AbstractWe solve the Milne, constant-source, and albedo problems for isotropic scattering in a two-dimensional “Flatland” half-space via the Wiener–Hopf method. The Flatland H-function is derived a...
In the study of energy-dependent neutron transport in three-dimensional volumes with plane symmetry, @cite_0 presented a general family of solutions to the Milne problem using the method of singular eigenfunctions. When their variable- @math factor @math takes on the specific quantity (in our notation) @math , their energy-dependent 3D solution becomes equivalent to our monoenergetic Flatland solution. Thus, the Flatland @math -function has, if only inadvertently, been presented long ago.
@cite_0
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Abstract Mathematical equivalence is demonstrated between problems for a separable scattering kernel in energy-dependent neutron transport and for the uniform line-blanketing model of nongrey radiative transfer. As an example, the solution of the Milne problem is rederived by the method of singular eigenfunctions, with the application of orthogonality relations.