Dimensional Analysis Beyond the Pi Theorem

Table of ContentsAbout the AuthorPrefaceAcknowledgmentCHAPTER ONE: Principles of the Dimensional Analysis1.1 Introduction1.2 Dimensional Analysis and Scaling Concept1.2.1 Fractal Dimension1.3 Scaling Analysis and Modeling1.4 Mathematical Basis for Scaling Analysis1.5 Dimensions, Dimensional Homogeneity, and Independent Dimensions1.6 Basics of Buckingham's pi (Pi) Theorem1.6.1 Some Examples of Buckingham's pi (Pi) Theorem1.7 Oscillations of a Star1.8 Gravity Waves on Water1.9 Dimensional Analysis Correlation for Cooking a Turkey1.10 Energy in a Nuclear Explosion1.10.1 The Basic Scaling Argument in a Nuclear Explosion1.10.2 Calculating the Differential Equations of Expanding Gas of Nuclear Explosion1.10.3 Solving the Differential Equations of Expanding Gas of Nuclear Explosion1.11 Energy in a High Intense Implosion1.12 Similarity and Estimating1.13 Self-Similarity1.14 General Results of Similarity1.14.1 Principles of Similarity1.15 Scaling Argument1.16 Self-Similarity Solutions of the First and Second Kind1.17 Conclusion1.18 ReferencesCHAPTER TWO: Dimensional Analysis: Similarity and Self-Similarity2.1 Lagrangian and Eulerian Coordinate Systems2.1.1 Arbitrary Lagrangian Eulerian (ALE) Systems2.2 Similar and Self-Similar Definitions"/div>2.3 Compressible and Incompressible Flows2.3.1 Limiting Condition for Compressibility2.4 Mathematical and Thermodynamic Aspect of Gas Dynamics2.4.1 Gas Dynamics Equations in Integral Form2.4.2 Gas Dynamics Equations in Differential Form2.4.3 Perfect Gas Equation of State2.5 Unsteady Motion of Continuous Media and Self-Similarity Methods2.5.1 Fundamental Equations of Gasdynamics in the Eulerian Form2.5.2 Fundamental Equations of Gasdynamics in the Lagrangian Form2.6 Study of Shock Waves and Normal Shock Waves2.6.1 Shock Diffraction and Reflection Processes2.7 ReferencesCHAPTER THREE: Shock Wave and High Pressure Phenomena3.1 Introduction to Blast Waves and Shock Waves3.2 Self-Similarity and Sedov - Taylor Problem3.3 Self-Similarity and Guderley Problem3.4 Physics of Nuclear Device Explosion3.4.1 Little Boy Uranium Bomb3.4.2 Fat Man Plutonium Bomb3.4.3 Problem of Implosion and Explosion3.4.4 Critical Mass and Neutron Initiator for Nuclear Devices3.5 Physics of Thermonuclear Explosion3.6 Nuclear Isomer and Self-Similar Approaches3.7 Pellet Implosion Driven Fusion Energy and Self-Similar Approaches3.7.1 Linear Stability of Self-Similar Flow in D-T Pellet Implosion3.8 Plasma Physics and Particle-in-Cell Solution (PIC)3.9 Similarity Solutions for Partial and Differential Equations3.10 Dimensional Analysis and Intermediate Asymptotic3.11 Asymptotic Analysis and Singular Perturbation Theory3.12 Regular and Singular Perturbation Problems3.13 Eigenvalue Problems3.14 Quantum Mechanics3.15 Summary3.16 ReferencesCHAPTER FOUR: Similarity Methods for Nonlinear Problems4.1 Similarity Solutions for Partial and Differential Equations4.2 Fundamental Solutions of the Diffusion Equation Using Similarity Method4.3 Similarity Method and Fundamental Solutions of the Fourier Equation4.4 Fundamental Solutions of the Diffusion Equation; Global Affinity4.5 Solution of the Boundary-Layer Equations for Flow over a Flat Plate4.6 Solving First Order Partial Differential Equations using Similarity Method4.6.1 Solving Quasilinear Partial Differential Equations of First Order using Similarity4.6.2 The Boundary Value problem for a First Order Partial Differential Equation4.6.3 Statement of the Cauchy Problem for First Order Partial Differential Equation4.7 Exact Similarity Solutions on Nonlinear Partial Differential Equations4.8 Asymptotic Solutions by Balancing Arguments4.9 ReferencesAPPENDIX A: Simple Harmonic MotionAPPENDIX B: Pendulum ProblemAPPENDIX C: Similarity Solutions Methods for Partial Differential Equations (PDEs)C-1 Self-Similar Solutions by Dimensional AnalysisC-2 Similarity Solutions by Stretching TransformationC-3 Similarity Solution for the Rayleigh ProblemINDEX