The Mathematics of Radiative Transfer

This tract gives a simple but rigorous treatment of some of the mathematical problems which arise in the theory of the transfer of radiation through the atmosphere of a star.

I. W. Busbridge (Author)

9780521090667, Cambridge University Press

Paperback / softback, published 27 November 2008

156 pages
21.6 x 14 x 0.9 cm, 0.21 kg

This tract gives a simple but rigorous treatment of some of the mathematical problems that arise in the theory of the transfer of radiation through the atmosphere of a star. Similar problems occur in the theory of the diffusion of neutrons and in the study of temperature-wave flow in solids; so the solutions found in one theory can often be applied in the others. Dr Busbridge's starting-point is the equation of transfer. The first section provides the auxiliary mathematics, and the second discusses the Milne equations. Some unsolved and incompletely solved problems are considered in an appendix. The language and notation of astrophysics is used throughout, for brevity and simplicity, but translation into other notations is usually fairly easy. Over the years the subject had grown considerably, and several outstanding problems have been solved, though the total amount of rigorous work is small. This tract will help to clear up confusions which exist and will provide an introduction to some of the more powerful mathematical techniques available.

Part I. Auxiliary Mathematics: 1. The Equation of Transfer
2. The H- Functions
3. Integral Operators
Part II. Milne Equations: 4. Iterative Solutions
5. The Wiener-Hopf Solution
6. Solutions of the Non-Homogeneous Equation
7. Finite Atmospheres: Preliminary Results
8. The X- and Y-Functions
9. Finite Atmospheres: Further Results
10. Anisothropic Scattering.

Subject Areas: Mathematics [PB]