Spectrum of one-speed Neutron transport operator with reflective boundary conditions in slab geometry

Sahni, D.C.; Garis, N.S.; Sjöstrand, N.G.

doi:10.1080/00411459508206019

Cited by 14 publications

(4 citation statements)

References 9 publications

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“…(7) (or from the corresponding integral equation (3 1)) the corresponding c-value is calculated using the boundary condition in Eq. (8). This gives the decay constant according to Eq.…”

Section: Sahni and Sjostrandmentioning

confidence: 99%

Time eigenvalues for one–speed neutrons in reflected spheres

Sahni

Sjöstrand

1998

Transport Theory and Statistical Physics

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The spectrum of time eigenvalues has been studied for one-speed neutrons in isotropically scattering spheres with a reflexion coefficient R in the interval -1 I ; R 5 1. It is proved that a continuous spectrum exists in the Hilbert space. This continuum disappears if we suitably enlarge the function space. It is also proved that for R 5 0 there are only discrete eigenvalues on the real axis. However, for R > 0 there is a continuum of eigenvalues beyond the Corngold limit. An expression is given for the lower boundary of the continuum, and it is supported through numerical calculations.

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“…(7) (or from the corresponding integral equation (3 1)) the corresponding c-value is calculated using the boundary condition in Eq. (8). This gives the decay constant according to Eq.…”

Section: Sahni and Sjostrandmentioning

confidence: 99%

Time eigenvalues for one–speed neutrons in reflected spheres

Sahni

Sjöstrand

1998

Transport Theory and Statistical Physics

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“…For a physical system d * s must be real. The transformation in equation ( 8) is valid and straightforward as long as the criticality factor c and the decay constant are real [5,14,57].…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…Negative or complex cross sections are frequently found in computing the time eigenvalues [3][4][5][6][7][8]. We note that the fundamental time eigenvalue is defined as the smallest number λ with a time behaviour of the form exp(−λt) for the neutron distribution [1,14].…”

Section: Introductionmentioning

confidence: 99%

“…Thus, the criticality problem can often be best approached by introducing auxiliary eigenvalues. Moreover, one usually deals with some approximation of the stationary transport operator [1][2][3][4]14]. Deviations in the eigenvalues, both the fundamental and the higher ones, yield information on the range of validity of an approximate operator [1,4].…”

Section: Introductionmentioning

confidence: 99%

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Influence of anisotropic scattering on the size of time-dependent systems in monoenergetic neutron transport

Yildiz¹

1999

J. Phys. D: Appl. Phys.

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Criticality type eigenvalues of the one-speed transport equation in a homogeneous slab with anisotropic scattering and Marshak boundary conditions are considered. The connection between the transport equations for a critical and for a time-decaying system is established, and thus the time-dependent equation is reduced to the stationary one. Variation of the size of the time-dependent system with anisotropic scattering is studied numerically. Calculations for different combinations of the scattering parameters and the selected values of the time decay constant using the method are reported. Results are discussed and compared with those already obtained using various methods available in the literature.

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Asymptotics of Transport Equations for Spherical Geometry in L2 with Reflecting Boundary Conditions

Song¹,

Greenberg

2001

Mathematical Modeling

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Spectrum of one-speed Neutron transport operator with reflective boundary conditions in slab geometry

Cited by 14 publications

References 9 publications

Time eigenvalues for one–speed neutrons in reflected spheres

Time eigenvalues for one–speed neutrons in reflected spheres

Influence of anisotropic scattering on the size of time-dependent systems in monoenergetic neutron transport

Asymptotics of Transport Equations for Spherical Geometry in L2 with Reflecting Boundary Conditions

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