دانلود کتاب Problems of High Frequency Diffraction by Elongated Bodies

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Contents
List of Figures
1 High-Frequency Diffraction and Elongated Bodies
1.1 High-Frequency Methods
1.2 Diffraction by a Smooth Convex Body
1.2.1 Analysis of the Field of Rays
1.2.2 The Parabolic Equation Method
1.2.3 Asymptotic Expansion in the Fock Domain
1.2.4 Generalizations to 3D and Electromagnetic Problems
1.2.5 The Higher Order Corrections
1.3 Accuracy of the Fock Approximation
1.4 The Transverse Curvature Effects
1.4.1 Transverse Curvature in the Classical Fock Asymptotic Approximation
1.4.2 Moderately Elongated Bodies
1.4.3 Strongly Elongated Bodies
1.5 Conclusion
References
2 Diffraction by an Elliptic Cylinder
2.1 Introduction
2.2 Stretched Coordinates and Separation of Variables
2.3 The Forward Wave
2.3.1 Asymptotic Representation
2.3.2 Integral Representation of the Incident Plane Wave
2.3.3 Integral Representation of the Line Source Field
2.4 The Backward Wave
2.4.1 Integral Representation for the Backward Wave
2.4.2 The Reflection Coefficients
2.5 The Induced Currents
2.5.1 Integral Representations for the Currents
2.5.2 The Case of Plane Wave Incidence
2.5.3 Reduction to Fock Asymptotics in the Case of χtoinfty
2.5.4 The Case of Line Source Field Incidence
2.5.5 Accuracy of Approximation and Test Examples
2.5.6 Results for the Line Source Field Diffraction
2.6 The Far Field
2.6.1 Far Field in the Forward Cone
2.6.2 Numerical Examples and Tests for the Far Field
2.6.3 Far Field in the Backward Cone
2.7 Conclusion
References
3 Acoustic Wave Diffraction by Spheroid
3.1 Introduction
3.2 Problem Formulation and Assumptions on the Parameters
3.3 Stretched Coordinates and Separation of Variables
3.4 The Forward Wave
3.4.1 Integral Representation
3.4.2 The Incident Plane Wave Representation
3.4.3 The Incident Spherical Wave Representation
3.4.4 The Currents
3.5 Vicinities of the End-points and the Backward Diffracted Wave
3.6 Numerical Results and Validations for the Currents
3.7 The Far Field
3.7.1 Kirchhoff Integral
3.7.2 The Far Field Approximation in the Forward Cone
3.7.3 The Far Field Approximation in the Backward Cone
3.8 Conclusion and Discussion
References
4 Electromagnetic Wave Diffraction by Spheroid
4.1 Introduction
4.2 The Problem Formulation and the Boundary-Layer Coordinates
4.3 Representation for the Forward Wave
4.4 Matching with the Incident Wave
4.4.1 The Plane Wave Incidence
4.4.2 Point Dipole Source Field Incidence
4.5 Backward Wave
4.5.1 Representation of the Field Near the Trailing Tip
4.5.2 Determining the Amplitudes λn,j and νn,j
4.5.3 Representation for the Backward Wave
4.6 Induced Currents
4.7 Validation Tests
4.8 The Far Field
4.9 Test Examples
References
5 Other Strongly Elongated Shapes
5.1 Introduction
5.2 The Boundary-Layer Coordinates
5.3 Surfaces Which Allow Variable Separation
5.4 Strongly Elongated Two-Sheeted Hyperboloid
5.4.1 Boundary-Layer Coordinates and the Parabolic Equation
5.4.2 Axial Incidence
5.4.3 Skew Incidence
5.5 Strongly Elongated Paraboloid
5.6 One-Sheeted Hyperboloid
5.7 Narrow Cone
5.7.1 Problem of Diffraction
5.7.2 Diffraction of the Plane Acoustic Wave
5.7.3 Diffraction of the Plane Electromagnetic Wave
5.8 Conclusion
References
Appendix A Airy and Whittaker Functions
A.1 Airy Functions
A.2 Whittaker Functions
A.2.1 Integral Representations and Functional Relations
A.2.2 The Coulomb Wave Functions
A.2.3 Asymptotic Expansions
A.3 Solutions of Dispersion Equations
A.4 The Integral Transform
A.5 Integrals Containing Whittaker Functions
References
Index