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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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Lebesgue Moment Method for Solving the Neutron Transport Equation
Mathematical Models and Computer Simulations, 2021Summary: The method of Lebesgue moments for simulating the reversal of resonances, resonance self-shielding, and block effect in the neutron spectra of extended heterogeneous objects, such as nuclear reactors, radiation shielding, and installations for studying the properties of matter, is developed.
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On the stochastic nonlinear neutron transport equation
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1992SynopsisThe probability that a neutron leads to a divergent chain reaction in a nuclear reactor is governed by a nonlinear integro-partial-differential equation [1]. A model case of this equation was completely analysed by Pazy and Rabinowitz [2,3].
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A family of transport equations in neutron transport theory
Annals of Nuclear Energy, 1991Abstract The backward formulation of problems in neutron transport is considered. Boundary conditions are developed from the adjoint system which in turn is rigorously obtained from a variational principle. The variational principle is derived by constraining the flux with the forward transport equation and affiliated boundary/initial conditions ...
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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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Kinetic diffusion equation in neutron transport theory
Atomic Energy, 2013The neutron transport equation can be expressed in a form identical to that of the diffusion equation in the elementary theory of diffusion. The kinetic equation expressed in such a form is defined as the kinetic diffusion equation. The kinetic diffusion equation in a one-dimensional planar geometry is derived and physical validation is given for the ...
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Solution of the Two-Group Neutron Transport Equation—I
Nuclear Science and Engineering, 1968Particular numerical methods are described for solving the two-group neutron transport equations obtained in a companion paper.
D. R. Metcalf, P. F. Zweifel
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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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Alternative forms of the time-dependent neutron transport equation
Progress in Nuclear Energy, 2008Abstract This work is devoted to the derivation of alternative formulations of the one-velocity neutron transport equation. The Peierl's integral form of the transport equation is considered as the starting point. Using a generalization of the mathematical procedure applied to derive the A N approximation, two formulations are obtained, both ...
COPPA, Gianni +3 more
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