and the Generalized Enskog Equations
10.4 Unsteady Flow of a Compressible Gas in a Cavity
10.5 Application of the GHE: To the Investigation of Gas Flows in Channels with a Step
10.6 Vortex and Turbulent Flow of Viscous Gas in Channel with Flat Plate
Chapter 11: Astrophysical Applications
Abstract
11.1 Solution of the Dark Matter Problem in the Frame of the Non-Local Physics
11.2 Plasma-Gravitational Analogy in the Generalized Theory of Landau Damping
11.3 Disk Galaxy Rotation and the Problem of Dark Matter
11.4 Hubble Expansion and the Problem of Dark Energy
11.5 Propagation of Plane Gravitational Waves in Vacuum with Cosmic Microwave Background
11.6 Application of the Non-Local Physics in the Theory of the Matter Movement in Black Hole
11.7 Self-similar Solutions of the Non-local Equations
Chapter 12: The Generalized Relativistic Kinetic Hydrodynamic Theory
Abstract
12.1 Hydrodynamic Form of the Dirac Quantum Relativistic Equation
12.6 The Limit Transfer to the non-Relativistic Generalized non-Local Euler Equations
12.7 Expansion of the Flat Harmonic Waves of Small Amplitudes in Ultra-relativistic Media
Some remarks to the conclusion of the monograph
Appendix 1: Perturbation Method of the Equation Solution Related to T[f]
Appendix 2: Using of Curvilinear Coordinates in the Generalized Hydrodynamic Theory
Appendix 3: Characteristic Scales in Plasma Physics
Appendix 4: Dispersion Relations in the Generalized Boltzmann Kinetic Theory Neglecting the Integral Collision Term
Appendix 5: Three-Diagonal Method of Gauss Elimination Techniques for the Differential Third- and Second-Order Equations
Appendix 6: Some Integral Calculations in the Generalized Navier-Stokes Approximation
Appendix 7: Derivation of Energy Equation for Invariant
Appendix 8: To the Non-Local Theory of Cold Nuclear Fusion
Appendix 9: To the Non-Local Theory of Variable Stars
Appendix 10: To the Non-Local Theory of Levitation
References
Index
No. of pages: 644
Language: English
Edition: 2
Published: February 5, 2015
Imprint: Elsevier
Hardback ISBN: 9780444634788
eBook ISBN: 9780444634870
BA
Boris V. Alexeev
Professor Boris V. Alexeev is Head of the Centre of the Theoretical Foundations of Nanotechnology and Head of the Physics Department at the Moscow Lomonosov University of Fine Chemical Technologies, Moscow, Russia. In the 1990s he was Visiting Professor at the University of Alabama, Huntsville, AL, USA, and Visiting Professor at the University of Provence, Marseille, France. Professor Alexeev has published over 290 articles in international scientific journals and 22 books. He has received several honors and awards, and is member of six societies.
Affiliations and expertise
Physics Department, Moscow Lomonosov University of Fine Chemical Technologies, Moscow, Russia
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