Radiative Transfer: An Introduction to Exact and Asymptotic Methods

1. An Overview of the Content.- Part I: Scalar Radiative Transfer Equations.- 2. Radiative Transfer Equations.- 3. Exact Methods of Solution: A Brief Survey.- 4. Singular Integral Equations.- 5. The Scattering Kernel and Associated Auxiliary Functions.- 6. The Surface Green Function and the Resolvent Function.- 7. The Emergent Intensity and the Source Function.- 8. Spectral Line with Continuous Absorption.- 9. Conservative Scattering: The Milne Problem.- 10. The Case Eigenfunction Expansion Method.- 11. The √ɛ-law and the Nonlinear H-Equation.- 12. The Wiener-Hopf Method.- Part II: Scattering Polarization.- 13. The Scattering of Polarized Radiation.- 14. Polarized Radiative Transfer Equations.- 15. The √ɛ-law, the Nonlinear H-Equation, and Matrix Singular Integral Equations. 16. Conservative Rayleigh Scattering: Exact Solutions.- 17. Scattering Problems with No Exact Solution I: The Auxiliary Matrices.- 18. Scattering Problems with No Exact Solution II: The Resolvent Matrix, the H-Matrix, and the I-Matrix.- Part III: Asymptotic Properties of Multiple Scattering.- 19. Asymptotic Properties of the Scattering Kernel K(τ).- 20. Large Scale Radiative Transfer Equations.- 21. The Photon Random Walk.- 22. Asymptotic Behavior of the Resolvent Function.- 23. The Asymptotics of the Diffusion Approximation.- 24. The Diffusion Approximation for Rayleigh Scattering.- 25. Anomalous Diffusion for Spectral Lines.- 26. Asymptotic Results for Partial Frequency Redistribution.