Boundary‐Value Problems of Linear‐Transport Theory—Green's Function Approach

Case's technique utilizing Green's functions for dealing with boundary‐value problems of the neutron linear‐transport theory is exploited. We show that the Fourier coefficients of the Green's function over the Case spectrum are precisely the normal modes. In particular, if we assume that the scattering kernel is rotationally invariant (which indeed we do assume) and approximate it by a degenerate kernel consisting of spherical harmonics, the set of modes is deficient for problems lacking azimuthal symmetry. We also show that the expansion of the scattering kernel, in terms of spherical harmonics (or any set of orthogonal functions for that matter), permits the linear factorization of the Fourier coefficients of the Green's function in terms of the lowest element, with the proportionality functions consisting of complete orthogonal polynomials. As a consequence of this attribute of Fourier coefficients, the eigenfunctions (continuum and discrete) also factorize, which then permits decoupling of the appropriate singular integral equations. To illustrate our idea, we solve half‐space and slab problems. However, the basic procedure is kept sufficiently general so that the extension to problems involving other geometrics remains straightforward.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71085/2/JMAPAQ-11-10-3042-1.pd

AFIT School of Engineering Contributions to Air Force Research and Technology Calendar Year 1973

This report contains abstracts of Master of Science Theses, Doctoral dissertations, and selected faculty publications completed during the 1973 calendar year at the School of Engineering, Air Force Institute of Technology, at Wright-Patterson Air Force Base, Ohio

AFIT School of Engineering Contributions to Air Force Research and Technology Calendar Year 1973

This report contains abstracts of Master of Science Theses, Doctoral dissertations, and selected faculty publications completed during the 1973 calendar year at the School of Engineering, Air Force Institute of Technology, at Wright-Patterson Air Force Base, Ohio

Singular self-adjoint boundary value problems for systems of first order linear differential equations

M.S.Frank W. Stallar