Stochastic transition matrix approach for treating particle transport problems in slab geometry i... more Stochastic transition matrix approach for treating particle transport problems in slab geometry is considered. It is argued that this approach is not suitable as the transition matrix lacks the property of positivity. It is also shown that for thick slabs, the transition matrix may not exist.
A~tract-Stationary, one-speed, spherically symmetric transport equations are considered in a cons... more A~tract-Stationary, one-speed, spherically symmetric transport equations are considered in a conservative medium. Closed-form expressions are obtained for the angular flux ~0(r, #) that yield a total flux varying as 1/r by using Sonine transforms. Properties of this solution are studied and it is shown that the solution can not be identified as a diffusion mode solution of the transport equation. Limitations of the Sonine transform technique are noted.
Journal of Computational and Theoretical Transport, 2021
Abstract We develop the density transform method for treating particle transport problems in sphe... more Abstract We develop the density transform method for treating particle transport problems in spherical geometry with linearly anisotropic scattering. We consider both, the interior and exterior problems of a homogeneous sphere and show that the transform satisfies an equation that resembles particle transport equation in slab geometry. The boundary conditions for these two problems are different. We also work out the density transform method for linearly anisotropic scattering for a region of arbitrary shape.
The paper reviews some recent adva,nces pertaining to the criticality and time eigenvalues of the... more The paper reviews some recent adva,nces pertaining to the criticality and time eigenvalues of the one-speed tra,nsport equation. We discuss the nature, real or complex of the k,~f, c and X eigenvalues and their variation with size and other parameters. Our empha.sis is on accurate numerical results that display some novel features. In some cases these are explained theoretically. We also discuss the recent findings about continuous spectrum of time eigenvalue problem as it consists of a set of discrete lines rather than a half plane.
The Indian nuclear power programme has a special interest in Accelerator Driven Subcritical Syste... more The Indian nuclear power programme has a special interest in Accelerator Driven Subcritical Systems (ADSS) from the point of view of utilization of .the large thorium deposits in the country. Our effort is directed towards devising an ADSS based on the 233U-Th cycle, which produces a net energy output. In view of the constraints in accelerator technology for achieving high currents, we have also been investigating the possibility of having an ADSS with a reduced accelerator current. In an earlier work, these investigations were carried out using a simple model based on two groups diffusion theory. It was shown that it is possible to achieve a high neutron multiplication by designing a subcritical assembly made up of a booster and a main reactor region and ensuring that there is a more or less one way coupling between the two regions. In the present work, we have studied an ADSS, consisting of a fast spectrum booster coupled one way to a thermal spectrum reactor, using multigroup tra...
The spectrum of time eigenvalues has been studied for one-speed neutrons in isotropically scatter... more 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 ≤ R ≤ 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 ≤ 0 there
The criticality eigenvalue problem has been studied for the one-speed neutron transport equation.... more The criticality eigenvalue problem has been studied for the one-speed neutron transport equation. Convex bodies of arbitrary shape and with vacuum boundary conditions have been considered. The cross sections may be space dependent, and the scattering is assumed to be anisotropic. Several new conditions have been derived which ensure that a point spectrum of eigenvalues exists and that all the
Abstract A new numerical method is developed for solving singular integral equations of particle ... more Abstract A new numerical method is developed for solving singular integral equations of particle transport theory. The singular integral equations are of index -1 and their solution exists if and only if their source terms satisfy certain orthogonality condition. The method exploits this condition for existence in a practical way.
The combination of strongly forward and backward scattering with usual linearly anisotropic scatt... more The combination of strongly forward and backward scattering with usual linearly anisotropic scattering has been studied for one-speed neutrons in infinite slabs with vacuum boundary conditions. For critical systems the criticality factor is given for two slab thicknesses and different degrees of the anisotropic scattering. The special case when the forward and backward scattering completely dominate over the 'ordinary' scattering
The one-speed transport equation normally used in neutron transport and radiative transfer studie... more The one-speed transport equation normally used in neutron transport and radiative transfer studies is applied to the process of vapour (mass) transport in a gaseous media to a spherical droplet. The rate of mass transfer has been obtained in the quasi-stationary approximation. The treatment is quite general and valid for any "accommodation coefficient" and any "saturated vapour pressure". A method for incorporating these concepts in the transport equation is outlined. It is shown that the use of Kelvin's equation in this theory leads to results quite different from those given by conventional diffusion theory.
The existence of certain reciprocity-like relations in neutron transport theory was shown earlier... more The existence of certain reciprocity-like relations in neutron transport theory was shown earlier under some quite restrictive conditions. Here, these relations are shown to be valid in more general situations by using a different approach based on individual neutron trajectories.
Journal of Computational and Theoretical Transport, 2020
Abstract We study numerical solution of Singular Integral Equations (SIE) of particle transport t... more Abstract We study numerical solution of Singular Integral Equations (SIE) of particle transport theory. We convert them into matrix equations by standard discretization process. It is found that the matrices are highly ill-conditioned and can be solved by Singular Value Decomposition (SVD) method. One expects that matrices resulting from expansions over Partial Range will not be ill-conditioned. We find this is not true though their ill-conditioning is an order of magnitude less than those of full or half range. Reasons for this phenomenon are explained.
Stochastic transition matrix approach for treating particle transport problems in slab geometry i... more Stochastic transition matrix approach for treating particle transport problems in slab geometry is considered. It is argued that this approach is not suitable as the transition matrix lacks the property of positivity. It is also shown that for thick slabs, the transition matrix may not exist.
A~tract-Stationary, one-speed, spherically symmetric transport equations are considered in a cons... more A~tract-Stationary, one-speed, spherically symmetric transport equations are considered in a conservative medium. Closed-form expressions are obtained for the angular flux ~0(r, #) that yield a total flux varying as 1/r by using Sonine transforms. Properties of this solution are studied and it is shown that the solution can not be identified as a diffusion mode solution of the transport equation. Limitations of the Sonine transform technique are noted.
Journal of Computational and Theoretical Transport, 2021
Abstract We develop the density transform method for treating particle transport problems in sphe... more Abstract We develop the density transform method for treating particle transport problems in spherical geometry with linearly anisotropic scattering. We consider both, the interior and exterior problems of a homogeneous sphere and show that the transform satisfies an equation that resembles particle transport equation in slab geometry. The boundary conditions for these two problems are different. We also work out the density transform method for linearly anisotropic scattering for a region of arbitrary shape.
The paper reviews some recent adva,nces pertaining to the criticality and time eigenvalues of the... more The paper reviews some recent adva,nces pertaining to the criticality and time eigenvalues of the one-speed tra,nsport equation. We discuss the nature, real or complex of the k,~f, c and X eigenvalues and their variation with size and other parameters. Our empha.sis is on accurate numerical results that display some novel features. In some cases these are explained theoretically. We also discuss the recent findings about continuous spectrum of time eigenvalue problem as it consists of a set of discrete lines rather than a half plane.
The Indian nuclear power programme has a special interest in Accelerator Driven Subcritical Syste... more The Indian nuclear power programme has a special interest in Accelerator Driven Subcritical Systems (ADSS) from the point of view of utilization of .the large thorium deposits in the country. Our effort is directed towards devising an ADSS based on the 233U-Th cycle, which produces a net energy output. In view of the constraints in accelerator technology for achieving high currents, we have also been investigating the possibility of having an ADSS with a reduced accelerator current. In an earlier work, these investigations were carried out using a simple model based on two groups diffusion theory. It was shown that it is possible to achieve a high neutron multiplication by designing a subcritical assembly made up of a booster and a main reactor region and ensuring that there is a more or less one way coupling between the two regions. In the present work, we have studied an ADSS, consisting of a fast spectrum booster coupled one way to a thermal spectrum reactor, using multigroup tra...
The spectrum of time eigenvalues has been studied for one-speed neutrons in isotropically scatter... more 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 ≤ R ≤ 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 ≤ 0 there
The criticality eigenvalue problem has been studied for the one-speed neutron transport equation.... more The criticality eigenvalue problem has been studied for the one-speed neutron transport equation. Convex bodies of arbitrary shape and with vacuum boundary conditions have been considered. The cross sections may be space dependent, and the scattering is assumed to be anisotropic. Several new conditions have been derived which ensure that a point spectrum of eigenvalues exists and that all the
Abstract A new numerical method is developed for solving singular integral equations of particle ... more Abstract A new numerical method is developed for solving singular integral equations of particle transport theory. The singular integral equations are of index -1 and their solution exists if and only if their source terms satisfy certain orthogonality condition. The method exploits this condition for existence in a practical way.
The combination of strongly forward and backward scattering with usual linearly anisotropic scatt... more The combination of strongly forward and backward scattering with usual linearly anisotropic scattering has been studied for one-speed neutrons in infinite slabs with vacuum boundary conditions. For critical systems the criticality factor is given for two slab thicknesses and different degrees of the anisotropic scattering. The special case when the forward and backward scattering completely dominate over the 'ordinary' scattering
The one-speed transport equation normally used in neutron transport and radiative transfer studie... more The one-speed transport equation normally used in neutron transport and radiative transfer studies is applied to the process of vapour (mass) transport in a gaseous media to a spherical droplet. The rate of mass transfer has been obtained in the quasi-stationary approximation. The treatment is quite general and valid for any "accommodation coefficient" and any "saturated vapour pressure". A method for incorporating these concepts in the transport equation is outlined. It is shown that the use of Kelvin's equation in this theory leads to results quite different from those given by conventional diffusion theory.
The existence of certain reciprocity-like relations in neutron transport theory was shown earlier... more The existence of certain reciprocity-like relations in neutron transport theory was shown earlier under some quite restrictive conditions. Here, these relations are shown to be valid in more general situations by using a different approach based on individual neutron trajectories.
Journal of Computational and Theoretical Transport, 2020
Abstract We study numerical solution of Singular Integral Equations (SIE) of particle transport t... more Abstract We study numerical solution of Singular Integral Equations (SIE) of particle transport theory. We convert them into matrix equations by standard discretization process. It is found that the matrices are highly ill-conditioned and can be solved by Singular Value Decomposition (SVD) method. One expects that matrices resulting from expansions over Partial Range will not be ill-conditioned. We find this is not true though their ill-conditioning is an order of magnitude less than those of full or half range. Reasons for this phenomenon are explained.
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Papers by Dinesh Sahni