Advanced Topics in Contemporary Physics for Engineering: Nanophysics, Plasma Physics, and Electrodynamics

Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Preface
1. Advanced Phenomena in Plasma
1.1 Introduction
1.2 The Plasma Universe Theory
1.2.1 Parametric Resonance and Nonlinear Phenomenon
1.2.2 Synergetics
1.2.3 The Birkeland's Terrella Experiment
1.2.4 Celsius and the Aurora Borealis
1.2.5 The Interplanetary Space
1.2.6 The Birkeland Current
1.2.7 The Jupiter-Io Generator
1.2.8 Electric Double Layers, Critical Velocity and Pinch Effect
1.2.9 The Electric Charge of the Sun
1.3 Transport Phenomena in Multicomponent Systems
1.3.1 Individual Trajectories
1.3.2 Microscopic Description of Plasma
1.3.2.1 Velocity Distribution Function
1.3.2.2 Evolution of the Distribution Function
1.3.3 The Principle of Detailed Balance
1.3.3.1 Momentum Transfert Cross Section
1.3.4 Hydrodynamic Models
1.3.4.1 The Equation of Continuity
1.3.5 The Stress Tensor in Newtonian Fluids
1.3.5.1 Homogeneous Reactions: Reaction Rates
1.3.5.2 Ponderomotive Forces Acting in a dielectric barrier discharge (DBD)
1.3.5.3 EHD Induced by Paraelectric Effects
1.3.6 The Miller's Force
1.3.6.1 A New Form of the Electromagnetic Energy Equation When Free Charges are Present
1.3.6.2 Equation of Conservation of Energy
1.3.7 Effects of Space Charge
1.4 Plasma Actuators Devices and Modeling
1.5 Numerical Model
1.5.1 Description
1.5.2 Transport Parameters and Rate Coefficients
1.5.3 Numerical Model
1.5.4 The First Order Orbit Theory
1.5.4.1 Particle Motion in the Presence of a Constant Magnetic Field
1.5.5 Circuital Model of Anomalous Diffusion in a Cold Magnetized Plasma
1.6 Simon's "Short-Circuit" Theory
1.7 Plasma Turbulence and Transport
1.8 Circuital Model of Anomalous Diffusion
1.9 Discussion and Summary
Notes
References
2. Topics in Electromagnetism
2.1 Classical Electrodynamics
2.1.1 The Maxwell's Equations
2.1.2 Retarded Potentials and Fields
2.1.3 Vortices of an Electric Field
2.1.4 Dependence of Electric Voltage on Integration Path
2.1.5 The Velocity Field and Radiation Fields
2.1.6 Schwinger's Variational Principle
2.1.7 Series of Fourier and Fourier Transform
2.1.8 Lagrangian Formulation of Classical Electrodynamics
2.1.8.1 Lagrangian of Free Classical Maxwell Fields
2.1.8.2 Lagrangian of Topologically Massive Spinor Electrodynamics
2.2 Chern-Simons Theory
2.3 Ergontropic Dynamics
2.3.1 Dynamics
2.3.2 Electrodynamics
2.4 An Overview of Other Electromagnetic Theories
2.4.1 The Experiment of Oersted
2.4.2 The Method of Hypothesis - Introduced by Ampère
2.4.3 Ampère's Law
2.4.4 The Experiment of Ampère
2.4.5 Weber's Law
2.4.5.1 "Catalytic Forces" and the Fundamental Length
2.4.5.2 Nuclear Forces Dependent on Velocity and Weber's Electrodynamics
2.4.6 Neumann's Principle of Electrodynamics
2.4.7 Field Theories and Action-at-a-Distance Theories
2.4.8 Maxwell's Electrodynamics
2.4.9 Helmholtz's Electrodynamics
2.4.10 The Biefeld-Brown Effect
2.4.11 Vacuum and Casimir Forces
Notes
References
3. Tensors, Spinors, and Higher Representations of the Electromagnetic Field
3.1 Tensorial Calculus, Differential Forms, and Spinorial Calculus
3.1.1 Introduction to Tensorial Calculus
3.1.1.1 Historical Introduction
3.1.2 Origin of Determinants
3.1.2.1 Matrix Characteristics
3.1.2.2 Eigenvectors and Eigenvalues of a Transformation Matrix
3.1.2.3 Application to the Special Theory of Relativity
3.1.3 Tangent Vectors and Mappings
3.1.4 Contravariant Tensors
3.1.5 Covariant Tensors
3.1.6 Higher Ranks and Mixed Tensors
3.1.7 Space Curves
3.1.8 The Tensors δij and ϵijk
3.1.8.1 Metric Tensors and the Line Element
3.1.8.2 Christoffel Symbols
3.1.8.3 Covariant Derivation
3.1.9 Curvature: The Riemann, Torsion, and Weyl Tensors
3.1.10 Dragging in the Kerr Field
3.1.11 Spinorial Calculus
3.1.12 Maxwell's Equations in Spinorial Representation
3.1.13 Differential Forms
3.1.13.1 Lorentz Force and Electromagnetic Field Tensor
3.1.13.2 Maxwell's Equations in Differential Form
3.1.13.3 Dyadic Notation
3.1.14 Topology and Turbulence
3.1.15 The Chern-Simon Lagrangian
3.1.16 The Lie Derivative
3.1.17 Elements of Set Theory
3.1.18 The Yang-Mills Field
3.1.19 Elements of Group Theory
3.1.20 Cyclic Groups
3.1.21 Permutation Groups
3.1.22 Classical Groups
3.1.23 Group Representations
3.1.23.1 Group of Rotations in Three Dimensions
3.1.23.2 Lie Algebra
3.1.23.3 Lie Algebras
3.1.24 SU(2) Representation of Maxwell's Equations
3.1.25 SO(3,1) Representation of Maxwell's Equations
3.1.26 Chirality
3.2 Zilch Densities Z
3.2.1 Retrograde Flow of Zilch
3.3 Fractional Calculus and Its Applications to Physics
3.3.1 Historical Perspective
3.3.2 Applications
3.3.2.1 Abel's Equation
3.3.3 Fractional Integrals
3.4 Short Note on String Theory
3.4.1 Historical Perspective
3.4.2 Some Properties of Veneziano and Virasoro Amplitudes
3.4.3 Regge Poles
Notes
References
4. The World of the Tiniest Building Blocks
4.1 Understanding Nature for Improving Processes and Devices
4.2 From Atoms to Nano-Objects
References
5. Nanophysics and Nanotechnology: From Quanta to Weak Forces Metrology
5.1 Quantum Physics in the Nanoworld
5.2 Measuring Increasingly Weak Forces
References
6. Lab-on-a-Tip and Plasmas for Sustainability
6.1 Lab-on-a-Tip in Applied Nanophysics
6.2 Plasmas and Nano for Sustainability
References
Index