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[en] A simple projectional technique combined with an equally simple parametric representation of the transient part of the neutron total flux is proposed for an elementary straightforward calculation of the extrapolation distance in diffusing media. (author)

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[en] The time dependence of a neutron population in a homogeneous sphere has been studied. The neutrons are of one speed and are assumed to be scattered with linear anisotropy. Vacuum boundary conditions are used. It is shown that the integral Boltzmann equation is simplified, when the decay constant is at the 'Corngold limit'. Using Carlvik's method it is possible to calculate the spectrum of sphere diameters corresponding to this decay constant. Detailed numerical results are given. (author)

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[en] A multigroup formalism is developed for the backward-forward-isotropic scattering model of neutron transport. Some exact solutions are obtained in two-group theory for slab and spherical geometry. The results are useful for benchmark problems involving multigroup anisotropic scattering. (author)

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[en] An approximate model based on an improved diffusion-type theory is established for treating multiple synthetic scattering in a homogeneous slab of finite thickness. As in the case of the exact treatment given in the preceding paper (Part I), it appears possible to transform the considered transport problem into an equivalent fictitious one involving multiple isotropic scattering, therefore permitting the application of an established corrected diffusion theory for treating isotropic scattering taking place in a convex homogeneous medium bounded by a vacuum in the presence of various types of sources. The approximate values of the reflection and transmission coefficients are compared with the rigorous values listed in Part I. In this way, the high accuracy of the approximation is clearly demonstrated. (author)

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Annals of Nuclear Energy (Oxford); ISSN 0306-4549; ; v. 12(1); p. 23-34

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[en] A completely boundary-free maximum principle for the first-order Boltzmann equation is derived from the completely boundary-free maximum principle for the mixed-parity Boltzmann equation. When continuity is imposed on the trial function for directions crossing interfaces the completely boundary-free principle for the first-order Boltzmann equation reduces to a maximum principle previously established directly from first principles and indirectly by the Euler-Lagrange method. Present finite element methods for the first-order Boltzmann equation are based on a weighted-residual method which permits the use of discontinuous trial functions. The new principle for the first-order equation can be used as a basis for finite-element methods with the same freedom from boundary conditions as those based on the weighted-residual method. The extremum principle as the parent of the variationally-derived weighted-residual equations ensures their good behaviour. (author)

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Annals of Nuclear Energy (Oxford); ISSN 0306-4549; ; v. 10(5); p. 243-261

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Ferguson, J.M.; Greenbaum, A.

Lawrence Livermore National Lab., CA (USA)

Lawrence Livermore National Lab., CA (USA)

AbstractAbstract

[en] A finite element method is introduced for solving the neutron transport equations. Our method falls into the category of Petrov-Galerkin solution, since the trial space differs from the test space. The close relationship between this method and the discrete ordinate method is discussed, and the methods are compared for simple test problems

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21 Mar 1984; 8 p; ANS topical meeting on reactor physics and shielding; Chicago, IL (USA); 17-19 Sep 1984; CONF-840901--19; Available from NTIS, PC A02/MF A01 as DE85001075

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[en] The F/sub N/ method is used to establish particularly accurate solutions, at modest cost, for the emerging angular fluxes basic to a class of multigroup particle-transport problems. A study of the fundamental computational aspects of the established solution is reported, and numerical results are given, accurate to five significant figures, for the reflected and transmitted angular fluxes relevant to a 16-group albedo problem and to a 19-group albedo problem. 10 refs

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Nuclear Science and Engineering; ISSN 0029-5639; ; v. 78(4); p. 315-323

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[en] The analytical determination of the spatial and angular moments of the monoenergetic neutron-transport equation in an infinite medium initiated by Case, de Hoffmann and Placzek 30 years ago is completed. Analytical expressions for the moments that are convenient for numerical evaluation are obtained, and several high-order moments are evaluated as a demonstration. (author)

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Annals of Nuclear Energy (Oxford); ISSN 0306-4549; ; v. 12(1); p. 35-38

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[en] The neutron wave propagation method has been applied in small graphite blocks to study the axial propagation of the neutron disturbance and the transverse wave propagation. No evidence of non-asymptotic behaviour within the limits of the wave frequencies investigated was found, and an effect of transverse wave propagation which points to a frequency-dependent complex transverse buckling has been demonstrated for the first time. (author)

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[en] Literature in the area of anisotropic neutron scattering is by no means lacking. Attention, however, is usually devoted to solution of some particular neutron transport problem and the model employed is at best approximate. The present approach to the problem in general is classically exact and may be of some particular value to individuals seeking exact numerical results in transport calculations. For attempts neutrons originally directed toward the unit vector Omega, it attempts the evaluation of p(theta'), defined such that p(theta') d theta' is that fraction of scattered neutrons that emerges in the vicinity of a cone i.e., having been scattered to between angles theta' and theta' + d theta' with the axis of preferred orientation i; Omega makes an angle theta with i. The relative simplicity of the final form of the solution for hydrogen, in spite of the complicated nature of the limits involved, is a trade-off that truly is not necessary. The exact general solution presented here in integral form, has exceedingly simple limits, i.e., 0 ≤ theta' ≤ π regardless of the material involved; but the form of the final solution is extraordinarily complicated

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American Nuclear Society winter meeting; San Francisco, CA (USA); 10-15 Nov 1985; CONF-851115--

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