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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:9 7 8 - 0 - 4 4 4 - 6 3 4 7 8 - 8
- eBook ISBN: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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Request a sales quote*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
- 12.2 Generalized Relativistic Kinetic Equation
- 12.3 Generalized Enskog Relativistic Hydrodynamic Equations
- 12.4 Generalized System of the Relativistic Hydrodynamics and Transfer to the Generalized Relativistic non-Local Euler Hydrodynamic Equations
- 12.5 Generalized non-Local Relativistic Euler Equations
- 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

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### Boris V. Alexeev

*Unified Non-Local Theory of Transport Processes*on ScienceDirect