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The solution of coupled fractional neutron diffusion equations with delayed neutrons
International Journal of Nuclear Energy Science and Technology, 2010The distribution of the neutron population in a nuclear reactor is described by using transport equations. One possible solution of the fractional neutron transport equation is given by the fractional neutron diffusion equation. This paper presents the application of an analytical approximation method for the solution of one group of fractional neutron
T. Sardar +4 more
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Discontinuous variational solutions for the neutron diffusion equation
Annals of Nuclear Energy, 1996Abstract A maximum variational principle derived by a least squares method is used to obtain discontinuous finite element solution to the neutron diffusion equation. Here the principle is applied with locally constant and locally linear trial functions to determine a discontinuous finite element solution for a number of one group diffusion problems ...
R.T. Ackroyd, A.M. Gashut, O.A. Abuzid
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Electrical circuit representations of the neutron diffusion equations
The 2004 47th Midwest Symposium on Circuits and Systems, 2004. MWSCAS '04., 2004In a nuclear power plant, the neutron diffusion equations are simulated in order to obtain information about unknown states of the nuclear reactor. One way to solve these nonlinear partial differential equations numerically is to use the wave digital concept. It is based on a reference circuit representing the neutron diffusion equations.
K. Luhmann, K. Ochs
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Homogenized Diffusion Approximations to the Neutron Transport Equation
Nuclear Science and Engineering, 1980A general problem of time-dependent neutron transport in a spatially heterogeneous medium is analyzed by two perturbation methods that have previously been applied to specialized problems. These ''bucking'' and ''asymptotic'' methods are shown to be equivalent in the sense that the asymptotic method leads to a time-dependent diffusion equation with ...
Edward W. Larsen, R. P. Hughes
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3D λ-modes of the neutron-diffusion equation
Annals of Nuclear Energy, 1994Abstract The paper deals with the calculation of the 3D harmonic lambda modes in a B.W.R. reactor. An algorithm to calculate the harmonic lambda modes corresponding to the steady state two-group 3D neutron-diffusion equation is presented. The algorithm uses subspace iteration method techniques combined with convergence acceleration based on ...
G. Verdú +3 more
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Wavelet Theory for Solution of the Neutron Diffusion Equation
Nuclear Science and Engineering, 1996We solve the neutron diffusion equation by a wavelet Galerkin scheme in this paper. Wavelet functions are generated by dilation and translation operation on a scaling function.
Nam Zin Cho, Chang Je Park
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Solution of the neutron diffusion equation in hexagonal geometries
Annals of Nuclear Energy, 1987Abstract Various ways to solve the neutron diffusion equation in hexagonal geometries are known in the literature. In this paper it is aimed to unify these approaches from different points of view. First conditions are developed for consistency and uniqueness of the various approximations; they are then used to derive estimates of the order of the ...
J. Gadó, F. Schmidt
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Quantum dynamical semigroups and the neutron diffusion equation
Reports on Mathematical Physics, 1977Abstract We construct a class of quantum dynamical semigroups with unbounded generators by first obtaining the quantum mechanical analogue of the Feller minimal solution of the Fokker-Planck equation of probability theory. The theory is then used to study a quantum- mechanical neutron diffusion equation at various levels of approximation.
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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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Homogeneous reactor and neutron diffusion equation
2021K. Devan, Abhitab Bachchan
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