# Unified Non-Local Theory of Transport Processes

## 2nd Edition

### Generalized Boltzmann Physical Kinetics

**Authors:**Boris Alexeev

**Hardcover ISBN:**9780444634788

**eBook ISBN:**9780444634870

**Imprint:**Elsevier

**Published Date:**5th February 2015

**Page Count:**644

## Description

*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.

## Key Features

- 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

## Readership

Theoretical and applied physicists, astrophysicists, astronomers, cosmologists, engineers

## Table of Contents

- 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

## Details

- No. of pages:
- 644

- Language:
- English

- Copyright:
- © Elsevier 2015

- Published:
- 5th February 2015

- Imprint:
- Elsevier

- Hardcover ISBN:
- 9780444634788

- eBook ISBN:
- 9780444634870

## About the Author

### Boris 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

## Reviews

"...contains a lot of illustrations and calculations supplied with the detailed discussions of the used approximations, their precision, parameters, etc. It is especially important within the first part of the book, where the method is introduced since these items allow for studying of the topic by newcomers." --**Zentralblatt MATH**