[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] 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

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[en] A method is developed to perform calculations for the sensitivities of integral quantities to geometric parameters using Monte Carlo techniques. This method was incorporated into a widely used Monte Carlo code for neutron and photon transport. The method is particularly useful when changes in integral quantities are required for small perturbations in surface parameters. The technique involved in calculating geometric sensitivities includes the usual weight adjustment based on the probability of the track occurring in the unperturbed and perturbed cases due to an infinitesimal perturbation of the geometric surface. This weight adjustment is then applied to all the relevant results of interest. In addition to this term, there are two other terms in the expression for sensitivity which account for the possible effects of scattering in the infinitesimal volume in space caused by a small perturbation of a surface. The first of these represents scattering in the perturbed case and the second the scattering in the unperturbed case. Weights are assigned to these two tracks and their contributions to various results are determined by separate tracking. The method is very powerful and versatile and represents a potentially useful extension to the Monte Carlo method

[en] A previously invented Fermi-Hypernetted-Chain technique is extended to the calculation of Landau parameters. The transport coefficients are shown to depend sensitively on the long ranged correlations in the system

[en] This paper reports that the experimental results on the dispersive diffusion of atoms in disordered solids cannot be explained by conventional diffusion theory. The random trap model is also shown to be irrelevant to the experimental situation, but the random bond problem is more promising. The accurate analysis of this model requires important and non-trivial extensions to customary percolation theory. Numerical simulations of the model could prove of great value in determining its relevance to the experimental results

[en] For a number of years the MORSE user community has requested additional help in setting up problems using various options. The sample problems distributed with MORSE did not fully demonstrate the capability of the code. At Oak Ridge National Laboratory the code originators had a complete set of sample problems, but funds for documenting and distributing them were never available. Recently the number of requests for listings of input data and results for running some particular option the user was trying to implement has increased to the point where it is not feasible to handle them on an individual basis. Consequently it was decided to package a set of sample problems which illustrates more adequately how to run MORSE. This write-up may be added to Part III of the MORSE report. These sample problems include a combined neutron-gamma case, a neutron only case, a gamma only case, an adjoint case, a fission case, a time-dependent fission case, the collision density case, an XCHEKR run and a PICTUR run

[en] We have shown that the transport equation can be solved with particles, like the Monte-Carlo method, but without random numbers. In the Monte-Carlo method, particles are created from the source, and are followed from collision to collision until either they are absorbed or they leave the spatial domain. In our method, particles are created from the original source, with a variable weight taking into account both collision and absorption. These particles are followed until they leave the spatial domain, and we use them to determine a first collision source. Another set of particles is then created from this first collision source, and tracked to determine a second collision source, and so on. This process introduces an approximation which does not exist in the Monte-Carlo method. However, we have analyzed the effect of this approximation, and shown that it can be limited. Our method is deterministic, gives reproducible results. Furthermore, when extra accuracy is needed in some region, it is easier to get more particles to go there. It has the same kind of applications: rather problems where streaming is dominant than collision dominated problems