Wave Motion

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Wave Motion / J. Billingham, A. C. King

資料種別:

図書

出版情報:

Cambridge : Cambridge University Press, 2000

形態:

ix, 468 p. ; 23 cm

シリーズ名:

Cambridge texts in applied mathematics <BA03474162>

著者名:

ISBN:

9780521632577 [0521632579] (: hard)
9780521634502 [0521634504] (: pbk.)

書誌ID:

BA50256495

子書誌情報

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書誌詳細

注記:

Bibliography: p. 455-458
Includes index

主題:

流体動力学

言語:

英語

目次情報:

Introduction

Linear Waves / Part 1：

Basic Ideas / 1：

Exercises

Waves on a Stretched String / 2：

Derivation of the Governing Equation / 2.1：

Standing Waves on Strings of Finite Length / 2.2：

D'Alembert's Solution for Strings of Infinite Length / 2.3：

Reflection and Transmission of Waves by Discontinuities in Density / 2.4：

A Single Discontinuity / 2.4.1：

Two Discontinuities: Impedance Matching / 2.4.2：

Sound Waves / 3：

Plane Waves / 3.1：

Acoustic Energy Transmission / 3.3：

Plane Waves In Tubes / 3.4：

Acoustic Waveguides / 3.5：

Reflection of a Plane Acoustic Wave by a Rigid Wall / 3.5.1：

A Planar Waveguide / 3.5.2：

A Circular Waveguide / 3.5.3：

Acoustic Sources / 3.6：

The Acoustic Source / 3.6.1：

Energy Radiated by Sources and Plane Waves / 3.6.2：

Radiation from Sources in a Plane Wall / 3.7：

Linear Water Waves / 4：

Derivation of the Governing Equations / 4.1：

Linear Gravity Waves / 4.2：

Progressive Gravity Waves / 4.2.1：

Standing Gravity Waves / 4.2.2：

The Wavemaker / 4.2.3：

The Extraction of Energy from Water Waves / 4.2.4：

The Effect of Surface Tension: Capillary--Gravity Waves / 4.3：

Edge Waves / 4.4：

Ship Waves / 4.5：

The Solution of Initial Value Problems / 4.6：

Shallow Water Waves: Linear Theory / 4.7：

The Reflection of Sea Swell by a Step / 4.7.1：

Wave Amplification at a Gently Sloping Beach / 4.7.2：

Wave Refraction / 4.8：

The Kinematics of Slowly Varying Waves / 4.8.1：

Wave Refraction at a Gently Sloping Beach / 4.8.2：

The Effect of Viscosity / 4.9：

Waves in Elastic Solids / 5：

Waves in an Infinite Elastic Body / 5.1：

One-Dimensional Dilatation Waves / 5.2.1：

One-Dimensional Rotational Waves / 5.2.2：

Plane Waves with General Orientation / 5.2.3：

Two-Dimensional Waves in Semi-infinite Elastic Bodies / 5.3：

Normally Loaded Surface / 5.3.1：

Stress-Free Surface / 5.3.2：

Waves in Finite Elastic Bodies / 5.4：

Flexural Waves in Plates / 5.4.1：

Waves in Elastic Rods / 5.4.2：

Torsional Waves / 5.4.3：

Longitudinal Waves / 5.4.4：

The Excitation and Propagation of Elastic Wavefronts / 5.5：

Wavefronts Caused by an Internal Line Force in an Unbounded Elastic Body / 5.5.1：

Wavefronts Caused by a Point Force on the Free Surface of a Semi-infinite Elastic Body / 5.5.2：

Electromagnetic Waves / 6：

Electric and Magnetic Forces and Fields / 6.1：

Electrostatics: Gauss's Law / 6.2：

Magnetostatics: Ampere's Law and the Displacement Current / 6.3：

Electromagnetic Induction: Farady's Law / 6.4：

Plane Electromagnetic Waves / 6.5：

Conductors and Insulators / 6.6：

Reflection and Transmission at Interfaces / 6.7：

Boundary Conditions at Interfaces / 6.7.1：

Reflection by a Perfect Conductor / 6.7.2：

Reflection and Refraction by Insulators / 6.7.3：

Waveguides / 6.8：

Metal Waveguides / 6.8.1：

Weakly Guiding Optical Fibres / 6.8.2：

Radiation / 6.9：

Scalar and Vector Potentials / 6.9.1：

The Electric Dipole / 6.9.2：

The Far Field of a Localised Current Distribution / 6.9.3：

The Centre Fed Linear Antenna / 6.9.4：

Nonlinear Waves / Part 2：

The Formation and Propagation of Shock Waves / 7：

Traffic Waves / 7.1：

Small Amplitude Disturbances of a Uniform State / 7.1.1：

The Nonlinear Initial Value Problem / 7.1.3：

The Speed of the Shock / 7.1.4：

Compressible Gas Dynamics / 7.2：

Some Essential Thermodynamics / 7.2.1：

Equations of Motion / 7.2.2：

Construction of the Characteristic Curves / 7.2.3：

The Rankine--Hugoniot Relations / 7.2.4：

Detonations / 7.2.5：

Nonlinear Water Waves / 8：

Nonlinear Shallow Water Waves / 8.1：

The Dam Break Problem / 8.1.1：

A Shallow Water Bore / 8.1.2：

The Effect of Nonlinearity on Deep Water Gravity Waves: Stokes' Expansion / 8.2：

The Korteweg-de Vries Equation for Shallow Water Waves: the Interaction of Nonlinear Steepening and Linear Dispersion / 8.3：

Derivation of the Korteweg-de Vries Equation / 8.3.1：

Travelling Wave Solutions of the KdV Equation / 8.3.2：

Nonlinear Capillary Waves / 8.4：

Chemical and Electrochemical Waves / 9：

The Law of Mass Action / 9.1：

Molecular Diffusion / 9.2：

Reaction-Diffusion Systems / 9.3：

Autocatalytic Chemical Waves with Unequal Diffusion Coefficients* / 9.4：

Existence of Travelling Wave Solutions / 9.4.1：

Asymptotic Solution for [delta] [[ 1 / 9.4.2：

The Transmission of Nerve Impulses: the Fitzhugh-Nagumo Equations / 9.5：

The Fitzhugh-Nagumo Model / 9.5.1：

The Existence of a Threshold / 9.5.2：

Travelling Waves / 9.5.3：

Advanced Topics / Part 3：

Burgers' Equation: Competition between Wave Steepening and Wave Spreading / 10：

Burgers' Equation for Traffic Flow / 10.1：

The Effect of Dissipation on Weak Shock Waves in an Ideal Gas / 10.2：

Simple Solutions of Burgers' Equation / 10.3：

Asymptotic Solutions for v [[ 1 / 10.3.1：

Diffraction and Scattering / 11：

Diffraction of Acoustic Waves by a Semi-infinite Barrier / 11.1：

Preliminary Estimates of the Potential / 11.1.1：

Pre-transform Considerations / 11.1.2：

The Fourier Transform Solution / 11.1.3：

The Diffraction of Waves by an Aperture / 11.2：

Scalar Diffraction: Acoustic Waves / 11.2.1：

Vector Diffraction: Electromagnetic Waves / 11.2.2：

Scattering of Linear, Deep Water Waves by a Surface Piercing Cylinder / 11.3：

Solitons and the Inverse Scattering Transform / 12：

The Korteweg-de Vries Equation / 12.1：

The Scattering Problem / 12.1.1：

The Inverse Scattering Problem / 12.1.2：

Scattering Data for KdV Potentials / 12.1.3：

Examples: Solutions of the KdV Equation / 12.1.4：

The Nonlinear Schrodinger Equation / 12.2：

Derivation of the Nonlinear Schrodinger Equation for Plane Electromagnetic Waves / 12.2.1：

Solitary Wave Solutions of the Nonlinear Schrodinger Equation / 12.2.2：

The Inverse Scattering Transform for the Nonlinear Schrodinger Equation / 12.2.3：

Useful Mathematical Formulas and Physical Data / Appendix 1：

Cartesian Coordinates / A1.1：

Cylindrical Polar Coordinates / A1.2：

Spherical Polar Coordinates / A1.3：

Some Vector Calculus Identities and Useful Results for Smooth Vector Fields / A1.4：

Physical constants / A1.5：

Bibliography

Index

Introduction

Linear Waves / Part 1：

Basic Ideas / 1：

Exercises

Waves on a Stretched String / 2：

Derivation of the Governing Equation / 2.1：

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