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A Simple Derivation of the Neutron Transport Equation
Nuclear Science and Engineering, 1992In this paper, a new and simple derivation of the neutron transport equation is given. The approach is similar to that used in the Liouville equation and its applications to the Boltzmann equation in that it is formulated in terms of the one-particle or one-point density function, as opposed to the traditional reactor physics approach of counting ...
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Quantum Corrections to the Neutron Transport Equation
Physical Review, 1969The singular behaviour of the neutron transport equation, in the limit of zero neutron velocity, comes into play in an essential manner when one wants to study the nature of its asymptotic solutions. From the physical point of view, the consistency of such a study can be checked only if one knows explicitly the behaviour of the quantum correction terms
E. Diana, A. Scotti
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The nonlinear transport equation with delayed neutrons
Transport Theory and Statistical Physics, 1997Abstract In this paper, we consider the nonlinear transport equation with delayed neutrons. By means of the tneory of nonlinear perturbations of Co -semigroups, the existence and uniqueness of the mild solution, strong solution and local solution in Lp (1 ≤ p < +00) are proved.
Li Xuezhi, Hao Yong
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Remark to the solution of the neutron transport equation
Il Nuovo Cimento, 1964The velocity space-distribution of neutrons from a point source is investigated. The main difficulty of this problem is first stated and then it is indicated how it can be overcome.
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An approximate solution to the neutron transport equation
Transport Theory and Statistical Physics, 1997Abstract This paper presents an approximate solution to the neutron transport equation by using the theory of reproducing kernels. The approximate solution can be constructed by only finite many values of a function. This method can be generalized in a tensor product space.
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A collocation method for the neutron transport equation
Transport Theory and Statistical Physics, 1983Abstract One of the dominant numerical approximation methods for the integro-differential equation for neutron transport is the discrete-ordinates method1. In this method one collocates the equation at preselected angular directions which are the quadrature points of the integral scattering term (the “discrete ordinates”), and then solves the resulting
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Nodal finite element approximations for the neutron transport equation
Mathematics and Computers in Simulation, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jean-Pierre Hennart, Edmundo del Valle
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Hermite Approximation of the Neutron Transport Equation
Nuclear Science and Engineering, 1981A semianalytical method is devised for solving the stationary neutron transport equation in plane geometry. The angular variable is treated fully analytically, while the spatial dependence is approximated by the two-point Hermite method of arbitrary order k.
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Nonlinear semigroup approach to transport equations with delayed neutrons
Acta Mathematica Scientia, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Al Izeri, Abdul Majeed, Latrach, Khalid
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A forward equation for stochastic neutron transport
Annals of Nuclear Energy, 1994Abstract A new formalism is developed for describing the stochastic neutron transport by the forward approach. This is used to derive a forward stochastic transport equation for this process. The first moment of this equation is the usual transport equation for the singlet density while higher moments yield equations for the doublet and higher ...
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