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Sahni, D.C.; Garis, N.S.; Pazsit, I.

Chalmers Univ. of Technology, Goeteborg (Sweden). Dept. of Reactor Physics

Chalmers Univ. of Technology, Goeteborg (Sweden). Dept. of Reactor Physics

AbstractAbstract

[en] Calculation of the neutron noise, induced by small amplitude vibrations of a strong absorber, is a difficult task because the traditional linearization technique cannot be applied. Two methods, based on two different representations of the absorber, were developed earlier to solve the problem. In both methods the rod displacements are described by a Taylor expansion, such that the boundary condition needs only to be considered at the surface of a static rod. Only one of the methods is applicable in two dimensions. In this paper an alternative method is developed and used for the solution of the problem. The essence of the method is a variable transformation by which the moving boundary is transformed into a static one without Taylor expansion. The corresponding equations are solved in a linear manner and the solution is transformed back to the original parameter space. The method is equally applicable in one and two dimensions. The solutions are in complete agreement with those of the previous methods

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Jun 1998; 19 p; ISSN 0281-9775; ; 6 refs

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Sahni, D.C., E-mail: dineshsahni@hotmail.com

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[en] Continuous spectrum of linear transport equation in a homogeneous slab is investigated for four different boundary conditions. These are vacuum, reflective, periodic and isotropic return conditions. It is found that the continuous spectrum is quite different for these four conditions. It is also shown that the continuous spectrum exists even if there are no infinite paths in the system.

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S0306-4549(17)30029-4; Available from http://dx.doi.org/10.1016/j.anucene.2017.01.018; Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

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[en] The density transform method has been extended to cover spherically symmetric neutron transport problems. The density transform is expanded in plane geometry normal modes and explicit singular integral equations are derived for the expansion coefficients. The method is thus an extension of Case's method of singular eigenfunctions to spherical geometry problems. The Green's function approach for transport problems in spherical geometry has been considered. It is shown that the reduction operators used in this method can solve only some of the problems in the interior of a solid homogeneous sphere

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International symposium on radiation physics; Calcutta, India; 30 Nov 1974; See CONF-741109--.

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Natl. Bur. Stand. (U.S.), Spec. Publ; (no.461); p. 87-90

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[en] The density transform method was extended to cover spherically symmetric transport problems in a spherical shell. The density transform is expanded in plane geometry normal modes and explicit singular integral equations are derived for the expansion coefficients. It is shown that the Green's function method, introduced by Case et al., gives the same representation of total flux. The singular integral equations for the expansion coefficients are rederived using the analytic properties of some sectionally holomorphic functions introduced previously. (auth)

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J. Math. Phys. (N.Y.); v. 16(11); p. 2260-2270

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[en] Many papers have been devoted to the study of the spectral properties of the linear (neutron) transport equation. Most of the theoretical investigations have concentrated on the existence (or otherwise) of a continuous spectrum, point spectrum, a leading/dominant eigenvalue, and a corresponding positive eigenvector. It is shown that the fundamental time eigenvalue of the linear transport operator increases with the size of the system. This follows from the increase in the largest eigenvalue of a non-negative irreducible matrix whenever any matrix element his increased. This result of matrix analysis is generalized to more general Krein-Rutman operators that leave a cone of vectors invariant

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[en] The integral form of one-speed, spherically symmetric neutron transport equation with isotropic scattering is considered. Two standard problems are solved using normal mode expansion technique. The expansion coefficients are obtained by solving their singular integral equations. It is shown that these expansion coefficients provide a representation of all spherical harmonics moments of the angular flux as a superposition of Bessel functions. It is seen that large errors occur in the computation of higher moments unless we take certain precautions. The reasons for this phenomenon are explained. They throw some light on the failure of spherical harmonics method in treating spherical geometry problems as observed by Aronsson

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S0306454999000626; Copyright (c) 2000 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

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Modak, R.S.; Sahni, D.C., E-mail: rsmodak@magnum.barc.ernet.in

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[en] Earlier, certain reciprocity-like relations have been shown to hold in some restricted steady state cases in neutron diffusion and transport theories. Here, the possibility of existence of similar relations in time-dependent situations is investigated

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S0306454901000287; Copyright (c) 2001 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

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[en] The general methods in solving neutron transport problems have been reviewed. These include the methods based on integral transport equation and the integro-differential Boltzmann equation of neutron transport theory. These methods broadly fall in two categories: (1) methods for solving reactor design problems such as spherical harmonics method, Ssub(n) method and collision probability methods and (2) methods developed for treating idealized problems that throw considerable light on the mathematical structure of Boltzmann equation and provide analytical or semi-analytical solutions of these problems. They serve as reference solutions against which numerical methods can be compared. These include Case's method of singular eigenfunctions, the Green's function approach and the integral transform methods. Present status of the subject in both the areas is outlined and the current trends are reviewed. (author)

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Department of Atomic Energy, Bombay (India); p. 17-36; 1978; p. 17-36; Department of Atomic Energy; Bombay; Symposium on reactor physics; Bombay, India; 1 - 3 Mar 1976; 18 refs.

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[en] Mathematical modelling is an integral part of the way physicists try to understand natural phenomena. It is well known that real life situations are very complicated and involve an interplay of many different forces. A physicist starts by guessing the most important, or the main features of the process. This helps him in making a mental picture of the phenomenon. It is a kind of an Abstract model of the physical system. He then puts the relationship of various factors in quantitative terms. This is what is commonly understood as a mathematical model of the system under study. There are many examples of mathematical modeling in reactor physics such as the diffusion model, Fermi age model, G-G model, Wigner Seitz cell and white boundary conditions, the point kinetics model etc. The paper will discuss some of them as well as a few others used in BARC for solving some specific problems. (author)

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Ganesan, S.; Koparde, R.V. (Reactor Physics Design Div., Bhabha Atomic Research Centre, Mumbai (India)) (eds.); Singh, R.K. (ed.) (Control Instrumentation Div., Bhabha Atomic Research Centre, Mumbai (India)); Thiyagarajan, T.K. (ed.) (Laser and Plasma Technology Div., Bhabha Atomic Research Centre, Mumbai (India)); Indian Nuclear Society, Mumbai (India); [1063 p.]; Nov 2005; [1 p.]; INSAC-2005: 16. annual conference of Indian Nuclear Society; Mumbai (India); 15-18 Nov 2005

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[en] In this paper the problem of resonance absorption in isolated Breit-Wigner resonances of an absorber in an infinite homogeneous mixture of the absorber and moderator with an explicit treatment of the moderator collision integral is treated. It is shown that Fourier transform techniques can profitably be used to treat this problem. The analysis also provides an analytical expression for the asymptotic flux distribution well below the resonance energy. Numerical results are presented to demonstrate the accuracy of the method. 24 refs

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Nuclear Science and Engineering; ISSN 0029-5639; ; v. 76(2); p. 181-197

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