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· 제목 : Elasticity and Fluid Dynamics: Volume 3 of Modern Classical Physics (Paperback)
· 분류 : 외국도서 > 과학/수학/생태 > 과학 > 물리학 > 일반
· ISBN : 9780691207346
· 쪽수 : 480쪽
· 출판일 : 2021-06-15
· 분류 : 외국도서 > 과학/수학/생태 > 과학 > 물리학 > 일반
· ISBN : 9780691207346
· 쪽수 : 480쪽
· 출판일 : 2021-06-15
목차
- List of Boxes
- Preface
- Contents of Modern Classical Physics, volumes 1?5
- PART IV ELASTICITY
- 11 Elastostatics
- 11.1 Overview
- 11.2 Displacement and Strain
- 11.2.1 Displacement Vector and Its Gradient
- 11.2.2 Expansion, Rotation, Shear, and Strain
- 11.3 Stress, Elastic Moduli, and Elastostatic Equilibrium
- 11.3.1 Stress Tensor
- 11.3.2 Realm of Validity for Hooke’s Law
- 11.3.3 Elastic Moduli and Elastostatic Stress Tensor
- 11.3.4 Energy of Deformation
- 11.3.5 Thermoelasticity
- 11.3.6 Molecular Origin of Elastic Stress; Estimate of Moduli
- 11.3.7 Elastostatic Equilibrium: Navier-Cauchy Equation
- 11.4 Young’s Modulus and Poisson’s Ratio for an Isotropic Material: A Simple Elastostatics Problem
- 11.5 Reducing the Elastostatic Equations to 1 Dimension for a Bent Beam: Cantilever Bridge, Foucault Pendulum, DNA Molecule, Elastica
- 11.6 Buckling and Bifurcation of Equilibria
- 11.6.1 Elementary Theory of Buckling and Bifurcation
- 11.6.2 Collapse of theWorld Trade Center Buildings
- 11.6.3 Buckling with Lateral Force; Connection to Catastrophe Theory
- 11.6.4 Other Bifurcations: Venus Fly Trap, Whirling Shaft, Triaxial Stars, and Onset of Turbulence
- 11.7 Reducing the Elastostatic Equations to 2 Dimensions for a Deformed Thin Plate: Stress Polishing a Telescope Mirror
- 11.8 Cylindrical and Spherical Coordinates: Connection Coefficients and Components of the Gradient of the Displacement Vector
- 11.9 Solving the 3-Dimensional Navier-Cauchy Equation in Cylindrical Coordinates
- 11.9.1 Simple Methods: Pipe Fracture and Torsion Pendulum
- 11.9.2 Separation of Variables and Green’s Functions: Thermoelastic Noise in Mirrors
- Bibliographic Note
- 12 Elastodynamics
- 12.1 Overview
- 12.2 Basic Equations of Elastodynamics; Waves in a Homogeneous Medium
- 12.2.1 Equation of Motion for a Strained Elastic Medium
- 12.2.2 Elastodynamic Waves
- 12.2.3 Longitudinal Sound Waves
- 12.2.4 Transverse Shear Waves
- 12.2.5 Energy of Elastodynamic Waves
- 12.3 Waves in Rods, Strings, and Beams
- 12.3.1 Compression Waves in a Rod
- 12.3.2 Torsion Waves in a Rod
- 12.3.3 Waves on Strings
- 12.3.4 Flexural Waves on a Beam
- 12.3.5 Bifurcation of Equilibria and Buckling (Once More)
- 12.4 Body Waves and Surface Waves?Seismology and Ultrasound
- 12.4.1 Body Waves
- 12.4.2 Edge Waves
- 12.4.3 Green’s Function for a Homogeneous Half-Space
- 12.4.4 Free Oscillations of Solid Bodies
- 12.4.5 Seismic Tomography
- 12.4.6 Ultrasound; Shock Waves in Solids
- 12.5 The Relationship of Classical Waves to Quantum Mechanical Excitations
- Bibliographic Note
- PART V FLUID DYNAMICS
- 13 Foundations of Fluid Dynamic
- 13.1 Overview
- 13.2 The Macroscopic Nature of a Fluid: Density, Pressure, Flow Velocity; Liquids versus Gases
- 13.3 Hydrostatics
- 13.3.1 Archimedes’ Law
- 13.3.2 Nonrotating Stars and Planets
- 13.3.3 Rotating Fluids
- 13.4 Conservation Laws
- 13.5 The Dynamics of an Ideal Fluid
- 13.5.1 Mass Conservation
- 13.5.2 Momentum Conservation
- 13.5.3 Euler Equation
- 13.5.4 Bernoulli’s Theorem
- 13.5.5 Conservation of Energy
- 13.6 Incompressible Flows
- 13.7 Viscous Flows with Heat Conduction
- 13.7.1 Decomposition of the Velocity Gradient into Expansion, Vorticity, and Shear
- 13.7.2 Navier-Stokes Equation
- 13.7.3 Molecular Origin of Viscosity
- 13.7.4 Energy Conservation and Entropy Production
- 13.7.5 Reynolds Number
- 13.7.6 Pipe Flow
- 13.8 Relativistic Dynamics of a Perfect Fluid
- 13.8.1 Stress-Energy Tensor and Equations of Relativistic Fluid Mechanics
- 13.8.2 Relativistic Bernoulli Equation and Ultrarelativistic Astrophysical Jets
- 13.8.3 Nonrelativistic Limit of the Stress-Energy Tensor
- Bibliographic Note
- 14 Vorticity
- 14.1 Overview
- 14.2 Vorticity, Circulation, and Their Evolution
- 14.3 Low-Reynolds-Number Flow?Stokes Flow and Sedimentation
- 14.3.1 Motivation: Climate Change
- 14.3.2 Stokes Flow
- 14.3.3 Sedimentation Rate
- 14.4 High-Reynolds-Number Flow?Laminar Boundary Layers
- 14.4.1 Blasius Velocity Profile Near a Flat Plate: Stream Function and Similarity Solution
- 14.4.2 Blasius Vorticity Profile
- 14.4.3 Viscous Drag Force on a Flat Plate
- 14.4.4 Boundary Layer Near a Curved Surface: Separation
- 14.5 Nearly Rigidly Rotating Flows?Earth’s Atmosphere and Oceans
- 14.5.1 Equations of Fluid Dynamics in a Rotating Reference Frame
- 14.5.2 Geostrophic Flows
- 14.5.3 Taylor-Proudman Theorem
- 14.5.4 Ekman Boundary Layers
- 14..6 Instabilities of Shear Flows?Billow Clouds and Turbulence in the Stratosphere
- 14.6.1 Discontinuous Flow: Kelvin-Helmholtz Instability
- 14.6.2 Discontinuous Flow with Gravity
- 14.6.3 Smoothly Stratified Flows: Rayleigh and Richardson Criteria for Instability
- Bibliographic Note
- 15 Turbulence
- 15.1 Overview
- 15.2 The Transition to Turbulence?Flow Past a Cylinder
- 15.3 Empirical Description of Turbulence
- 15.4 Semiquantitative Analysis of Turbulence
- 15.4.1 Weak-Turbulence Formalism
- 15.4.2 Turbulent Viscosity
- 15.4.3 TurbulentWakes and Jets; Entrainment; the Coanda Effect
- 15.4.4 Kolmogorov Spectrum for Fully Developed, Homogeneous, Isotropic Turbulence
- 15.5 Turbulent Boundary Layers
- 15.5.1 Profile of a Turbulent Boundary Layer
- 15.5.2 Coanda Effect and Separation in a Turbulent Boundary Layer
- 15.5.3 Instability of a Laminar Boundary Layer
- 15.5.4 Flight of a Ball
- 15.6 The Route to Turbulence?Onset of Chaos
- 15.6.1 Rotating Couette Flow
- 15.6.2 Feigenbaum Sequence, Poincaré Maps, and the Period-Doubling Route to Turbulence in Convection
- 15.6.3 Other Routes to Turbulent Convection
- 15.6.4 Extreme Sensitivity to Initial Conditions
- Bibliographic Note
- 16 Waves
- 16.1 Overview
- 16.2 Gravity Waves on and beneath the Surface of a Fluid
- 16.2.1 Deep-Water Waves and Their Excitation and Damping
- 16.2.2 Shallow-Water Waves
- 16.2.3 Capillary Waves and Surface Tension
- 16.2.4 Helioseismology
- 16.3 Nonlinear Shallow-Water Waves and Solitons
- 16.3.1 Korteweg?de Vries (KdV) Equation
- 16.3.2 Physical Effects in the KdV Equation
- 16.3.3 Single-Soliton Solution
- 16.3.4 Two-Soliton Solution
- 16.3.5 Solitons in Contemporary Physics
- 16.4 Rossby Waves in a Rotating Fluid
- 16.5 Sound Waves
- 16.5.1 Wave Energy
- 16.5.2 Sound Generation
- 16.5.3 Radiation Reaction, Runaway Solutions, and Matched Asymptotic Expansions
- Bibliographic Note
- 17 Compressible and Supersonic Flow
- 17.1 Overview
- 17.2 Equations of Compressible Flow
- 17.3 Stationary, Irrotational, Quasi-1-Dimensional Flow
- 17.3.1 Basic Equations; Transition from Subsonic to Supersonic Flow
- 17.3.2 Setting up a Stationary, Transonic Flow
- 17.3.3 Rocket Engines
- 17.4 Dimensional, Time-Dependent Flow
- 17.4.1 Riemann Invariants
- 17.4.2 Shock Tube
- 17.5 Shock Fronts
- 17.5.1 Junction Conditions across a Shock; Rankine-Hugoniot Relations
- 17.5.2 Junction Conditions for Ideal Gas with Constant γ
- 17.5.3 Internal Structure of a Shock
- 17.5.4 Mach Cone
- 17.6 Self-Similar Solutions?Sedov-Taylor BlastWave
- 17.6.1 The Sedov-Taylor Solution
- 17.6.2 Atomic Bomb
- 17.6.3 Supernovae
- Bibliographic Note
- 18.1 Overview
- 18.2 Diffusive Heat Conduction?Cooling a Nuclear Reactor; Thermal Boundary Layers
- 18.3 Boussinesq Approximation
- 18.4 Rayleigh-Bénard Convection
- 18.5 Convection in Stars
- 18.6 Double Diffusion?Salt Fingers
- Bibliographic Note
- 1.1 Introduction
- 1.1.1 The Geometric Viewpoint on the Laws of Physics
- 1.1.2 Purposes of This Chapter
- 1.1.3 Overview of This Chapter
- 1.2 Foundational Concepts
- 1.3 Tensor Algebra without a Coordinate System
- 1.4 Particle Kinetics and Lorentz Force in Geometric Language
- 1.5 Component Representation of Tensor Algebra
- 1.5.1 Slot-Naming Index Notation
- 1.5.2 Particle Kinetics in Index Notation
- 1.6 Orthogonal Transformations of Bases
- 1.7 Differentiation of Scalars, Vectors, and Tensors; Cross Product and Curl
- 1.8 Volumes, Integration, and Integral Conservation Laws
- 1.8.1 Gauss’s and Stokes’ Theorems
- 11.9 The Stress Tensor and Momentum Conservation
- 1.9.1 Examples: Electromagnetic Field and Perfect Fluid
- 1.9.2 Conservation of Momentum
- 1.10 Geometrized Units and Relativistic Particles for Newtonian Readers
- 1.10.1 Geometrized Units
- 1.10.2 Energy and Momentum of a Moving Particle
- Bibliographic Note
