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# Unified Non-Local Relativistic Theory of Transport Processes

- 1st Edition - August 18, 2016
- Author: Boris V. Alexeev
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 4 - 6 3 8 5 4 - 0

Unified Non-Local Relativistic Theory of Transport Processes highlights the most significant features of non-local relativistic theory, which is a highly effective tool for solvi… Read more

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Request a sales quote*Unified Non-Local Relativistic Theory of Transport Processes* highlights the most significant features of non-local relativistic theory, which is a highly effective tool for solving many physical problems in areas where the classical local theory runs into difficulties. The book provides the fundamental science behind new non-local physics – generalized for relativistic cases and applied in a range of scales – from transport phenomena in massless physical systems to unified theory of dissipative structures.

The book complements the author’s previous monograph on *Unified Non-Local Theory of Transport Processes* (Elsevier, 2015), which is mainly devoted to non-relativistic non-local physics. Nevertheless, the theory as handled in this new work is outlined independently so the book can be studied on its own.

- Comprehensive collection of non-local relativistic theory with examples that could previously only be found scattered in the literature
- Provides applications in quantum non-local relativistic hydrodynamics, quantum solitons in solid matter, and plasmas
- Uses generalized non-local kinetic theory as a highly effective tool for solving many physical problems beyond classical physics
- Presents non-local relativistic physics in many related problems of hydrodynamics, gravity, nonlinear optics, time quantization, and applied mathematics
- Includes concrete mathematical problems that are physically consistent and can be solved and studied both analytically and numerically

- Preface
- Introduction: Review of the Main Principles of the Unified Nonlocal Theory of Transport Processes
- I.1 The Principles of Nonlocal Physics
- I.2 On the Solution of Fundamental Problems of Nonlocal Statistical Theory of Dissipative Processes
- I.3 Fundamental Postulates of the Special Theory of Relativity

- Chapter 1: Hydrodynamic Form of the Dirac Quantum Relativistic Equation
- Abstract
- 1.1 “Derivation” of the Dirac Equation
- 1.2 Hydrodynamic Form of Dirac Equation in the Absence of an External Field
- 1.3 Hydrodynamic Form of the Dirac Equation in an External Electromagnetic Field

- Chapter 2: Generalized Relativistic Nonlocal Kinetic Equation Without Taking Into Account the External Forces
- Abstract
- 2.1 The Collision Integral
- 2.2 Nonlocal Relativistic Kinetic Equation
- 2.3 Model Generalized Relativistic Kinetic Equation

- Chapter 3: Classical Relativistic Equilibrium Distribution Function and Computation of Equilibrium Values of Some Macroscopic Quantities
- Abstract
- 3.1 The Derivation of the Formula for the Classical Equilibrium Distribution Function
- 3.2 The Calculation of the Number Density
- 3.3 The Calculation of the Energy Density and Pressure
- 3.4 The Calculation of the Density of Entropy

- Chapter 4: Generalized Relativistic Hydrodynamic Enskog Equations Without Regard to External Forces
- Abstract
- 4.1 Derivation of the Continuity Equation
- 4.2 Derivation of the Motion Equation
- 4.3 Derivation of the Energy Equation
- 4.4 Generalized Enskog System of Relativistic Hydrodynamic Equations

- Chapter 5: Generalized Relativistic Hydrodynamic Euler Equations Without Taking Into Account the External Forces
- Abstract
- 5.1 Components of Tensor Physical Quantities in the Local Rest System
- 5.2 The Lorentz Transformation Law for Tensor Physical Quantities in One-Dimensional Case
- 5.3 Generalized Relativistic Euler Equations for One-Dimensional Motion
- 5.4 Generalized One-Dimensional Nonrelativistic Euler Equations as the Asymptotic Behavior of the Relativistic Equations
- 5.5 Generalized Relativistic Euler Equations for Arbitrary Motion
- 5.6 Generalized Nonrelativistic Euler Equations for an Arbitrary Motion as an Asymptotic Form of the Relativistic Equations

- Chapter 6: The Solution of Some Physical Problems on the Basis of the Nonlocal Relativistic Equations Without Taking Into Account the External Forces
- Abstract
- 6.1 The Propagation of Plane Harmonic Waves of Small Amplitude in the Ultra-Relativistic Medium
- 6.2 Shock Waves in Relativistic Gas
- 6.3 The Collision of Nucleons

- Chapter 7: Nonlocal Relativistic Kinetic Equation and Hydrodynamic Enskog Equations Taking Into Account the External Forces
- Abstract
- 7.1 Nonlocal Relativistic Kinetic Equation Taking Into Account the External Forces
- 7.2 The Derivation of the Continuity Equation
- 7.3 The Derivation of the Motion Equation
- 7.4 The Derivation of the Energy Equation
- 7.5 Generalized System of Relativistic Hydrodynamic Enskog Equations
- 7.6 Generalized System of Relativistic Hydrodynamic Enskog Equations for Multicomponent Mixture

- Chapter 8: Generalized Relativistic Euler Equations Taking Into Account External Forces
- Abstract
- 8.1 Components of Tensor Physical Quantities in the Local Rest System
- 8.2 The Lorentz Transformation Law for Tensor Physical Quantities in One-Dimensional Case
- 8.3 Generalized Relativistic Euler Equations for One-Dimensional Motion
- 8.4 Generalized One-Dimensional Nonrelativistic Euler Equations as the Asymptotic Behavior of the Relativistic Equations

- Chapter 9: Application of the Generalized Relativistic Kinetic and Hydrodynamic Equations to the Study of Graphene
- Abstract
- 9.1 Features of the Band Structure of Graphene
- 9.2 Generalized Kinetic and Hydrodynamic Equations for Graphene in an Electric Field
- 9.3 Wave Transfer in Graphene
- 9.4 The Hall Effect in the Relativistic Nonlocal Theory of Massless Particles

- Chapter 10: Application of Relativistic Nonlocal Physics in the Theory of Gravitational Field Interaction With a Laser Beam
- Abstract
- 10.1 Nonlocal Physics and Gravitational Waves
- 10.2 Basic Equations of Relativistic Nonlocal Physics Having Regard to External Forces
- 10.3 Calculation of the Tensor Moments for the Laser Beam Evolution
- 10.4 Nonlocal Relativistic Equations in the Explicit Form
- 10.5 Wave Solutions for GFR-Interaction

- Chapter 11: Application of the Generalized Relativistic Hydrodynamic Equations to the Study of the Interaction of Planck Radiation With the Gravitational Field
- Abstract
- 11.1 About the Influence of Gravitational Field on Radiation
- 11.2 Nonlocal Relativistic Hydrodynamic Equations for Equilibrium Radiation
- 11.3 Local Equilibrium Radiation in Gravitational Field for the One-Dimensional Stationary Case
- 11.4 Self-Similar Solutions of Hydrodynamic Equations for Planck Radiation in Gravitational Field

- Chapter 12: Connection Between Time Quantization in the Frame of Nonlocal Relativistic Physics and Shannon-Nyquist-Kotelnikov Theorem
- Abstract
- 12.1 About the Time Quantization
- 12.2 Systems of Generalized Relativistic Hydrodynamic Equations in the Shannon-Nyquist-Kotelnikov Theory
- 12.3 Shannon-Nyquist-Kotelnikov Theorem as a Consequence of Nonlocal Physics: Time Quantization

- Appendices
- Appendix 1 Elements of the Theory of Tensors
- Appendix 2 Conservation of Phase Volume dx
^{1}dx^{,2}dx^{,3}dt Under the Lorentz Transformations - Appendix 3 The Relativistic Invariance of the Substantial Derivative in One-Dimensional Motion
- Appendix 4 Integration of Four-Dimensional Divergence in Momentum Space
- Appendix 5 Calculation of the Tensor

- Index

- No. of pages: 466
- Language: English
- Edition: 1
- Published: August 18, 2016
- Imprint: Elsevier
- Paperback ISBN: 9780444638540

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### Boris V. Alexeev

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