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[en] A generalized nodal finite element formalism is presented, which covers virtually all known finite difference approximations to the discrete ordinates equations in slab geometry. This paper (hereafter referred to as Part II) presents the theory of the so-called discontinuous moment methods, which include such well-known methods as the linear discontinuous scheme. It is the sequel of a first paper (Part I) where continuous moment methods were presented. Corresponding numerical results for all the schemes of both parts will be presented in a third paper (Part III)

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[en] The criticality eigenvalue problem has been studied for the one-speed neutron transport equation. Convex bodies of arbitrary shape and with vacuum boundary conditions have been considered. The cross sections may be space dependent, and the scattering is assumed to be anisotropic. Several new conditions have been derived which ensure that a point spectrum of eigenvalues exists and that all th eigenvalues are real. The most general such condition is that the even order coefficients in the development of the scattering function have a different sign than the odd order ones. As a consequence, for linearly anisotropic scattering the eignevalues are all real if the average cosine of the scattering angle is negative. Numerical results computed for homogeneous bodies in the form of spheres and infinite slabs and cylinders confirm the theoretical considerations. 14 refs., 1 fig., 3 tabs

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[en] The spectral radius of the integral neutron transport operator in unbounded regions is analyzed. A suitable integral operator in a bounded region is found, where previously found monotoneity and continuity results hold and a transitional relation is established. 7 refs., 1 fig

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[en] The index of the eigenvalue of the monoenergetic neutron transport operator is studied under the assumptions of homogeneity and boundedness of the medium and of isotropy of scattering. It is shown that all isolated real eigenvalues are with index one. In addition, the authors show that there is no nonreal eigenvalues in (λ C | Re λ > - Σ). 8 refs

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[en] Calculations of the diffusion of unpolarized photons in thin thickness targets have been performed with recourse to a vector transport model taking rigorously into account the polarization introduced by the scattering interactions. An order-of-interactions solution of the Boltzmann transport equation for photons was used to describe the multiple scattering terms due to the prevailing effects in the X-ray regime. An analytical expression for the correction factor to the attenuation coefficient is given in term of the solid angle subtended by the detector and the energy interval characterizing the detection response. Although the main corrections are due to the influence of the pure Rayleigh effect, first- and second-order chains involving the Rayleigh and Compton effects have been considered as possible sources of overlapping contributions to the transmitted intensity. The extent of the corrections is estimated and some examples are given for pure element targets

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[en] A generalized nodal finite element formalism is presented, which covers virtually all known finit difference approximation to the discrete ordinates equations in slab geometry. This paper (Part 1) presents the theory of the so called open-quotes continuous moment methodsclose quotes, which include such well-known methods as the open-quotes diamond differenceclose quotes and the open-quotes characteristicclose quotes schemes. In a second paper (hereafter referred to as Part II), the authors will present the theory of the open-quotes discontinuous moment methodsclose quotes, consisting in particular of the open-quotes linear discontinuousclose quotes scheme as well as of an entire new class of schemes. Corresponding numerical results are available for all these schemes and will be presented in a third paper (Part III). 12 refs

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[en] An angular finite element technique is used within the integro-differential neutron transport equation. The model is cast into a discrete ordinate form, where a suitable modification induced by the numerical procedure is introduced on removal and scattering cross sections, as well as on the source term. The artificial increase of the scattering term produced a reduction of ray effects. The present paper shows that such a reduction can be remarkably enhanced by an appropriate choice of the shape function utilized to represent the angular dependence of the neutron flux. Shape functions can be chosen to yield usual spherical harmonics equations; however, they do not allow a discrete ordinate formulation of the equations, owing to their singular behaviour. Therefore, the use of shape functions close to those showing such a singular behaviour is proposed. The technique allows a ray effect reduction as much as desired, through the solution of equations having a discrete ordinate form. Results are presented to enlighten features and performance of the method. 11 refs., 6 figs

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[en] Nonmonotonic variation of the open-quotes Cclose quotes eigenvalue (average number of secondaries per collision) with increasing α, the strength of forward scattering, has been observed earlier for one-dimensional infinite homogeneous slabs and infinitely long homogeneous cylinders. The authors have developed the Integral Transform (IT) method, an accurate semi-analytical method to obtain the C eigenvalue for a homogeneous cylinder (two-dimensional system). They are thus able to detect any nonmonotonic variation of C (with α) using the Sahni and Sjoestrand criterion. Along with the IT method, the authors also present the results obtained by the well-known numerical techniques like the discrete ordinates method using a high quadrature order and the Monte Carlo method for the same problem. The S

_{N}results show disagreement with the other two methods when one of the dimensions is very small (<0.05λ_{t}). They believe that even the 16th order quadrature set cannot integrate the angular flux accurately in these extreme situations. 12 refs., 9 tabsPrimary Subject

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[en] The present paper deals with the fine structure of the real point spectrum of a class of transport operators with unsymmetric scattering kernels. The author gives necessary and sufficient conditions for existence, finiteness and sufficient conditions for infiniteness of the real point spectrum. Estimates of the number of eigenvalues and localization results are given. 33 refs

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[en] The author constructs discrete Boltzmann equations describing the reactions between any number of chemicals. By including a heat particle to balance the energy, a model is constructed for the chemistry of liquids that obeys the Arrhenius relation. It is proven that all isolated systems within this class of models converge to equilibrium. The models are used to describe cotransport through membranes, and prove that the systems converge to the static head equilibrium, for both symport and antiport. For open systems either the static head is trivial or is numerically ambiguous. For the continuum limit heat equations are found, with nonlinear boundary conditions across the membrane, in which the ambiguity reappears as due to the lack of boundary conditions at ∞. A stationary solution is found which represents flow in which the concentrations do not satisfy the predictions of equilibrium thermodynamics. 27 refs., 8 figs

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