Linked e-resources
Details
Table of Contents
Intro
Preface
References
Contents
List of Figures
List of Tables
1 An Overview of the Content
1.1 Part I: Scalar Radiative Transfer Equations
1.2 Part II: Scattering Polarization
1.3 Part III: Asymptotic Properties of Multiple Scattering
References
Part I Scalar Radiative Transfer Equations
2 Radiative Transfer Equations
2.1 The Integro-Differential Radiative Transfer Equations
2.1.1 Monochromatic Scattering
2.1.2 Complete Frequency Redistribution
2.1.3 The Diffuse Radiation Field
2.2 Integral Equations for the Source Function
2.2.1 Monochromatic Scattering
2.2.2 The Milne Problem
2.2.3 Complete Frequency Redistribution
2.3 Neumann Series Expansion
2.4 The Green Function and Associated Functions
2.4.1 Some Definitions
2.4.2 A Lemma on Wiener-Hopf Equations
2.4.3 The Source Function and the Resolvent Function
2.4.4 Some Properties of the Green Function
References
3 Exact Methods of Solution: A Brief Survey
3.1 The Infinite Medium and the Dispersion Function
3.2 Exact Methods for a Semi-Infinite Medium
3.2.1 The Wiener-Hopf Method
3.2.2 Traditional Real-Space Methods
3.2.3 The Singular Integral Equation Approach
References
4 Singular Integral Equations
4.1 The Inverse Laplace Transformation
4.1.1 The Half-Space Case
4.1.2 The Full-Space Case
4.2 The Direct Laplace Transformation
4.3 The Hilbert Transform Method of Solution
4.3.1 A Special Case
4.3.2 The General Case
4.3.3 Application to Radiative Transfer
Appendix A: Hilbert Transforms
A.1 Definition and Properties
A.2 The Plemelj Formulae
A.3 The Plemelj Formulae for a Dirac Distribution
References
5 The Scattering Kernel and Associated Auxiliary Functions
B.5 Moments of X(z) and H(z)
References
6 The Surface Green Function and the Resolvent Function
6.1 Infinite Medium
6.1.1 The Fourier Transform Method
6.1.1.1 Complete Frequency Redistribution
6.1.1.2 Monochromatic Scattering
6.1.2 The Inverse Laplace Transform Method
6.2 Semi-infinite Medium. The Inverse Laplace Transform Method
6.2.1 Complete Frequency Redistribution
6.2.2 Monochromatic Scattering
6.3 The H-Function
Appendix C: The Direct Laplace Transform Method
C.1 Complete Frequency Redistribution
C.2 Monochromatic Scattering
References
Preface
References
Contents
List of Figures
List of Tables
1 An Overview of the Content
1.1 Part I: Scalar Radiative Transfer Equations
1.2 Part II: Scattering Polarization
1.3 Part III: Asymptotic Properties of Multiple Scattering
References
Part I Scalar Radiative Transfer Equations
2 Radiative Transfer Equations
2.1 The Integro-Differential Radiative Transfer Equations
2.1.1 Monochromatic Scattering
2.1.2 Complete Frequency Redistribution
2.1.3 The Diffuse Radiation Field
2.2 Integral Equations for the Source Function
2.2.1 Monochromatic Scattering
2.2.2 The Milne Problem
2.2.3 Complete Frequency Redistribution
2.3 Neumann Series Expansion
2.4 The Green Function and Associated Functions
2.4.1 Some Definitions
2.4.2 A Lemma on Wiener-Hopf Equations
2.4.3 The Source Function and the Resolvent Function
2.4.4 Some Properties of the Green Function
References
3 Exact Methods of Solution: A Brief Survey
3.1 The Infinite Medium and the Dispersion Function
3.2 Exact Methods for a Semi-Infinite Medium
3.2.1 The Wiener-Hopf Method
3.2.2 Traditional Real-Space Methods
3.2.3 The Singular Integral Equation Approach
References
4 Singular Integral Equations
4.1 The Inverse Laplace Transformation
4.1.1 The Half-Space Case
4.1.2 The Full-Space Case
4.2 The Direct Laplace Transformation
4.3 The Hilbert Transform Method of Solution
4.3.1 A Special Case
4.3.2 The General Case
4.3.3 Application to Radiative Transfer
Appendix A: Hilbert Transforms
A.1 Definition and Properties
A.2 The Plemelj Formulae
A.3 The Plemelj Formulae for a Dirac Distribution
References
5 The Scattering Kernel and Associated Auxiliary Functions
B.5 Moments of X(z) and H(z)
References
6 The Surface Green Function and the Resolvent Function
6.1 Infinite Medium
6.1.1 The Fourier Transform Method
6.1.1.1 Complete Frequency Redistribution
6.1.1.2 Monochromatic Scattering
6.1.2 The Inverse Laplace Transform Method
6.2 Semi-infinite Medium. The Inverse Laplace Transform Method
6.2.1 Complete Frequency Redistribution
6.2.2 Monochromatic Scattering
6.3 The H-Function
Appendix C: The Direct Laplace Transform Method
C.1 Complete Frequency Redistribution
C.2 Monochromatic Scattering
References