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[en] The sufficient condition are formulated for the existence and uniqueness of the solution to the critical problem for the neutron transport equation. The conditions admit singular scattering kernels and black regions for certain neutron energy range. 14 references

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Sufficient conditions

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Transport Theory and Statistical Physics; ISSN 0041-1450; ; v. 7(4); p. 139-160

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[en] Riemann-Hilbert problems arising in two-group neutron transport theory and linearly anisotropic scattering, connected with half-space homogeneous media, are considered. A detailed procedure for obtaining a fundamental matrix for the case of the same total cross sections in both groups is given following a recent idea of Cercignani. Next, a first order correction to the fundamental matrix is obtained by applying a perturbation technique with respect to the difference between total cross sections as an expansion parameter. Stability of the total index to the Riemann-Hilbert problem is also considered

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Transport Theory and Statistical Physics; ISSN 0041-1450; ; v. 11(1); p. 5-28

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[en] The standard iterative procedure for solving fixed-source discrete-ordinates problems converges very slowly for problems in optically thick regions with scattering ratios c near unity. The diffusion-synthetic acceleration method has been proposed to make use of the fact that for this class of problems, the diffusion equation is often an accurate approximation to the transport equation. However, stability difficulties have historically hampered the implementation of this method for general transport differencing schemes. In this article we discuss a recently developed procedure for obtaining unconditionally stable diffusion-synthetic acceleration methods for various transport differencing schemes. We motivate the analysis by first discussing the exact transport equation; then we illustrate the procedure by deriving a new stable acceleration method for the linear discontinuous transport differencing scheme. We also provide some numerical results

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Transport Theory and Statistical Physics; ISSN 0041-1450; ; v. 11(1); p. 29-52

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[en] The abstract differential equation (Tf)' = -Af with ''partial range'' boundary conditions is solved on a Hilbert space. T and A are (possible unbounded) self-adjoint operators, A> or =0 and semi-Fredholm. Examples from kinetic theory are given

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Transport Theory and Statistical Physics; ISSN 0041-1450; ; v. 11(3); p. 155-181

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[en] A review of reports presented at the third Oberwolfach Conference is given. Existence proofs of solutions to the nonlinear Boltzmann equation drew the most attention. Also discussed were chaotic systems and the Vlasov problem

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Transport Theory and Statistical Physics; ISSN 0041-1450; ; v. 12(1); p. 85-101

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[en] In the past several years, with the development of the coarse-mesh schemes for the spatial discretization of the diffusion equations, the computing time for the static neutron flux calculations has been reduced considerably over the conventional finite difference scheme. For the temporal discretization in the time-dependent case, a fully implicit method (FIM) was found to be more efficient than either the explicit or the alternating-direction explicit method. In this paper, a new approach using the collocation method is investigated for the temporal discretization in an effort to further improve the computing time over that of the FIM

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Transport Theory and Statistical Physics; ISSN 0041-1450; ; v. 12(3); p. 285-306

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[en] Multidimensional transport theory involving the inverse problem, which presents results applicable to radiative transfer and neutron transport theory for a homogeneous medium, is discussed. The Legendre expansion is used to construct the scattering kernel (or phase function) from assumed known experimental data described herein. Two cases are considered, the interior problem in which the medium contains a monodirectional point source and the exterior problem in which the medium is free of sources but is subjected to a plane wave source at infinity. Use of the principles of invariance is made to relate results of measurements with different geometries. The paper is an extension of earlier work on the one-dimensional case with azimuthal symmetry by Kanal and Moses

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Transport Theory and Statistical Physics; ISSN 0041-1450; ; v. 8(2); p. 99-115

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[en] The results of previous calculations are extended to the full (linearized) Fokker--Planck collision model originally introduced by Chandrasekhar. As in previous papers, we study longitudinal oscillations of an infinite, one-dimensional plasma described by the equations partialphi(x,v,t)/partialt+v partialphi/partialx+e/m(E/sub A/ +E)partialphi/partialt = (partialphi/partialt)/sub coll/, partialE/partialx = 4πrho

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Transport Theory and Statistical Physics; ISSN 0041-1450; ; v. 10(4); p. 149-160

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[en] A method is developed using the variational principle to solve a two-region, monoenergetic, one-dimensional transport problem arising in the calculation of the neutron flux-distortion factor. The Roussopoulos functional for the problem is modified with the help of a Lagrangian multiplier accommodating the interface conditions. The complete set of Case eigenfunctions in each region are selected as the trial functions. The stationarity condition of the modified functional leads to a decoupled set of equations for each set unknown coefficients. These are solved using Gauss quadrature to approximate integrals. Two problems are solved using the formalism developed; the problem of computing the flux-depression ue to a foil placed in a medium with a constant source, and the problem of evaluating the flux-distortion due to a foil placed in an exponentially varying flux. The results are compared with the previously reported values and excellent agreement is observed

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Transport Theory and Statistical Physics; ISSN 0041-1450; ; v. 12(1); p. 1-33

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[en] Equations are developed with which to evaluate the coefficients used in the one-speed Boltzmann-Fokker-Planck transport equation for strongly anisotropic scattering of photons or neutrons. The inverse equations, which are derived for a homogeneous slab target, require only measurements outside the medium. One set of equations is useful when the external illumination is nonuniformly incident over the surface, and the other set is valid for a uniform illumination of the target

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Transport Theory and Statistical Physics; ISSN 0041-1450; ; v. 12(2); p. 129-156

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