[en] For the past several years, a series of papers by the transport group at the University of Arizona dealing with benchmark solutions of the monoenergetic transport equation has appeared. The approach has been to take advantage of highly successful numerical Laplace Fourier transform inversions to provide benchmark quality solutions in infinite media, half-space in one and two dimensions and in homogeneous slabs. This paper extends the set of solutions to include heterogeneous slab geometry by using the recently established Green's Function Method (GFM). Analytical benchmark solutions are an essential part of the quality control of computational algorithms developed for particle transport. In addition, benchmarking methods have applications in the classroom by providing examples of how computational mathematics is used to solve physical problems to obtain meaningful answers. In a structural context, monoenergetic solutions are directly applicable to the investigation of the microlight environment within a leaf. The leaf is considered to be a composition of alternating layers of highly absorbing pigments and water superimposed on a refractively scattering background

[en] The Seminar on Deterministic Methods in Radiation Transport was held February 4--5, 1992, in Oak Ridge, Tennessee. Eleven presentations were made and the full papers are published in this report, along with three that were submitted but not given orally. These papers represent a good overview of the state of the art in the deterministic solution of radiation transport problems for a variety of applications of current interest to the Radiation Shielding Information Center user community

[en] Inverse problems for a class of linear kinetic equations are investigated. The aim is to identify the scattering kernel of a transport equation (corresponding to the structure of a background medium) by observing the 'albedo' part of the solution operator for the corresponding direct initial boundary value problem. This means to get information on some integral operator in an integrodifferential equation through on overdetermined boundary value problem. We first derive a constructive method for solving direct halfspace problems and prove a new factorization theorem for the solutions. Using this result we investigate stationary inverse problems with respect to well posedness (e.g. reduce them to classical ill-posed problems, such as integral equations of first kind). In the time-dependent case we show that a quite general inverse problem is well posed and solve it constructively. (orig.)

[en] Embedded in multidimensional nodal transport codes is the solution of transverse integrated ID transport equations. Since, in this solution, fluxes on boundaries are DP₁, it is generally assumed that the ID solutions, in the small-mesh limit, approach DP₁ solutions. It will be shown that this is not true. Small-mesh limits of the ID nodal equations will be derived, and it will be shown that these are substantially worse than the DP₁ equations under certain circumstances. Alternate ID nodal equations (which do have a DP₁ small-mesh limit) are proposed

[en] Angular biasing in deep-penetration problems can enhance the efficiency of Monte Carlo calculations. In the case of anisotropic scattering the angular biasing results in a joint probability distribution which is difficult to handle. In the present paper a simple angular biasing has been suggested which is easy to implement and helps to reduce the variance. Transmission probabilities were calculated in a 1-D 20 m.f.p. problem with different scattering probabilities and anisotropy factors. It was found that the present scheme gives a benefit factor of more than 10 in most of the cases studied. (author)

[en] In earlier work by Gelbard and Lell, arguments based on perturbation theory were used to obtain relations between mean-square chord lengths and lattice eigenvalues for given bucklings. We show here that first-order perturbation theory does not give the lattice eigenvalue correctly to order B². When all missing terms in B² are inserted, the eigenvalue buckling relations remain formally unchanged, but the mean-square chord lengths must be redefined. The original and redefined mean-square chord lengths differ only insofar as events in successive fission generations are correlated. A reexamination of work based on the original relations indicates that earlier numerical results were substantially correct

[en] The direct operational method and Pade's approximation is used to transform the integro-differential form of the transport equation to differential form. The moment method and the similarity method are used to solve the space-energy problem in the slowing down region with energy-dependent cross section. The energy deposition factor is calculated in terms of the spatial-angular moments, without using the integral transform. (author)

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[en] An improved model for calculating collision probabilities in spatially stochastic media is described based upon a method developed by Cassell and Williams [Cassell, J.S., Williams, M.M.R., in press. An approximate method for solving radiation and neutron transport problems in spatially stochastic media. Annals of Nuclear Energy] and is applicable to three-dimensional problems. We shall show how to evaluate the collision probability in an arbitrarily shaped non-re-entrant lump, consisting of a random dispersal of two phases, for any form of autocorrelation function. Specific examples, with numerical values, are given for a sphere and a slab. In the case of the slab we allow the material to have different stochastic properties in the x, y and z directions