Zobrazeno 1 - 10
of 118
pro vyhledávání: '"M. M. R. Williams"'
Autor:
M. M. R. Williams
Publikováno v:
Nuclear Science and Engineering. 197:104-131
Autor:
M. M. R. Williams, Eugene d'Eon
We 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 and benchmark values and some identities unique to Flatland a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::36b25060d112683fe0df5c2cb4853503
http://arxiv.org/abs/1802.02120
http://arxiv.org/abs/1802.02120
Autor:
M. M. R. Williams
Publikováno v:
Applied Mathematics and Computation. 215:3906-3928
We present a novel approach for calculating the stochastic eigenvalues of a linear operator. This is an extension of our earlier work on the subject and introduces a significant simplification that reduces the amount of numerical work required when e
Autor:
M M R Williams
Publikováno v:
Physica Scripta. 76:303-313
A study is made of radiative transfer along a cylindrical duct using the one-dimensional approximation of Larsen. This method enables three-dimensional effects to be included in a one-dimensional equation. We have generalised Larsen's approach so tha
Autor:
M M R Williams
Publikováno v:
Journal of Physics A: Mathematical and Theoretical. 40:6407-6425
We extend the range of the searchlight problem in radiative transfer to include internal reflection arising from Fresnel and Lambert processes. For an isotropic beam and a normal beam, we calculate the albedo, the surface intensity and the mean dista
Autor:
M M R Williams
Publikováno v:
Journal of Physics A: Mathematical and Theoretical. 40:1513-1523
The classic constant source problem for a half-space is generalized to include the effect of refraction at the boundary by inclusion of the Fresnel boundary conditions. The problem is solved using the Wiener–Hopf technique with both specular and di
Autor:
M M R Williams, J S Cassell
Publikováno v:
Journal of Physics A: Mathematical and General. 36:8003-8023
An integral equation describing the fuel distribution necessary to maintain a flat flux in a nuclear reactor in two group transport theory is reduced to the solution of a singular integral equation. The formalism developed enables the physical aspect
Autor:
M. M. R. Williams
Publikováno v:
Transport Theory and Statistical Physics. 32:239-251
In Canada, during the autumn of 1942, a group of physicists, chemists and engineers were assembled to work on what was to become the Canadian atomic energy project. The base for this work was Montreal. This paper concentrates on the contributions of
Autor:
M. M. R. Williams
Publikováno v:
Nuclear Science and Engineering. 143:1-18
A model of neutron multiplication for aggregates of randomly placed fissile spheres with random material properties in a background medium is presented in terms of the transport equation. Two distinct problems are examined: (1) small spheres in an in