Dimensional Analysis Beyond the Pi Theorem

'Table of Contents About the Author Preface Acknowledgment CHAPTER ONE: Principles of the Dimensional Analysis 1.1 Introduction 1.2 Dimensional Analysis and Scaling Concept 1.2.1 Fractal Dimension 1.3 Scaling Analysis and Modeling 1.4 Mathematical Basis for Scaling Analysis 1.5 Dimensions, Dimensional Homogeneity, and Independent Dimensions 1.6 Basics of Buckingham's pi (Pi) Theorem 1.6.1 Some Examples of Buckingham's pi (Pi) Theorem 1.7 Oscillations of a Star 1.8 Gravity Waves on Water 1.9 Dimensional Analysis Correlation for Cooking a Turkey 1.10 Energy in a Nuclear Explosion 1.10.1 The Basic Scaling Argument in a Nuclear Explosion 1.10.2 Calculating the Differential Equations of Expanding Gas of Nuclear Explosion 1.10.3 Solving the Differential Equations of Expanding Gas of Nuclear Explosion1.11 Energy in a High Intense Implosion 1.12 Similarity and Estimating 1.13 Self-Similarity 1.14 General Results of Similarity 1.14.1 Principles of Similarity 1.15 Scaling Argument 1.16 Self-Similarity Solutions of the First and Second Kind 1.17 Conclusion 1.18 References CHAPTER TWO: Dimensional Analysis: Similarity and Self-Similarity 2.1 Lagrangian and Eulerian Coordinate Systems 2.1.1 Arbitrary Lagrangian Eulerian (ALE) Systems 2.2 Similar and Self-Similar Definitions< 2.3 Compressible and Incompressible Flows 2.3.1 Limiting Condition for Compressibility 2.4 Mathematical and Thermodynamic Aspect of Gas Dynamics 2.4.1 Gas Dynamics Equations in Integral Form 2.4.2 Gas Dynamics Equations in Differential Form 2.4.3 Perfect Gas Equation of State 2.5 Unsteady Motion of Continuous Media and Self-Similarity Methods 2.5.1 Fundamental Equations of Gasdynamics in the Eulerian Form 2.5.2 Fundamental Equations of Gasdynamics in the Lagrangian Form 2.6 Study of Shock Waves and Normal Shock Waves 2.6.1 Shock Diffraction and Reflection Processes 2.7 References CHAPTER THREE: Shock Wave and High Pressure Phenomena 3.1 Introduction to Blast Waves and Shock Waves 3.2 Self-Similarity and Sedov - Taylor Problem 3.3 Self-Similarity and Guderley Problem 3.4 Physics of Nuclear Device Explosion 3.4.1 Little Boy Uranium Bomb 3.4.2 Fat Man Plutonium Bomb 3.4.3 Problem of Implosion and Explosion 3.4.4 Critical Mass and Neutron Initiator for Nuclear Devices 3.5 Physics of Thermonuclear Explosion 3.6 Nuclear Isomer and Self-Similar Approaches 3.7 Pellet Implosion Driven Fusion Energy and Self-Similar Approaches 3.7.1 Linear Stability of Self-Similar Flow in D-T Pellet Implosion 3.8 Plasma Physics and Particle-in-Cell Solution (PIC) 3.9 Similarity Solutions for Partial and Differential Equations 3.10 Dimensional Analysis and Intermediate Asymptotic 3.11 Asymptotic Analysis and Singular Perturbation Theory 3.12 Regular and Singular Perturbation Problems 3.13 Eigenvalue Problems 3.14 Quantum Mechanics 3.15 Summary 3.16 References CHAPTER FOUR: Similarity Methods for Nonlinear Problems 4.1 Similarity Solutions for Partial and Differential Equations 4.2 Fundamental Solutions of the Diffusion Equation Using Similarity Method 4.3 Similarity Method and Fundamental Solutions of the Fourier Equation 4.4 Fundamental Solutions of the Diffusion Equation; Global Affinity 4.5 Solution of the Boundary-Layer Equations for Flow over a Flat Plate 4.6 Solving First Order Partial Differential Equations using Similarity Method 4.6.1 Solving Quasilinear Partial Differential Equations of First Order using Similarity 4.6.2 The Boundary Value problem for a First Order Partial Differential Equation 4.6.3 Statement of the Cauchy Problem for First Order Partial Differential Equation 4.7 Exact Similarity Solutions on Nonlinear Partial Differential Equations 4.8 Asymptotic Solutions by Balancing Arguments 4.9 References APPENDIX A: Simple Harmonic Motion APPENDIX B: Pendulum Problem APPENDIX C: Similarity Solutions Methods for Partial Differential Equations (PDEs) C-1 Self-Similar Solutions by