VENTURE: a code block for solving multigroup neutronics problems applying the finite-difference diffusion-theory approximation to neutron transport, version II. [LMFBR

Energy Technology Data Exchange (ETDEWEB)

Vondy, D.R.; Fowler, T.B.; Cunningham, G.W.

1977-11-01

The report documents the computer code block VENTURE designed to solve multigroup neutronics problems with application of the finite-difference diffusion-theory approximation to neutron transport (or alternatively simple P/sub 1/) in up to three-dimensional geometry. It uses and generates interface data files adopted in the cooperative effort sponsored by the Reactor Physics Branch of the Division of Reactor Research and Development of the Energy Research and Development Administration. Several different data handling procedures have been incorporated to provide considerable flexibility; it is possible to solve a wide variety of problems on a variety of computer configurations relatively efficiently.

Procedure for obtaining neutron diffusion coefficients from neutron transport Monte Carlo calculations (AWBA Development Program)

International Nuclear Information System (INIS)

Gast, R.C.

1981-08-01

A procedure for defining diffusion coefficients from Monte Carlo calculations that results in suitable ones for use in neutron diffusion theory calculations is not readily obtained. This study provides a survey of the methods used to define diffusion coefficients from deterministic calculations and provides a discussion as to why such traditional methods cannot be used in Monte Carlo. This study further provides the empirical procedure used for defining diffusion coefficients from the RCP01 Monte Carlo program

Size dependent diffusive parameters and tensorial diffusion equations in neutronic models for optically small nuclear systems

International Nuclear Information System (INIS)

Premuda, F.

1983-01-01

Two lines in improved neutron diffusion theory extending the efficiency of finite-difference diffusion codes to the field of optically small systems, are here reviewed. The firs involves the nodal solution for tensorial diffusion equation in slab geometry and tensorial formulation in parallelepiped and cylindrical gemometry; the dependence of critical eigenvalue from small slab thicknesses is also analitically investigated and finally a regularized tensorial diffusion equation is derived for slab. The other line refer to diffusion models formally unchanged with respect to the classical one, but where new size-dependent RTGB definitions for diffusion parameters are adopted, requiring that they allow to reproduce, in diffusion approach, the terms of neutron transport global balance; the trascendental equation for the buckling, arising in slab, sphere and parallelepiped geometry from the above requirement, are reported and the sizedependence of the new diffusion coefficient and extrapolated end point is investigated

Three-group albedo method applied to the diffusion phenomenon with up-scattering of neutrons

International Nuclear Information System (INIS)

Terra, Andre M. Barge Pontes Torres; Silva, Jorge A. Valle da; Cabral, Ronaldo G.

2007-01-01

The main objective of this research is to develop a three-group neutron Albedo algorithm considering the up-scattering of neutrons in order to analyse the diffusion phenomenon in nonmultiplying media. The neutron Albedo method is an analytical method that does not try to solve describing explicit equations for the neutron fluxes. Thus the neutron Albedo methodology is very different from the conventional methodology, as the neutron diffusion theory model. Graphite is analyzed as a model case. One major application is in the determination of the nonleakage probabilities with more understandable results in physical terms than conventional radiation transport method calculations. (author)

Single Crystal Diffuse Neutron Scattering

Directory of Open Access Journals (Sweden)

Richard Welberry

2018-01-01

Full Text Available Diffuse neutron scattering has become a valuable tool for investigating local structure in materials ranging from organic molecular crystals containing only light atoms to piezo-ceramics that frequently contain heavy elements. Although neutron sources will never be able to compete with X-rays in terms of the available flux the special properties of neutrons, viz. the ability to explore inelastic scattering events, the fact that scattering lengths do not vary systematically with atomic number and their ability to scatter from magnetic moments, provides strong motivation for developing neutron diffuse scattering methods. In this paper, we compare three different instruments that have been used by us to collect neutron diffuse scattering data. Two of these are on a spallation source and one on a reactor source.

Huang diffuse scattering of neutrons

International Nuclear Information System (INIS)

Burkel, E.; Guerard, B. v.; Metzger, H.; Peisl, J.

1979-01-01

Huang diffuse neutron scattering was measured for the first time on niobium with interstitially dissolved deuterium as well as on MgO after neutron irradiation and Li 7 F after γ-irradiation. With Huang diffuse scattering the strength and symmetry of the distortion field around lattice defects can be determined. Our results clearly demonstrate that this method is feasible with neutrons. The present results are compared with X-ray experiments and the advantages of using neutrons is discussed in some detail. (orig.)

Estimating anisotropic diffusion of neutrons near the boundary of a pebble bed random system

Energy Technology Data Exchange (ETDEWEB)

Vasques, R. [Department of Mathematics, Center for Computational Engineering Science, RWTH Aachen University, Schinkel Strasse 2, D-52062 Aachen (Germany)

2013-07-01

Due to the arrangement of the pebbles in a Pebble Bed Reactor (PBR) core, if a neutron is located close to a boundary wall, its path length probability distribution function in directions of flight parallel to the wall is significantly different than in other directions. Hence, anisotropic diffusion of neutrons near the boundaries arises. We describe an analysis of neutron transport in a simplified 3-D pebble bed random system, in which we investigate the anisotropic diffusion of neutrons born near one of the system's boundary walls. While this simplified system does not model the actual physical process that takes place near the boundaries of a PBR core, the present work paves the road to a formulation that may enable more accurate diffusion simulations of such problems to be performed in the future. Monte Carlo codes have been developed for (i) deriving realizations of the 3-D random system, and (ii) performing 3-D neutron transport inside the heterogeneous model; numerical results are presented for three different choices of parameters. These numerical results are used to assess the accuracy of estimates for the mean-squared displacement of neutrons obtained with the diffusion approximations of the Atomic Mix Model and of the recently introduced [1] Non-Classical Theory with angular-dependent path length distribution. The Non-Classical Theory makes use of a Generalized Linear Boltzmann Equation in which the locations of the scattering centers in the system are correlated and the distance to collision is not exponentially distributed. We show that the results predicted using the Non-Classical Theory successfully model the anisotropic behavior of the neutrons in the random system, and more closely agree with experiment than the results predicted by the Atomic Mix Model. (authors)

Estimating anisotropic diffusion of neutrons near the boundary of a pebble bed random system

International Nuclear Information System (INIS)

Vasques, R.

2013-01-01

Due to the arrangement of the pebbles in a Pebble Bed Reactor (PBR) core, if a neutron is located close to a boundary wall, its path length probability distribution function in directions of flight parallel to the wall is significantly different than in other directions. Hence, anisotropic diffusion of neutrons near the boundaries arises. We describe an analysis of neutron transport in a simplified 3-D pebble bed random system, in which we investigate the anisotropic diffusion of neutrons born near one of the system's boundary walls. While this simplified system does not model the actual physical process that takes place near the boundaries of a PBR core, the present work paves the road to a formulation that may enable more accurate diffusion simulations of such problems to be performed in the future. Monte Carlo codes have been developed for (i) deriving realizations of the 3-D random system, and (ii) performing 3-D neutron transport inside the heterogeneous model; numerical results are presented for three different choices of parameters. These numerical results are used to assess the accuracy of estimates for the mean-squared displacement of neutrons obtained with the diffusion approximations of the Atomic Mix Model and of the recently introduced [1] Non-Classical Theory with angular-dependent path length distribution. The Non-Classical Theory makes use of a Generalized Linear Boltzmann Equation in which the locations of the scattering centers in the system are correlated and the distance to collision is not exponentially distributed. We show that the results predicted using the Non-Classical Theory successfully model the anisotropic behavior of the neutrons in the random system, and more closely agree with experiment than the results predicted by the Atomic Mix Model. (authors)

Interpretation of active neutron measurements by the heterogeneous theory

International Nuclear Information System (INIS)

Birkhoff, G.; Depraz, J.; Descieux, J.P.

1979-01-01

In this paper are presented results from a study on the application of the heterogeneous method for the interpretation of active neutron measurements. The considered apparatus consists out of a cylindrical lead pile, which is provided with two axial channels: a central channel incorporates an antimony beryllium photoneutron source and an excentric channel serves for the insertion of the sample to be assayed for fissionable materials contents. The mathematical model of this apparatus is the heterogeneous group diffusion theory. Sample and source channel are described by multigroup monopolar and dipolar sources and sinks. Monopolar sources take account of neutron production within energy group and in-scatter from upper groups. Monopolar sinks represent neutron removal by absorption within energy group and outscatter to lower groups. Dipol sources describe radial streaming of neutrons across the sample channel. Multigroup diffusion theory is applied throughout the lead pile. The strengths of the monopolar and dipolar sources and sinks are determined by linear extrapolation distances of azimuthal mean and first harmonic flux values at the channels' surface. In an experiment we may measure the neutrons leaking out of the lead pile and linear extrapolation distances at the channels' surface. Such informations are utilized for interpretation in terms of fission neutron source strengh and mean neutron flux values in the sample. In this paper we summarized the theoretical work in course

Ohmic ion temperature and thermal diffusivity profiles from the JET neutron emission profile monitor

Energy Technology Data Exchange (ETDEWEB)

Esposito, B. (ENEA, Frascati (Italy). Centro Ricerche Energia); Marcus, F.B.; Conroy, S.; Jarvis, O.N.; Loughlin, M.J.; Sadler, G.; Belle, P. van (Commission of the European Communities, Abingdon (United Kingdom). JET Joint Undertaking); Adams, J.M.; Watkins, N. (AEA Industrial Technology, Harwell (United Kingdom))

1993-10-01

The JET neutron emission profile monitor was used to study ohmically heated deuterium discharges. The radial profile of the neutron emissivity is deduced from the line-integral data. The profiles of ion temperature, T[sub i], and ion thermal diffusivity, [chi][sub i], are derived under steady-state conditions. The ion thermal diffusivity is higher than, and its scaling with plasma current opposite to, that predicted by neoclassical theory. (author).

Ohmic ion temperature and thermal diffusivity profiles from the JET neutron emission profile monitor

International Nuclear Information System (INIS)

Esposito, B.

1993-01-01

The JET neutron emission profile monitor was used to study ohmically heated deuterium discharges. The radial profile of the neutron emissivity is deduced from the line-integral data. The profiles of ion temperature, T i , and ion thermal diffusivity, χ i , are derived under steady-state conditions. The ion thermal diffusivity is higher than, and its scaling with plasma current opposite to, that predicted by neoclassical theory. (author)

Multigroup neutron transport equation in the diffusion and P{sub 1} approximation

Energy Technology Data Exchange (ETDEWEB)

Obradovic, D [Boris Kidric Institute of nuclear sciences Vinca, Belgrade (Yugoslavia)

1970-07-01

Investigations of the properties of the multigroup transport operator, width and without delayed neutrons in the diffusion and P{sub 1} approximation, is performed using Keldis's theory of operator families as well as a technique . recently used for investigations into the properties of the general linearized Boltzmann operator. It is shown that in the case without delayed neutrons, multigroup transport operator in the diffusion and P{sub 1} approximation possesses a complete set of generalized eigenvectors. A formal solution to the initial value problem is also given. (author)

An extension of diffusion theory for thermal neutrons near boundaries; Extension del campo de validez de la teoria de difusion para neutrones termico en las proximidades de bordes

Energy Technology Data Exchange (ETDEWEB)

Alvarez Rivas, J L

1963-07-01

The distribution of thermal neutron flux has been measured inside and outside copper rods of several diameters, immersed in water. It has been found that these distributions can be calculated by means of elemental diffusion theory if the value of the coefficient of diffusion is changed. this parameter is truly a diffusion coefficient, which now also depends on the diameter of the rod. Through a model an expression of this coefficient is introduced which takes account of the measurements of the author and of those reported in PUGC P/928 (1995), ANL-5872 (1959), DEGR 319 (D) (1961). This model could be extended also to plane geometry. (Author) 19 refs.

Neutron transport equation - indications on homogenization and neutron diffusion

International Nuclear Information System (INIS)

Argaud, J.P.

1992-06-01

In PWR nuclear reactor, the practical study of the neutrons in the core uses diffusion equation to describe the problem. On the other hand, the most correct method to describe these neutrons is to use the Boltzmann equation, or neutron transport equation. In this paper, we give some theoretical indications to obtain a diffusion equation from the general transport equation, with some simplifying hypothesis. The work is organised as follows: (a) the most general formulations of the transport equation are presented: integro-differential equation and integral equation; (b) the theoretical approximation of this Boltzmann equation by a diffusion equation is introduced, by the way of asymptotic developments; (c) practical homogenization methods of transport equation is then presented. In particular, the relationships with some general and useful methods in neutronic are shown, and some homogenization methods in energy and space are indicated. A lot of other points of view or complements are detailed in the text or the remarks

Incoherent neutron scattering functions for random jump diffusion in bounded and infinite media

International Nuclear Information System (INIS)

Hall, P.L.; Ross, D.K.

1981-01-01

The incoherent neutron scattering function for unbounded jump diffusion is calculated from random walk theory assuming a gaussian distribution of jump lengths. The method is then applied to calculate the scattering function for spatially bounded random jumps in one dimension. The dependence on momentum transfer of the quasi-elastic energy broadenings predicted by this model and a previous model for bounded one-dimensional continuous diffusion are calculated and compared with the predictions of models for diffusion in unbounded media. The one-dimensional solutions can readily be generalized to three dimensions to provide a description of quasi-elastic scattering of neutrons by molecules undergoing localized random motions. (author)

DWARF, 1-D Few-Group Neutron Diffusion with Thermal Feedback for Burnup and Xe Oscillation

International Nuclear Information System (INIS)

Anderson, E.C.; Putnam, G.E.

1975-01-01

1 - Description of problem or function: DWARF allows one-dimensional simulation of reactor burnup and xenon oscillation problems in slab, cylindrical, or spherical geometry using a few-group diffusion theory model. 2 - Method of solution: The few-group, neutron diffusion theory equations are reduced to a system of finite-difference equations that are solved for each group by the Gauss method at each time point. Fission neutron source iteration can be accelerated with Chebyshev extrapolation. A thermal feedback iterative loop is used to obtain consistent solutions for the distributions of reactor power, neutron flux, and fuel and coolant properties with the neutron group constants functions of the latter. Solutions for the new nuclide concentrations of a time-point are made with the flux assumed constant in the time interval. 3 - Restrictions on the complexity of the problem - Maxima of: 4 groups; 40 regions; 50 macroscopic materials (Only 10 are functions of the feedback variables); 50 nuclides per region; 250 mesh points

Diffuse scattering of neutrons

International Nuclear Information System (INIS)

Novion, C.H. de.

1981-02-01

The use of neutron scattering to study atomic disorder in metals and alloys is described. The diffuse elastic scattering of neutrons by a perfect crystal lattice leads to a diffraction spectrum with only Bragg spreads. the existence of disorder in the crystal results in intensity and position modifications to these spreads, and above all, to the appearance of a low intensity scatter between Bragg peaks. The elastic scattering of neutrons is treated in this text, i.e. by measuring the number of scattered neutrons having the same energy as the incident neutrons. Such measurements yield information on the static disorder in the crystal and time average fluctuations in composition and atomic displacements [fr

Asymptotic neutron scattering laws for anomalously diffusing quantum particles

Energy Technology Data Exchange (ETDEWEB)

Kneller, Gerald R. [Centre de Biophysique Moléculaire, CNRS, Rue Charles Sadron, 45071 Orléans (France); Université d’Orléans, Chateau de la Source-Ave. du Parc Floral, 45067 Orléans (France); Synchrotron-SOLEIL, L’Orme de Merisiers, 91192 Gif-sur-Yvette (France)

2016-07-28

The paper deals with a model-free approach to the analysis of quasielastic neutron scattering intensities from anomalously diffusing quantum particles. All quantities are inferred from the asymptotic form of their time-dependent mean square displacements which grow ∝t{sup α}, with 0 ≤ α < 2. Confined diffusion (α = 0) is here explicitly included. We discuss in particular the intermediate scattering function for long times and the Fourier spectrum of the velocity autocorrelation function for small frequencies. Quantum effects enter in both cases through the general symmetry properties of quantum time correlation functions. It is shown that the fractional diffusion constant can be expressed by a Green-Kubo type relation involving the real part of the velocity autocorrelation function. The theory is exact in the diffusive regime and at moderate momentum transfers.

Systematic homogenization and self-consistent flux and pin power reconstruction for nodal diffusion methods. 1: Diffusion equation-based theory

International Nuclear Information System (INIS)

Zhang, H.; Rizwan-uddin; Dorning, J.J.

1995-01-01

A diffusion equation-based systematic homogenization theory and a self-consistent dehomogenization theory for fuel assemblies have been developed for use with coarse-mesh nodal diffusion calculations of light water reactors. The theoretical development is based on a multiple-scales asymptotic expansion carried out through second order in a small parameter, the ratio of the average diffusion length to the reactor characteristic dimension. By starting from the neutron diffusion equation for a three-dimensional heterogeneous medium and introducing two spatial scales, the development systematically yields an assembly-homogenized global diffusion equation with self-consistent expressions for the assembly-homogenized diffusion tensor elements and cross sections and assembly-surface-flux discontinuity factors. The rector eigenvalue 1/k eff is shown to be obtained to the second order in the small parameter, and the heterogeneous diffusion theory flux is shown to be obtained to leading order in that parameter. The latter of these two results provides a natural procedure for the reconstruction of the local fluxes and the determination of pin powers, even though homogenized assemblies are used in the global nodal diffusion calculation

Diffuse neutron scattering signatures of rough films

International Nuclear Information System (INIS)

Pynn, R.; Lujan, M. Jr.

1992-01-01

Patterns of diffuse neutron scattering from thin films are calculated from a perturbation expansion based on the distorted-wave Born approximation. Diffuse fringes can be categorised into three types: those that occur at constant values of the incident or scattered neutron wavevectors, and those for which the neutron wavevector transfer perpendicular to the film is constant. The variation of intensity along these fringes can be used to deduce the spectrum of surface roughness for the film and the degree of correlation between the film's rough surfaces

Neutron stochastic transport theory with delayed neutrons

International Nuclear Information System (INIS)

Munoz-Cobo, J.L.; Verdu, G.

1987-01-01

From the stochastic transport theory with delayed neutrons, the Boltzmann transport equation with delayed neutrons for the average flux emerges in a natural way without recourse to any approximation. From this theory a general expression is obtained for the Feynman Y-function when delayed neutrons are included. The single mode approximation for the particular case of a subcritical assembly is developed, and it is shown that Y-function reduces to the familiar expression quoted in many books, when delayed neutrons are not considered, and spatial and source effects are not included. (author)

THEORY OF CORRELATIONS AND FLUCTUATIONS IN NEUTRON DISTRIBUTIONS

Energy Technology Data Exchange (ETDEWEB)

Osborn, R. K.; Yip, S.

1963-06-15

Equations are derived for the first and second order densities for neutrons and alpha particles. The implications of the equations are examined by reducing them to their diffusion theory equivalents, and the one-speed equations are obtained. Results show that in cases where the singlet density can be approximated as spatially uniform, the same approximation may not apply to the doublet density. (D.C.W.)

Thermal neutron diffusion parameters in homogeneous mixtures

Energy Technology Data Exchange (ETDEWEB)

Drozdowicz, K.; Krynicka, E. [Institute of Nuclear Physics, Cracow (Poland)

1995-12-31

A physical background is presented for a computer program which calculates the thermal neutron diffusion parameters for homogeneous mixtures of any compounds. The macroscopic absorption, scattering and transport cross section of the mixture are defined which are generally function of the incident neutron energy. The energy-averaged neutron parameters are available when these energy dependences and the thermal neutron energy distribution are assumed. Then the averaged diffusion coefficient and the pulsed thermal neutron parameters (the absorption rare and the diffusion constant) are also defined. The absorption cross section is described by the 1/v law and deviations from this behaviour are considered. The scattering cross section can be assumed as being almost constant in the thermal neutron region (which results from the free gas model). Serious deviations are observed for hydrogen atoms bound in molecules and a special study in the paper is devoted to this problem. A certain effective scattering cross section is found in this case on a base of individual exact data for a few hydrogenous media. Approximations assumed for the average cosine of the scattering angle are also discussed. The macroscopic parameters calculated are averaged over the Maxwellian energy distribution for the thermal neutron flux. An information on the input data for the computer program is included. (author). 10 refs, 4 figs, 5 tabs.

Thermal neutron diffusion parameters in homogeneous mixtures

International Nuclear Information System (INIS)

Drozdowicz, K.; Krynicka, E.

1995-01-01

A physical background is presented for a computer program which calculates the thermal neutron diffusion parameters for homogeneous mixtures of any compounds. The macroscopic absorption, scattering and transport cross section of the mixture are defined which are generally function of the incident neutron energy. The energy-averaged neutron parameters are available when these energy dependences and the thermal neutron energy distribution are assumed. Then the averaged diffusion coefficient and the pulsed thermal neutron parameters (the absorption rare and the diffusion constant) are also defined. The absorption cross section is described by the 1/v law and deviations from this behaviour are considered. The scattering cross section can be assumed as being almost constant in the thermal neutron region (which results from the free gas model). Serious deviations are observed for hydrogen atoms bound in molecules and a special study in the paper is devoted to this problem. A certain effective scattering cross section is found in this case on a base of individual exact data for a few hydrogenous media. Approximations assumed for the average cosine of the scattering angle are also discussed. The macroscopic parameters calculated are averaged over the Maxwellian energy distribution for the thermal neutron flux. An information on the input data for the computer program is included. (author). 10 refs, 4 figs, 5 tabs

A boundary integral equation for boundary element applications in multigroup neutron diffusion theory

International Nuclear Information System (INIS)

Ozgener, B.

1998-01-01

A boundary integral equation (BIE) is developed for the application of the boundary element method to the multigroup neutron diffusion equations. The developed BIE contains no explicit scattering term; the scattering effects are taken into account by redefining the unknowns. Boundary elements of the linear and constant variety are utilised for validation of the developed boundary integral formulation

Study of the critical scattering of neutrons by iron; Etude de la diffusion critique des neutrons par le fer

Energy Technology Data Exchange (ETDEWEB)

Galula, M; Jacrot, B; Mangin, J P [Commissariat a l' Energie Atomique, Saclay (France)

1959-07-01

The critical scattering of very slow neutrons by iron near critical point is measured by time of flight techniques. The VAN HOVE formula is verified and the geometrical parameters K{sub 1} et r{sub 1} introduced in this theory are determined. (author) [French] On etudie la diffusion critique des neutrons tres lents par le fer dans la region du point de Curie par une methode de temps de vol. On verifie la formule de VAN HOVE et on determine les parametres geometriques K{sub 1} et r{sub 1} introduit par ce dernier. (auteur)

Derivation of a volume-averaged neutron diffusion equation; Atomos para el desarrollo de Mexico

Energy Technology Data Exchange (ETDEWEB)

Vazquez R, R.; Espinosa P, G. [UAM-Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, Mexico D.F. 09340 (Mexico); Morales S, Jaime B. [UNAM, Laboratorio de Analisis en Ingenieria de Reactores Nucleares, Paseo Cuauhnahuac 8532, Jiutepec, Morelos 62550 (Mexico)]. e-mail: rvr@xanum.uam.mx

2008-07-01

This paper presents a general theoretical analysis of the problem of neutron motion in a nuclear reactor, where large variations on neutron cross sections normally preclude the use of the classical neutron diffusion equation. A volume-averaged neutron diffusion equation is derived which includes correction terms to diffusion and nuclear reaction effects. A method is presented to determine closure-relationships for the volume-averaged neutron diffusion equation (e.g., effective neutron diffusivity). In order to describe the distribution of neutrons in a highly heterogeneous configuration, it was necessary to extend the classical neutron diffusion equation. Thus, the volume averaged diffusion equation include two corrections factor: the first correction is related with the absorption process of the neutron and the second correction is a contribution to the neutron diffusion, both parameters are related to neutron effects on the interface of a heterogeneous configuration. (Author)

Comparison of neutron diffusion theory codes in two and three space dimensions using a sodium cooled fast reactor benchmark

International Nuclear Information System (INIS)

Butland, A.T.D.; Putney, J.; Sweet, D.W.

1980-04-01

This report describes work performed to compare two UK neutron diffusion theory codes, TIGAR and SNAP, with published results for eight other codes available abroad. Both mesh edge and mesh centred finite difference diffusion theory codes as well as one axial synthesis code are included in the comparison and a range of iteration procedures are used by them. Comparison is made of calculations for a model of the sodium cooled fast reactor SNR-300 in both triangular and rectangular geometry and for a range of spatial meshes, enabling extrapolations to infinite mesh to be made. Calculated values of the effective multiplication constant, keff, for all the codes, agree very well when extrapolated to infinite mesh, indicating that no significant errors arising from the finite difference approximation but independent of mesh spacing are present in the calculations. The variation of keff with mesh area is found to be linear for the small meshes considered here, with the gradients for the mesh centred and mesh edged codes being of opposite sign. The results obtained using the mesh centred codes TIGAR, SNAP and CITATION agree closely with one another for all the meshes considered; the mesh edge codes agree less closely. (author)

DIF3D nodal neutronics option for two- and three-dimensional diffusion theory calculations in hexagonal geometry

International Nuclear Information System (INIS)

Lawrence, R.D.

1983-03-01

A nodal method is developed for the solution of the neutron-diffusion equation in two- and three-dimensional hexagonal geometries. The nodal scheme has been incorporated as an option in the finite-difference diffusion-theory code DIF3D, and is intended for use in the analysis of current LMFBR designs. The nodal equations are derived using higher-order polynomial approximations to the spatial dependence of the flux within the hexagonal-z node. The final equations, which are cast in the form of inhomogeneous response-matrix equations for each energy group, involved spatial moments of the node-interior flux distribution plus surface-averaged partial currents across the faces of the node. These equations are solved using a conventional fission-source iteration accelerated by coarse-mesh rebalance and asymptotic source extrapolation. This report describes the mathematical development and numerical solution of the nodal equations, as well as the use of the nodal option and details concerning its programming structure. This latter information is intended to supplement the information provided in the separate documentation of the DIF3D code

Dynamical theory of neutron diffraction

International Nuclear Information System (INIS)

Sears, V.F.

1978-01-01

We present a review of the dynamical theory of neutron diffraction by macroscopic bodies which provides the theoretical basis for the study of neutron optics. We consider both the theory of dispersion, in which it is shown that the coherent wave in the medium satisfies a macroscopic one-body Schroedinger equation, and the theory of reflection, refraction, and diffraction in which the above equation is solved for a number of special cases of interest. The theory is illustrated with the help of experimental results obtained over the past 10 years by a number of new techniques such as neutron gravity refractometry. Pendelloesung interference, and neutron interferometry. (author)

Diffuse scattering of neutrons and X-rays

International Nuclear Information System (INIS)

Novion, C.H. de

1978-01-01

Diffuse scattering is used to study defect concentrations of about 10 -4 in the case of X-rays and 10 -3 in the case of neutrons. The foundations of diffuse scattering formalism are given, some experimental devices described and a few applications discussed: study by diffraction on powders of defects in CeOsub(2-x); short-range order study by X-rays on Cusub(0.75) Ausub(0.25); short-range order study by neutrons on Cusub(0.435)Nisub(0.565); short-range order study by electrons TiOx; study of irradiation-induced self-interstitials in Al; study of holes created by neutrons in Al [fr

SNAP - a three dimensional neutron diffusion code

International Nuclear Information System (INIS)

McCallien, C.W.J.

1993-02-01

This report describes a one- two- three-dimensional multi-group diffusion code, SNAP, which is primarily intended for neutron diffusion calculations but can also carry out gamma calculations if the diffusion approximation is accurate enough. It is suitable for fast and thermal reactor core calculations and for shield calculations. SNAP can solve the multi-group neutron diffusion equations using finite difference methods. The one-dimensional slab, cylindrical and spherical geometries and the two-dimensional case are all treated as simple special cases of three-dimensional geometries. Numerous reflective and periodic symmetry options are available and may be used to reduce the number of mesh points necessary to represent the system. Extrapolation lengths can be specified at internal and external boundaries. (Author)

Neutron spin-echo spectroscopy for diffusion in crystalline solids

International Nuclear Information System (INIS)

Kaisermayr, M.; Rennhofer, M.; Vogl, G.; Pappas, C.; Longeville, S.

2002-01-01

Neutron spin-echo spectroscopy (NSE) offers unprecedented opportunities in the investigation of diffusion in crystalline systems due to its outstanding energy resolution. NSE not only enables measurements at lower diffusivities than the established techniques of neutron spectroscopy, but it also gives a very immediate access to the different time scales involved in the diffusion process. This is demonstrated in detail on the example of the binary alloy NiGa where the Ni atoms hop between regular sites on the Ni sublattice and anti-sites on the Ga sublattice. Experiments on two different NSE instruments are compared to measurements using neutron backscattering spectroscopy. The potential of NSE for the investigation of jump diffusion and experimental requirements are discussed

Evaluation for the models of neutron diffusion theory in terms of power density distributions of the HTTR

International Nuclear Information System (INIS)

Takamatsu, Kuniyoshi; Shimakawa, Satoshi; Nojiri, Naoki; Fujimoto, Nozomu

2003-10-01

In the case of evaluations for the highest temperature of the fuels in the HTTR, it is very important to expect the power density distributions accurately; therefore, it is necessary to improve the analytical model with the neutron diffusion and the burn-up theory. The power density distributions are analyzed in terms of two models, the one mixing the fuels and the burnable poisons homogeneously and the other modeling them heterogeneously. Moreover these analytical power density distributions are compared with the ones derived from the gross gamma-ray measurements and the Monte Carlo calculational code with continuous energy. As a result the homogeneous mixed model isn't enough to expect the power density distributions of the core in the axial direction; on the other hand, the heterogeneous model improves the accuracy. (author)

Investigation of the local component of power-reactor noise via diffusion theory

International Nuclear Information System (INIS)

Kosaly, G.

1975-03-01

The aim of the paper is to provide a theoretical background for the phenomenological model, which postulates the existence of a local component in the neutron noise of a light water cooled boiling water reactor. After the introductory review of the phenomenological model, noise calculation are performed by help of the one-group and two-group diffusion theory. Only in the two-group diffusion model it is succeeded to find a term in the response to a propagating disturbance of density which results in a small volume of neutrons physical sensivity around the point of observation. The problem, whether this local component can be a dominating term in the solution or not, is investigated in the Appenix. (Sz.Z.)

Chemical order-disorder in alloys. Study by neutrons diffuse diffusion

International Nuclear Information System (INIS)

Novion, C. de; Beuneu, B.

1993-01-01

Applications of neutrons diffuse diffusion for short distance chemical order in FCC transition metals solid solutions (Pd-V, Ni-V, Ni-Cr) and understoichiometric carbides or nitrides of transition metals (TiC 1-x , NbC 1-x , TiN 1-x ) are shortly presented with theoretical and experimental aspects. (A.B.)

DIF3D nodal neutronics option for two- and three-dimensional diffusion theory calculations in hexagonal geometry. [LMFBR

Energy Technology Data Exchange (ETDEWEB)

Lawrence, R.D.

1983-03-01

A nodal method is developed for the solution of the neutron-diffusion equation in two- and three-dimensional hexagonal geometries. The nodal scheme has been incorporated as an option in the finite-difference diffusion-theory code DIF3D, and is intended for use in the analysis of current LMFBR designs. The nodal equations are derived using higher-order polynomial approximations to the spatial dependence of the flux within the hexagonal-z node. The final equations, which are cast in the form of inhomogeneous response-matrix equations for each energy group, involved spatial moments of the node-interior flux distribution plus surface-averaged partial currents across the faces of the node. These equations are solved using a conventional fission-source iteration accelerated by coarse-mesh rebalance and asymptotic source extrapolation. This report describes the mathematical development and numerical solution of the nodal equations, as well as the use of the nodal option and details concerning its programming structure. This latter information is intended to supplement the information provided in the separate documentation of the DIF3D code.

Decay constants of subcritical system by diffusion theory for two groups

International Nuclear Information System (INIS)

Moura Neto, C. de.

1977-01-01

The effects of a neutronic pulse applied to a subcritical multiplicative medium are analysed on the basis of the diffusion theory for one and two groups. The decay constants of the system for various values of geometric buckling were determined from the experimental data. A natural uranium-light water lattice was pulsed employing a Texas Nuclear 9905 neutron generator. The least square method was employed in the data reduction procedures to determine the decay constants. The separation of the decay constants associated with thermal and epithermal fluxes is attempted through two groups formulation. (author)

Decay constants of a subcritical system by two-group diffusion theory

International Nuclear Information System (INIS)

Moura Neto, C. de.

1979-08-01

The effects of a neutronic pulse applied to a subcritical multiplicative medium are analyzed on the basis of the diffusion theory for one and two groups. The decay constants of the system were determined from the experimental data, for various values geometric buckling. A natural uranium light-water configuration was pulsed employing a Texas Nuclear 9905 neutron generator. The least square method was employed in the data reduction procedures to determine the decay constants. The separation of the decay constants associated with thermal and epithermal fluxes are verified through two groups formulation. (Author) [pt

Derivation of the neutron diffusion equation

International Nuclear Information System (INIS)

Mika, J.R.; Banasiak, J.

1994-01-01

We discuss the diffusion equation as an asymptotic limit of the neutron transport equation for large scattering cross sections. We show that the classical asymptotic expansion procedure does not lead to the diffusion equation and present two modified approaches to overcome this difficulty. The effect of the initial layer is also discussed. (authors). 9 refs

Reflector modelization for neutronic diffusion and parameters identification

International Nuclear Information System (INIS)

Argaud, J.P.

1993-04-01

Physical parameters of neutronic diffusion equations can be adjusted to decrease calculations-measurements errors. The reflector being always difficult to modelize, we choose to elaborate a new reflector model and to use the parameters of this model as adjustment coefficients in the identification procedure. Using theoretical results, and also the physical behaviour of neutronic flux solutions, the reflector model consists then in its replacement by boundary conditions for the diffusion equations on the core only. This theoretical result of non-local operator relations leads then to some discrete approximations by taking into account the multiscaled behaviour, on the core-reflector interface, of neutronic diffusion solutions. The resulting model of this approach is then compared with previous reflector modelizations, and first results indicate that this new model gives the same representation of reflector for the core than previous. (author). 12 refs

The quasi-diffusive approximation in transport theory: Local solutions

International Nuclear Information System (INIS)

Celaschi, M.; Montagnini, B.

1995-01-01

The one velocity, plane geometry integral neutron transport equation is transformed into a system of two equations, one of them being the equation of continuity and the other a generalized Fick's law, in which the usual diffusion coefficient is replaced by a self-adjoint integral operator. As the kernel of this operator is very close to the Green function of a diffusion equation, an approximate inversion by means of a second order differential operator allows to transform these equations into a purely differential system which is shown to be equivalent, in the simplest case, to a diffusion-like equation. The method, the principles of which have been exposed in a previous paper, is here extended and applied to a variety of problems. If the inversion is properly performed, the quasi-diffusive solutions turn out to be quite accurate, even in the vicinity of the interface between different material regions, where elementary diffusion theory usually fails. 16 refs., 3 tabs

Contribution to the neutronic theory of random stacks (diffusion coefficient and first-flight collision probabilities) with a general theorem on collision probabilities

International Nuclear Information System (INIS)

Dixmier, Marc.

1980-10-01

A general expression of the diffusion coefficient (d.c.) of neutrons was given, with stress being put on symmetries. A system of first-flight collision probabilities for the case of a random stack of any number of types of one- and two-zoned spherical pebbles, with an albedo at the frontiers of the elements or (either) consideration of the interstital medium, was built; to that end, the bases of collision probability theory were reviewed, and a wide generalisation of the reciprocity theorem for those probabilities was demonstrated. The migration area of neutrons was expressed for any random stack of convex, 'simple' and 'regular-contact' elements, taking into account the correlations between free-paths; the average cosinus of re-emission of neutrons by an element, in the case of a homogeneous spherical pebble and the transport approximation, was expressed; the superiority of the so-found result over Behrens' theory, for the type of media under consideration, was established. The 'fine structure current term' of the d.c. was also expressed, and it was shown that its 'polarisation term' is negligible. Numerical applications showed that the global heterogeneity effect on the d.c. of pebble-bed reactors is comparable with that for Graphite-moderated, Carbon gas-cooled, natural Uranium reactors. The code CARACOLE, which integrates all the results here obtained, was introduced [fr

Prediction of the neutrons subcritical multiplication using the diffusion hybrid equation with external neutron sources

Energy Technology Data Exchange (ETDEWEB)

Costa da Silva, Adilson; Carvalho da Silva, Fernando [COPPE/UFRJ, Programa de Engenharia Nuclear, Caixa Postal 68509, 21941-914, Rio de Janeiro (Brazil); Senra Martinez, Aquilino, E-mail: aquilino@lmp.ufrj.br [COPPE/UFRJ, Programa de Engenharia Nuclear, Caixa Postal 68509, 21941-914, Rio de Janeiro (Brazil)

2011-07-15

Highlights: > We proposed a new neutron diffusion hybrid equation with external neutron source. > A coarse mesh finite difference method for the adjoint flux and reactivity calculation was developed. > 1/M curve to predict the criticality condition is used. - Abstract: We used the neutron diffusion hybrid equation, in cartesian geometry with external neutron sources to predict the subcritical multiplication of neutrons in a pressurized water reactor, using a 1/M curve to predict the criticality condition. A Coarse Mesh Finite Difference Method was developed for the adjoint flux calculation and to obtain the reactivity values of the reactor. The results obtained were compared with benchmark values in order to validate the methodology presented in this paper.

Prediction of the neutrons subcritical multiplication using the diffusion hybrid equation with external neutron sources

International Nuclear Information System (INIS)

Costa da Silva, Adilson; Carvalho da Silva, Fernando; Senra Martinez, Aquilino

2011-01-01

Highlights: → We proposed a new neutron diffusion hybrid equation with external neutron source. → A coarse mesh finite difference method for the adjoint flux and reactivity calculation was developed. → 1/M curve to predict the criticality condition is used. - Abstract: We used the neutron diffusion hybrid equation, in cartesian geometry with external neutron sources to predict the subcritical multiplication of neutrons in a pressurized water reactor, using a 1/M curve to predict the criticality condition. A Coarse Mesh Finite Difference Method was developed for the adjoint flux calculation and to obtain the reactivity values of the reactor. The results obtained were compared with benchmark values in order to validate the methodology presented in this paper.

Development of 3D multi-group neutron diffusion code for hexagonal geometry

International Nuclear Information System (INIS)

Sun Wei; Wang Kan; Ni Dongyang; Li Qing

2013-01-01

Based on the theory of new flux expansion nodal method to solve the neutron diffusion equations, the intra-nodal fluence rate distribution was expanded in a series of analytic basic functions for each group. In order to improve the accuracy of calculation result, continuities of neutron fluence rate and current were utilized across the nodal surfaces. According to the boundary conditions, the iteration method was adopted to solve the diffusion equation, where inner iteration speedup method is Gauss-Seidel method and outer is Lyusternik-Wagner. A new speedup method (one-outer-iteration and multi-inner-iteration method) was proposed according to the characteristic that the convergence speed of multiplication factor is faster than that of neutron fluence rate and the update of inner iteration matrix is slow. Based on the proposed model, the code HANDF-D was developed and tested by 3D two-group vver440 benchmark, experiment 2 of HFETR, 3D four-group thermal reactor benchmark, and 3D seven-group fast reactor benchmark. The numerical results show that HANDF-D can predict accurately the multiplication factor and nodal powers. (authors)

SHREDI, Neutron Flux and Neutron Activation in 2-D Shields by Removal Diffusion

International Nuclear Information System (INIS)

Daneri, A.; Toselli, G.

1976-01-01

1 - Nature of physical problem solved: SHREDI is a removal - diffusion neutron shielding code. The program computes neutron fluxes and activations in bidimensional sections (x,y or r,z) of the shield. It is also possible to consider shielding points with the same y or z coordinate (mono-dimensional problems). 2 - Method of solution: The integrals which define the removal fluxes are computed in some shield points by means of a particular algorithm based on the Simpson's and trapezoidal rules. For the diffusion calculation the finite difference method is used. The removal sources are interpolated in all diffusion points by Chebyshev polynomials. 3 - Restrictions on the complexity of the problem: Maxima: number of removal energy groups NGR = 40; number of diffusion energy groups NGD = 40; number of the reactor core and shield materials NCMP = 50; number of core mesh points in r (or x) direction for integral calculation = 75; number of core mesh points in z (or y) direction for integral calculation = 75; number of core mesh points in theta (or z) direction for integral calculation = 75; number of shield mesh points for the neutron flux calculation in r (or x) direction NPX = 200; number of shield mesh points for the neutron flux calculation in z (or y) direction NPY = 200; n.b. (NPX * NPY) le 12000

Quasi-elastic neutron scattering studies of the diffusion of hydrogen in metals

Energy Technology Data Exchange (ETDEWEB)

Ross, D K [Birmingham Univ. (UK). School of Physics and Space Research

1989-01-01

Quasi-elastic neutron scattering provides a uniquely detailed way of investigating microscopic models for diffusion in lattice gases. In the present paper we discuss extensions of the original Chudley-Elliott model to cover systems containing high concentrations of interacting particles for both the incoherent and coherent cases. In the former case, the peak width is changed by site blocking and by interactions and its shape is altered by correlation effects between successive jumps. In the coherent case, although interactions introduce different correlation effects, the most important changes are due to the short-range order caused by the interactions. A simple Mean Field theory is described which predicts peak narrowing where the diffuse scattering is at a maximum. Experimental tests of both coherent and incoherent theories are described for the case of {alpha}'NbD{sub x}. (orig.).

Quasi-elastic neutron scattering studies of the diffusion of hydrogen in metals

International Nuclear Information System (INIS)

Ross, D.K.

1989-01-01

Quasi-elastic neutron scattering provides a uniquely detailed way of investigating microscopic models for diffusion in lattice gases. In the present paper we discuss extensions of the original Chudley-Elliott model to cover systems containing high concentrations of interacting particles for both the incoherent and coherent cases. In the former case, the peak width is changed by site blocking and by interactions and its shape is altered by correlation effects between successive jumps. In the coherent case, although interactions introduce different correlation effects, the most important changes are due to the short-range order caused by the interactions. A simple Mean Field theory is described which predicts peak narrowing where the diffuse scattering is at a maximum. Experimental tests of both coherent and incoherent theories are described for the case of α'NbD x . (orig.)

The numerical analysis of eigenvalue problem solutions in multigroup neutron diffusion theory

International Nuclear Information System (INIS)

Woznicki, Z.I.

1995-01-01

The main goal of this paper is to present a general iteration strategy for solving the discrete form of multidimensional neutron diffusion equations equivalent mathematically to an eigenvalue problem. Usually a solution method is based on different levels of iterations. The presented matrix formalism allows us to visualize explicitly how the used matrix splitting influences the matrix structure in an eigenvalue problem to be solved as well as the interdependence between inner and outer iterations within global iterations. Particular iterative strategies are illustrated by numerical results obtained for several reactor problems. (author). 21 refs, 35 figs, 16 tabs

Measurement of the diffusion length of thermal neutrons in the beryllium oxide; Mesure de la longueur de diffusion des neutrons thermiques dans l'oxyde de beryllium

Energy Technology Data Exchange (ETDEWEB)

Koechlin, J C; Martelly, J; Duggal, V P [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1955-07-01

The diffusion length of thermal neutrons in the beryllium oxide has been obtained while studying the spatial distribution of the neutrons in a massive parallelepiped of this matter placed before the thermal column of the reactor core of Saclay. The mean density of the beryllium oxide (BeO) is 2,95 gr/cm{sup 3}, the mean density of the massif is 2,92 gr/cm{sup 3}. The value of the diffusion length, deducted of the done measures, is: L = 32,7 {+-} 0,5 cm (likely gap). Some remarks are formulated about the influence of the spectral distribution of the neutrons flux used. (authors) [French] La longueur de diffusion des neutrons thermiques dans l'oxyde de beryllium a ete obtenue en etudiant la repartition spatiale des neutrons dans un massif parallelepipedique de cette matiere placee devant la colonne thermique de la Pile de Saclay. La densite moyenne de l'oxyde de beryllium (BeO) est de 2,95 gr/cm{sup 3}, la densite moyenne du massif de 2,92 gr/cm{sup 3}. La valeur de la longueur de diffusion, deduite des mesures effectuees est: L 32,7 {+-} 0,5 cm (ecart probable). Des remarques sont formulees quant a l'influence de la repartition spectrale du flux de neutrons utilise. (auteurs)

Finite difference solution of the time dependent neutron group diffusion equations

International Nuclear Information System (INIS)

Hendricks, J.S.; Henry, A.F.

1975-08-01

In this thesis two unrelated topics of reactor physics are examined: the prompt jump approximation and alternating direction checkerboard methods. In the prompt jump approximation it is assumed that the prompt and delayed neutrons in a nuclear reactor may be described mathematically as being instantaneously in equilibrium with each other. This approximation is applied to the spatially dependent neutron diffusion theory reactor kinetics model. Alternating direction checkerboard methods are a family of finite difference alternating direction methods which may be used to solve the multigroup, multidimension, time-dependent neutron diffusion equations. The reactor mesh grid is not swept line by line or point by point as in implicit or explicit alternating direction methods; instead, the reactor mesh grid may be thought of as a checkerboard in which all the ''red squares'' and '' black squares'' are treated successively. Two members of this family of methods, the ADC and NSADC methods, are at least as good as other alternating direction methods. It has been found that the accuracy of implicit and explicit alternating direction methods can be greatly improved by the application of an exponential transformation. This transformation is incompatible with checkerboard methods. Therefore, a new formulation of the exponential transformation has been developed which is compatible with checkerboard methods and at least as good as the former transformation for other alternating direction methods

Criticality problems for slabs and spheres in energy dependent neutron transport theory

International Nuclear Information System (INIS)

Victory, H.D. Jr.

1980-01-01

The steady-state equation for energy-dependent neutron transport in isotropically scattering slabs and spheres is formulated as an integral equation. The Perron-Frobenius-Jentzsch theory of positive operators is used to analyze criticality problems for transport in slab and spherical media consisting of core and reflector. In addition, with an adroit selection of diffusion-like solutions, this theory is used to obtain an expression relating the critical radius of a homogeneous sphere to a parameter characterizing fission production. 21 refs

Calculation of the power factor using the neutron diffusion hybrid equation

International Nuclear Information System (INIS)

Costa da Silva, Adilson; Carvalho da Silva, Fernando; Senra Martinez, Aquilino

2013-01-01

Highlights: ► A neutron diffusion hybrid equation with an external neutron source was used. ► Nodal expansion method to obtain the neutron flux was used. ► Nuclear power factors in each fuel element in the reactor core were calculated. ► The results obtained were very accurate. -- Abstract: In this paper, we used a neutron diffusion hybrid equation with an external neutron source to calculate nuclear power factors in each fuel element in the reactor core. We used the nodal expansion method to obtain the neutron flux for a given control rods bank position. The results were compared with results obtained for eigenvalue problem near criticality condition and fixed source problem during the start-up of the reactor, where external neutron sources are extremely important for the stabilization of external neutron detectors.

Analytical synthetic methods of solution of neutron transport equation with diffusion theory approaches energy multigroup

International Nuclear Information System (INIS)

Moraes, Pedro Gabriel B.; Leite, Michel C.A.; Barros, Ricardo C.

2013-01-01

In this work we developed a software to model and generate results in tables and graphs of one-dimensional neutron transport problems in multi-group formulation of energy. The numerical method we use to solve the problem of neutron diffusion is analytic, thus eliminating the truncation errors that appear in classical numerical methods, e.g., the method of finite differences. This numerical analytical method increases the computational efficiency, since they are not refined spatial discretization necessary because for any spatial discretization grids used, the numerical result generated for the same point of the domain remains unchanged unless the rounding errors of computational finite arithmetic. We chose to develop a computational application in MatLab platform for numerical computation and program interface is simple and easy with knobs. We consider important to model this neutron transport problem with a fixed source in the context of shielding calculations of radiation that protects the biosphere, and could be sensitive to ionizing radiation

Discrete formulation for two-dimensional multigroup neutron diffusion equations

Energy Technology Data Exchange (ETDEWEB)

Vosoughi, Naser E-mail: vosoughi@mehr.sharif.edu; Salehi, Ali A.; Shahriari, Majid

2003-02-01

The objective of this paper is to introduce a new numerical method for neutronic calculation in a reactor core. This method can produce the final finite form of the neutron diffusion equation by classifying the neutronic variables and using two kinds of cell complexes without starting from the conventional differential form of the neutron diffusion equation. The method with linear interpolation produces the same convergence as the linear continuous finite element method. The quadratic interpolation is proven; the convergence order depends on the shape of the dual cell. The maximum convergence order is achieved by choosing the dual cell based on two Gauss' points. The accuracy of the method was examined with a well-known IAEA two-dimensional benchmark problem. The numerical results demonstrate the effectiveness of the new method.

Discrete formulation for two-dimensional multigroup neutron diffusion equations

International Nuclear Information System (INIS)

Vosoughi, Naser; Salehi, Ali A.; Shahriari, Majid

2003-01-01

The objective of this paper is to introduce a new numerical method for neutronic calculation in a reactor core. This method can produce the final finite form of the neutron diffusion equation by classifying the neutronic variables and using two kinds of cell complexes without starting from the conventional differential form of the neutron diffusion equation. The method with linear interpolation produces the same convergence as the linear continuous finite element method. The quadratic interpolation is proven; the convergence order depends on the shape of the dual cell. The maximum convergence order is achieved by choosing the dual cell based on two Gauss' points. The accuracy of the method was examined with a well-known IAEA two-dimensional benchmark problem. The numerical results demonstrate the effectiveness of the new method

Mathematical methods in neutronics

International Nuclear Information System (INIS)

Planchard, J.

1995-01-01

This book presents the mathematical theory of nuclear reactors. It applies to engineers in neutronics and applied mathematicians. After a recall of the elementary notions of neutronics and of diffusion-type partial derivative equations, the theory of reactors criticality calculation is described. (J.S.)

Pulsed neutron method for diffusion, slowing down, and reactivity measurements

International Nuclear Information System (INIS)

Sjoestrand, N.G.

1985-01-01

An outline is given on the principles of the pulsed neutron method for the determination of thermal neutron diffusion parameters, for slowing-down time measurements, and for reactivity determinations. The historical development is sketched from the breakthrough in the middle of the nineteen fifties and the usefulness and limitations of the method are discussed. The importance for the present understanding of neutron slowing-down, thermalization and diffusion are point out. Examples are given of its recent use for e.g. absorption cross section measurements and for the study of the properties of heterogeneous systems

Investigation of the response of a neutron moisture meter using a multigroup, two-dimensional diffusion theory code

International Nuclear Information System (INIS)

Ritchie, A.I.M.; Wilson, D.J.

1984-12-01

A multigroup diffusion code has been used to predict the count rate from a neutron moisture meter for a range of values of soil water content ω, thermal neutron absorption cross section Ssub(a) (defined as Σsub(a)/rho) of the soil matrix and soil matrix density rho. Two dimensions adequately approximated the geometry of the source, detector and soil surrounding the detector. Seven energy groups, the data for which were condensed from 128 group data set over the neutron energy spectrum appropriate to the soil-water mixture under study, proved adequate to describe neutron slowing-down and diffusion. The soil-water mixture was an SiO 2 →water mixture, with the absorption cross section of SiO 2 increased to cover the range of Σsub(a) required. The response to changes in matrix density is, in general, linear but the response to changes in water content is not linear over the range of parameter values investigated. Tabular results are presented which allow interpolation of the response for a particular ω, Ssub(a) and rho. It is shown that R(ω, Ssub(a), rho) rho M(Ssub(a)) + C(ω) is a crude representation of the response over a very limited range of variation of ω, and Ssub(a). As the response is a slowly varying function of rho, Ssub(a) and ω, a polynomial fit will provide a better estimate of the response for values of rho, Ssub(a) and ω not tabulated

Measurement of neutron diffusion length in heavy concrete

International Nuclear Information System (INIS)

Krejci, D.

2007-04-01

Using an aluminium sampler filled with heavy concrete the neutron diffusion length was determined, measuring thermal and fast neutrons over the whole beam hole with various threshold detectors using gold samples. These calculations should describe the neutron distribution in the whole concrete shield of the reactor and contribute to the investigation of the activation of the concrete shield using reactor parameters like operating time, power and neutron flux. Instrumentation, activation and positioning of the samples in the beam hole of the TRIGA Mark II reactor are described. (nevyjel)

On the numerical solution of the neutron fractional diffusion equation

International Nuclear Information System (INIS)

Maleki Moghaddam, Nader; Afarideh, Hossein; Espinosa-Paredes, Gilberto

2014-01-01

Highlights: • The new version of neutron diffusion equation which established on the fractional derivatives is presented. • The Neutron Fractional Diffusion Equation (NFDE) is solved in the finite differences frame. • NFDE is solved using shifted Grünwald-Letnikov definition of fractional operators. • The results show that “K eff ” strongly depends on the order of fractional derivative. - Abstract: In order to core calculation in the nuclear reactors there is a new version of neutron diffusion equation which is established on the fractional partial derivatives, named Neutron Fractional Diffusion Equation (NFDE). In the NFDE model, neutron flux in each zone depends directly on the all previous zones (not only on the nearest neighbors). Under this circumstance, it can be said that the NFDE has the space history. We have developed a one-dimension code, NFDE-1D, which can simulate the reactor core using arbitrary exponent of differential operators. In this work a numerical solution of the NFDE is presented using shifted Grünwald-Letnikov definition of fractional derivative in finite differences frame. The model is validated with some numerical experiments where different orders of fractional derivative are considered (e.g. 0.999, 0.98, 0.96, and 0.94). The results show that the effective multiplication factor (K eff ) depends strongly on the order of fractional derivative

Cosmic ray diffusion: report of the workshop in cosmic ray diffusion theory

International Nuclear Information System (INIS)

Birmingham, T.J.; Jones, F.C.

1975-02-01

A workshop in cosmic ray diffusion theory was held at Goddard Space Flight Center on May 16-17, 1974. Topics discussed and summarized are: (1) cosmic ray measurements as related to diffusion theory; (2) quasi-linear theory, nonlinear theory, and computer simulation of cosmic ray pitch-angle diffusion; and (3) magnetic field fluctuation measurements as related to diffusion theory. (auth)

Time-of-flight and vector polarization analysis for diffuse neutron scattering

International Nuclear Information System (INIS)

Schweika, W.

2003-01-01

The potential of pulsed neutron sources for diffuse scattering including time-of-flight (TOF) and polarization analysis is discussed in comparison to the capabilities of the present instrument diffuse neutron scattering at the research center Juelich. We present first results of a new method for full polarization analysis using precessing neutron polarization. A proposal is made for a new type of instrument at pulsed sources, which allows for vector polarization analysis in TOF instruments with multi-detectors

The numerical analysis of eigenvalue problem solutions in the multigroup neutron diffusion theory

International Nuclear Information System (INIS)

Woznicki, Z.I.

1994-01-01

The main goal of this paper is to present a general iteration strategy for solving the discrete form of multidimensional neutron diffusion equations equivalent mathematically to an eigenvalue problem. Usually a solution method is based on different levels of iterations. The presented matrix formalism allows us to visualize explicitly how the used matrix splitting influences the matrix structure in an eigenvalue problem to be solved as well as the interdependence between inner and outer iteration within global iterations. Particular interactive strategies are illustrated by numerical results obtained for several reactor problems. (author). 21 refs, 32 figs, 15 tabs

The numerical analysis of eigenvalue problem solutions in the multigroup neutron diffusion theory

Energy Technology Data Exchange (ETDEWEB)

Woznicki, Z I [Institute of Atomic Energy, Otwock-Swierk (Poland)

1994-12-31

The main goal of this paper is to present a general iteration strategy for solving the discrete form of multidimensional neutron diffusion equations equivalent mathematically to an eigenvalue problem. Usually a solution method is based on different levels of iterations. The presented matrix formalism allows us to visualize explicitly how the used matrix splitting influences the matrix structure in an eigenvalue problem to be solved as well as the interdependence between inner and outer iteration within global iterations. Particular interactive strategies are illustrated by numerical results obtained for several reactor problems. (author). 21 refs, 32 figs, 15 tabs.

Neutron transport. Physics and calculation of nuclear reactors with applications to pressurized water reactors and fast neutron reactors. 2 ed.

International Nuclear Information System (INIS)

Bussac, J.; Reuss, P.

1985-01-01

This book presents the main physical bases of neutron theory and nuclear reactor calculation. 1) Interactions of neutrons with matter and basic principles of neutron transport; 2) Neutron transport in homogeneous medium and the neutron field: kinetic behaviour, slowing-down, resonance absorption, diffusion equation, processing methods; 3) Theory of a reactor constituted with homogeneous zones: critical condition, kinetics, separation of variables, calculation and neutron balance of the fundamental mode, one-group and multigroup theories; 4) Study of heterogeneous cell lattices: fast fission factor, resonance absorption, thermal output factor, diffusion coefficient, computer codes; 5) Operation and control of reactors: perturbation theory, reactivity, fuel properties evolution, poisoning by fission products, calculation of a reactor and fuel management; 6) Study of some types of reactors: PWR and fast breeder reactors, the main reactor types of the present French program [fr

Study of fast neutron scattering. The displacement cross-section (1962); Etude de la diffusion des neutrons rapides. Section efficace de deplacement (1962)

Energy Technology Data Exchange (ETDEWEB)

Millot, J P [Commissariat a l' Energie Atomique, Fontenay-aux-Roses (France). Centre d' Etudes Nucleaires

1962-07-01

We propose a method for calculating the biological efficiency of fast neutrons emitted by in-pile fission sources. This method justifies the empirical theory of Albert and Welton. In making simple assumptions concerning the cross-sections, we have supposed that the propagation can ben reduced to a mono-kinetic problem. A system of orthonormal functions is then set up making it possible to calculate the flux leaving a planar source. This method generalises the results obtained by Platzek to the case where the elastic cross-sections are not isotropic, and make it possible in particular to define a displacement cross-section: extension of the diffusion coefficient. This method can be generalised to the case of neutron diffraction as a function of time, and to the study of slowing-down. Numerical results are given in an appendix for the following: H{sub 2}O, D{sub 2}O, Fe, Be, Pb, CH, CH{sub 2}. These cross-sections have been verified experimentally in water and in graphite for neutrons of 2.5 and 14 MeV using a SAMES accelerator and a 2 MeV Van De Graaff. (author) [French] Nous proposons une methode permettant de calculer l'efficacite biologique des neutrons rapides issus des sources de fission dans la protection d'une pile. Cette methode justifie la theorie empirique d'Albert et Welton. En faisant des hypotheses simples sur les sections efficaces, nous avons suppose que la propagation pouvait etre ramenee a un probleme monocinetique. Nous construisons alors un systeme de fonctions orthonormales qui permet de calculer le flux issu d'une source plane. Cette methode generalise les resultats obtenus par Platzek au cas ou les sections efficaces elastiques ne sont pas isotropes et en particulier permet de definir une section efficace de deplacement: extension du coefficient de diffusion. Cette methode peut etre generalisee a la diffusion des neutrons en fonction du temps et a l'etude du ralentissement. Les resultats numeriques sont donnes en annexe pour les corps. H{sub 2

Theory study of global density influence and soils chemical composition at neutron probes response

International Nuclear Information System (INIS)

Crispino, M.L.

1980-06-01

Three energy group diffusion theory is applied to calculate the thermal neutron flux through a soil-water mixture at the neutron source. The soils studies are taken from two horizons of different composition, of a representative soil of the Litoral-Mata Zone of Pernambuco State. The thermal flux is obtained taking into consideration increasing values of the water volume percent, H, and the bulk density of the soil. The cross-sections of the mixture are calculated from the chemical composition of the soils. (author)

TASK, 1-D Multigroup Diffusion or Transport Theory Reactor Kinetics with Delayed Neutron

International Nuclear Information System (INIS)

Buhl, A.R.; Hermann, O.W.; Hinton, R.J.; Dodds, H.L. Jr.; Robinson, J.C.; Lillie, R.A.

1975-01-01

1 - Description of problem or function: TASK solves the one-dimensional multigroup form of the reactor kinetics equations, using either transport or diffusion theory and allowing an arbitrary number of delayed neutron groups. The program can also be used to solve standard static problems efficiently such as eigenvalue problems, distributed source problems, and boundary source problems. Convergence problems associated with sources in highly multiplicative media are circumvented, and such problems are readily calculable. 2 - Method of solution: TASK employs a combination scattering and transfer matrix method to eliminate certain difficulties that arise in classical finite difference approximations. As such, within-group (inner) iterations are eliminated and solution convergence is independent of spatial mesh size. The time variable is removed by Laplace transformation. (A later version will permit direct time solutions.) The code can be run either in an outer iteration mode or in closed (non-iterative) form. The running mode is dictated by the number of groups times the number of angles, consistent with available storage. 3 - Restrictions on the complexity of the problem: The principal restrictions are available storage and computation time. Since the code is flexibly-dimensioned and has an outer iteration option there are no internal restrictions on group structure, quadrature, and number of ordinates. The flexible-dimensioning scheme allows optional use of core storage. The generalized cylindrical geometry option is not complete in Version I of the code. The feedback options and omega-mode search options are not included in Version I

A comparison of certain variational solutions of neutron diffusion equation

International Nuclear Information System (INIS)

Altiparmakov, D.V.; Milgram, M.S.

1987-01-01

Using the R-function theory and the variational method of Kantorovich, an approximate solution of the neutron diffusion equation is constructed for a homogeneous spatial domain of arbitrary shape. Calculations have been carried out by five different types of trial functions for certain characteristic domains of polygonal shape (square, triangle, hexagon, rhombus nad L-shaped domain). In the case of non-convex polygons, the consequence of the R-function solution is very poor and a separate treatment of singularity seems to be necessary. Compared to the R-function solution, the singular function development is mathematically more complicated but superior in respect to convergence rate. (author)

Contribution to the experimental study of the critical scattering of cold neutrons in iron; Contriiution a l'etude experimentale de la diffusion critique des neutrons froids par le fer

Energy Technology Data Exchange (ETDEWEB)

Konstantinovic, J [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1967-03-15

The aim of the present work is a study of magnetic fluctuations which are produced in iron in the neighbourhood of the Curie temperature, by neutron scattering. We start by briefly recalling the theory of scattering of neutrons by magnetic substances and Landau's theory of second order phase transitions which enables one to derive the magnetic cross section near the Curie temperature. Following this is a description of the experimental apparatus after which we present the experimental results. The analysis of the results confirms the four-third law obeyed by the magnetic susceptibility near the Curie point, predicted by recent theories based on the Heisenberg model. However, the analysis reveals a non-zero relaxation time for the magnetic fluctuations at the Curie point, which is in disagreement with theoretical conclusions. (author) [French] L'objet du present travail est l'etude des fluctuations d'aimantation qui prennent naissance dans le fer au voisinage de sa temperature de Curie par la diffusion des neutrons. Nous commencons par rappeler brievement les generalites sur la diffusion des neutrons par les substances magnetiques et la theorie de Landau des transitions de phase du second ordre qui permet de deriver une expression de la section efficace magnetique pres de la temperature de Curie. Ensuite, apres la description du dispositif experimental, nous presentons les resultats experimentaux. L'analyse de ces resultats confirme les theories recentes suivant le modele d'Heisenberg en ce qui concerne la 'loi en 4/3' de la susceptibilite magnetique au voisinage du point de Curie; mais par ailleurs elle revele l'existence d'un temps de relaxation des fluctuations d'aimantation non nul en ce point, ce qui est en desaccord avec les previsions theoriques actuelles. (auteur)

Research on GPU-accelerated algorithm in 3D finite difference neutron diffusion calculation method

International Nuclear Information System (INIS)

Xu Qi; Yu Ganglin; Wang Kan; Sun Jialong

2014-01-01

In this paper, the adaptability of the neutron diffusion numerical algorithm on GPUs was studied, and a GPU-accelerated multi-group 3D neutron diffusion code based on finite difference method was developed. The IAEA 3D PWR benchmark problem was calculated in the numerical test. The results demonstrate both high efficiency and adequate accuracy of the GPU implementation for neutron diffusion equation. (authors)

Determination of neutron buildup factor using analytical solution of one-dimensional neutron diffusion equation in cylindrical geometry

Energy Technology Data Exchange (ETDEWEB)

Fernandes, Julio Cesar L.; Vilhena, Marco Tullio, E-mail: julio.lombaldo@ufrgs.b, E-mail: vilhena@pq.cnpq.b [Universidade Federal do Rio Grande do Sul (DMPA/UFRGS), Porto Alegre, RS (Brazil). Dept. de Matematica Pura e Aplicada. Programa de Pos Graduacao em Matematica Aplicada; Borges, Volnei; Bodmann, Bardo Ernest, E-mail: bardo.bodmann@ufrgs.b, E-mail: borges@ufrgs.b [Universidade Federal do Rio Grande do Sul (PROMEC/UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica

2011-07-01

The principal idea of this work, consist on formulate an analytical method to solved problems for diffusion of neutrons with isotropic scattering in one-dimensional cylindrical geometry. In this area were develop many works that study the same problem in different system of coordinates as well as cartesian system, nevertheless using numerical methods to solve the shielding problem. In view of good results in this works, we starting with the idea that we can represent a source in the origin of the cylindrical system by a Delta Dirac distribution, we describe the physical modeling and solved the neutron diffusion equation inside of cylinder of radius R. For the case of transport equation, the formulation of discrete ordinates S{sub N} consists in discretize the angular variables in N directions and in using a quadrature angular set for approximate the sources of scattering, where the Diffusion equation consist on S{sub 2} approximated transport equation in discrete ordinates. We solved the neutron diffusion equation with an analytical form by the finite Hankel transform. Was presented also the build-up factor for the case that we have neutron flux inside the cylinder. (author)

Determination of neutron buildup factor using analytical solution of one-dimensional neutron diffusion equation in cylindrical geometry

International Nuclear Information System (INIS)

Fernandes, Julio Cesar L.; Vilhena, Marco Tullio; Borges, Volnei; Bodmann, Bardo Ernest

2011-01-01

The principal idea of this work, consist on formulate an analytical method to solved problems for diffusion of neutrons with isotropic scattering in one-dimensional cylindrical geometry. In this area were develop many works that study the same problem in different system of coordinates as well as cartesian system, nevertheless using numerical methods to solve the shielding problem. In view of good results in this works, we starting with the idea that we can represent a source in the origin of the cylindrical system by a Delta Dirac distribution, we describe the physical modeling and solved the neutron diffusion equation inside of cylinder of radius R. For the case of transport equation, the formulation of discrete ordinates S N consists in discretize the angular variables in N directions and in using a quadrature angular set for approximate the sources of scattering, where the Diffusion equation consist on S 2 approximated transport equation in discrete ordinates. We solved the neutron diffusion equation with an analytical form by the finite Hankel transform. Was presented also the build-up factor for the case that we have neutron flux inside the cylinder. (author)

A numerical study of the eigenvalues in the neutron diffusion theory

International Nuclear Information System (INIS)

Lima Bezerra, J. de.

1982-12-01

A systematic numerical study for the eigenvalue problem in one dimension was carried out. A computer code RED2G was developed to obtain and to discuss a number of numerical solutions concerning eigenvalues problems originating from the discretization of the two groups neutron diffusion equation in one dimension and steady state. The problem of eigenvalues was created from the discretization by the method of finite differences. The solutions were obtained by four different iterative methods, i.e. Power, Wielandt-1, Wielandt-2 and accelerated Power with the Chebyshev polinomials. The numerical results given by the solution of the two test-problems indicate that the RED2G code is fast and efficient in these calculations and the Wielandt-2 method has been found to be the best both in respect of rapidity of calculations as well as programation effort required. (E.G.) [pt

Fast solution of neutron diffusion problem by reduced basis finite element method

International Nuclear Information System (INIS)

Chunyu, Zhang; Gong, Chen

2018-01-01

Highlights: •An extremely efficient method is proposed to solve the neutron diffusion equation with varying the cross sections. •Three orders of speedup is achieved for IAEA benchmark problems. •The method may open a new possibility of efficient high-fidelity modeling of large scale problems in nuclear engineering. -- Abstract: For the important applications which need carry out many times of neutron diffusion calculations such as the fuel depletion analysis and the neutronics-thermohydraulics coupling analysis, fast and accurate solutions of the neutron diffusion equation are demanding but necessary. In the present work, the certified reduced basis finite element method is proposed and implemented to solve the generalized eigenvalue problems of neutron diffusion with variable cross sections. The order reduced model is built upon high-fidelity finite element approximations during the offline stage. During the online stage, both the k eff and the spatical distribution of neutron flux can be obtained very efficiently for any given set of cross sections. Numerical tests show that a speedup of around 1100 is achieved for the IAEA two-dimensional PWR benchmark problem and a speedup of around 3400 is achieved for the three-dimensional counterpart with the fission cross-sections, the absorption cross-sections and the scattering cross-sections treated as parameters.

Neutron transport in hexagonal reactor cores modeled by trigonal-geometry diffusion and simplified P{sub 3} nodal methods

Energy Technology Data Exchange (ETDEWEB)

Duerigen, Susan

2013-05-15

The superior advantage of a nodal method for reactor cores with hexagonal fuel assemblies discretized as cells consisting of equilateral triangles is its mesh refinement capability. In this thesis, a diffusion and a simplified P{sub 3} (or SP{sub 3}) neutron transport nodal method are developed based on trigonal geometry. Both models are implemented in the reactor dynamics code DYN3D. As yet, no other well-established nodal core analysis code comprises an SP{sub 3} transport theory model based on trigonal meshes. The development of two methods based on different neutron transport approximations but using identical underlying spatial trigonal discretization allows a profound comparative analysis of both methods with regard to their mathematical derivations, nodal expansion approaches, solution procedures, and their physical performance. The developed nodal approaches can be regarded as a hybrid NEM/AFEN form. They are based on the transverse-integration procedure, which renders them computationally efficient, and they use a combination of polynomial and exponential functions to represent the neutron flux moments of the SP{sub 3} and diffusion equations, which guarantees high accuracy. The SP{sub 3} equations are derived in within-group form thus being of diffusion type. On this basis, the conventional diffusion solver structure can be retained also for the solution of the SP{sub 3} transport problem. The verification analysis provides proof of the methodological reliability of both trigonal DYN3D models. By means of diverse hexagonal academic benchmark and realistic detailed-geometry full-transport-theory problems, the superiority of the SP{sub 3} transport over the diffusion model is demonstrated in cases with pronounced anisotropy effects, which is, e.g., highly relevant to the modeling of fuel assemblies comprising absorber material.

Enhanced finite difference scheme for the neutron diffusion equation using the importance function

International Nuclear Information System (INIS)

Vagheian, Mehran; Vosoughi, Naser; Gharib, Morteza

2016-01-01

Highlights: • An enhanced finite difference scheme for the neutron diffusion equation is proposed. • A seven-step algorithm is considered based on the importance function. • Mesh points are distributed through entire reactor core with respect to the importance function. • The results all proved that the proposed algorithm is highly efficient. - Abstract: Mesh point positions in Finite Difference Method (FDM) of discretization for the neutron diffusion equation can remarkably affect the averaged neutron fluxes as well as the effective multiplication factor. In this study, by aid of improving the mesh point positions, an enhanced finite difference scheme for the neutron diffusion equation is proposed based on the neutron importance function. In order to determine the neutron importance function, the adjoint (backward) neutron diffusion calculations are performed in the same procedure as for the forward calculations. Considering the neutron importance function, the mesh points can be improved through the entire reactor core. Accordingly, in regions with greater neutron importance, density of mesh elements is higher than that in regions with less importance. The forward calculations are then performed for both of the uniform and improved non-uniform mesh point distributions and the results (the neutron fluxes along with the corresponding eigenvalues) for the two cases are compared with each other. The results are benchmarked against the reference values (with fine meshes) for Kang and Rod Bundle BWR benchmark problems. These benchmark cases revealed that the improved non-uniform mesh point distribution is highly efficient.

Application of synthetic diffusion method in the numerical solution of the equations of neutron transport in slab geometry

International Nuclear Information System (INIS)

Valdes Parra, J.J.

1986-01-01

One of the main problems in reactor physics is to determine the neutron distribution in reactor core, since knowing that, it is possible to calculate the rapidity of occurrence of different nuclear reaction inside the reactor core. Within different theories existing in nuclear reactor physics, is neutron transport the one in which equation who govern the exact behavior of neutronic distribution are developed even inside the proper neutron transport theory, there exist different methods of solution which are approximations to exact solution; still more, with the purpose to reach a more precise solution, the majority of methods have been approached to the obtention of solutions in numerical form with the aim of take the advantages of modern computers, and for this reason a great deal of effort is dedicated to numerical solution of the equations of neutron transport. In agreement with the above mentioned, in this work has been developed a computer program which uses a relatively new techniques known as 'acceleration of synthetic diffusion' which has been applied to solve the neutron transport equation with 'classical schemes of spatial integration' obtaining results with a smaller quantity of interactions, if they compare to done without using such equation (Author)

Measurement of the diffusion length of thermal neutrons inside graphite; Mesure de la longueur de diffusion des neutrons thermiques dans le graphite

Energy Technology Data Exchange (ETDEWEB)

Ertaud, A; Beauge, R; Fauquez, H; De Laboulay, H; Mercier, C; Vautrey, L

1948-11-01

The diffusion length of thermal neutrons inside a given industrial graphite is determined by measuring the neutron density inside a parallelepipedal piling up of graphite bricks (2.10 x 2.10 x 2.442 m). A 3.8 curies (Ra {alpha} {yields} Be) source is placed inside the parallelepipedal block of graphite and thin manganese detectors are used. Corrections are added to the unweighted measurements to take into account the effects of the damping of supra-thermal neutrons in the measurement area. These corrections are experimentally deduced from the differential measurements made with a cadmium screen interposed between the source and the first plane of measurement. An error analysis completes the report. The diffusion length obtained is: L = 45.7 cm {+-} 0.3. The average density of the graphite used is 1.76 and the average apparent density of the piling up is 1.71. (J.S.)

Determination of diffusion parameters of Thermal neutrons for non-moderator media by a pulsed method and a time independent method

International Nuclear Information System (INIS)

Boufraqech, A.

1991-01-01

Two methods for determining the diffusion parameters of thermal neutrons for non-moderator and non-multiplicator media have been developped: The first one, which is a pulsed method, is based on thermal neutrons relaxation coefficients measurement in a moderator, with and without the medium of interest that plays the role of reflector. For the experimental results interpretation using the diffusion theory, a corrective factor which takes into account the neutron cooling by diffusion has been introduced. Its dependence on the empirically obtained relaxation coefficients is in a good agreement with the calculations made in P3L2 approximation. The difference between linear extrapolation lengths of the moderator and the reflector has been taken into account, by developping the scalar fluxes in Bessel function series which automatically satisfy the boundary conditions at the extra-polated surfaces of the two media. The obtained results for Iron are in a good agreement with those in the literature. The second method is time independent, based on the 'flux albedo' measurements interpretation (Concept introduced by Amaldi and Fermi) by P3 approximation in the one group trans-port theory. The independent sources are introduced in the Marshak boundary conditions. An angular albedo matrix has been used to deal with multiple reflections and to take into account the distortion of the current vector when entring a medium, after being reflected by this latter. The results obtained by this method are slightly different from those given in the literature. The analysis of the possible sources causing this discrepancy, particulary the radial distribution of flux in cylindrical geometry and the flux depression at medium-black body interface, has shown that the origin of this discrepancy is the neutron heating by diffusion. 47 figs., 20 tabs., 39 refs. (author)

Multi-group neutron transport theory

International Nuclear Information System (INIS)

Zelazny, R.; Kuszell, A.

1962-01-01

Multi-group neutron transport theory. In the paper the general theory of the application of the K. M. Case method to N-group neutron transport theory in plane geometry is given. The eigenfunctions (distributions) for the system of Boltzmann equations have been derived and the completeness theorem has been proved. By means of general solution two examples important for reactor and shielding calculations are given: the solution of a critical and albedo problem for a slab. In both cases the system of singular integral equations for expansion coefficients into a full set of eigenfunction distributions has been reduced to the system of Fredholm-type integral equations. Some results can be applied also to some spherical problems. (author) [fr

Solution of two energy-group neutron diffusion equation by triangular elements

International Nuclear Information System (INIS)

Correia Filho, A.

1981-01-01

The application of the triangular finite elements of first order in the solution of two energy-group neutron diffusion equation in steady-state conditions is aimed at. The EFTDN (triangular finite elements in neutrons diffusion) computer code in FORTRAN IV language is developed. The discrete formulation of the diffusion equation is obtained applying the Galerkin method. The power method is used to solve the eigenvalues' problem and the convergence is accelerated through the use of Chebshev polynomials. For the equation systems solution the Gauss method is applied. The results of the analysis of two test-problems are presented. (Author) [pt

Multi-group diffusion perturbation calculation code. PERKY (2002)

Energy Technology Data Exchange (ETDEWEB)

Iijima, Susumu; Okajima, Shigeaki [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment

2002-12-01

Perturbation calculation code based on the diffusion theory ''PERKY'' is designed for nuclear characteristic analyses of fast reactor. The code calculates reactivity worth on the multi-group diffusion perturbation theory in two or three dimensional core model and kinetics parameters such as effective delayed neutron fraction, prompt neutron lifetime and absolute reactivity scale factor ({rho}{sub 0} {delta}k/k) for FCA experiments. (author)

Chapman--Enskog approach to flux-limited diffusion theory

International Nuclear Information System (INIS)

Levermore, C.D.

1979-01-01

Using the technique developed by Chapman and Enskog for deriving the Navier--Stokes equations from the Boltzmann equation, a framework is set up for deriving diffusion theories from the transport equation. The procedure is first applied to give a derivation of isotropic diffusion theory and then of a completely new theory which is naturally flux-limited. This new flux-limited diffusion theory is then compared with asymptotic diffusion theory

Determination of thermal neutrons diffusion length in graphite

International Nuclear Information System (INIS)

Garcia Fite, J.

1959-01-01

The diffusion length of thermal neutrons in graphite using the less possible quantity of material has been determined. The proceeding used was the measurement in a graphite pile which has a punctual source of rapid neutrons inside surrounded by a reflector medium (paraffin or water). The measurement was done in the following conditions: a) introducing an aluminium plate between both materials. b) Introducing a cadmium plate between both materials. (Author) 91 refs

Exact and approximate interior corner problem in neutron diffusion by integral transform methods

International Nuclear Information System (INIS)

Bareiss, E.H.; Chang, K.S.J.; Constatinescu, D.A.

1976-09-01

The mathematical solution of the neutron diffusion equation exhibits singularities in its derivatives at material corners. A mathematical treatment of the nature of these singularities and its impact on coarse network approximation methods in computational work is presented. The mathematical behavior is deduced from Green's functions, based on a generalized theory for two space dimensions, and the resulting systems of integral equations, as well as from the Kontorovich--Lebedev Transform. The effect on numerical calculations is demonstrated for finite difference and finite element methods for a two-region corner problem

Nodal spectrum method for solving neutron diffusion equation

International Nuclear Information System (INIS)

Sanchez, D.; Garcia, C. R.; Barros, R. C. de; Milian, D.E.

1999-01-01

Presented here is a new numerical nodal method for solving static multidimensional neutron diffusion equation in rectangular geometry. Our method is based on a spectral analysis of the nodal diffusion equations. These equations are obtained by integrating the diffusion equation in X, Y directions and then considering flat approximations for the current. These flat approximations are the only approximations that are considered in this method, as a result the numerical solutions are completely free from truncation errors. We show numerical results to illustrate the methods accuracy for coarse mesh calculations

Quasielastic neutron scattering in biology: Theory and applications.

Science.gov (United States)

Vural, Derya; Hu, Xiaohu; Lindner, Benjamin; Jain, Nitin; Miao, Yinglong; Cheng, Xiaolin; Liu, Zhuo; Hong, Liang; Smith, Jeremy C

2017-01-01

Neutrons scatter quasielastically from stochastic, diffusive processes, such as overdamped vibrations, localized diffusion and transitions between energy minima. In biological systems, such as proteins and membranes, these relaxation processes are of considerable physical interest. We review here recent methodological advances and applications of quasielastic neutron scattering (QENS) in biology, concentrating on the role of molecular dynamics simulation in generating data with which neutron profiles can be unambiguously interpreted. We examine the use of massively-parallel computers in calculating scattering functions, and the application of Markov state modeling. The decomposition of MD-derived neutron dynamic susceptibilities is described, and the use of this in combination with NMR spectroscopy. We discuss dynamics at very long times, including approximations to the infinite time mean-square displacement and nonequilibrium aspects of single-protein dynamics. Finally, we examine how neutron scattering and MD can be combined to provide information on lipid nanodomains. This article is part of a Special Issue entitled "Science for Life" Guest Editor: Dr. Austen Angell, Dr. Salvatore Magazù and Dr. Federica Migliardo. Copyright © 2016 Elsevier B.V. All rights reserved.

One dimensional benchmark calculations using diffusion theory

International Nuclear Information System (INIS)

Ustun, G.; Turgut, M.H.

1986-01-01

This is a comparative study by using different one dimensional diffusion codes which are available at our Nuclear Engineering Department. Some modifications have been made in the used codes to fit the problems. One of the codes, DIFFUSE, solves the neutron diffusion equation in slab, cylindrical and spherical geometries by using 'Forward elimination- Backward substitution' technique. DIFFUSE code calculates criticality, critical dimensions and critical material concentrations and adjoint fluxes as well. It is used for the space and energy dependent neutron flux distribution. The whole scattering matrix can be used if desired. Normalisation of the relative flux distributions to the reactor power, plotting of the flux distributions and leakage terms for the other two dimensions have been added. Some modifications also have been made for the code output. Two Benchmark problems have been calculated with the modified version and the results are compared with BBD code which is available at our department and uses same techniques of calculation. Agreements are quite good in results such as k-eff and the flux distributions for the two cases studies. (author)

Diffusion Parameters of BeO by the Pulsed Neutron Method

International Nuclear Information System (INIS)

Joshi, B.V.; Nargundkar, V.R.; Subbarao, K.

1965-01-01

The use of the pulsed neutron method for the precise determination of the diffusion parameters of moderators is described. The diffusion parameters of BeO have been obtained by this method. The neutron bursts were produced from a cascade accelerator by pulsing the ion source and using the Be (d, n) reaction. The detector was an enriched boron trifluoride proportional counter. It is shown that by a proper choice of the counter position arid length, and the source position, most of the space harmonics can be eliminated. Any constant background can be accounted for in the calculation of the decay constant. Very large bucklings were not used to avoid time harmonics. Any remaining harmonic content was rendered ineffective by the use of adequate time delay. The decay constant of the fundamental mode of the thermal neutron population was determined for several bucklings. Conditions to be satisfied for an accurate determination of the diffusion cooling constant C are discussed. The following values are obtained for BeO: λ 0 = absorption constant = 156.02 ± 4.37 s -1 D = diffusion coefficient = (1.3334 ± 0.0128) x 10 5 cm 2 /s C = diffusion cooling constant = (-4.8758 ± 0.5846) x 10 5 cm 4 /s. The effect of neglecting the contribution of the B 6 term on the determination of the diffusion parameters was estimated and is shown to be considerable. The reason for the longstanding discrepancy between the values of C obtained for the same moderator by different workers is attributed to this. (author) [fr

Asymptotic time dependent neutron transport in multidimensional systems

International Nuclear Information System (INIS)

Nagy, M.E.; Sawan, M.E.; Wassef, W.A.; El-Gueraly, L.A.

1983-01-01

A model which predicts the asymptotic time behavior of the neutron distribution in multi-dimensional systems is presented. The model is based on the kernel factorization method used for stationary neutron transport in a rectangular parallelepiped. The accuracy of diffusion theory in predicting the asymptotic time dependence is assessed. The use of neutron pulse experiments for predicting the diffusion parameters is also investigated

Theory of Pulsed Neutron Experiments in Highly Heterogeneous Multiplying Media

International Nuclear Information System (INIS)

Corno, S.E.

1965-01-01

In this work we investigate the time and space dependence of the neutron flux within a highly heterogeneous assembly, in which pulsed or sinusoidally modulated neutrons are injected. We consider, for the sake of simplicity, a device consisting of a cylindrical block of heavy moderator, along the axis of which a line-shaped region of fissionable material is located. The driving neutron source is assumed to be located on one of the end faces of the cylinder. The extent of the fissionable region allows us to deal with it as with an absorbing and multiplying singularity of the neutron field. As our attention is mostly concentrated on space and time variation of the neutron flux, rather crude approximations are assumed as far as the energy dependence of the neutron population is concerned. Within the limits of the age-diffusion theory, the response of the device to any neutron excitation may be found in closed form. For a sinusoidally modulated source of given frequency, it may easily be shown that, if the axial singularity were a purely absorbing one, the neutron waves being propagated along the device would possess a phase shift; a wavelength and an attenuation constant depending on the absorbing properties of the singularity. This picture becomes more and more complicated when neutron multiplication occurs. For this general case the solution derived in our paper obviously turns out to be dependent on both absorption and multiplication properties of the singularity. This circumstance suggests, among others, the idea of using a device of the type described above for testing fuel elements of heterogeneous reactors. (author) [fr

HAMMER, 1-D Multigroup Neutron Transport Infinite System Cell Calculation for Few-Group Diffusion Calculation

International Nuclear Information System (INIS)

Honeck, H.C.

1984-01-01

1 - Description of problem or function: HAMMER performs infinite lattice, one-dimensional cell multigroup calculations, followed (optionally) by one-dimensional, few-group, multi-region reactor calculations with neutron balance edits. 2 - Method of solution: Infinite lattice parameters are calculated by means of multigroup transport theory, composite reactor parameters by few-group diffusion theory. 3 - Restrictions on the complexity of the problem: - Cell calculations - maxima of: 30 thermal groups; 54 epithermal groups; 20 space points; 20 regions; 18 isotopes; 10 mixtures; 3 thermal up-scattering mixtures; 200 resonances per group; no overlap or interference; single level only. - Reactor calculations - maxima of : 40 regions; 40 mixtures; 250 space points; 4 groups

Analysis of critical neutron- scattering data from iron and dynamical scaling theory

DEFF Research Database (Denmark)

Als-Nielsen, Jens Aage

1970-01-01

Experimental three- axis spectrometer data of critical neutron- scattering data from Fe are reanalyzed and compared with the recent theoretical prediction by P. Resibois and C. Piette. The reason why the spin- diffusion parameter did not obey the prediction of dynamical scaling theory is indicated....... Double- axis spectrometer data have previously been interpreted in terms of a non- Lorentzian susceptibility. It is shown that with proper corrections for the inelasticity of the scattering the data are consistent with a Lorentzian form of susceptibility....

Accounting for the thermal neutron flux depression in voluminous samples for instrumental neutron activation analysis

International Nuclear Information System (INIS)

Overwater, R.M.W.; Hoogenboom, J.E.

1994-01-01

At the Delft University of Technology Interfaculty Reactor Institute, a facility has been installed to irradiate cylindrical samples with diameters up to 15 cm and weights up to 50 kg for instrumental neutron activation analysis (INAA) purposes. To be able to do quantitative INAA on voluminous samples, it is necessary to correct for gamma-ray absorption, gamma-ray scattering, neutron absorption, and neutron scattering in the sample. The neutron absorption and the neutron scattering are discussed. An analytical solution is obtained for the diffusion equation in the geometry of the irradiation facility. For samples with known composition, the neutron flux--as a function of position in the sample--can be calculated directly. Those of unknown composition require additional flux measurements on which least-squares fitting must be done to obtain both the thermal neutron diffusion coefficient D s and the diffusion length L s of the sample. Experiments are performed to test the theory

Evaluation of energy collapsing effect on reactor kinetics parameters by diffusion theory

International Nuclear Information System (INIS)

Unesaki, Hironobu

1989-01-01

Reactor kinetics parameters play an important role as scaling factors between observed and calculated reactivities in the analysis of reactor physics experiments. In this report, energy collapsing errors in two kinetic parameters, the effective delayed neutron fraction and the neutron life time, are investigated by means of the diffusion theory. Coarse group calculations are made for various energy group structures. Cores of various moderator-to-fuel volume ratios are selected to investigate the influence of neutron spectrum changes on the energy collapsing error. The energy collapsing errors in the effective delayed neutron fraction and neutron life time are much larger than those in k eff . This might be because the former two parameters are functions of both the foward and adjoint flux, whereas the latter is a function of the forward flux alone. The use of coarse constants will cause errors in both fluxes, and the resulting errors in the former will be much more emphasized. As the effective delayed neutron fraction is sensitive to the treatment of an energy region in the vicinity of the fission spectrum peak, the coarse group error in it might differ between cores with different enrichment and composition. Inaccurate weighting of group constants leads to neutron spectra which do not conserve the fine group spectra, and those errors will be emphasized in calculated integral parameters. (N.K.)

DNS: Diffuse scattering neutron time-of-flight spectrometer

Directory of Open Access Journals (Sweden)

Yixi Su

2015-08-01

Full Text Available DNS is a versatile diffuse scattering instrument with polarisation analysis operated by the Jülich Centre for Neutron Science (JCNS, Forschungszentrum Jülich GmbH, outstation at the Heinz Maier-Leibnitz Zentrum (MLZ. Compact design, a large double-focusing PG monochromator and a highly efficient supermirror-based polarizer provide a polarized neutron flux of about 107 n cm-2 s-1. DNS is used for the studies of highly frustrated spin systems, strongly correlated electrons, emergent functional materials and soft condensed matter.

Theory of the diffusion coefficient of neutrons in a lattice containing cavities; Theorie du coefficient de diffusion des neutrons dans un reseau comportant des cavites

Energy Technology Data Exchange (ETDEWEB)

Benoist, P [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1964-01-15

In an previous publication, a simple and general formulation of the diffusion coefficient, which defines the mode of weighting of the mean free paths of the various media, in introducing the collision probabilities in each medium, was established. This expression is demonstrated again here through a more direct method, and the velocity is introduced; new terms are emphasised, the existence of which implies that the representation of the diffusion area as the mean square of the straight line distance from source to absorption is not correct in a lattice. However these terms are of small enough an order of magnitude to he treated as a correction. The general expression also shows the existence, for the radial coefficient, of the series of angular correlation terms, which is seen to converge very slowly for large channels. The term by term computation which was initiated in the first work was then interrupted and a global formulation, which emphasize a resemblance with the problem of the thermal utilisation factor, was adopted. An integral method, analogous to that use for the computation of this factor, gives the possibility to establish new and simple practical formulae, which require the use of a few basic functions only. These formulae are very accurate, as seen from the results of a variational method which was studied as a reference. Various correction effects are reviewed. Expressions which allow the exact treatment of fuel rod clusters are presented. The theory is confronted with various experimental results, and a new method of measuring the radial coefficient is proposed. (author) [French] Dans une publication anterieure, on a etablie une formulation simple et generale du coefficient de diffusion, qui definit le mode de ponderation des libres parcours des differents milieux constituants en faisant apparaitre les probabilites de collision dans chaque milieu. On redemontre ici cette expression d'une maniere plus directe, tout en introduisant la variable

Evolution of diffusion and dissemination theory.

Science.gov (United States)

Dearing, James W

2008-01-01

The article provides a review and considers how the diffusion of innovations Research paradigm has changed, and offers suggestions for the further development of this theory of social change. Main emphases of diffusion Research studies are compared over time, with special attention to applications of diffusion theory-based concepts as types of dissemination science. A considerable degree of paradigmatic evolution is observed. The classical diffusion model focused on adopter innovativeness, individuals as the locus of decision, communication channels, and adoption as the primary outcome measures in post hoc observational study designs. The diffusion systems in question were centralized, with fidelity of implementation often assumed. Current dissemination Research and practice is better characterized by tests of interventions that operationalize one or more diffusion theory-based concepts and concepts from other change approaches, involve complex organizations as the units of adoption, and focus on implementation issues. Foment characterizes dissemination and implementation Research, Reflecting both its interdisciplinary Roots and the imperative of spreading evidence-based innovations as a basis for a new paradigm of translational studies of dissemination science.

Measurement of the diffusion length of thermal neutrons in the beryllium oxide

International Nuclear Information System (INIS)

Koechlin, J.C.; Martelly, J.; Duggal, V.P.

1955-01-01

The diffusion length of thermal neutrons in the beryllium oxide has been obtained while studying the spatial distribution of the neutrons in a massive parallelepiped of this matter placed before the thermal column of the reactor core of Saclay. The mean density of the beryllium oxide (BeO) is 2,95 gr/cm 3 , the mean density of the massif is 2,92 gr/cm 3 . The value of the diffusion length, deducted of the done measures, is: L = 32,7 ± 0,5 cm (likely gap). Some remarks are formulated about the influence of the spectral distribution of the neutrons flux used. (authors) [fr

Monte Carlo simulation of neutron transport phenomena

International Nuclear Information System (INIS)

Srinivasan, P.

2009-01-01

Neutron transport is one of the central problems in nuclear reactor related studies and other applied sciences. Some of the major applications of neutron transport include nuclear reactor design and safety, criticality safety of fissile material handling, neutron detector design and development, nuclear medicine, assessment of radiation damage to materials, nuclear well logging, forensic analysis etc. Most reactor and dosimetry studies assume that neutrons diffuse from regions of high to low density just like gaseous molecules diffuse to regions of low concentration or heat flow from high to low temperature regions. However while treatment of gaseous or heat diffusion is quite accurately modeled, treatment of neutron transport as simple diffusion is quite limited. In simple diffusion, the neutron trajectories are irregular, random and zigzag - where as in neutron transport low reaction cross sections (1 barn- 10 -24 cm 2 ) lead to long mean free paths which again depend on the nature and irregularities of the medium. Hence a more accurate representation of the neutron transport evolved based on the Boltzmann equation of kinetic gas theory. In fact the neutron transport equation is a linearized version of the Boltzmann gas equation based on neutron conservation with seven independent variables. The transport equation is difficult to solve except in simple cases amenable to numerical methods. The diffusion (equation) approximation follows from removing the angular dependence of the neutron flux

Carmen system: a code block for neutronic PWR calculation by diffusion theory with spacedependent feedback effects

International Nuclear Information System (INIS)

Ahnert, C.; Aragones, J.M.

1982-01-01

The Carmen code (theory and user's manual) is described. This code for assembly and core calculations uses diffusion theory (Citation), with feedback in the cross sections by zone due to the effects of burnup, water density, fuel temperature, Xenon and Samarium. The burnup calculation of a full cycle is solved in only an execution of Carmen, and in a reduced computer time. (auth.)

Measurement of the diffusion length of thermal neutrons inside graphite

International Nuclear Information System (INIS)

Ertaud, A.; Beauge, R.; Fauquez, H.; De Laboulay, H.; Mercier, C.; Vautrey, L.

1948-11-01

The diffusion length of thermal neutrons inside a given industrial graphite is determined by measuring the neutron density inside a parallelepipedal piling up of graphite bricks (2.10 x 2.10 x 2.442 m). A 3.8 curies (Ra α → Be) source is placed inside the parallelepipedal block of graphite and thin manganese detectors are used. Corrections are added to the unweighted measurements to take into account the effects of the damping of supra-thermal neutrons in the measurement area. These corrections are experimentally deduced from the differential measurements made with a cadmium screen interposed between the source and the first plane of measurement. An error analysis completes the report. The diffusion length obtained is: L = 45.7 cm ± 0.3. The average density of the graphite used is 1.76 and the average apparent density of the piling up is 1.71. (J.S.)

Hydrogen rotational and translational diffusion in calcium borohydride from quasielastic neutron scattering and DFT

DEFF Research Database (Denmark)

Blanchard, Didier; Riktor, M.D.; Maronsson, Jon Bergmann

2010-01-01

Hydrogen dynamics in crystalline calcium borohydride can be initiated by long-range diffusion or localized motion such as rotations, librations, and vibrations. Herein, the rotational and translational diffusion were studied by quasielastic neutron scattering (QENS) by using two instruments...... with different time scales in combination with density functional theory (DFT) calculations. Two thermally activated reorientational motions were observed, around the 2-fold (C2) and 3-fold (C3) axes of the BH4− units, at temperature from 95 to 280K. The experimental energy barriers (EaC2 = 0.14 eV and EaC3 = 0...... of the interstitial H2 might come from the synthesis of the compound or a side reaction with trapped synthesis residue leading to the partial oxidation of the compound and hydrogen release....

Dynamical theory of neutron diffraction. [One-body Schroedinger equation, review

Energy Technology Data Exchange (ETDEWEB)

Sears, V F [Atomic Energy of Canada Ltd., Chalk River, Ontario. Chalk River Nuclear Labs.

1978-10-01

We present a review of the dynamical theory of neutron diffraction by macroscopic bodies which provides the theoretical basis for the study of neutron optics. We consider both the theory of dispersion, in which it is shown that the coherent wave in the medium satisfies a macroscopic one-body Schroedinger equation, and the theory of reflection, refraction, and diffraction in which the above equation is solved for a number of special cases of interest. The theory is illustrated with the help of experimental results obtained over the past 10 years by a number of new techniques such as neutron gravity refractometry. Pendelloesung interference, and neutron interferometry.

Thermal diffuse scattering in angular-dispersive neutron diffraction

International Nuclear Information System (INIS)

Popa, N.C.; Willis, B.T.M.

1998-01-01

The theoretical treatment of one-phonon thermal diffuse scattering (TDS) in single-crystal neutron diffraction at fixed incident wavelength is reanalysed in the light of the analysis given by Popa and Willis [Acta Cryst. (1994), (1997)] for the time-of-flight method. Isotropic propagation of sound with different velocities for the longitudinal and transverse modes is assumed. As in time-of-flight diffraction, there exists, for certain scanning variables, a forbidden range in the one-phonon TDS of slower-than-sound neutrons, and this permits the determination of the sound velocity in the crystal. A fast algorithm is given for the TDS correction of neutron diffraction data collected at a fixed wavelength: this algorithm is similar to that reported earlier for the time-of-flight case. (orig.)

Diffuse neutron scattering study of Cu2−xSe

DEFF Research Database (Denmark)

Cava, R. J.; Andersen, Niels Hessel; Clausen, Kurt Nørgaard

1986-01-01

We have measured the diffuse neutron scattering in the hkk plane for Cu2Se and Cu1.8Se at 180°C and 51°C, respectively, in the cubic antifluorite type phase. The diffuse scattering shows significant structure, indicative of correlated short range mobile ion ordering. The short range order is foun...

Diffuse neutron scattering from anion-excess strontium chloride

DEFF Research Database (Denmark)

Goff, J.P.; Clausen, K.N.; Fåk, B.

1992-01-01

The defect structure and diffusional processes have been studied in the anion-excess fluorite (Sr, Y)Cl2.03 by diffuse neutron scattering techniques. Static cuboctahedral clusters found at ambient temperature break up at temperatures below 1050 K, where the anion disorder is highly dynamic. The a...

Chemical shift of neutron resonances and some ideas on neutron resonances and scattering theory

International Nuclear Information System (INIS)

Ignatovich, V.K.; )

2002-01-01

The dependence of positions of neutron resonances in nuclei in condensed matter on chemical environment is considered. A possibility of theoretical description of neutron resonances, different from R-matrix theory is investigated. Some contradictions of standard scattering theory are discussed and a new approach without these contradictions is formulated [ru

Measurement of diffusion length of thermal neutrons in concrete

International Nuclear Information System (INIS)

Moser, M.

2007-04-01

The diffusion length of neutrons with a medium energy < 0.025 eV in concrete were determined using 4π-β detector and gamma detectors. Then it was possible to determine how deep can neutrons penetrate diverse concrete construction parts in a reactor in operation, with this method the dismantling process of a reactor can be planned in terms of what parts can be removed without danger and what parts can be assumed still are activated. (nevyjel)

Theory of the diffusion coefficient of neutrons in a lattice containing cavities; Theorie du coefficient de diffusion des neutrons dans un reseau comportant des cavites

Energy Technology Data Exchange (ETDEWEB)

Benoist, P. [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1964-01-15

In an previous publication, a simple and general formulation of the diffusion coefficient, which defines the mode of weighting of the mean free paths of the various media, in introducing the collision probabilities in each medium, was established. This expression is demonstrated again here through a more direct method, and the velocity is introduced; new terms are emphasised, the existence of which implies that the representation of the diffusion area as the mean square of the straight line distance from source to absorption is not correct in a lattice. However these terms are of small enough an order of magnitude to he treated as a correction. The general expression also shows the existence, for the radial coefficient, of the series of angular correlation terms, which is seen to converge very slowly for large channels. The term by term computation which was initiated in the first work was then interrupted and a global formulation, which emphasize a resemblance with the problem of the thermal utilisation factor, was adopted. An integral method, analogous to that use for the computation of this factor, gives the possibility to establish new and simple practical formulae, which require the use of a few basic functions only. These formulae are very accurate, as seen from the results of a variational method which was studied as a reference. Various correction effects are reviewed. Expressions which allow the exact treatment of fuel rod clusters are presented. The theory is confronted with various experimental results, and a new method of measuring the radial coefficient is proposed. (author) [French] Dans une publication anterieure, on a etablie une formulation simple et generale du coefficient de diffusion, qui definit le mode de ponderation des libres parcours des differents milieux constituants en faisant apparaitre les probabilites de collision dans chaque milieu. On redemontre ici cette expression d'une maniere plus directe, tout en introduisant la variable

Neutron star structure: Theory, observation, and speculation

International Nuclear Information System (INIS)

Pandharipande, V.R.; Pines, D.; Smith, R.A.

1976-01-01

The broad physical aspects of the neutron-neutron interaction in dense matter are reviewed, and an examination is made of the extent to which the equation of state of neutron star matter is influenced by phase transitions which have been proposed for the high-density regime. The dependence of the maximum neutron star mass and the stellar structure on the neutron-neutron interaction is studied through calculations of the equation of state of neutron matter based on four different models for this interaction: the Reid (R) and Bethe-Johnson (BJ) models, a tensor-interaction (TI) model which assumes that the attraction between nucleons comes from the higher order contribution of the pion-exchange tensor interaction, and a mean field (MF) model which assumes that all the attraction between nucleons is due to the exchange of an effective scalar meson. It is shown that the harder equations of state which result from the BJ, TI, and MF models give rise to significant modifications in the structure of neutron stars; heavy neutron stars (approximately-greater-than1 M/sub sun/) have both larger radii and thicker crusts than were predicted using the R model.These stars are used as a basis for comparing theory with observation for the mass and structure of neutron stars such as the Crab and Vela pulsars, and the compact X-ray sources Her X-1 and Vela X-1. We find that both theory and observation tend to favor an equation of state that is stiff in the region of 10 14 --10 15 g cm -3 and that a neutron star such as Her X-1 (Mapprox.1.3 M/sub sun/) has a radius of the order of 15 km with a crust thickness of order 5 km. Based on starquake theory, it is concluded that the Crab pulsar could have a mass as large as 1.3 M/sub sun/, with a critical strain angle approx.10 -3 , comparable to that suggested for Her X-1. The possibility of solid-core neutron stars and some of their observational consequences is discussed

Linear stochastic neutron transport theory

International Nuclear Information System (INIS)

Lewins, J.

1978-01-01

A new and direct derivation of the Bell-Pal fundamental equation for (low power) neutron stochastic behaviour in the Boltzmann continuum model is given. The development includes correlation of particle emission direction in induced and spontaneous fission. This leads to generalizations of the backward and forward equations for the mean and variance of neutron behaviour. The stochastic importance for neutron transport theory is introduced and related to the conventional deterministic importance. Defining equations and moment equations are derived and shown to be related to the backward fundamental equation with the detector distribution of the operational definition of stochastic importance playing the role of an adjoint source. (author)

SYN3D: a single-channel, spatial flux synthesis code for diffusion theory calculations

Energy Technology Data Exchange (ETDEWEB)

Adams, C. H.

1976-07-01

This report is a user's manual for SYN3D, a computer code which uses single-channel, spatial flux synthesis to calculate approximate solutions to two- and three-dimensional, finite-difference, multigroup neutron diffusion theory equations. SYN3D is designed to run in conjunction with any one of several one- and two-dimensional, finite-difference codes (required to generate the synthesis expansion functions) currently being used in the fast reactor community. The report describes the theory and equations, the use of the code, and the implementation on the IBM 370/195 and CDC 7600 of the version of SYN3D available through the Argonne Code Center.

SYN3D: a single-channel, spatial flux synthesis code for diffusion theory calculations

International Nuclear Information System (INIS)

Adams, C.H.

1976-07-01

This report is a user's manual for SYN3D, a computer code which uses single-channel, spatial flux synthesis to calculate approximate solutions to two- and three-dimensional, finite-difference, multigroup neutron diffusion theory equations. SYN3D is designed to run in conjunction with any one of several one- and two-dimensional, finite-difference codes (required to generate the synthesis expansion functions) currently being used in the fast reactor community. The report describes the theory and equations, the use of the code, and the implementation on the IBM 370/195 and CDC 7600 of the version of SYN3D available through the Argonne Code Center

Thermal neutron diffusion parameters dependent on the flux energy distribution in finite hydrogenous media

International Nuclear Information System (INIS)

Drozdowicz, K.

1999-01-01

Macroscopic parameters for a description of the thermal neutron transport in finite volumes are considered. A very good correspondence between the theoretical and experimental parameters of hydrogenous media is attained. Thermal neutrons in the medium possess an energy distribution, which is dependent on the size (characterized by the geometric buckling) and on the neutron transport properties of the medium. In a hydrogenous material the thermal neutron transport is dominated by the scattering cross section which is strongly dependent on energy. A monoenergetic treatment of the thermal neutron group (admissible for other materials) leads in this case to a discrepancy between theoretical and experimental results. In the present paper the theoretical definitions of the pulsed thermal neutron parameters (the absorption rate, the diffusion coefficient, and the diffusion cooling coefficient) are based on Nelkin's analysis of the decay of a neutron pulse. Problems of the experimental determination of these parameters for a hydrogenous medium are discussed. A theoretical calculation of the pulsed parameters requires knowledge of the scattering kernel. For thermal neutrons it is individual for each hydrogenous material because neutron scattering on hydrogen nuclei bound in a molecule is affected by the molecular dynamics (characterized with internal energy modes which are comparable to the incident neutron energy). Granada's synthetic model for slow-neutron scattering is used. The complete up-dated formalism of calculation of the energy transfer scattering kernel after this model is presented in the paper. An influence of some minor variants within the model on the calculated differential and integral neutron parameters is shown. The theoretical energy-dependent scattering cross section (of Plexiglas) is compared to experimental results. A particular attention is paid to the calculation of the diffusion cooling coefficient. A solution of an equation, which determines the

Parallel diffusion length on thermal neutrons in rod type lattices

International Nuclear Information System (INIS)

Ahmed, T.; Siddiqui, S.A.M.M.; Khan, A.M.

1981-11-01

Calculation of diffusion lengths of thermal neutrons in lead-water and aluminum water lattices in direction parallel to the rods are performed using one group diffusion equation together with Shevelev transport correction. The formalism is then applied to two practical cases, the Kawasaki (Hitachi) and the Douglas point (Candu) reactor lattices. Our results are in good agreement with the observed values. (author)

Benchmarking a first-principles thermal neutron scattering law for water ice with a diffusion experiment

Directory of Open Access Journals (Sweden)

Holmes Jesse

2017-01-01

Full Text Available The neutron scattering properties of water ice are of interest to the nuclear criticality safety community for the transport and storage of nuclear materials in cold environments. The common hexagonal phase ice Ih has locally ordered, but globally disordered, H2O molecular orientations. A 96-molecule supercell is modeled using the VASP ab initio density functional theory code and PHONON lattice dynamics code to calculate the phonon vibrational spectra of H and O in ice Ih. These spectra are supplied to the LEAPR module of the NJOY2012 nuclear data processing code to generate thermal neutron scattering laws for H and O in ice Ih in the incoherent approximation. The predicted vibrational spectra are optimized to be representative of the globally averaged ice Ih structure by comparing theoretically calculated and experimentally measured total cross sections and inelastic neutron scattering spectra. The resulting scattering kernel is then supplied to the MC21 Monte Carlo transport code to calculate time eigenvalues for the fundamental mode decay in ice cylinders at various temperatures. Results are compared to experimental flux decay measurements for a pulsed-neutron die-away diffusion benchmark.

GPU-accelerated 3D neutron diffusion code based on finite difference method

Energy Technology Data Exchange (ETDEWEB)

Xu, Q.; Yu, G.; Wang, K. [Dept. of Engineering Physics, Tsinghua Univ. (China)

2012-07-01

Finite difference method, as a traditional numerical solution to neutron diffusion equation, although considered simpler and more precise than the coarse mesh nodal methods, has a bottle neck to be widely applied caused by the huge memory and unendurable computation time it requires. In recent years, the concept of General-Purpose computation on GPUs has provided us with a powerful computational engine for scientific research. In this study, a GPU-Accelerated multi-group 3D neutron diffusion code based on finite difference method was developed. First, a clean-sheet neutron diffusion code (3DFD-CPU) was written in C++ on the CPU architecture, and later ported to GPUs under NVIDIA's CUDA platform (3DFD-GPU). The IAEA 3D PWR benchmark problem was calculated in the numerical test, where three different codes, including the original CPU-based sequential code, the HYPRE (High Performance Pre-conditioners)-based diffusion code and CITATION, were used as counterpoints to test the efficiency and accuracy of the GPU-based program. The results demonstrate both high efficiency and adequate accuracy of the GPU implementation for neutron diffusion equation. A speedup factor of about 46 times was obtained, using NVIDIA's Geforce GTX470 GPU card against a 2.50 GHz Intel Quad Q9300 CPU processor. Compared with the HYPRE-based code performing in parallel on an 8-core tower server, the speedup of about 2 still could be observed. More encouragingly, without any mathematical acceleration technology, the GPU implementation ran about 5 times faster than CITATION which was speeded up by using the SOR method and Chebyshev extrapolation technique. (authors)

GPU-accelerated 3D neutron diffusion code based on finite difference method

International Nuclear Information System (INIS)

Xu, Q.; Yu, G.; Wang, K.

2012-01-01

Finite difference method, as a traditional numerical solution to neutron diffusion equation, although considered simpler and more precise than the coarse mesh nodal methods, has a bottle neck to be widely applied caused by the huge memory and unendurable computation time it requires. In recent years, the concept of General-Purpose computation on GPUs has provided us with a powerful computational engine for scientific research. In this study, a GPU-Accelerated multi-group 3D neutron diffusion code based on finite difference method was developed. First, a clean-sheet neutron diffusion code (3DFD-CPU) was written in C++ on the CPU architecture, and later ported to GPUs under NVIDIA's CUDA platform (3DFD-GPU). The IAEA 3D PWR benchmark problem was calculated in the numerical test, where three different codes, including the original CPU-based sequential code, the HYPRE (High Performance Pre-conditioners)-based diffusion code and CITATION, were used as counterpoints to test the efficiency and accuracy of the GPU-based program. The results demonstrate both high efficiency and adequate accuracy of the GPU implementation for neutron diffusion equation. A speedup factor of about 46 times was obtained, using NVIDIA's Geforce GTX470 GPU card against a 2.50 GHz Intel Quad Q9300 CPU processor. Compared with the HYPRE-based code performing in parallel on an 8-core tower server, the speedup of about 2 still could be observed. More encouragingly, without any mathematical acceleration technology, the GPU implementation ran about 5 times faster than CITATION which was speeded up by using the SOR method and Chebyshev extrapolation technique. (authors)

Interpretation of the quasi-elastic neutron scattering on PAA by rotational diffusion models

International Nuclear Information System (INIS)

Bata, L.; Vizi, J.; Kugler, S.

1974-10-01

First the most important data determined by other methods for para azoxy anisolon (PAA) are collected. This molecule makes a rotational oscillational motion around the mean molecular direction. The details of this motion can be determined by inelastic neutron scattering. Quasielastic neutron scattering measurements were carried out without orienting magnetic field on a time-of-flight facility with neutron beam of 4.26 meV. For the interpretation of the results two models, the spherical rotation diffusion model and the circular random walk model are investigated. The comparison shows that the circular random walk model (with N=8 sites, d=4A diameter and K=10 10 s -1 rate constant) fits very well with the quasi-elastic neutron scattering, while the spherical rotational diffusion model seems to be incorrect. (Sz.N.Z.)

Theory of neutron star magnetospheres

CERN Document Server

Curtis Michel, F

1990-01-01

An incomparable reference for astrophysicists studying pulsars and other kinds of neutron stars, "Theory of Neutron Star Magnetospheres" sums up two decades of astrophysical research. It provides in one volume the most important findings to date on this topic, essential to astrophysicists faced with a huge and widely scattered literature. F. Curtis Michel, who was among the first theorists to propose a neutron star model for radio pulsars, analyzes competing models of pulsars, radio emission models, winds and jets from pulsars, pulsating X-ray sources, gamma-ray burst sources, and other neutron-star driven phenomena. Although the book places primary emphasis on theoretical essentials, it also provides a considerable introduction to the observational data and its organization. Michel emphasizes the problems and uncertainties that have arisen in the research as well as the considerable progress that has been made to date.

Fast neutron irradiation effects on diffusion processes in the aluminum-magnesium system; Effets de l'irradiation aux neutrons rapides sur les phenomenes lies a la diffusion dans le systeme aluminium-magnesium

Energy Technology Data Exchange (ETDEWEB)

Moreau, G [Commissariat a l' Energie Atomique, Fontenay-aux-Roses (France). Centre d' Etudes Nucleaires

1969-06-01

Examination of bulky diffusion couples Al (Mg) - Al and Mg (Al) - Mg handled in same thermal conditions (between 200 and 440 C) out of pile and under fast neutron irradiation show, in the latter case: 1 - An increase of the growth kinetics of {beta} phase which can be explained with KIDSON' s formula. 2 - An apparent increase of solubility caused by migration of a part of excess vacancies as complexes (vacancy - solute atom) to sinks (stacking faults, grain boundaries) or to sub-microscopical clusters. 3 - An enhancement of chemical diffusion at low temperature. At infinite dilution, chemical diffusion coefficient of Mg in Al can be expressed in normal conditions as: D = 1 exp(- 31000/RT {+-} 1200/RT cal/mole) cm{sup 2}.s{sup -1} and under irradiation as: D = 8.10{sup -3} exp(-24500/RT {+-} 1200/RT cal/mole) cm{sup 2}.s{sup -1}. Interpretation can be carried out by DIENES and Damask's theory. Excess defects (vacancies and interstitials generated in equal numbers by radiation) annihilate by migration to sinks and by direct recombination. Sinks density varies with temperature and irradiation time. The part of complexes (vacancy-solute atom) is important in the vacancies annealing kinetics. (author) [French] L'examen de couples de diffusion massifs Al (Mg) - Al et Mg (Al) - Mg traites dans les memes conditions thermiques (entre 200 et 440 C) hors pile et sous flux de neutrons rapides montre dans le dernier cas: 1 - Une acceleration de la cinetique de croissance de la phase {beta} a basse temperature dont on peut rendre compte a l'aide de la formule de KIDSON. 2 - Une augmentation apparente de la solubilite due a l'elimination d'une partie des lacunes en exces sous forme de complexes (lacune -solute) sur des pieges (dislocations, joints) ou sous forme d'amas sub-microscopiques. 3 - Une acceleration de la diffusion a basse temperature. A dilution infinie la diffusion (en cm{sup 2}/s) du Mg dans l'Al passe de: 1 exp(- 31000/RT {+-} 1200/RT cal/mole) a 8.10{sup -3} exp

Computational complexity in multidimensional neutron transport theory calculations. Progress report, September 1, 1975--August 31, 1976

International Nuclear Information System (INIS)

Bareiss, E.H.

1976-05-01

The objectives of the work are to develop mathematically and computationally founded for the design of highly efficient and reliable multidimensional neutron transport codes to solve a variety of neutron migration and radiation problems, and to analyze existing and new methods for performance. As new analytical insights are gained, new numerical methods are developed and tested. Significant results obtained include implementation of the integer-preserving Gaussian elimination method (two-step method) in a CDC 6400 computer code, modes analysis for one-dimensional transport solutions, and a new method for solving the 1-T transport equation. Some of the work dealt with the interface and corner problem in diffusion theory

X-ray and neutron diffuse scattering in LiNbO3 from 38 to 1200 K

International Nuclear Information System (INIS)

Zotov, N.; Mayer, H.M.; Guethoff, F.; Hohlwein, D.

1995-01-01

A semi-quantitative description of X-ray and neutron diffuse scattering from congruent lithium niobate, LiNbO 3 , is given. The diffuse scattering is concentrated in three sets of diffuse planes perpendicular to the pseudo-cubic symmetry-related [221], [241] and [ anti 4 anti 21] directions and can be attributed to one-dimensional displacive and chemical disorder along these directions. The variation of the X-ray and neutron diffuse intensities with the scattering vector, as well as the comparison between X-ray and neutron data, indicate that more than one type of atom is involved. Temperature variations are followed from 38 to 1200 K. Different disorder models are discussed. The increase of the integrated intensities of the diffuse lines along the [0 1k 2l] * and [0 anti 1k 4l] * directions (i.e. sections of the diffuse planes) up to 800 K followed by a slight decrease at higher temperatures may be interpreted either by static disorder related to temperature-dependent variation of disorder/defect clusters or by dynamic disorder. Inelastic neutron scattering experiments do not show any anomaly of the transversal acoustic (TA) modes. (orig.)

Angular distributions of fast neutrons scattered by Al, Si, P, S and Zn; Distributions angulaires des neutrons rapides diffuses par Al, Si, P, S et Zn; Usloviya raspredeleniya bystrykh nejtronov, rasseyannykh alyuminiem, kremniem, fosforom i tsinkom; Distribuciones angulares de neutrones rapidos dispersados por Al, Si, P, S y Zn

Energy Technology Data Exchange (ETDEWEB)

Tstjkaija, K; Tanaka, S; Maeuyama, M; Tomita, Y [Japan Atomic Energy Research Institute, Tokai-Mtjea (Japan)

1962-03-15

Differential scattering cross-sections of Al, Si, P, S and Zn for fast neutrons have been measured in an energy range of 3.4 to 4.6 MeV by using the time-of-flight method. Angular distributions of the inelastically scattered neutrons are nearly isotropic in all cases. These results are discussed on the basis of the Hauser-Feshbach theory. (author) [French] Les sections efficaces differentielles de diffusion de Al, Si, P, S et Zn pour des neutrons rapides ont ete mesurees dans la gamme d'energies de 3,4 a 4,6 MeV, en employant la methode du temps de vol. Les distributions angulaires des neutrons diffuses inelastiquement sont presque isotropes dans tous les cas. Les auteurs analysent ces resultats en se fondant sur la theorie de Hauser-Feshbach. (author) [Spanish] Los autores han medido por el metodo del tiempo de vuelo las secciones eficaces diferenciales de dispersion del Al, Si, P, S y Zn para neutrones rapidos de energia comprendida entre 3,4 y 4,6 MeV. Las distribuciones angulares de los neutrones dispersados inelasticamente son casi isotropicas en todos los casos. Los autores analizan los resultados obtenidos basandose en la teoria de Hauser-Feshbach . (author) [Russian] Differentsial'no e sechenie rasseyaniya alyuminiya, kremniya, fosfora, sery i tsinka dlya bystrykh nejtronov izmereno v diapazone ehnergii ot 3,4 do 4,6 Megaehlektronvol't ispol'zovanie m metoda vremeni proleta. Uglovye raspredeleniya neuprugo rasseyannykh nejtronov yavlyayutsya pochti vo vsekh sluchayakh izotropnymi. Jeti rezul'taty obsuzhdayutsya na osnove teorii Hauzera-Feshbakha. (author)

On the group approximation errors in description of neutron slowing-down at large distances from a source. Diffusion approach

International Nuclear Information System (INIS)

Kulakovskij, M.Ya.; Savitskij, V.I.

1981-01-01

The errors of multigroup calculating the neutron flux spatial and energy distribution in the fast reactor shield caused by using group and age approximations are considered. It is shown that at small distances from a source the age theory rather well describes the distribution of the slowing-down density. With the distance increase the age approximation leads to underestimating the neutron fluxes, and the error quickly increases at that. At small distances from the source (up to 15 lengths of free path in graphite) the multigroup diffusion approximation describes the distribution of slowing down density quite satisfactorily and at that the results almost do not depend on the number of groups. With the distance increase the multigroup diffusion calculations lead to considerable overestimating of the slowing-down density. The conclusion is drawn that the group approximation proper errors are opposite in sign to the error introduced by the age approximation and to some extent compensate each other

Theoretical study of the paramagnetic scattering of neutrons; Etude theorique de la diffusion paramagnetique des neutrons

Energy Technology Data Exchange (ETDEWEB)

Saint-James, D [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1962-02-15

General paramagnetic scattering of neutrons is investigated in the situation where the orbital moment of the magnetic scattering ions is not quenched. The general relevant expression of the cross-section is given. The proceeding results are applied to rare earths and iron group ions. It is shown that if crystalline actions lift the free ion ground state degeneracy the neutron may induce transitions between the various levels, the distances of which are typically of the order of several hundred cm{sup -1}. The various scattering cross-sections (elastic and inelastic) are calculated for the rare earths in a cubic crystal field, for the holmium and erbium sesquioxide and for the anhydrous iron chloride (Cl{sub 2}Fe). These cross-sections are high enough to allow for an experimental detection, thus providing a direct determination of the levels distances through the measurement of the neutron wave-length shift. Moreover it is shown that, for neodymium, holmium, erbium, the total cross-section for neutrons of one angstrom wave length is rather insensitive to the crystal field effects. The results are then compared with the available experimental studies. The influence of the orbital moment on the angular dependence of the scattering for polarised ions is then investigated. The well-known formula: I = I{sub 0}sin{sup 2}{beta} is only an approximation, the validity of which is discussed. (author) [French] On envisage le cas general de la diffusion paramagnetique de neutrons. Le moment orbital des ions magnetiques ne peut etre considere comme bloque. On donne l'expression generale de la section efficace. Les resultats obtenus sont appliques au cas des terres rares et des ions du groupe du fer. On montre que, si les actions cristallines levent la degenerescence du niveau fondamental de l'ion libre, le neutron peut induire des transitions entre les divers sous-niveaux, dont la distance est ordinairement de l'ordre de quelques centaines de cm{sup -1}. La section efficace des

Neutron resonance absorption theory

International Nuclear Information System (INIS)

Reuss, P.

1991-11-01

After some recalls on the physics of neutron resonance absorption during their slowing down, this paper presents the main features of the theoretical developments performed by the french school of reactor physics: the effective reaction rate method so called Livolant-Jeanpierre theory, the generalizations carried out by the author, and the probability table method [fr

Neutronics equations: Positiveness; compactness; spectral theory; time asymptotic behavior

International Nuclear Information System (INIS)

Mokhtar-Kharroubi, M.

1987-12-01

Neutronics equations are studied: the continuous model (with and without delayed neutrons) and the multigroup model. Asymptotic descriptions of these equations (t→+∞) are obtained, either by the Dunford method or by using semigroup perturbation techniques, after deriving the spectral theory for the equations. Compactness problems are reviewed, and a general theory of compact injection in neutronic functional space is derived. The effects of positiveness in neutronics are analyzed: the irreducibility of the transport semigroup, and the properties of the main eigenvalue (existence, nonexistence, frame, strict dominance, strict monotony in relation to all the parameters). A class of transport operators whose real spectrum can be completely described is shown [fr

Neutron matter, neutron pairing, and neutron drops based on chiral effective field theory interactions

Energy Technology Data Exchange (ETDEWEB)

Krueger, Thomas

2016-10-19

The physics of neutron-rich systems is of great interest in nuclear and astrophysics. Precise knowledge of the properties of neutron-rich nuclei is crucial for understanding the synthesis of heavy elements. Infinite neutron matter determines properties of neutron stars, a final stage of heavy stars after a core-collapse supernova. It also provides a unique theoretical laboratory for nuclear forces. Strong interactions are determined by quantum chromodynamics (QCD). However, QCD is non-perturbative at low energies and one presently cannot directly calculate nuclear forces from it. Chiral effective field theory circumvents these problems and connects the symmetries of QCD to nuclear interactions. It naturally and systematically includes many-nucleon forces and gives access to uncertainty estimates. We use chiral interactions throughout all calculation in this thesis. Neutron stars are very extreme objects. The densities in their interior greatly exceed those in nuclei. The exact composition and properties of neutron stars is still unclear but they consist mainly of neutrons. One can explore neutron stars theoretically with calculations of neutron matter. In the inner core of neutron stars exist very high densities and thus maybe exotic phases of matter. To investigate whether there exists a phase transition to such phases even at moderate densities we study the chiral condensate in neutron matter, the order parameter of chiral symmetry breaking, and find no evidence for a phase transition at nuclear densities. We also calculate the more extreme system of spin-polarised neutron matter. With this we address the question whether there exists such a polarised phase in neutron stars and also provide a benchmark system for lattice QCD. We find spin-polarised neutron matter to be an almost non-interacting Fermi gas. To understand the cooling of neutron stars neutron pairing is of great importance. Due to the high densities especially triplet pairing is of interest. We

Study by neutron diffusion of magnetic fluctuations in iron in the curie temperature region; Etude des fluctuations d'aimantation dans le fer au voisinage de la temperature de curie par diffusion des neutrons

Energy Technology Data Exchange (ETDEWEB)

Ericson-Galula, M [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1958-12-15

The critical diffusion of neutrons in iron is due to the magnetisation fluctuations which occur in ferromagnetic substances in the neighbourhood of the Curie temperature. The fluctuations can be described in correlation terms; a correlation function {gamma}{sub R{sub vector}} (t) is defined, {gamma}{sub R{sub vector}} (t) = mean value of the scalar product of a reference spin and a spin situated at a distance (R) from the first and considered at the instant t. In chapter I we recall the generalities on neutron diffusion cross-sections; a brief summary is given of the theory of VAN HOVE, who has shown that the magnetic diffusion cross section of neutrons is the Fourier transformation of the correlation function. In chapter Il we study the spatial dependence of the correlation function, assumed to be independent of time. It can then be characterised by two parameters K{sub 1} and r{sub 1}, by means of which the range and intensity of the correlations can be calculated respectively. After setting out the principle of the measurement of these parameters, we shall describe the experimental apparatus. The experimental values obtained are in good agreement with the calculations, and the agreement is better if it is supposed that the second and not the first neighbours of an iron atom are magnetically active, as proposed by Neel. In chapter III we study the evolution with time of the correlation function; this evolution is characterised by a parameter {lambda} depending on the temperature, which occurs in the diffusion equation obeyed by the magnetisation fluctuations: {delta}M{sub vector}/{delta}t = {lambda} {nabla}{sup 2} M{sub vector}. The principle of the measurement of {lambda} is given, after which the modifications carried out on the experimental apparatus mentioned in chapter II are described. The results obtained are then discussed and compared with the theoretical forecasts of De Gennes, mode by using the

Neutron Star Models in Alternative Theories of Gravity

Science.gov (United States)

Manolidis, Dimitrios

We study the structure of neutron stars in a broad class of alternative theories of gravity. In particular, we focus on Scalar-Tensor theories and f(R) theories of gravity. We construct static and slowly rotating numerical star models for a set of equations of state, including a polytropic model and more realistic equations of state motivated by nuclear physics. Observable quantities such as masses, radii, etc are calculated for a set of parameters of the theories. Specifically for Scalar-Tensor theories, we also calculate the sensitivities of the mass and moment of inertia of the models to variations in the asymptotic value of the scalar field at infinity. These quantities enter post-Newtonian equations of motion and gravitational waveforms of two body systems that are used for gravitational-wave parameter estimation, in order to test these theories against observations. The construction of numerical models of neutron stars in f(R) theories of gravity has been difficult in the past. Using a new formalism by Jaime, Patino and Salgado we were able to construct models with high interior pressure, namely pc > rho c/3, both for constant density models and models with a polytropic equation of state. Thus, we have shown that earlier objections to f(R) theories on the basis of the inability to construct viable neutron star models are unfounded.

Benchmarks with diffusion theory and transport theory

International Nuclear Information System (INIS)

Cunha Menezes Filho, A. da; Souza, A.L. de.

1984-01-01

The multiplication factor and some spectral indices for five critical assemblies (ZPR-6-7, ZPR-3-11, GODIVA, BIG-TEN and FLATTOP) are calculated by Diffusion and Transport Theory, with group constants generated by MC 2 (for diffusion calculations) and by NJOY (for transport calculations). The discrepancies encountered in the ZPR-6-7 spectra, can be tracked to the large differences in the elastic cross section for Iron, calculated by MC 2 and NJOY. (Author) [pt

Applied neutron resonance theory

International Nuclear Information System (INIS)

Froehner, F.H.

1980-01-01

Utilisation of resonance theory in basic and applications-oriented neutron cross section work is reviewed. The technically important resonance formalisms, principal concepts and methods as well as representative computer programs for resonance parameter extraction from measured data, evaluation of resonance data, calculation of Doppler-broadened cross sections and estimation of level-statistical quantities from resonance parameters are described. (author)

Neutronics codes

International Nuclear Information System (INIS)

Buckel, G.

1983-01-01

The objectives are the development, testing and cultivation of reliable, efficient and user-optimized neutron-physical calculation methods and conformity with users' requirements concerning design of power reactors, planning and analysis of experiments necessary for their protection as well as research on physical key problems. A short outline of available computing programmes for the following objectives is given: - Provision of macroscopic group constants, - Calculation of neutron flux distribution in transport theory and diffusion approximation, - Evaluation of neutron flux-distribution, - Execution of disturbance calculations for the determination reactivity coefficients, and - graphical representation of results. (orig./RW) [de

Neutrons in a highly diffusive medium a new propulsion tool for deep space exploration?

CERN Document Server

Rubbia, Carlo

1998-01-01

The recently completed TARC Experiment at the CERN-PS has shown how it is possible to confine neutrons by diffusion in a limited volume of a highly transparent medium for very long times (tens of milliseconds), with correspondingly very long diffusive paths (> 60 m neutron path ÒwoundÓ within a ~ 60 cm effective radius). Assume an empty cavity is introduced inside the previous volume of diffusing medium. The inner walls of the cavity are covered with a thin layer of highly fissionable material, which acts as a neutron multiplying source. This configuration, called Òn-HohlraumÓ, is reminiscent of a classic black-body radiator, with the exception that now neutrons rather than photons are propagated. The flux can be sufficiently enhanced as to permit to reach criticality with a ~ 1 mm thick Americium deposit, corresponding to a mere 1100 atomic layers. Such a layer is so thin that the Fission Fragments (FF) exit freely into the cavity. The energy carried by FF can be recovered directly, thus making use of th...

Study on neutron diffusion and time dependence heat ina fluidized bed nuclear reactor

International Nuclear Information System (INIS)

Vilhena, M.T. de.

1988-01-01

The purpose of this work is to model the neutron diffusion and heat transfer for a Fluidized Bed Nuclear Reactor and its solution by Laplace Transform Technique with numerical inversion using Fourier Series. Also Gaussian quadrature and residues techniques were applied for numerical inversion. The neutron transport, diffusion, and point Kinetic equation for this nuclear reactor concept are developed. A matricial and Taylor Series methods are proposed for the solution of the point Kinetic equation which is a time scale problem of Stiff type

CINESP - computational program of spatial kinetics for nuclear reactors in the one-two dimension multigroup diffusion theory

International Nuclear Information System (INIS)

Santos, R.S. dos

1993-01-01

This paper presents a computational program to solve numerically the reactor kinetics equations in the multigroup diffusion theory. One or two-dimensional problems in cylindrical or Cartesian geometries, with any number of energy and delayed-neutron precursors groups are dealt with. The main input and output of the program are briefly discussed. Various results demonstrate the accuracy and versatility of the program, when compared with other kinetics programs. (author)

Study by neutron diffusion of magnetic fluctuations in iron in the curie temperature region

International Nuclear Information System (INIS)

Ericson-Galula, M.

1958-12-01

The critical diffusion of neutrons in iron is due to the magnetisation fluctuations which occur in ferromagnetic substances in the neighbourhood of the Curie temperature. The fluctuations can be described in correlation terms; a correlation function γ R vector (t) is defined, γ R vector (t) = 0 vector (0) S R vector (t)> mean value of the scalar product of a reference spin and a spin situated at a distance (R) from the first and considered at the instant t. In chapter I we recall the generalities on neutron diffusion cross-sections; a brief summary is given of the theory of VAN HOVE, who has shown that the magnetic diffusion cross section of neutrons is the Fourier transformation of the correlation function. In chapter Il we study the spatial dependence of the correlation function, assumed to be independent of time. It can then be characterised by two parameters K 1 and r 1 , by means of which the range and intensity of the correlations can be calculated respectively. After setting out the principle of the measurement of these parameters, we shall describe the experimental apparatus. The experimental values obtained are in good agreement with the calculations, and the agreement is better if it is supposed that the second and not the first neighbours of an iron atom are magnetically active, as proposed by Neel. In chapter III we study the evolution with time of the correlation function; this evolution is characterised by a parameter Λ depending on the temperature, which occurs in the diffusion equation obeyed by the magnetisation fluctuations: δM vector /δt = Λ ∇ 2 M vector . The principle of the measurement of Λ is given, after which the modifications carried out on the experimental apparatus mentioned in chapter II are described. The results obtained are then discussed and compared with the theoretical forecasts of De Gennes, mode by using the Heinsenberg model and a simple band model; our values in good agreement with those calculated in the Heisenberg

Fe and N diffusion in nitrogen-rich FeN measured using neutron ...

Indian Academy of Sciences (India)

E-mail: mgupta@csr.ernet.in. Abstract. Grazing incidence neutron reflectometry provides an opportunity to measure the depth profile of a thin film sample with a resolution <1 nm, in a non-destructive way. In this way the diffusion across the interfaces can also be measured. In addition, neutrons have contrast among the ...

Some improved methods in neutron transport theory

Energy Technology Data Exchange (ETDEWEB)

Pop-Jordanov, J; Stefanovic, D; Kocic, A; Matausek, M; Bosevski, T [Boris Kidric Institute of Nuclear Sciences Vinca, Beograd (Yugoslavia)

1973-07-01

The methods described in this paper are: analytical approach to neutron spectra in case of energy dependent anisotropy of elastic scattering; Monte Carlo estimations of neutron absorption reaction rate during slowing down process; spherical harmonics treatment of space-angle-lethargy dependent slowing down transport equation; integral transport theory based on point-wise representation of variables.

Introduction to the theory of thermal neutron scattering

CERN Document Server

Squires, G L

2012-01-01

Since the advent of the nuclear reactor, thermal neutron scattering has proved a valuable tool for studying many properties of solids and liquids, and research workers are active in the field at reactor centres and universities throughout the world. This classic text provides the basic quantum theory of thermal neutron scattering and applies the concepts to scattering by crystals, liquids and magnetic systems. Other topics discussed are the relation of the scattering to correlation functions in the scattering system, the dynamical theory of scattering and polarisation analysis. No previous knowledge of the theory of thermal neutron scattering is assumed, but basic knowledge of quantum mechanics and solid state physics is required. The book is intended for experimenters rather than theoreticians, and the discussion is kept as informal as possible. A number of examples, with worked solutions, are included as an aid to the understanding of the text.

Applied neutron resonance theory

International Nuclear Information System (INIS)

Froehner, F.H.

1978-07-01

Utilisation of resonance theory in basic and applications-oriented neutron cross section work is reviewed. The technically important resonance formalisms, principal concepts and methods as well as representative computer programs for resonance parameter extraction from measured data, evaluation of resonance data, calculation of Doppler-broadened cross sections and estimation of level-statistical quantities from resonance parameters are described. (orig.) [de

Neuro-diffuse algorithm for neutronic power identification of TRIGA Mark III reactor

International Nuclear Information System (INIS)

Rojas R, E.; Benitez R, J. S.; Segovia de los Rios, J. A.; Rivero G, T.

2009-10-01

In this work are presented the results of design and implementation of an algorithm based on diffuse logic systems and neural networks like method of neutronic power identification of TRIGA Mark III reactor. This algorithm uses the punctual kinetics equation as data generator of training, a cost function and a learning stage based on the descending gradient algorithm allow to optimize the parameters of membership functions of a diffuse system. Also, a series of criteria like part of the initial conditions of training algorithm are established. These criteria according to the carried out simulations show a quick convergence of neutronic power estimated from the first iterations. (Author)

A multidimensional multigroup diffusion model for the determination of the frequency-dependent field of view of a neutron detector

International Nuclear Information System (INIS)

van der Hagen, T.H.J.J.; Hoogenboom, J.E.; van Dam, H.

1992-01-01

This paper reports on the sensitivity of a neutron detector to parametric fluctuations in the core of a reactor which depends on the position and the frequency of the perturbation. The basic neutron diffusion model for the calculation of this so-called field of view (FOV) of the detector is extended with respect to the dimensionality of the problem and the number of energy groups involved. The physical meaning of the FOV concept is illustrated by means of some simple examples, which can be handled analytically. The possibility of calculating the FOV by a conventional neutron diffusion code is demonstrated. In that case, the calculation in n neutron energy groups leads to 2n modified neutron diffusion equations

Simulation of a parallel processor on a serial processor: The neutron diffusion equation

International Nuclear Information System (INIS)

Honeck, H.C.

1981-01-01

Parallel processors could provide the nuclear industry with very high computing power at a very moderate cost. Will we be able to make effective use of this power. This paper explores the use of a very simple parallel processor for solving the neutron diffusion equation to predict power distributions in a nuclear reactor. We first describe a simple parallel processor and estimate its theoretical performance based on the current hardware technology. Next, we show how the parallel processor could be used to solve the neutron diffusion equation. We then present the results of some simulations of a parallel processor run on a serial processor and measure some of the expected inefficiencies. Finally we extrapolate the results to estimate how actual design codes would perform. We find that the standard numerical methods for solving the neutron diffusion equation are still applicable when used on a parallel processor. However, some simple modifications to these methods will be necessary if we are to achieve the full power of these new computers. (orig.) [de

Elastic neutron diffuse scattering in Zr(Ca, Y)O2-x

International Nuclear Information System (INIS)

Barberis, P.; Beuneu, B.; Novion, C.H. de.

1990-01-01

Elastic neutron diffuse scattering has been measured in cubic Zr(Ca, Y)O 2-x at room temperature. The very high diffuse scattering (up to 70 Laue) is explained mostly by the oxygen displacements along directions, and by Ca displacements along . The weak short-range order contribution strongly suggests that oxygen vacancies tend to place as second rather than at first neighbours of a Ca stabilizing ion

Neutron diffuse scattering in magnetite due to molecular polarons

International Nuclear Information System (INIS)

Yamada, Y.; Wakabayashi, N.; Nicklow, R.M.

1980-01-01

A detailed neutron diffuse scattering study has been carried out in order to verify a model which describes the property of valence fluctuations in magnetite above T/sub V/. This model assumes the existence of a complex which is composed of two excess electrons and a local displacement mode of oxygens within the fcc primitive cell. The complex is called a molecular polaron. It is assumed that at sufficiently high temperatures there is a random distribution of molecular polarons, which are fluctuating independently by making hopping motions through the crystal or by dissociating into smaller polarons. The lifetime of each molecular polaron is assumed to be long enough to induce an instantaneous strain field around it. Based on this model, the neutron diffuse scattering cross section due to randomly distributed dressed molecular polarons has been calculated. A precise measurement of the quasielastic scattering of neutrons has been carried out at 150 K. The observed results definitely show the characteristics which are predicted by the model calculation and, thus, give evidence for the existence of the proposed molecular polarons. From this standpoint, the Verwey transition of magnetite may be viewed as the cooperative ordering process of dressed molecular polarons. Possible extensions of the model to describe the ordering and the dynamical behavior of the molecular polarons are discussed

A method to measure the diffusion coefficient by neutron wave propagation for limited samples

International Nuclear Information System (INIS)

Woznicka, U.

1986-03-01

A study has been made of the use of the neutron wave and pulse propagation method for measurement of thermal neutron diffusion parameters. Earlier works an homogenous and heterogeneous media are reviewed. A new method is sketched for the determination of the diffusion coefficient for samples of limited size. The principle is to place a relatively thin slab of the material between two blocks of a medium with known properties. The advantages and disadvantages of the method are discussed. (author)

A coupled diffusion-transport computational method and its application for the determination of space dependent angular flux distributions at a cold neutron source

International Nuclear Information System (INIS)

Turgut, M.H.

1985-01-01

A fast calculation program ''BRIDGE'' was developed for the calculation of a Cold Neutron Source (CNS) at a radial beam tube of the FRG-I reactor, which couples a total assembly diffusion calculation to a transport calculation for a certain subregion. For the coupling flux and current boundary values at the common surfaces are taken from the diffusion calculation and are used as driving conditions in the transport calculation. 'Equivalence Theorie' is used for the transport feedback effect on the diffusion calculation to improve the consistency of the boundary values. The optimization of a CNS for maximizing the subthermal flux in the wavelength range 4 - 6 A is discussed. (orig.) [de

A diffuse neutron scattering study of clustering in copper-nickel alloys

International Nuclear Information System (INIS)

Vrijen, J.

1977-01-01

The amount of clustering in Cu-Ni alloys in thermal equilibrium at several temperatures between 400degC and 700degC and ranging in composition between 20 and 80 atomic percent Ni has been determined by means of diffuse neutron scattering. A rough calculation of the excess elastic energy due to alloying Cu with Ni shows that the contribution of size effects to the configurational energy is asymmetric in the composition with its maximum located between 60 and 70 atomic percent Ni. This asymmetry is caused by different elastic constants for Cu and Ni and it might explain part of the asymmetry of clustering in Cu-Ni and its temperature dependence. With the help of the measured cluster parameters, the magnetic diffuse neutron scattering cross-sections of several differently clustered compositions in Cu-Ni could be interpreted, both well inside the ferromagnetic phase and in the transition region between ferromagnetism and superparamagnetism. Giants moments have been observed. Non-equilibrium distributions and their changes during relaxing towards equilibrium have been investigated by measuring the time-evolution of the diffuse scattering. The relaxation of the null matrix (composition without Bragg reflections for neutron scattering) has been measured at five temperatures between 320degC and 450degC. The results of these relaxations were compared with a few available kinetic models

Non probabilistic solution of uncertain neutron diffusion equation for imprecisely defined homogeneous bare reactor

International Nuclear Information System (INIS)

Chakraverty, S.; Nayak, S.

2013-01-01

Highlights: • Uncertain neutron diffusion equation of bare square homogeneous reactor is studied. • Proposed interval arithmetic is extended for fuzzy numbers. • The developed fuzzy arithmetic is used to handle uncertain parameters. • Governing differential equation is modelled by modified fuzzy finite element method. • Fuzzy critical eigenvalues and effective multiplication factors are investigated. - Abstract: The scattering of neutron collision inside a reactor depends upon geometry of the reactor, diffusion coefficient and absorption coefficient etc. In general these parameters are not crisp and hence we get uncertain neutron diffusion equation. In this paper we have investigated the above equation for a bare square homogeneous reactor. Here the uncertain governing differential equation is modelled by a modified fuzzy finite element method. Using modified fuzzy finite element method, obtained eigenvalues and effective multiplication factors are studied. Corresponding results are compared with the classical finite element method in special cases and various uncertain results have been discussed

A scatter model for fast neutron beams using convolution of diffusion kernels

International Nuclear Information System (INIS)

Moyers, M.F.; Horton, J.L.; Boyer, A.L.

1988-01-01

A new model is proposed to calculate dose distributions in materials irradiated with fast neutron beams. Scattered neutrons are transported away from the point of production within the irradiated material in the forward, lateral and backward directions, while recoil protons are transported in the forward and lateral directions. The calculation of dose distributions, such as for radiotherapy planning, is accomplished by convolving a primary attenuation distribution with a diffusion kernel. The primary attenuation distribution may be quickly calculated for any given set of beam and material conditions as it describes only the magnitude and distribution of first interaction sites. The calculation of energy diffusion kernels is very time consuming but must be calculated only once for a given energy. Energy diffusion distributions shown in this paper have been calculated using a Monte Carlo type of program. To decrease beam calculation time, convolutions are performed using a Fast Fourier Transform technique. (author)

Diffusive epidemic process: theory and simulation

International Nuclear Information System (INIS)

Maia, Daniel Souza; Dickman, Ronald

2007-01-01

We study the continuous absorbing-state phase transition in the one-dimensional diffusive epidemic process via mean-field theory and Monte Carlo simulation. In this model, particles of two species (A and B) hop on a lattice and undergo reactions B → A and A+B → 2B; the total particle number is conserved. We formulate the model as a continuous-time Markov process described by a master equation. A phase transition between the (absorbing) B-free state and an active state is observed as the parameters (reaction and diffusion rates, and total particle density) are varied. Mean-field theory reveals a surprising, nonmonotonic dependence of the critical recovery rate on the diffusion rate of B particles. A computational realization of the process that is faithful to the transition rates defining the model is devised, allowing for direct comparison with theory. Using the quasi-stationary simulation method we determine the order parameter and the survival time in systems of up to 4000 sites. Due to strong finite-size effects, the results converge only for large system sizes. We find no evidence for a discontinuous transition. Our results are consistent with the existence of three distinct universality classes, depending on whether A particles diffusive more rapidly, less rapidly or at the same rate as B particles. We also perform quasi-stationary simulations of the triplet creation model, which yield results consistent with a discontinuous transition at high diffusion rates

Contribution to the study of magnetic diffusion of neutrons; Contribution a l'etude de la diffusion magnetique des neutrons

Energy Technology Data Exchange (ETDEWEB)

Gennes, P.G. de [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1959-07-01

Certain statistical aspects of a large collection of electronic spins coupled by exchange forces are examined. The treatment is limited to substances where the orbital magnetic moment can be considered fixed, and where the effect of thermal agitation of the ions can be neglected. A system of this kind can be followed experimentally by elastic and inelastic diffusion of neutrons. At high temperatures, inelastic diffusion allows the microscopic aspect, reversible, and the macroscopic aspect, irreversible, to be studied simultaneously and these 2 fields to be linked. At temperatures around the Curie point, the average phenomenon is the appearance of a critical opalescence. At low temperatures, collective spin excitations can be observed. In the neighborhood of the Curie point, the spin coefficient {lambda}, which governs the relaxation of fluctuations of magnetization, is calculated. An intrinsic factor is discussed in {lambda}, bound to the microscopic frequency of the spin exchanges, and to a factor due to the damping of the diffusion by the magnetic field. At the transition point, {lambda} is cancelled. The spectrum of the spin excitations in metals is discussed. (author)

Homogenization of neutronic diffusion models

International Nuclear Information System (INIS)

Capdebosq, Y.

1999-09-01

In order to study and simulate nuclear reactor cores, one needs to access the neutron distribution in the core. In practice, the description of this density of neutrons is given by a system of diffusion equations, coupled by non differential exchange terms. The strong heterogeneity of the medium constitutes a major obstacle to the numerical computation of this models at reasonable cost. Homogenization appears as compulsory. Heuristic methods have been developed since the origin by nuclear physicists, under a periodicity assumption on the coefficients. They consist in doing a fine computation one a single periodicity cell, to solve the system on the whole domain with homogeneous coefficients, and to reconstruct the neutron density by multiplying the solutions of the two computations. The objectives of this work are to provide mathematically rigorous basis to this factorization method, to obtain the exact formulas of the homogenized coefficients, and to start on geometries where two periodical medium are placed side by side. The first result of this thesis concerns eigenvalue problem models which are used to characterize the state of criticality of the reactor, under a symmetry assumption on the coefficients. The convergence of the homogenization process is proved, and formulas of the homogenized coefficients are given. We then show that without symmetry assumptions, a drift phenomenon appears. It is characterized by the mean of a real Bloch wave method, which gives the homogenized limit in the general case. These results for the critical problem are then adapted to the evolution model. Finally, the homogenization of the critical problem in the case of two side by side periodic medium is studied on a one dimensional on equation model. (authors)

An analytical solution for the two-group kinetic neutron diffusion equation in cylindrical geometry

International Nuclear Information System (INIS)

Fernandes, Julio Cesar L.; Vilhena, Marco Tullio; Bodmann, Bardo Ernst

2011-01-01

Recently the two-group Kinetic Neutron Diffusion Equation with six groups of delay neutron precursor in a rectangle was solved by the Laplace Transform Technique. In this work, we report on an analytical solution for this sort of problem but in cylindrical geometry, assuming a homogeneous and infinite height cylinder. The solution is obtained applying the Hankel Transform to the Kinetic Diffusion equation and solving the transformed problem by the same procedure used in the rectangle. We also present numerical simulations and comparisons against results available in literature. (author)

Theory of quantum diffusion in biased semiconductors

CERN Document Server

Bryksin, V V

2003-01-01

A general theory is developed to describe diffusion phenomena in biased semiconductors and semiconductor superlattices. It is shown that the Einstein relation is not applicable for all field strengths so that the calculation of the field-mediated diffusion coefficient represents a separate task. Two quite different diffusion contributions are identified. The first one disappears when the dipole operator commutes with the Hamiltonian. It plays an essential role in the theory of small polarons. The second contribution is obtained from a quantity that is the solution of a kinetic equation but that cannot be identified with the carrier distribution function. This is in contrast to the drift velocity, which is closely related to the distribution function. A general expression is derived for the quantum diffusion regime, which allows a clear physical interpretation within the hopping picture.

SNAP-3D: a three-dimensional neutron diffusion code

International Nuclear Information System (INIS)

McCallien, C.W.J.

1975-10-01

A preliminary report is presented describing the data requirements of a one- two- or three-dimensional multi-group diffusion code, SNAP-3D. This code is primarily intended for neutron diffusion calculations but it can also carry out gamma calculations if the diffuse approximation is accurate enough. It is suitable for fast and thermal reactor core calculations and for shield calculations. It is assumed the reader is familiar with the older, two-dimensional code SNAP and can refer to the report [TRG-Report-1990], describing it. The present report concentrates on the enhancements to SNAP that have been made to produce the three-dimensional version, SNAP-3D, and is intended to act a a guide on data preparation until a single, comprehensive report can be published. (author)

Diffusion in the special theory of relativity.

Science.gov (United States)

Herrmann, Joachim

2009-11-01

The Markovian diffusion theory is generalized within the framework of the special theory of relativity. Since the velocity space in relativity is a hyperboloid, the mathematical stochastic calculus on Riemanian manifolds can be applied but adopted here to the velocity space. A generalized Langevin equation in the fiber space of position, velocity, and orthonormal velocity frames is defined from which the generalized relativistic Kramers equation in the phase space in external force fields is derived. The obtained diffusion equation is invariant under Lorentz transformations and its stationary solution is given by the Jüttner distribution. Besides, a nonstationary analytical solution is derived for the example of force-free relativistic diffusion.

Matrix-type multiple reciprocity boundary element method for solving three-dimensional two-group neutron diffusion equations

International Nuclear Information System (INIS)

Itagaki, Masafumi; Sahashi, Naoki.

1997-01-01

The multiple reciprocity boundary element method has been applied to three-dimensional two-group neutron diffusion problems. A matrix-type boundary integral equation has been derived to solve the first and the second group neutron diffusion equations simultaneously. The matrix-type fundamental solutions used here satisfy the equation which has a point source term and is adjoint to the neutron diffusion equations. A multiple reciprocity method has been employed to transform the matrix-type domain integral related to the fission source into an equivalent boundary one. The higher order fundamental solutions required for this formulation are composed of a series of two types of analytic functions. The eigenvalue itself is also calculated using only boundary integrals. Three-dimensional test calculations indicate that the present method provides stable and accurate solutions for criticality problems. (author)

Diffusion, quantum theory, and radically elementary mathematics (MN-47)

CERN Document Server

Faris, William G

2014-01-01

Diffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein''s work on Brownian motion. It is also relevant to understanding various aspects of quantum theory. This book explains diffusive motion and its relation to both nonrelativistic quantum theory and quantum field theory. It shows how diffusive motion concepts lead to a radical reexamination of the structure of mathematical analysis. The book''s inspiration is Princeton University mathematics professor Edward Nelson''s influential work in

Homotopy analysis method for neutron diffusion calculations

International Nuclear Information System (INIS)

Cavdar, S.

2009-01-01

The Homotopy Analysis Method (HAM), proposed in 1992 by Shi Jun Liao and has been developed since then, is based on a fundamental concept in differential geometry and topology, the homotopy. It has proved useful for problems involving algebraic, linear/non-linear, ordinary/partial differential and differential-integral equations being an analytic, recursive method that provides a series sum solution. It has the advantage of offering a certain freedom for the choice of its arguments such as the initial guess, the auxiliary linear operator and the convergence control parameter, and it allows us to effectively control the rate and region of convergence of the series solution. HAM is applied for the fixed source neutron diffusion equation in this work, which is a part of our research motivated by the question of whether methods for solving the neutron diffusion equation that yield straightforward expressions but able to provide a solution of reasonable accuracy exist such that we could avoid analytic methods that are widely used but either fail to solve the problem or provide solutions through many intricate expressions that are likely to contain mistakes or numerical methods that require powerful computational resources and advanced programming skills due to their very nature or intricate mathematical fundamentals. Fourier basis are employed for expressing the initial guess due to the structure of the problem and its boundary conditions. We present the results in comparison with other widely used methods of Adomian Decomposition and Variable Separation.

An analytical solution of the one-dimensional neutron diffusion kinetic equation in cartesian geometry

International Nuclear Information System (INIS)

Ceolin, Celina; Vilhena, Marco T.; Petersen, Claudio Z.

2009-01-01

In this work we report an analytical solution for the monoenergetic neutron diffusion kinetic equation in cartesian geometry. Bearing in mind that the equation for the delayed neutron precursor concentration is a first order linear differential equation in the time variable, to make possible the application of the GITT approach to the kinetic equation, we introduce a fictitious diffusion term multiplied by a positive small value ε. By this procedure, we are able to solve this set of equations. Indeed, applying the GITT technique to the modified diffusion kinetic equation, we come out with a matrix differential equation which has a well known analytical solution when ε goes to zero. We report numerical simulations as well study of numerical convergence of the results attained. (author)

Hydrogen dynamics in Na3AlH6: A combined density functional theory and quasielastic neutron scattering study

DEFF Research Database (Denmark)

Voss, Johannes; Shi, Qing; Jacobsen, Hjalte Sylvest

2007-01-01

alanate with TiCl3, and here we study hydrogen dynamics in doped and undoped Na3AlH6 using a combination of density functional theory calculations and quasielastic neutron scattering. The hydrogen dynamics is found to be vacancy mediated and dominated by localized jump events, whereas long-range bulk......Understanding the elusive catalytic role of titanium-based additives on the reversible hydrogenation of complex hydrides is an essential step toward developing hydrogen storage materials for the transport sector. Improved bulk diffusion of hydrogen is one of the proposed effects of doping sodium...... defect motion in sodium alanate could result from vacancy-mediated sodium diffusion....

The perturbation theory in the fundamental mode. Its application to the analysis of neutronic experiments involving small amounts of materials in fast neutron multiplying media

International Nuclear Information System (INIS)

Remsak, Stanislav.

1975-01-01

The formalism of the perturbation theory at the first order, is developed in its simplest form: diffusion theory in the fundamental mode and then the more complex formalism of the transport theory in the fundamental mode. A comparison shows the effect of the angular correlation between the fine structures of the flux and its adjoint function, the difference in the treatment of neutron leakage phenomena, and the existence of new terms in the perturbation formula, entailing a reactivity representation in the diffusion theory that is not quite exact. Problems of using the formalism developed are considered: application of the multigroup formalism, transients of the flux and its adjoint function, validity of the first order approximation etc. A detailed analysis allows the formulation of a criterion specifying the validity range. Transients occuring in the reference medium are also treated. A set of numerical tests for determining a method of elimination of transient effects is presented. Some differential experiments are then discussed: sodium blowdown in enriched uranium or plutonium cores, experiments utilizing some structural materials (iron and oxygen) and plutonium sample oscillations. The Cadarache version II program was systematically used but the analysis of the experiments of plutonium sample oscillation in Ermine required the Cadarache version III program [fr

Solving the uncommon nuclear reactor core neutronics problems

International Nuclear Information System (INIS)

Vondy, D.R.; Fowler, T.B.

1983-01-01

Calculational procedures have been implemented for solving importance and higher harmonic neutronics problems. Solutions are obtained routinely to support analysis of reactor core performance, treating up to three space coordinates with the multigroup diffusion theory approximation to neutron transport. The techniques used and some of the calculational difficulties are discussed

Calculation of neutron flux distribution of thermal neutrons from microtron converter in a graphite moderator with water reflector

International Nuclear Information System (INIS)

Andrejsek, K.

1977-01-01

The calculation is made of the thermal neutron flux in the moderator and reflector by solving the neutron diffusion equation using the four-group theory. The correction for neutron absorption in the moderator was carried out using the perturbation theory. The calculation was carried out for four groups with the following energy ranges: the first group 2 MeV to 3 keV, the second group 3 keV to 5 eV, the third group 5 eV to 0.025 eV and the fourth group 0.025 eV. The values of the macroscopic cross section of capture and scattering, of the diffusion coefficient, the macroscopic cross section of the moderator, of the neutron age and the extrapolation length for the water-graphite moderator used in the calculations are given. The spatial distribution of the thermal neutron flux is graphically represented for graphite of a 30, 40, and 50 cm radius and for graphite of a 30 and 40 cm radius with a 10 cm water reflector; a graphic comparison is made of the distribution of the thermal neutron flux in water and in graphite, both 40 cm in radius. The system of graphite with reflector proved to be the best and most efficient system for raising the flux density of thermal neutrons. (J.P.)

MODICO, 1-D Time-Dependent 1 Group, 2 Group Neutron Diffusion with Delayed Neutron Precursors

International Nuclear Information System (INIS)

Camiciola, P.; Cundari, D.; Montagnini, B.

1992-01-01

1 - Description of program or function: The program solves the 1-D time-dependent one and two group coarse-mesh neutron diffusion equations, coupled with the equations for the delayed-neutron precursor, in plane geometry. 2 - Method of solution: The program is based on a simple coarse-mesh cubic approximation formula for the spatial behaviour of the flux inside each interval. An implicit scheme (the time-integrated method) is used for the advancement of the solution. The resulting (block three-diagonal) matrix is inverted at each time step by Thomas' method. 3 - Restrictions on the complexity of the problem: Number of coarse- mesh intervals LE 80; number of material regions LE 10; number of delayed-neutron precursor groups LE 10. Typical mesh sizes range from 5 cm to 20 cm; typical step length (non-prompt critical transients) ranges from 0.005 to 0.1 seconds

Classical diffusion: theory and simulation codes

International Nuclear Information System (INIS)

Grad, H.; Hu, P.N.

1978-03-01

A survey is given of the development of classical diffusion theory which arose from the observation of Grad and Hogan that the Pfirsch-Schluter and Neoclassical theories are very special and frequently inapplicable because they require that plasma mass flow be treated as transport rather than as a state variable of the plasma. The subsequent theory, efficient numerical algorithms, and results of various operating codes are described

Neutron spectroscopy of fast hydrogen diffusion in BCC transition metals

International Nuclear Information System (INIS)

Richter, D.; Lottner, V.

1979-01-01

Quasielastic neutron scattering reveals microscopic details of both the time and space development of the H-diffusion process on an atomic scale. After outlining the method on the example of PdH/sub x/, new results on the jump geometry in bcc metals are surveyed. In particular, the anomalous diffusion behavior of H in Nb, Ta, and V at elevated temperature is emphasized, where correlated jump processes are important. The influence of impurities on the H-diffusion process is demonstrated by experiments performed on NbH/sub x/ doped with nitrogen impurities, which act as trapping centers for the diffusing hydrogen. The results are discussed in terms of a two-state random walk model which includes multiple trapping and detrapping processes. The concentration and temperature dependence of the capture and escape rates of traps are obtained

Parallel solutions of the two-group neutron diffusion equations

International Nuclear Information System (INIS)

Zee, K.S.; Turinsky, P.J.

1987-01-01

Recent efforts to adapt various numerical solution algorithms to parallel computer architectures have addressed the possibility of substantially reducing the running time of few-group neutron diffusion calculations. The authors have developed an efficient iterative parallel algorithm and an associated computer code for the rapid solution of the finite difference method representation of the two-group neutron diffusion equations on the CRAY X/MP-48 supercomputer having multi-CPUs and vector pipelines. For realistic simulation of light water reactor cores, the code employees a macroscopic depletion model with trace capability for selected fission product transients and critical boron. In addition to this, moderator and fuel temperature feedback models are also incorporated into the code. The validity of the physics models used in the code were benchmarked against qualified codes and proved accurate. This work is an extension of previous work in that various feedback effects are accounted for in the system; the entire code is structured to accommodate extensive vectorization; and an additional parallelism by multitasking is achieved not only for the solution of the matrix equations associated with the inner iterations but also for the other segments of the code, e.g., outer iterations

Applications of a general random-walk theory for confined diffusion.

Science.gov (United States)

Calvo-Muñoz, Elisa M; Selvan, Myvizhi Esai; Xiong, Ruichang; Ojha, Madhusudan; Keffer, David J; Nicholson, Donald M; Egami, Takeshi

2011-01-01

A general random walk theory for diffusion in the presence of nanoscale confinement is developed and applied. The random-walk theory contains two parameters describing confinement: a cage size and a cage-to-cage hopping probability. The theory captures the correct nonlinear dependence of the mean square displacement (MSD) on observation time for intermediate times. Because of its simplicity, the theory also requires modest computational requirements and is thus able to simulate systems with very low diffusivities for sufficiently long time to reach the infinite-time-limit regime where the Einstein relation can be used to extract the self-diffusivity. The theory is applied to three practical cases in which the degree of order in confinement varies. The three systems include diffusion of (i) polyatomic molecules in metal organic frameworks, (ii) water in proton exchange membranes, and (iii) liquid and glassy iron. For all three cases, the comparison between theory and the results of molecular dynamics (MD) simulations indicates that the theory can describe the observed diffusion behavior with a small fraction of the computational expense. The confined-random-walk theory fit to the MSDs of very short MD simulations is capable of accurately reproducing the MSDs of much longer MD simulations. Furthermore, the values of the parameter for cage size correspond to the physical dimensions of the systems and the cage-to-cage hopping probability corresponds to the activation barrier for diffusion, indicating that the two parameters in the theory are not simply fitted values but correspond to real properties of the physical system.

Solution of two-dimensional neutron diffusion equation for triangular region by finite Fourier transformation

International Nuclear Information System (INIS)

Kobayashi, Keisuke; Ishibashi, Hideo

1978-01-01

A two-dimensional neutron diffusion equation for a triangular region is shown to be solved by the finite Fourier transformation. An application of the Fourier transformation to the diffusion equation for triangular region yields equations whose unknowns are the expansion coefficients of the neutron flux and current in Fourier series or Legendre polynomials expansions only at the region boundary. Some numerical calculations have revealed that the present technique gives accurate results. It is shown also that the solution using the expansion in Legendre polynomials converges with relatively few terms even if the solution in Fourier series exhibits the Gibbs' phenomenon. (auth.)

New methods in transport theory. Part of a coordinated programme on methods in neutron transport theory

International Nuclear Information System (INIS)

Stefanovic, D.

1975-09-01

The research work of this contract was oriented towards the study of different methods in neutron transport theory. Authors studied analytical solution of the neutron slowing down transport equation and extension of this solution to include the energy dependence of the anisotropy of neutron scattering. Numerical solution of the fast and resonance transport equation for the case of mixture of scatterers including inelastic effects were also reviewed. They improved the existing formalism for treating the scattering of neutrons on water molecules; Identifying modal analysis as the Galerkin method, general conditions for modal technique applications have been investigated. Inverse problems in transport theory were considered. They obtained the evaluation of an advanced level distribution function, made improvement of the standard formalism for treating the inelastic scattering and development of a cluster nuclear model for this evaluation. Authors studied the neutron transport treatment in space energy groups for criticality calculation of a reactor core, and development of the Monte Carlo sampling scheme from the neutron transport equation

System of adjoint P1 equations for neutron moderation; Sistema de equacoes P1 adjuntas para a moderacao de neutrons

Energy Technology Data Exchange (ETDEWEB)

Martinez, Aquilino Senra; Silva, Fernando Carvalho da; Cardoso, Carlos Eduardo Santos [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear

2000-07-01

In some applications of perturbation theory, it is necessary know the adjoint neutron flux, which is obtained by the solution of adjoint neutron diffusion equation. However, the multigroup constants used for this are weighted in only the direct neutron flux, from the solution of direct P1 equations. In this work, this procedure is questioned and the adjoint P1 equations are derived by the neutron transport equation, the reversion operators rules and analogies between direct and adjoint parameters. (author)

Nested element method in multidimensional neutron diffusion calculations

International Nuclear Information System (INIS)

Altiparmakov, D.V.

1983-01-01

A new numerical method is developed that is particularly efficient in solving the multidimensional neutron diffusion equation in geometrically complex systems. The needs for a generally applicable and fast running computer code have stimulated the inroad of a nonclassical (R-function) numerical method into the nuclear field. By using the R-functions, the geometrical components of the diffusion problem are a priori analytically implemented into the approximate solution. The class of functions, to which the approximate solution belongs, is chosen as close to the exact solution class as practically acceptable from the time consumption point of view. That implies a drastic reduction of the number of degrees of freedom, compared to the other methods. Furthermore, the reduced number of degrees of freedom enables calculation of large multidimensional problems on small computers

Application of multicomponent diffusion theory for description of impurities distribution in complex diffusive doping of semiconductors

International Nuclear Information System (INIS)

Uskov, V.A.; Kondrachenko, O.E.; Kondrachenko, L.A.

1977-01-01

A phenomenological theory of multicomponent diffusion involving interaction between the components is employed to analyze how the interaction between two admixtures affects their simultaneous or consequent diffusion into a semiconductor. The theory uses the equations of multicomponent dissusion under common conditions (constant diffusion coefficients and equilibrium distribution of vacancies). The experiments are described on In and Sb simultaneous diffusion into Ge. The diffusion is performed according to the routine gas phase technology with the use of radioactive isotopes In 114 and Sb 124 . It is shown that the introduction of an additional diffusion coefficient D 12 makes it possible to simply and precisely describe the distribution of interacting admixtures in complex diffusion alloying of semiconductors

Domain decomposition methods for the neutron diffusion problem

International Nuclear Information System (INIS)

Guerin, P.; Baudron, A. M.; Lautard, J. J.

2010-01-01

The neutronic simulation of a nuclear reactor core is performed using the neutron transport equation, and leads to an eigenvalue problem in the steady-state case. Among the deterministic resolution methods, simplified transport (SPN) or diffusion approximations are often used. The MINOS solver developed at CEA Saclay uses a mixed dual finite element method for the resolution of these problems. and has shown his efficiency. In order to take into account the heterogeneities of the geometry, a very fine mesh is generally required, and leads to expensive calculations for industrial applications. In order to take advantage of parallel computers, and to reduce the computing time and the local memory requirement, we propose here two domain decomposition methods based on the MINOS solver. The first approach is a component mode synthesis method on overlapping sub-domains: several Eigenmodes solutions of a local problem on each sub-domain are taken as basis functions used for the resolution of the global problem on the whole domain. The second approach is an iterative method based on a non-overlapping domain decomposition with Robin interface conditions. At each iteration, we solve the problem on each sub-domain with the interface conditions given by the solutions on the adjacent sub-domains estimated at the previous iteration. Numerical results on parallel computers are presented for the diffusion model on realistic 2D and 3D cores. (authors)

Multicomponent diffusivities from the free volume theory

NARCIS (Netherlands)

Wesselingh, J.A; Bollen, A.M

In this paper the free volume theory of diffusion is extended to multicomponent mixtures. The free volume is taken to be accessible for any component according to its surface. fraction. The resulting equations predict multicomponent (Maxwell-Stefan) diffusivities in simple liquid mixtures from pure

Theory of the diffusion coefficient of neutrons in a lattice containing cavities

International Nuclear Information System (INIS)

Benoist, P.

1964-01-01

In an previous publication, a simple and general formulation of the diffusion coefficient, which defines the mode of weighting of the mean free paths of the various media, in introducing the collision probabilities in each medium, was established. This expression is demonstrated again here through a more direct method, and the velocity is introduced; new terms are emphasised, the existence of which implies that the representation of the diffusion area as the mean square of the straight line distance from source to absorption is not correct in a lattice. However these terms are of small enough an order of magnitude to he treated as a correction. The general expression also shows the existence, for the radial coefficient, of the series of angular correlation terms, which is seen to converge very slowly for large channels. The term by term computation which was initiated in the first work was then interrupted and a global formulation, which emphasize a resemblance with the problem of the thermal utilisation factor, was adopted. An integral method, analogous to that use for the computation of this factor, gives the possibility to establish new and simple practical formulae, which require the use of a few basic functions only. These formulae are very accurate, as seen from the results of a variational method which was studied as a reference. Various correction effects are reviewed. Expressions which allow the exact treatment of fuel rod clusters are presented. The theory is confronted with various experimental results, and a new method of measuring the radial coefficient is proposed. (author) [fr

Theory of neutron slowing down in nuclear reactors

CERN Document Server

Ferziger, Joel H; Dunworth, J V

2013-01-01

The Theory of Neutron Slowing Down in Nuclear Reactors focuses on one facet of nuclear reactor design: the slowing down (or moderation) of neutrons from the high energies with which they are born in fission to the energies at which they are ultimately absorbed. In conjunction with the study of neutron moderation, calculations of reactor criticality are presented. A mathematical description of the slowing-down process is given, with particular emphasis on the problems encountered in the design of thermal reactors. This volume is comprised of four chapters and begins by considering the problems

Some Aspects of Diffusion Theory

CERN Document Server

Pignedoli, A

2011-01-01

This title includes: V.C.A. Ferraro: Diffusion of ions in a plasma with applications to the ionosphere; P.C. Kendall: On the diffusion in the atmosphere and ionosphere; F. Henin: Kinetic equations and Brownian motion; T. Kahan: Theorie des reacteurs nucleaires: methodes de resolution perturbationnelles, interactives et variationnelles; C. Cattaneo: Sulla conduzione del calore; C. Agostinelli: Formule di Green per la diffusione del campo magnetico in un fluido elettricamente conduttore; A. Pignedoli: Transformational methods applied to some one-dimensional problems concerning the equations of t

Diffusion in a liquid alloy - theories and experiments

International Nuclear Information System (INIS)

Chastang, C.

1997-01-01

Different theories concerning the calculation of diffusion coefficients in liquid metals, as well for auto as for hetero-diffusion are presented and some experimental procedures using tracer techniques in shear cells and capillary tubes are described. Diffusion curves are calculated with the TRIO-EF code. Calculated and measured values of diffusion coefficients are compared and discussed with regard to various diffusion mechanisms. Copper gadolinium mixtures have been investigated in more detail. (C.B.)

Numerical analysis for multi-group neutron-diffusion equation using Radial Point Interpolation Method (RPIM)

International Nuclear Information System (INIS)

Kim, Kyung-O; Jeong, Hae Sun; Jo, Daeseong

2017-01-01

Highlights: • Employing the Radial Point Interpolation Method (RPIM) in numerical analysis of multi-group neutron-diffusion equation. • Establishing mathematical formation of modified multi-group neutron-diffusion equation by RPIM. • Performing the numerical analysis for 2D critical problem. - Abstract: A mesh-free method is introduced to overcome the drawbacks (e.g., mesh generation and connectivity definition between the meshes) of mesh-based (nodal) methods such as the finite-element method and finite-difference method. In particular, the Point Interpolation Method (PIM) using a radial basis function is employed in the numerical analysis for the multi-group neutron-diffusion equation. The benchmark calculations are performed for the 2D homogeneous and heterogeneous problems, and the Multiquadrics (MQ) and Gaussian (EXP) functions are employed to analyze the effect of the radial basis function on the numerical solution. Additionally, the effect of the dimensionless shape parameter in those functions on the calculation accuracy is evaluated. According to the results, the radial PIM (RPIM) can provide a highly accurate solution for the multiplication eigenvalue and the neutron flux distribution, and the numerical solution with the MQ radial basis function exhibits the stable accuracy with respect to the reference solutions compared with the other solution. The dimensionless shape parameter directly affects the calculation accuracy and computing time. Values between 1.87 and 3.0 for the benchmark problems considered in this study lead to the most accurate solution. The difference between the analytical and numerical results for the neutron flux is significantly increased in the edge of the problem geometry, even though the maximum difference is lower than 4%. This phenomenon seems to arise from the derivative boundary condition at (x,0) and (0,y) positions, and it may be necessary to introduce additional strategy (e.g., the method using fictitious points and

Fast neutron physics

International Nuclear Information System (INIS)

Moura Neto, C. de; Amorim, E.S. do.

1979-12-01

Finite systems of small dimensions were investigated in comparison with systems where the diffusion theory is valid with reasonable precision. Elaborated methods were introduced for the study of small systems, based on different approximations of the neutron transport equation. Experimental data, obtained from the literature, were compared with values by the ANISN-DLC/2D system. (Author) [pt

On diffusion process generators and scattering theory

International Nuclear Information System (INIS)

Demuth, M.

1980-01-01

In scattering theory the existence of wave operators is one of the mainly interesting points. For two selfadjoint operators K and H defined in separable Hilbertspaces H tilde and H' tilde, respectively, the usual two space wave operator is defined by Ωsub(+-)(H,J,K) = s-lim esup(itH)Jesup(-itK)Psup(ac), t → +-infinity, if these limits exist. J is the identification operator mapping H tilde into H' tilde. Psup(ac) is the orthogonal projection onto the absolutely continuous subspace of K. The objective is to prove the existence and completeness of the wave operator for K and K+V where K is a diffusion process generator and V a singular perturbation. Because generators of diffusion processes can be obtained by extension of second order differential operators with variable coefficients the result connects hard-core potential problems and wave operator existence for diffusion process generators including scattering theory for second order elliptic differential operators by means of the stochastic process theory and stochastic differential equation solutions. (author)

Statistical theory of neutron nuclear reactions

International Nuclear Information System (INIS)

Moldauer, P.A.

1978-02-01

The statistical theory of average neutron nucleus reaction cross sections is reviewed with emphasis on the justification of the Hauser Feshbach formula and its modifications for situations including isolated compound nucleus resonances, overlapping and interfering resonances, the competition of compound and direct reactions, and continuous treatment of residual nuclear states

Statistical theory of neutron nuclear reactions

International Nuclear Information System (INIS)

Moldauer, P.A.

1980-01-01

The statistical theory of average neutron nucleus reaction cross sections is reviewed with emphasis on the justification of the Hauser Feshbach formula and its modifications for situations including isolated compound nucleus resonances, overlapping and interfering resonances, the competition of compound and direct reactions, and continuous treatment of residual nuclear states. (author)

Numerical method for solving the three-dimensional time-dependent neutron diffusion equation

International Nuclear Information System (INIS)

Khaled, S.M.; Szatmary, Z.

2005-01-01

A numerical time-implicit method has been developed for solving the coupled three-dimensional time-dependent multi-group neutron diffusion and delayed neutron precursor equations. The numerical stability of the implicit computation scheme and the convergence of the iterative associated processes have been evaluated. The computational scheme requires the solution of large linear systems at each time step. For this purpose, the point over-relaxation Gauss-Seidel method was chosen. A new scheme was introduced instead of the usual source iteration scheme. (author)

Time Evolving Fission Chain Theory and Fast Neutron and Gamma-Ray Counting Distributions

International Nuclear Information System (INIS)

Kim, K. S.; Nakae, L. F.; Prasad, M. K.; Snyderman, N. J.; Verbeke, J. M.

2015-01-01

Here, we solve a simple theoretical model of time evolving fission chains due to Feynman that generalizes and asymptotically approaches the point model theory. The point model theory has been used to analyze thermal neutron counting data. This extension of the theory underlies fast counting data for both neutrons and gamma rays from metal systems. Fast neutron and gamma-ray counting is now possible using liquid scintillator arrays with nanosecond time resolution. For individual fission chains, the differential equations describing three correlated probability distributions are solved: the time-dependent internal neutron population, accumulation of fissions in time, and accumulation of leaked neutrons in time. Explicit analytic formulas are given for correlated moments of the time evolving chain populations. The equations for random time gate fast neutron and gamma-ray counting distributions, due to randomly initiated chains, are presented. Correlated moment equations are given for both random time gate and triggered time gate counting. There are explicit formulas for all correlated moments are given up to triple order, for all combinations of correlated fast neutrons and gamma rays. The nonlinear differential equations for probabilities for time dependent fission chain populations have a remarkably simple Monte Carlo realization. A Monte Carlo code was developed for this theory and is shown to statistically realize the solutions to the fission chain theory probability distributions. Combined with random initiation of chains and detection of external quanta, the Monte Carlo code generates time tagged data for neutron and gamma-ray counting and from these data the counting distributions.

Applications of a systematic homogenization theory for nodal diffusion methods

International Nuclear Information System (INIS)

Zhang, Hong-bin; Dorning, J.J.

1992-01-01

The authors recently have developed a self-consistent and systematic lattice cell and fuel bundle homogenization theory based on a multiple spatial scales asymptotic expansion of the transport equation in the ratio of the mean free path to the reactor characteristics dimension for use with nodal diffusion methods. The mathematical development leads naturally to self-consistent analytical expressions for homogenized diffusion coefficients and cross sections and flux discontinuity factors to be used in nodal diffusion calculations. The expressions for the homogenized nuclear parameters that follow from the systematic homogenization theory (SHT) are different from those for the traditional flux and volume-weighted (FVW) parameters. The calculations summarized here show that the systematic homogenization theory developed recently for nodal diffusion methods yields accurate values for k eff and assembly powers even when compared with the results of a fine mesh transport calculation. Thus, it provides a practical alternative to equivalence theory and GET (Ref. 3) and to simplified equivalence theory, which requires auxiliary fine-mesh calculations for assemblies embedded in a typical environment to determine the discontinuity factors and the equivalent diffusion coefficient for a homogenized assembly

Physics of pitch angle scattering and velocity diffusion. I - Theory

Science.gov (United States)

Karimabadi, H.; Krauss-Varban, D.; Terasawa, T.

1992-01-01

A general theory for the pitch angle scattering and velocity diffusion of particles in the field of a spectrum of waves in a magnetized plasma is presented. The test particle theory is used to analyze the particle motion. The form of diffusion surfaces is examined, and analytical expressions are given for the resonance width and bounce frequency. The resonance widths are found to vary strongly as a function of harmonic number. The resulting diffusion can be quite asymmetric with respect to pitch angle of 90 deg. The conditions for the onset of pitch angle scattering and energy diffusion are explained in detail. Some of the known shortcomings of the standard quasi-linear theory are also addressed, and ways to overcome them are shown. In particular, the often stated quasi-linear gap at 90 deg is found to exist only under very special cases. For instance, oblique wave propagation can easily remove the gap. The conditions for the existence of the gap are described in great detail. A new diffusion equation which takes into account the finite resonance widths is also discussed. The differences between this new theory and the standard resonance broadening theory is explained.

Determination of thermal neutrons diffusion length in graphite; Determinacion de la Longitud de Difusion de los Neutrones Termicos en Grafito

Energy Technology Data Exchange (ETDEWEB)

Garcia Fite, J

1959-07-01

The diffusion length of thermal neutrons in graphite using the less possible quantity of material has been determined. The proceeding used was the measurement in a graphite pile which has a punctual source of rapid neutrons inside surrounded by a reflector medium (paraffin or water). The measurement was done in the following conditions: a) introducing an aluminium plate between both materials. b) Introducing a cadmium plate between both materials. (Author) 91 refs.

Time-dependent pseudo-reciprocity relations in neutronics

International Nuclear Information System (INIS)

Modak, R.S.; Sahni, D.C.

2002-01-01

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

A comparison of Nodal methods in neutron diffusion calculations

Energy Technology Data Exchange (ETDEWEB)

Tavron, Barak [Israel Electric Company, Haifa (Israel) Nuclear Engineering Dept. Research and Development Div.

1996-12-01

The nuclear engineering department at IEC uses in the reactor analysis three neutron diffusion codes based on nodal methods. The codes, GNOMERl, ADMARC2 and NOXER3 solve the neutron diffusion equation to obtain flux and power distributions in the core. The resulting flux distributions are used for the furl cycle analysis and for fuel reload optimization. This work presents a comparison of the various nodal methods employed in the above codes. Nodal methods (also called Coarse-mesh methods) have been designed to solve problems that contain relatively coarse areas of homogeneous composition. In the nodal method parts of the equation that present the state in the homogeneous area are solved analytically while, according to various assumptions and continuity requirements, a general solution is sought out. Thus efficiency of the method for this kind of problems, is very high compared with the finite element and finite difference methods. On the other hand, using this method one can get only approximate information about the node vicinity (or coarse-mesh area, usually a feel assembly of a 20 cm size). These characteristics of the nodal method make it suitable for feel cycle analysis and reload optimization. This analysis requires many subsequent calculations of the flux and power distributions for the feel assemblies while there is no need for detailed distribution within the assembly. For obtaining detailed distribution within the assembly methods of power reconstruction may be applied. However homogenization of feel assembly properties, required for the nodal method, may cause difficulties when applied to fuel assemblies with many absorber rods, due to exciting strong neutron properties heterogeneity within the assembly. (author).

Application of diffusion theory to neutral atom transport in fusion plasmas

International Nuclear Information System (INIS)

Hasan, M.Z.; Conn, R.W.; Pomraning, G.C.

1987-01-01

It is found that the energy dependent diffusion theory provides excellent accuracy in the modelling of transport of neutral atoms in fusion plasmas. Two reasons in particular explain the good accuracy. First, while the plasma is optically thick for low energy neutrals, it is optically thin for high energy neutrals and the diffusion theory with Marshak boundary conditions gives accurate results for an optically thin medium, even for small values of c, the ratio of the scattering cross-section to the total cross-section. Second, the effective value of c at low energy is very close to 1 because of the downscattering via collisions of high energy neutrals. The first reason is proven computationally and theoretically by solving the transport equation in a power series in c and solving the diffusion equation with 'general' Marshak boundary conditions. The second reason is established numerically by comparing the results from a one-dimensional, general geometry, multigroup diffusion theory code, written for this purpose, with the results obtained using the transport code ANISN. Earlier studies comparing one-speed diffusion and transport theory indicated that the diffusion theory would be inaccurate. A detailed analysis shows that this conclusion is limited to a very specific case. Surprisingly, for a very wide range of conditions and when energy dependence is included, the diffusion theory is highly accurate. (author)

Statistical theory of neutron nuclear reactions

International Nuclear Information System (INIS)

Moldauer, P.A.

1975-01-01

The statistical theory of average neutron nucleus reaction cross sections is reviewed with emphasis on the justification of the Hauser Feshbach formula and its modifications for situations including isolated compound nucleus resonances, overlapping and interfering resonances, the competition of compound and direct reactions, and continuous treatment of residual nuclear states. 3 figures

Theory of neutron resonance cross sections for safety applications

International Nuclear Information System (INIS)

Froehner, F.H.

1992-09-01

Neutron resonances exert a strong influence on the behaviour of nuclear reactors, especially on their response to the temperature changes accompanying power excursions, and also on the efficiency of shielding materials. The relevant theory of neutron resonance cross sections including the practically important approximations is reviewed, both for the resolved and the unresolved resonance region. Numerical techniques for Doppler broadening of resonances are presented, and the construction of group constants and especially of self-shielding factors for neutronics calculations is outlined. (orig.) [de

On the reciprocity-like relations in linear neutron transport theory

International Nuclear Information System (INIS)

Modak, R.S.; Sahni, D.C.

1997-01-01

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. (author)

System of adjoint P1 equations for neutron moderation

International Nuclear Information System (INIS)

Martinez, Aquilino Senra; Silva, Fernando Carvalho da; Cardoso, Carlos Eduardo Santos

2000-01-01

In some applications of perturbation theory, it is necessary know the adjoint neutron flux, which is obtained by the solution of adjoint neutron diffusion equation. However, the multigroup constants used for this are weighted in only the direct neutron flux, from the solution of direct P1 equations. In this work, this procedure is questioned and the adjoint P1 equations are derived by the neutron transport equation, the reversion operators rules and analogies between direct and adjoint parameters. (author)

Point defect dynamics in sodium aluminum hydrides - a combined quasielastic neutron scattering and density functional theory study

DEFF Research Database (Denmark)

Shi, Qing; Voss, Johannes; Jacobsen, H.S.

2007-01-01

we study hydrogen dynamics in undoped and TiCl3-doped samples of NaAlH4 and Na3AlH6 using a combination of density functional theory calculations and quasielastic neutron scattering. Hydrogen dynamics is found to be limited and mediated by hydrogen vacancies in both alanate phases, requiring......Understanding the catalytic role of titanium-based additives on the reversible hydrogenation of complex metal hydrides is an essential step towards developing hydrogen storage materials for the transport sector. Improved bulk diffusion of hydrogen is one of the proposed catalytic effects, and here...

Generalization of the Fourier Convergence Analysis in the Neutron Diffusion Eigenvalue Problem

International Nuclear Information System (INIS)

Lee, Hyun Chul; Noh, Jae Man; Joo, Hyung Kook

2005-01-01

Fourier error analysis has been a standard technique for the stability and convergence analysis of linear and nonlinear iterative methods. Lee et al proposed new 2- D/1-D coupling methods and demonstrated several advantages of the new methods by performing a Fourier convergence analysis of the methods as well as two existing methods for a fixed source problem. We demonstrated the Fourier convergence analysis of one of the 2-D/1-D coupling methods applied to a neutron diffusion eigenvalue problem. However, the technique cannot be used directly to analyze the convergence of the other 2-D/1-D coupling methods since some algorithm-specific features were used in our previous study. In this paper we generalized the Fourier convergence analysis technique proposed and analyzed the convergence of the 2-D/1-D coupling methods applied to a neutron diffusion Eigenvalue problem using the generalized technique

Algorithm development and verification of UASCM for multi-dimension and multi-group neutron kinetics model

International Nuclear Information System (INIS)

Si, S.

2012-01-01

The Universal Algorithm of Stiffness Confinement Method (UASCM) for neutron kinetics model of multi-dimensional and multi-group transport equations or diffusion equations has been developed. The numerical experiments based on transport theory code MGSNM and diffusion theory code MGNEM have demonstrated that the algorithm has sufficient accuracy and stability. (authors)

Chapter 9: Experimental measurements of the diffusion area of neutrons in graphite

International Nuclear Information System (INIS)

Brown, G.; McCulloch, D.B.

1963-01-01

This report describes measurements of the diffusion area of neutrons in a solid graphite exponential stack, and in a stack containing cylindrical air channels of 4.5 in. diameter, arranged on a square lattice of 8 in. pitch. The resulting diffusion area ratios are compared with the theoretical predictions of a number of authors. The diffusion area ratios deduced from a pair of experiments in which the orientation of the air channels with respect to the source-plane is changed are found to be in agreement with those deduced from experiments in which the stack size is changed but a constant air channel orientation maintained. (author)

Differential Neutron Scattering from Hydrogenous Moderators; Diffusion Differentielle des Neutrons par des Ralentisseurs Hydrogenes; Differentsial'noe rasseyanie nejtronov iz vodorodosoderzhashchikh zamedlitelej; Dispersion Diferencial de Neutrones en Moderadores Hidrogenados

Energy Technology Data Exchange (ETDEWEB)

Beyster, J. R.; Young, J. C.; Neill, J. M.; Mowry, W. R. [General Atomic Division of General Dynamics Corporation, John Jay Hopkins Laboratory for Pure and Applied Science, San Diego, CA (United States)

1965-08-15

de realite physique. En outre, ce modele simple ne permet pas de prevoir avec exactitude la diffusion selon de grands angles. Les donnees experimentales sont utilisees a diverses fins pratiques. Tout d'abord, les distributions angulaires sont tres sensibles aux proprietes physiques du modele de diffusion et elles servent a les verifier. Deuxiemement, les resultats experimentaux sont sensibles aux ordres superieurs de la diffusion Pn, par opposition a plusieurs experiences integrales qui sont surtout sensibles a la diffusion P{sub 0}. En particulier, on peut verifier le noyau de diffusion P{sub 1} approprie a un modele moleculaire donne. Troisiemement, on peut calculer la section efficace de transport directement a partir des experiences en vue de l'utiliser dans l'analyse des reacteurs en theorie multigroupe. (author) [Spanish] Los autores estan midiendo, por el metodo del tiempo de vuelo, las secciones eficaces diferenciales de dispersion neutronica (d{sigma}/d {Omega}) de los moderadores de uso corriente. Para ello emplean una intensa fuente pulsada de neutrones termicos producidos por el acelerador lineal de la General Atomic, y una trayectoria de vuelo de 12 m, al final de la cual se encuentra una muestra delgada del moderador. Ademas, hay una breve trayectoria final de vuelo para los neutrones dispersados que va desde la muestra hasta varios detectores de neutrones totalmente absorbentes. Con este procedimiento puede medirse simultaneamente la distribucion angular de dispersion correspondiente a mas de 50 energias de incidencia de los neutrones. Las intensidades son elevadas, la actividad de fondo es baja y bien definida, y las mediciones pueden efectuarse rapidamente en todos los angulos de dispersion comprendidos entre 10 Degree-Sign y 155 Degree-Sign . Se presentan mediciones de las secciones eficaces de dispersion diferencial del vanadio, H{sub 2}O, D{sub 2}O y ZrH. El V se ha investigado para comprobar el aparato experimental. Se han efectuado mediciones en

Importance estimation in Monte Carlo modelling of neutron and photon transport

International Nuclear Information System (INIS)

Mickael, M.W.

1992-01-01

The estimation of neutron and photon importance in a three-dimensional geometry is achieved using a coupled Monte Carlo and diffusion theory calculation. The parameters required for the solution of the multigroup adjoint diffusion equation are estimated from an analog Monte Carlo simulation of the system under investigation. The solution of the adjoint diffusion equation is then used as an estimate of the particle importance in the actual simulation. This approach provides an automated and efficient variance reduction method for Monte Carlo simulations. The technique has been successfully applied to Monte Carlo simulation of neutron and coupled neutron-photon transport in the nuclear well-logging field. The results show that the importance maps obtained in a few minutes of computer time using this technique are in good agreement with Monte Carlo generated importance maps that require prohibitive computing times. The application of this method to Monte Carlo modelling of the response of neutron porosity and pulsed neutron instruments has resulted in major reductions in computation time. (Author)

Thermal neutron scattering from a hydrogen-metal system in terms of a general multi-sublattice jump diffusion model

International Nuclear Information System (INIS)

Kutner, R.; Sosnowska, I.

1977-01-01

A Multi-Sublattice Jump Diffusion Model (MSJD) for hydrogen diffusion through interstitial-site lattices is presented. The MSJD approach may, in principle, be considered as an extension of the Rowe et al (J. Phys. Chem. Solids; 32:41 (1971)) model. Jump diffusion to any neighbours with different jump times which may be asymmetric in space is discussed. On the basis of the model a new method of calculating the diffusion tensor is advanced. The quasielastic, double differential cross section for thermal neutron scattering is obtained in terms of the MSJD model. The model can be used for systems in which interstitial jump diffusion of impurity particles occurs. In Part II the theoretical results are compared with those for quasielastic neutron scattering from the αNbHsub(x) system. (author)

An incident flux expansion transport theory method suitable for coupling to diffusion theory methods in hexagonal geometry

International Nuclear Information System (INIS)

Hayward, Robert M.; Rahnema, Farzad; Zhang, Dingkang

2013-01-01

Highlights: ► A new hybrid stochastic–deterministic transport theory method to couple with diffusion theory. ► The method is implemented in 2D hexagonal geometry. ► The new method produces excellent results when compared with Monte Carlo reference solutions. ► The method is fast, solving all test cases in less than 12 s. - Abstract: A new hybrid stochastic–deterministic transport theory method, which is designed to couple with diffusion theory, is presented. The new method is an extension of the incident flux response expansion method, and it combines the speed of diffusion theory with the accuracy of transport theory. With ease of use in mind, the new method is derived in such a way that it can be implemented with only minimal modifications to an existing diffusion theory method. A new angular expansion, which is necessary for the diffusion theory coupling, is developed in 2D and 3D. The method is implemented in 2D hexagonal geometry, and an HTTR benchmark problem is used to test its accuracy in a standalone configuration. It is found that the new method produces excellent results (with average relative error in partial current less than 0.033%) when compared with Monte Carlo reference solutions. Furthermore, the method is fast, solving all test cases in less than 12 s

Analysis of EBR-II neutron and photon physics by multidimensional transport-theory techniques

International Nuclear Information System (INIS)

Jacqmin, R.P.; Finck, P.J.; Palmiotti, G.

1994-01-01

This paper contains a review of the challenges specific to the EBR-II core physics, a description of the methods and techniques which have been developed for addressing these challenges, and the results of some validation studies relative to power-distribution calculations. Numerical tests have shown that the VARIANT nodal code yields eigenvalue and power predictions as accurate as finite difference and discrete ordinates transport codes, at a small fraction of the cost. Comparisons with continuous-energy Monte Carlo results have proven that the errors introduced by the use of the diffusion-theory approximation in the collapsing procedure to obtain broad-group cross sections, kerma factors, and photon-production matrices, have a small impact on the EBR-II neutron/photon power distribution

Inter-atomic force constants of BaF{sub 2} by diffuse neutron scattering measurement

Energy Technology Data Exchange (ETDEWEB)

Sakuma, Takashi, E-mail: sakuma@mx.ibaraki.ac.jp; Makhsun,; Sakai, Ryutaro [Institute of Applied Beam Science, Ibaraki University, Mito 310-8512 (Japan); Xianglian [College of Physics and Electronics Information, Inner Mongolia University for the Nationalities, Tongliao 028043 (China); Takahashi, Haruyuki [Institute of Applied Beam Science, Ibaraki University, Hitachi 316-8511 (Japan); Basar, Khairul [Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung 40132 (Indonesia); Igawa, Naoki [Quantum Beam Science Directorate, Japan Atomic Energy Agency, Tokai 319-1195 (Japan); Danilkin, Sergey A. [Bragg Institute, Australian Nuclear Science and Technology Organisation, Kirrawee DC NSW 2232 (Australia)

2015-04-16

Diffuse neutron scattering measurement on BaF{sub 2} crystals was performed at 10 K and 295 K. Oscillatory form in the diffuse scattering intensity of BaF{sub 2} was observed at 295 K. The correlation effects among thermal displacements of F-F atoms were obtained from the analysis of oscillatory diffuse scattering intensity. The force constants among neighboring atoms in BaF{sub 2} were determined and compared to those in ionic crystals and semiconductors.

Linear response theory of activated surface diffusion with interacting adsorbates

Energy Technology Data Exchange (ETDEWEB)

Marti' nez-Casado, R. [Department of Chemistry, Imperial College London, South Kensington, London SW7 2AZ (United Kingdom); Sanz, A.S.; Vega, J.L. [Instituto de Fi' sica Fundamental, Consejo Superior de Investigaciones Cientificas, Serrano 123, 28006 Madrid (Spain); Rojas-Lorenzo, G. [Instituto Superior de Tecnologi' as y Ciencias Aplicadas, Ave. Salvador Allende, esq. Luaces, 10400 La Habana (Cuba); Instituto de Fi' sica Fundamental, Consejo Superior de Investigaciones Cienti' ficas, Serrano 123, 28006 Madrid (Spain); Miret-Artes, S., E-mail: s.miret@imaff.cfmac.csic.es [Instituto de Fi' sica Fundamental, Consejo Superior de Investigaciones Cienti' ficas, Serrano 123, 28006 Madrid (Spain)

2010-05-12

Graphical abstract: Activated surface diffusion with interacting adsorbates is analyzed within the Linear Response Theory framework. The so-called interacting single adsorbate model is justified by means of a two-bath model, where one harmonic bath takes into account the interaction with the surface phonons, while the other one describes the surface coverage, this leading to defining a collisional friction. Here, the corresponding theory is applied to simple systems, such as diffusion on flat surfaces and the frustrated translational motion in a harmonic potential. Classical and quantum closed formulas are obtained. Furthermore, a more realistic problem, such as atomic Na diffusion on the corrugated Cu(0 0 1) surface, is presented and discussed within the classical context as well as within the framework of Kramer's theory. Quantum corrections to the classical results are also analyzed and discussed. - Abstract: Activated surface diffusion with interacting adsorbates is analyzed within the Linear Response Theory framework. The so-called interacting single adsorbate model is justified by means of a two-bath model, where one harmonic bath takes into account the interaction with the surface phonons, while the other one describes the surface coverage, this leading to defining a collisional friction. Here, the corresponding theory is applied to simple systems, such as diffusion on flat surfaces and the frustrated translational motion in a harmonic potential. Classical and quantum closed formulas are obtained. Furthermore, a more realistic problem, such as atomic Na diffusion on the corrugated Cu(0 0 1) surface, is presented and discussed within the classical context as well as within the framework of Kramer's theory. Quantum corrections to the classical results are also analyzed and discussed.

Domain decomposition methods for the mixed dual formulation of the critical neutron diffusion problem; Methodes de decomposition de domaine pour la formulation mixte duale du probleme critique de la diffusion des neutrons

Energy Technology Data Exchange (ETDEWEB)

Guerin, P

2007-12-15

The neutronic simulation of a nuclear reactor core is performed using the neutron transport equation, and leads to an eigenvalue problem in the steady-state case. Among the deterministic resolution methods, diffusion approximation is often used. For this problem, the MINOS solver based on a mixed dual finite element method has shown his efficiency. In order to take advantage of parallel computers, and to reduce the computing time and the local memory requirement, we propose in this dissertation two domain decomposition methods for the resolution of the mixed dual form of the eigenvalue neutron diffusion problem. The first approach is a component mode synthesis method on overlapping sub-domains. Several Eigenmodes solutions of a local problem solved by MINOS on each sub-domain are taken as basis functions used for the resolution of the global problem on the whole domain. The second approach is a modified iterative Schwarz algorithm based on non-overlapping domain decomposition with Robin interface conditions. At each iteration, the problem is solved on each sub domain by MINOS with the interface conditions deduced from the solutions on the adjacent sub-domains at the previous iteration. The iterations allow the simultaneous convergence of the domain decomposition and the eigenvalue problem. We demonstrate the accuracy and the efficiency in parallel of these two methods with numerical results for the diffusion model on realistic 2- and 3-dimensional cores. (author)

On the calibration methods for neutron moisture gauges

International Nuclear Information System (INIS)

Apostol, I.

1975-01-01

Theoretical and experimental calibration methods for devices using neutron sources to measure the water content in subsurface soil and other samples are investigated. Neutron flux density is evaluated by means of the two and three group diffusion and Fermi age theories. The correction criteria for the calibration curves are presented. The agreement of the theoretical curves with the determined experimental data may be considered as excellent. (author)

Domain decomposition method for solving the neutron diffusion equation

International Nuclear Information System (INIS)

Coulomb, F.

1989-03-01

The aim of this work is to study methods for solving the neutron diffusion equation; we are interested in methods based on a classical finite element discretization and well suited for use on parallel computers. Domain decomposition methods seem to answer this preoccupation. This study deals with a decomposition of the domain. A theoretical study is carried out for Lagrange finite elements and some examples are given; in the case of mixed dual finite elements, the study is based on examples [fr

INNOVATION DIFFUSION THEORY MAIN DEVELOPMENT STAGES

Directory of Open Access Journals (Sweden)

S. V. Lisafiev

2011-01-01

Full Text Available Abstract: Main innovation diffusion development theory stages are: Rogers model of moving new products to the market including characteristics of its segments; mathematic substantiation of this model by Bass; Moor model taking into account gaps between adjacent market segments; Goldenberg model making it possible to predict sales drops at new product life cycle initial stages. It is reasonable to use this theory while moving innovative products to the market.

One-velocity neutron diffusion calculations based on a two-group reactor model

Energy Technology Data Exchange (ETDEWEB)

Bingulac, S; Radanovic, L; Lazarevic, B; Matausek, M; Pop-Jordanov, J [Boris Kidric Institute of Nuclear Sciences, Vinca, Belgrade (Yugoslavia)

1965-07-01

Many processes in reactor physics are described by the energy dependent neutron diffusion equations which for many practical purposes can often be reduced to one-dimensional two-group equations. Though such two-group models are satisfactory from the standpoint of accuracy, they require rather extensive computations which are usually iterative and involve the use of digital computers. In many applications, however, and particularly in dynamic analyses, where the studies are performed on analogue computers, it is preferable to avoid iterative calculations. The usual practice in such situations is to resort to one group models, which allow the solution to be expressed analytically. However, the loss in accuracy is rather great particularly when several media of different properties are involved. This paper describes a procedure by which the solution of the two-group neutron diffusion. equations can be expressed analytically in the form which, from the computational standpoint, is as simple as the one-group model, but retains the accuracy of the two-group treatment. In describing the procedure, the case of a multi-region nuclear reactor of cylindrical geometry is treated, but the method applied and the results obtained are of more general application. Another approach in approximate solution of diffusion equations, suggested by Galanin is applicable only in special ideal cases.

Domain decomposition methods for the mixed dual formulation of the critical neutron diffusion problem

International Nuclear Information System (INIS)

Guerin, P.

2007-12-01

The neutronic simulation of a nuclear reactor core is performed using the neutron transport equation, and leads to an eigenvalue problem in the steady-state case. Among the deterministic resolution methods, diffusion approximation is often used. For this problem, the MINOS solver based on a mixed dual finite element method has shown his efficiency. In order to take advantage of parallel computers, and to reduce the computing time and the local memory requirement, we propose in this dissertation two domain decomposition methods for the resolution of the mixed dual form of the eigenvalue neutron diffusion problem. The first approach is a component mode synthesis method on overlapping sub-domains. Several Eigenmodes solutions of a local problem solved by MINOS on each sub-domain are taken as basis functions used for the resolution of the global problem on the whole domain. The second approach is a modified iterative Schwarz algorithm based on non-overlapping domain decomposition with Robin interface conditions. At each iteration, the problem is solved on each sub domain by MINOS with the interface conditions deduced from the solutions on the adjacent sub-domains at the previous iteration. The iterations allow the simultaneous convergence of the domain decomposition and the eigenvalue problem. We demonstrate the accuracy and the efficiency in parallel of these two methods with numerical results for the diffusion model on realistic 2- and 3-dimensional cores. (author)

Defects and diffusion, theory & simulation II

CERN Document Server

Fisher, David J

2010-01-01

This second volume in a new series covering entirely general results in the fields of defects and diffusion includes 356 abstracts of papers which appeared between the end of 2009 and the end of 2010. As well as the abstracts, the volume includes original papers on theory/simulation, semiconductors and metals: ""Predicting Diffusion Coefficients from First Principles ..."" (Mantina, Chen & Liu), ""Gouge Assessment for Pipes ..."" (Meliani, Pluvinage & Capelle), ""Simulation of the Impact Behaviour of ... Hollow Sphere Structures"" (Ferrano, Speich, Rimkus, Merkel & Öchsner), ""Elastic-Plastic

Asymptotic equivalence of neutron diffusion and transport in time-independent reactor systems

International Nuclear Information System (INIS)

Borysiewicz, M.; Mika, J.; Spiga, G.

1982-01-01

Presented in this paper is the asymptotic analysis of the time-independent neutron transport equation in the second-order variational formulation. The small parameter introduced into the equation is an estimate of the ratio of absorption and leakage to scattering in the system considered. When the ratio tends to zero, the weak solution to the transport problem tends to the weak solution of the diffusion problem, including properly defined boundary conditions. A formula for the diffusion coefficient different from that based on averaging the transport mean-free-path is derived

Solution of the multilayer multigroup neutron diffusion equation in cartesian geometry by fictitious borders power method

Energy Technology Data Exchange (ETDEWEB)

Zanette, Rodrigo; Petersen, Caudio Zen [Univ. Federal de Pelotas, Capao do Leao (Brazil). Programa de Pos Graduacao em Modelagem Matematica; Schramm, Marcello [Univ. Federal de Pelotas (Brazil). Centro de Engenharias; Zabadal, Jorge Rodolfo [Univ. Federal do Rio Grande do Sul, Tramandai (Brazil)

2017-05-15

In this paper a solution for the one-dimensional steady state Multilayer Multigroup Neutron Diffusion Equation in cartesian geometry by Fictitious Borders Power Method and a perturbative analysis of this solution is presented. For each new iteration of the power method, the neutron flux is reconstructed by polynomial interpolation, so that it always remains in a standard form. However when the domain is long, an almost singular matrix arises in the interpolation process. To eliminate this singularity the domain segmented in R regions, called fictitious regions. The last step is to solve the neutron diffusion equation for each fictitious region in analytical form locally. The results are compared with results present in the literature. In order to analyze the sensitivity of the solution, a perturbation in the nuclear parameters is inserted to determine how a perturbation interferes in numerical results of the solution.

Adjoint P1 equations solution for neutron slowing down; Solucao das equacoes P1 adjuntas para moderacao de neutrons

Energy Technology Data Exchange (ETDEWEB)

Cardoso, Carlos Eduardo Santos; Martinez, Aquilino Senra; Silva, Fernando Carvalho da [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear

2002-07-01

In some applications of perturbation theory, it is necessary know the adjoint neutron flux, which is obtained by the solution of adjoint neutron diffusion equation. However, the multigroup constants used for this are weighted in only the direct neutron flux, from the solution of direct P1 equations. In this work, the adjoint P1 equations are derived by the neutron transport equation, the reversion operators rules and analogies between direct and adjoint parameters. The direct and adjoint neutron fluxes resulting from the solution of P{sub 1} equations were used to three different weighting processes, to obtain the macrogroup macroscopic cross sections. It was found out noticeable differences among them. (author)

Diffusion coefficient calculations for cylindrical cells

International Nuclear Information System (INIS)

Lam-Hime, M.

1983-03-01

An accurate and general diffusion coefficient calculation for cylindrical cells is described using isotropic scattering integral transport theory. This method has been particularly applied to large regular lattices of graphite-moderated reactors with annular coolant channels. The cells are divided into homogeneous zones, and a zone-wise flux expansion is used to formulate a collision probability problem. The reflection of neutrons at the cell boundary is accounted for by the conservation of the neutron momentum. The uncorrected diffusion coefficient Benoist's definition is used, and the described formulation does not neglect any effect. Angular correlation terms, energy coupling non-uniformity and anisotropy of the classical flux are exactly taken into account. Results for gas-graphite typical cells are given showing the importance of these approximations

Theory of deep inelastic neutron scattering: Hard-core perturbation theory

International Nuclear Information System (INIS)

Silver, R.N.

1988-01-01

Details are presented of a new many-body theory for deep inelastic neutron scattering (DINS) experiments to measure momentum distributions in quantum fluids and solids. The high-momentum and energy-transfer scattering law in helium is shown to be a convolution of the impulse approximation with a final-state broadening function which depends on the scattering phase shifts and the radial distribution function. The predicted broadening satisfies approximate Y scaling, is neither Lorentzian nor Gaussian, and obeys the f, ω 2 , and ω 3 sum rules. The derivation uses a combination of Liouville perturbation theory, projection superoperators, and semiclassical methods which I term ''hard-core perturbation theory.'' A review is presented of the predictions of prior theories for DINS experiments in relation to the present work. A subsequent paper will present massive numerical predictions and a discussion of DINS experiments on superfluid 4 He

Rhodium SPND's Error Reduction using Extended Kalman Filter combined with Time Dependent Neutron Diffusion Equation

International Nuclear Information System (INIS)

Lee, Jeong Hun; Park, Tong Kyu; Jeon, Seong Su

2014-01-01

The Rhodium SPND is accurate in steady-state conditions but responds slowly to changes in neutron flux. The slow response time of Rhodium SPND precludes its direct use for control and protection purposes specially when nuclear power plant is used for load following. To shorten the response time of Rhodium SPND, there were some acceleration methods but they could not reflect neutron flux distribution in reactor core. On the other hands, some methods for core power distribution monitoring could not consider the slow response time of Rhodium SPND and noise effect. In this paper, time dependent neutron diffusion equation is directly used to estimate reactor power distribution and extended Kalman filter method is used to correct neutron flux with Rhodium SPND's and to shorten the response time of them. Extended Kalman filter is effective tool to reduce measurement error of Rhodium SPND's and even simple FDM to solve time dependent neutron diffusion equation can be an effective measure. This method reduces random errors of detectors and can follow reactor power level without cross-section change. It means monitoring system may not calculate cross-section at every time steps and computing time will be shorten. To minimize delay of Rhodium SPND's conversion function h should be evaluated in next study. Neutron and Rh-103 reaction has several decay chains and half-lives over 40 seconds causing delay of detection. Time dependent neutron diffusion equation will be combined with decay chains. Power level and distribution change corresponding movement of control rod will be tested with more complicated reference code as well as xenon effect. With these efforts, final result is expected to be used as a powerful monitoring tool of nuclear reactor core

Rhodium SPND's Error Reduction using Extended Kalman Filter combined with Time Dependent Neutron Diffusion Equation

Energy Technology Data Exchange (ETDEWEB)

Lee, Jeong Hun; Park, Tong Kyu; Jeon, Seong Su [FNC Technology Co., Ltd., Yongin (Korea, Republic of)

2014-05-15

The Rhodium SPND is accurate in steady-state conditions but responds slowly to changes in neutron flux. The slow response time of Rhodium SPND precludes its direct use for control and protection purposes specially when nuclear power plant is used for load following. To shorten the response time of Rhodium SPND, there were some acceleration methods but they could not reflect neutron flux distribution in reactor core. On the other hands, some methods for core power distribution monitoring could not consider the slow response time of Rhodium SPND and noise effect. In this paper, time dependent neutron diffusion equation is directly used to estimate reactor power distribution and extended Kalman filter method is used to correct neutron flux with Rhodium SPND's and to shorten the response time of them. Extended Kalman filter is effective tool to reduce measurement error of Rhodium SPND's and even simple FDM to solve time dependent neutron diffusion equation can be an effective measure. This method reduces random errors of detectors and can follow reactor power level without cross-section change. It means monitoring system may not calculate cross-section at every time steps and computing time will be shorten. To minimize delay of Rhodium SPND's conversion function h should be evaluated in next study. Neutron and Rh-103 reaction has several decay chains and half-lives over 40 seconds causing delay of detection. Time dependent neutron diffusion equation will be combined with decay chains. Power level and distribution change corresponding movement of control rod will be tested with more complicated reference code as well as xenon effect. With these efforts, final result is expected to be used as a powerful monitoring tool of nuclear reactor core.

Performance characteristics of specified power reactors in multidimensional neutron diffusion problems

International Nuclear Information System (INIS)

Kim, M.G.

1980-01-01

The multigroup neutron diffusion equations with the constraint of specified power distributions are investigated by the application of the straight-line method which can be considered as the limiting case of zero mesh space in the finite difference method. The standard partial differential form of the diffusion equation is reduced to sets of ordinary differential equations and then converted into sets of integral equations by using Green's functions defined on the pseudo straight lines. Coupling of each straight line to the adjacent lines arises from the application of a three-point central difference formula. The interfaces encountered between two regions are taken into account by imposing the continuity conditions for the grown fluxes and net currents with Taylor expansions of internal fluxes at the interface positions. A few sample problems are selected to test the validity of the method. It is found that the proposed method of solution is similar to the finite Fourier sine transform. Numerical results for the solutions obtained by the method of straight lines are compared with the results of the exact analytical solutions for simple geometries. These comparisons indicate that the proposed method is compatible with the analytical method, and in some problems considered the straight-line solutions are much more efficient than the exact solutions. The method is also extended to the reactor kinetics problem by expressing the kinetics parameters in terms of the basis functions which are used to obtain the solutions of the steady-state neutron diffusion equations

Fast diffusion in the intermetallics Ni3Sb and Fe3Si: a neutron scattering study

International Nuclear Information System (INIS)

Randl, O.G.

1994-02-01

We present the results of neutron scattering experiments designed to elucidate the reason for the extraordinarily fast majority component diffusion in two intermetallic alloys of DO 3 structure, Fe 3 Si and Ni 3 Sb: We have performed diffraction measurements in order to determine the crystal structure and the state of order of both alloys as a function of composition and temperature. The results on Fe 3 Si essentially confirm the classical phase diagram: The alloys of a composition between 16 and 25 at % Si are DO 3 -ordered at room temperature and disorder at high temperatures. The high-temperature phase Ni 3 Sb also crystallizes in the DO 3 structure. Vacancies are created in one Ni sublattice at Sb contents beyond 25 at %. In a second step the diffusion mechanism in Ni 3 Sb has been studied by means of quasielastic neutron scattering. The results are reconcileable with a very simple NN jump model between the two different Ni sublattices. Finally, the lattice dynamics of Fe 3 Si and Ni 3 Sb has been studied by inelastic neutron scattering in dependence of temperature (both alloys) and alloy composition (Fe 3 Si only). The results on Fe 3 Si indicate clearly that phonon enhancement is not the main reason for fast diffusion in this alloy. In Ni 3 Sb no typical signs of phonon-enhanced diffusion have been found either. As a conclusion, fast diffusion in DO 3 intermetallics is explained by extraordinarily high vacancy concentrations (several atomic percent) in the majority component sublattices. (author)

Mesh-size errors in diffusion-theory calculations using finite-difference and finite-element methods

International Nuclear Information System (INIS)

Baker, A.R.

1982-07-01

A study has been performed of mesh-size errors in diffusion-theory calculations using finite-difference and finite-element methods. As the objective was to illuminate the issues, the study was performed for a 1D slab model of a reactor with one neutron-energy group for which analytical solutions were possible. A computer code SLAB was specially written to perform the finite-difference and finite-element calculations and also to obtain the analytical solutions. The standard finite-difference equations were obtained by starting with an expansion of the neutron current in powers of the mesh size, h, and keeping terms as far as h 2 . It was confirmed that these equations led to the well-known result that the criticality parameter varied with the square of the mesh size. An improved form of the finite-difference equations was obtained by continuing the expansion for the neutron current as far as the term in h 4 . In this case, the critical parameter varied as the fourth power of the mesh size. The finite-element solutions for 2 and 3 nodes per element revealed that the criticality parameter varied as the square and fourth power of the mesh size, respectively. Numerical results are presented for a bare reactive core of uniform composition with 2 zones of different uniform mesh and for a reactive core with an absorptive reflector. (author)

A solution of the thermal neutron diffusion equation for a two-region cyclindrical system program for ODRA-1305 computer

International Nuclear Information System (INIS)

Drozdowicz, K.; Woznicka, U.

1982-01-01

The program in FORTRAN for the ODRA-1305 computer is described. The dependence of the decay constant of the thermal neutron flux upon the dimensions of the two-region concentric cylindrical system is the result of the program. The solution (with a constant neutron flux in the inner medium assumed) is generally obtained in the one-group diffusion approximation by the method of the perturbation calculation. However, the energy distribution of the thermal neutron flux and the diffusion cooling are taken into account. The program is written for the case when the outer medium is hydrogenous. The listing of the program and an example of calculation results are included. (author)

An analytical multigroup benchmark for (n, γ) and (n, n', γ) verification of diffusion theory algorithms

International Nuclear Information System (INIS)

Ganapol, B.D.

2011-01-01

Highlights: → Coupled neutron and gamma transport is considered in the multigroup diffusion approximation. → The model accommodates fission, up- and down-scattering and common neutron-gamma interactions. → The exact solution to the diffusion equation in a heterogeneous media of any number of regions is found. → The solution is shown to parallel the one-group case in a homogeneous medium. → The discussion concludes with a heterogeneous, 2 fuel-plate 93.2% enriched reactor fuel benchmark demonstration. - Abstract: The angular flux for the 'rod model' describing coupled neutron/gamma (n, γ) diffusion has a particularly straightforward analytical representation when viewed from the perspective of a one-group homogeneous medium. Cast in the form of matrix functions of a diagonalizable matrix, the solution to the multigroup equations in heterogeneous media is greatly simplified. We shall show exactly how the one-group homogeneous medium solution leads to the multigroup solution.

Diffuse reflectance relations based on diffusion dipole theory for large absorption and reduced scattering.

Science.gov (United States)

Bremmer, Rolf H; van Gemert, Martin J C; Faber, Dirk J; van Leeuwen, Ton G; Aalders, Maurice C G

2013-08-01

Diffuse reflectance spectra are used to determine the optical properties of biological samples. In medicine and forensic science, the turbid objects under study often possess large absorption and/or scattering properties. However, data analysis is frequently based on the diffusion approximation to the radiative transfer equation, implying that it is limited to tissues where the reduced scattering coefficient dominates over the absorption coefficient. Nevertheless, up to absorption coefficients of 20  mm-1 at reduced scattering coefficients of 1 and 11.5  mm-1, we observed excellent agreement (r2=0.994) between reflectance measurements of phantoms and the diffuse reflectance equation proposed by Zonios et al. [Appl. Opt.38, 6628-6637 (1999)], derived as an approximation to one of the diffusion dipole equations of Farrell et al. [Med. Phys.19, 879-888 (1992)]. However, two parameters were fitted to all phantom experiments, including strongly absorbing samples, implying that the reflectance equation differs from diffusion theory. Yet, the exact diffusion dipole approximation at high reduced scattering and absorption also showed agreement with the phantom measurements. The mathematical structure of the diffuse reflectance relation used, derived by Zonios et al. [Appl. Opt.38, 6628-6637 (1999)], explains this observation. In conclusion, diffuse reflectance relations derived as an approximation to the diffusion dipole theory of Farrell et al. can analyze reflectance ratios accurately, even for much larger absorption than reduced scattering coefficients. This allows calibration of fiber-probe set-ups so that the object's diffuse reflectance can be related to its absorption even when large. These findings will greatly expand the application of diffuse reflection spectroscopy. In medicine, it may allow the use of blue/green wavelengths and measurements on whole blood, and in forensic science, it may allow inclusion of objects such as blood stains and cloth at crime

Diffusion theory in biology: a relic of mechanistic materialism.

Science.gov (United States)

Agutter, P S; Malone, P C; Wheatley, D N

2000-01-01

Diffusion theory explains in physical terms how materials move through a medium, e.g. water or a biological fluid. There are strong and widely acknowledged grounds for doubting the applicability of this theory in biology, although it continues to be accepted almost uncritically and taught as a basis of both biology and medicine. Our principal aim is to explore how this situation arose and has been allowed to continue seemingly unchallenged for more than 150 years. The main shortcomings of diffusion theory will be briefly reviewed to show that the entrenchment of this theory in the corpus of biological knowledge needs to be explained, especially as there are equally valid historical grounds for presuming that bulk fluid movement powered by the energy of cell metabolism plays a prominent note in the transport of molecules in the living body. First, the theory's evolution, notably from its origins in connection with the mechanistic materialist philosophy of mid nineteenth century physiology, is discussed. Following this, the entrenchment of the theory in twentieth century biology is analyzed in relation to three situations: the mechanism of oxygen transport between air and mammalian tissues; the structure and function of cell membranes; and the nature of the intermediary metalbolism, with its implicit presumptions about the intracellular organization and the movement of molecules within it. In our final section, we consider several historically based alternatives to diffusion theory, all of which have their precursors in nineteenth and twentieth century philosophy of science.

Application of Van Hove theory to fast neutron inelastic scattering

International Nuclear Information System (INIS)

Stanicicj, V.

1974-11-01

The Vane Hove general theory of the double differential scattering cross section has been used to derive the particular expressions of the inelastic fast neutrons scattering kernel and scattering cross section. Since the considered energies of incoming neutrons being less than 10 MeV, it enables to use the Fermi gas model of nucleons. In this case it was easy to derive an analytical expression for the time-dependent correlation function of the nucleus. Further, by using an impulse approximation and a short-collision time approach, it was possible to derive the analytical expression of the scattering kernel and scattering cross section for the fast neutron inelastic scattering. The obtained expressions have been used for Fe nucleus. It has been shown a surprising agreement with the experiments. The main advantage of this theory is in its simplicity for some practical calculations and for some theoretical investigations of nuclear processes

Thermal hydraulic and neutronic interaction in the rotating bed reactor

International Nuclear Information System (INIS)

Lee, C.C.

1986-01-01

Power transient characteristics in a rotating fluidized bed reactor (RBR) are investigated theoretically. A propellant flow perturbation is assumed to occur in an initially equilibrium state of the core. Transfer functions representing quasi-one-dimensional mutual feedback between thermal hydraulics and neutronics are developed and analyzed in the frequency domain. Neutronic responses are determined by Fermi-age theory for slowing down of fast neutrons and diffusion theory for thermal neutron distribution. Neutron leakage through the exhaust nozzle is accounted for by applying diffuse view factors similar to those applied in radiative heat transfer. The bed expansion behavior is described by a kinematic wave equation derived from the continuity of the gas phase. The drift flux approach is used to determine the yield fractions in the equilibrium bed. Thermal responses of fuel are evaluated by dividing it into several volume-averaged zones to better account for the transient effects over single zone models. Sample calculations are undertaken for the various operation conditions and design parameters of the RBR based on 250 MW/sub t/, 1000 MW/sub t/, and 5000 MW/sub t/ power reactors. The results show that power transients are dependent on the parametric changes of optical thickness and view factors

Solution of the multigroup neutron diffusion Eigenvalue problem in slab geometry by modified power method

Energy Technology Data Exchange (ETDEWEB)

Zanette, Rodrigo [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Programa de Pós-Graduação em Matemática Aplicada; Petersen, Claudio Z.; Tavares, Matheus G., E-mail: rodrigozanette@hotmail.com, E-mail: claudiopetersen@yahoo.com.br, E-mail: matheus.gulartetavares@gmail.com [Universidade Federal de Pelotas (UFPEL), RS (Brazil). Programa de Pós-Graduação em Modelagem Matemática

2017-07-01

We describe in this work the application of the modified power method for solve the multigroup neutron diffusion eigenvalue problem in slab geometry considering two-dimensions for nuclear reactor global calculations. It is well known that criticality calculations can often be best approached by solving eigenvalue problems. The criticality in nuclear reactors physics plays a relevant role since establishes the ratio between the numbers of neutrons generated in successive fission reactions. In order to solve the eigenvalue problem, a modified power method is used to obtain the dominant eigenvalue (effective multiplication factor (K{sub eff})) and its corresponding eigenfunction (scalar neutron flux), which is non-negative in every domain, that is, physically relevant. The innovation of this work is solving the neutron diffusion equation in analytical form for each new iteration of the power method. For solve this problem we propose to apply the Finite Fourier Sine Transform on one of the spatial variables obtaining a transformed problem which is resolved by well-established methods for ordinary differential equations. The inverse Fourier transform is used to reconstruct the solution for the original problem. It is known that the power method is an iterative source method in which is updated by the neutron flux expression of previous iteration. Thus, for each new iteration, the neutron flux expression becomes larger and more complex due to analytical solution what makes propose that it be reconstructed through an polynomial interpolation. The methodology is implemented to solve a homogeneous problem and the results are compared with works presents in the literature. (author)

Adjoint P1 equations solution for neutron slowing down

International Nuclear Information System (INIS)

Cardoso, Carlos Eduardo Santos; Martinez, Aquilino Senra; Silva, Fernando Carvalho da

2002-01-01

In some applications of perturbation theory, it is necessary know the adjoint neutron flux, which is obtained by the solution of adjoint neutron diffusion equation. However, the multigroup constants used for this are weighted in only the direct neutron flux, from the solution of direct P1 equations. In this work, the adjoint P1 equations are derived by the neutron transport equation, the reversion operators rules and analogies between direct and adjoint parameters. The direct and adjoint neutron fluxes resulting from the solution of P 1 equations were used to three different weighting processes, to obtain the macrogroup macroscopic cross sections. It was found out noticeable differences among them. (author)

Homogenization of neutronic diffusion models; Homogeneisation des modeles de diffusion en neutronique

Energy Technology Data Exchange (ETDEWEB)

Capdebosq, Y

1999-09-01

In order to study and simulate nuclear reactor cores, one needs to access the neutron distribution in the core. In practice, the description of this density of neutrons is given by a system of diffusion equations, coupled by non differential exchange terms. The strong heterogeneity of the medium constitutes a major obstacle to the numerical computation of this models at reasonable cost. Homogenization appears as compulsory. Heuristic methods have been developed since the origin by nuclear physicists, under a periodicity assumption on the coefficients. They consist in doing a fine computation one a single periodicity cell, to solve the system on the whole domain with homogeneous coefficients, and to reconstruct the neutron density by multiplying the solutions of the two computations. The objectives of this work are to provide mathematically rigorous basis to this factorization method, to obtain the exact formulas of the homogenized coefficients, and to start on geometries where two periodical medium are placed side by side. The first result of this thesis concerns eigenvalue problem models which are used to characterize the state of criticality of the reactor, under a symmetry assumption on the coefficients. The convergence of the homogenization process is proved, and formulas of the homogenized coefficients are given. We then show that without symmetry assumptions, a drift phenomenon appears. It is characterized by the mean of a real Bloch wave method, which gives the homogenized limit in the general case. These results for the critical problem are then adapted to the evolution model. Finally, the homogenization of the critical problem in the case of two side by side periodic medium is studied on a one dimensional on equation model. (authors)

Neutron pulse propagation in natural UO sub(2) subcritical assembly moderated by heavy water

International Nuclear Information System (INIS)

Prado Souza, R.M.G. do.

1976-01-01

Short neutron bursts are fed to the graphite base of CAPITU, a D sub(2)O - natural uranium subcritical assembly. Due to the dispersive properties of the media the wave -components of the neutron pulses are attenuated and phase shifted along the axial direction. The experimental impulse response is Fourier transformed to yield the system's dispersion law, a relationship connecting the neutron diffusion parameters and the inverse complex relaxation length K (ω). The experimental results for five assemblies studied in CAPITU are compared with the theoretical dispersion law obtained from the two group diffusion theory. (author)

PHISICS multi-group transport neutronic capabilities for RELAP5

Energy Technology Data Exchange (ETDEWEB)

Epiney, A.; Rabiti, C.; Alfonsi, A.; Wang, Y.; Cogliati, J.; Strydom, G. [Idaho National Laboratory (INL), 2525 N. Fremont Ave., Idaho Falls, ID 83402 (United States)

2012-07-01

PHISICS is a neutronic code system currently under development at INL. Its goal is to provide state of the art simulation capability to reactor designers. This paper reports on the effort of coupling this package to the thermal hydraulic system code RELAP5. This will enable full prismatic core and system modeling and the possibility to model coupled (thermal-hydraulics and neutronics) problems with more options for 3D neutron kinetics, compared to the existing diffusion theory neutron kinetics module in RELAP5 (NESTLE). The paper describes the capabilities of the coupling and illustrates them with a set of sample problems. (authors)

Field theory of propagating reaction-diffusion fronts

International Nuclear Information System (INIS)

Escudero, C.

2004-01-01

The problem of velocity selection of reaction-diffusion fronts has been widely investigated. While the mean-field limit results are well known theoretically, there is a lack of analytic progress in those cases in which fluctuations are to be taken into account. Here, we construct an analytic theory connecting the first principles of the reaction-diffusion process to an effective equation of motion via field-theoretic arguments, and we arrive at results already confirmed by numerical simulations

Performance modeling of parallel algorithms for solving neutron diffusion problems

International Nuclear Information System (INIS)

Azmy, Y.Y.; Kirk, B.L.

1995-01-01

Neutron diffusion calculations are the most common computational methods used in the design, analysis, and operation of nuclear reactors and related activities. Here, mathematical performance models are developed for the parallel algorithm used to solve the neutron diffusion equation on message passing and shared memory multiprocessors represented by the Intel iPSC/860 and the Sequent Balance 8000, respectively. The performance models are validated through several test problems, and these models are used to estimate the performance of each of the two considered architectures in situations typical of practical applications, such as fine meshes and a large number of participating processors. While message passing computers are capable of producing speedup, the parallel efficiency deteriorates rapidly as the number of processors increases. Furthermore, the speedup fails to improve appreciably for massively parallel computers so that only small- to medium-sized message passing multiprocessors offer a reasonable platform for this algorithm. In contrast, the performance model for the shared memory architecture predicts very high efficiency over a wide range of number of processors reasonable for this architecture. Furthermore, the model efficiency of the Sequent remains superior to that of the hypercube if its model parameters are adjusted to make its processors as fast as those of the iPSC/860. It is concluded that shared memory computers are better suited for this parallel algorithm than message passing computers

Study of reactor analysis codes available at IPEN and their application to problems involving the diffusion theory

International Nuclear Information System (INIS)

Mendonca, A.G.

1980-01-01

Two computer codes that are available at IPEN for analyses of static neutron diffusion problems are studied and applied. The CITATION code is animed at analyses of criticality, fuel burnup, flux and power distributions etc, in one, two, and three spatial dimensions in multigroup. The EXTERMINATOR code can be used for the same purposes as for CITATION with a limitation to one or two spatial dimensions. Basic theories and numerical techniques used in the codes are studied and summarized. Benchmark problems have been solved using the codes. Comparisons of the results show that both codes can be used with confidence in the analyses of nuclear reactor problems. (author) [pt

Dense fluid self-diffusion coefficient calculations using perturbation theory and molecular dynamics

Directory of Open Access Journals (Sweden)

COELHO L. A. F.

1999-01-01

Full Text Available A procedure to correlate self-diffusion coefficients in dense fluids by using the perturbation theory (WCA coupled with the smooth-hard-sphere theory is presented and tested against molecular simulations and experimental data. This simple algebraic expression correlates well the self-diffusion coefficients of carbon dioxide, ethane, propane, ethylene, and sulfur hexafluoride. We have also performed canonical ensemble molecular dynamics simulations by using the Hoover-Nosé thermostat and the mean-square displacement formula to compute self-diffusion coefficients for the reference WCA intermolecular potential. The good agreement obtained from both methods, when compared with experimental data, suggests that the smooth-effective-sphere theory is a useful procedure to correlate diffusivity of pure substances.

From microscopic to macroscopic dynamics in mean-field theory: effect of neutron skin on fusion barrier and dissipation

Energy Technology Data Exchange (ETDEWEB)

Lacroix, D

2001-07-01

In this work, we introduce a method to reduce the microscopic mean-field theory to a classical macroscopic dynamics at the initial stage of fusion reaction. We show that TDHF (Time-dependent Hartree-Fock) could be a useful tool to infer information on the fusion barrier as well as on one-body dissipation effect. We apply the reduction of information to the case of head-on reaction between a {sup 16}O and {sup 16,22,24,28}O in order to quantify the effect of neutron skin on fusion. We show that the precise determination of fusion barrier requires, in addition to the relative distance between center of mass, the introduction of an additional collective coordinate that explicitly breaks the neutron-proton symmetry. With this additional collective variable, we obtain a rather precise determination of the barrier position, height and diffuseness as well as one-body friction. (author)

Natural equilibria in steady-state neutron diffusion with temperature feedback

International Nuclear Information System (INIS)

Pounders, J. M.; Ingram, R.

2013-01-01

The critical diffusion equation with feedback is investigated within the context of steady-state multiphysics. It is proposed that for critical configurations there is no need to include the multiplication factor k in the formulation of the diffusion equation. This is notable because exclusion of k from the coupled system of equations precludes the mathematically tenuous notion of a nonlinear eigenvalue problem. On the other hand, it is shown that if the factor k is retained in the diffusion equation, as is currently common practice, then the resulting problem is equivalent to the constrained minimization of a functional representing the critical equilibrium of neutron and temperature distributions. The unconstrained solution corresponding to k = 1 represents the natural equilibrium of a critical system at steady-state. Computational methods for solving the constrained problem (with k) are briefly reviewed from the literature and a method for the unconstrained problem (without k) is outlined. A numerical example is studied to examine the effects of the constraint in the nonlinear system. (authors)

Differential and integral characteristics of prompt fission neutrons in the statistical theory

International Nuclear Information System (INIS)

Gerasimenko, B.F.; Rubchenya, V.A.

1989-01-01

Hauser-Feshbach statistical theory is the most consistent approach to the calculation of both spectra and prompt fission neutrons characteristics. On the basis of this approach a statistical model for calculation of differential prompt fission neutrons characteristics of low energy fission has been proposed and improved in order to take into account the anisotropy effects arising at prompt fission neutrons emission from fragments. 37 refs, 6 figs

Study by neutron diffusion of local order liquid sulfur around the polymerization transition

International Nuclear Information System (INIS)

Descotes, L.

1994-05-01

We studied the liquid sulfur according to the temperature. The sulfur is one of the most complicated elementary liquid. We experimented the neutron diffusion by the powder orthorhombic sulfur. The complexity at the polymerization transition are only accompanied by weak local structural transfer. 231 refs., 48 figs., 8 tabs., 3 annexes

Theory of spin-lattice relaxation of diffusing light nuclei in glasses

International Nuclear Information System (INIS)

Schirmer, A.; Schirmacher, W.

1988-01-01

NMR data of diffusion-induced spin-lattice relaxation in glasses cannot generally be interpreted in the framework of the classical theory of Bloembergen, Purcell and Pound (BPP). Since it is based on exponential density relaxation, generally bnot found in glasses, the BPP formula must be generalized. Here a combination of standard relaxation theory with a hopping model for diffusion in glasses is present. It is shown that the observed anomaties in the NMR data can be explained as a result of anomalous diffusion. 25 refs.; 1 figure

Point defects and magnetic properties of neutron irradiated MgO single crystal

Directory of Open Access Journals (Sweden)

Mengxiong Cao

2017-05-01

Full Text Available (100-oriented MgO single crystals were irradiated to introduce point defects with different neutron doses ranging from 1.0×1016 to 1.0×1020 cm-2. The point defect configurations were studied with X-ray diffuse scattering and UV-Vis absorption spectra. The isointensity profiles of X-ray diffuse scattering caused by the cubic and double-force point defects in MgO were theoretically calculated based on the Huang scattering theory. The magnetic properties at different temperature were measured with superconducting quantum interference device (SQUID. The reciprocal space mappings (RSMs of irradiated MgO revealed notable diffuse scattering. The UV-Vis spectra indicated the presence of O Frenkel defects in irradiated MgO. Neutron-irradiated MgO was diamagnetic at room temperature and became ferromagnetic at low temperature due to O Frenkel defects induced by neutron-irradiation.

Study by neutron diffusion of local order liquid sulfur around the polymerization transition; Etude par diffusion de neutrons de l`ordre local du soufre liquide autour de la transition de polymerisation

Energy Technology Data Exchange (ETDEWEB)

Descotes, L

1994-05-01

We studied the liquid sulfur according to the temperature. The sulfur is one of the most complicated elementary liquid. We experimented the neutron diffusion by the powder orthorhombic sulfur. The complexity at the polymerization transition are only accompanied by weak local structural transfer. 231 refs., 48 figs., 8 tabs., 3 annexes.

Some basic mathematical methods of diffusion theory. [emphasis on atmospheric applications

Science.gov (United States)

Giere, A. C.

1977-01-01

An introductory treatment of the fundamentals of diffusion theory is presented, starting with molecular diffusion and leading up to the statistical methods of turbulent diffusion. A multilayer diffusion model, designed to permit concentration and dosage calculations downwind of toxic clouds from rocket vehicles, is described. The concepts and equations of diffusion are developed on an elementary level, with emphasis on atmospheric applications.

Development of the hierarchical domain decomposition boundary element method for solving the three-dimensional multiregion neutron diffusion equations

International Nuclear Information System (INIS)

Chiba, Gou; Tsuji, Masashi; Shimazu, Yoichiro

2001-01-01

A hierarchical domain decomposition boundary element method (HDD-BEM) that was developed to solve a two-dimensional neutron diffusion equation has been modified to deal with three-dimensional problems. In the HDD-BEM, the domain is decomposed into homogeneous regions. The boundary conditions on the common inner boundaries between decomposed regions and the neutron multiplication factor are initially assumed. With these assumptions, the neutron diffusion equations defined in decomposed homogeneous regions can be solved respectively by applying the boundary element method. This part corresponds to the 'lower level' calculations. At the 'higher level' calculations, the assumed values, the inner boundary conditions and the neutron multiplication factor, are modified so as to satisfy the continuity conditions for the neutron flux and the neutron currents on the inner boundaries. These procedures of the lower and higher levels are executed alternately and iteratively until the continuity conditions are satisfied within a convergence tolerance. With the hierarchical domain decomposition, it is possible to deal with problems composing a large number of regions, something that has been difficult with the conventional BEM. In this paper, it is showed that a three-dimensional problem even with 722 regions can be solved with a fine accuracy and an acceptable computation time. (author)

Analysis of the HTTR with Monte-Carlo and diffusion theory. An IRI-ECN intercomparison

International Nuclear Information System (INIS)

De Haas, J.B.M.; Wallerbos, E.J.M.

2000-09-01

In the framework of the IAEA Co-ordinated Research Program (CRP) 'Evaluation of HTGR Performance' for the start-up core physics benchmark of the High Temperature Engineering Test Reactor (HTTR) two-group cross section data for a fuel compact lattice and for a two-dimensional R-Z model have been generated for comparison purposes. For this comparison, 5.2% enriched uranium was selected. Furthermore, a simplified core configuration utilising only the selected type of fuel has been analysed with both the Monte Carlo code KENO and with the diffusion theory codes BOLD VENTURE and PANTHER. With a very detailed KENO model of this simplified core, k eff was calculated to be 1.1278±0.0005. Homogenisation of the core region was seen to increase k eff by 0.0340 which can be attributed to streaming of neutrons in the detailed model. The difference in k eff between the homogenised models of KENO and BOLD VENTURE amounts then only,Δk =0.0025. The PANTHER result for this core is k eff = 1. 1251, which is in good agreement with the KENO result. The fully loaded core configuration, with a range of enrichments, has also been analysed with both KENO and BOLD VENTURE. In this case the homogenisation was seen to increase k eff by 0.0375 (streaming effect). In BOLD VENTURE the critical state could be reached by the insertion of the control rods through adding an effective 10 B density over the insertion depth while the streaming of neutrons was accounted for by adjustment of the diffusion coefficient. The generation time and the effective fraction of delayed neutrons in the critical state have been calculated to be 1.11 ms and 0.705 %, respectively. This yields a prompt decay constant at critical of 6.9 s -1 . The analysis with PANTHER resulted in a k eff =1.1595 and a critical control rod setting of 244.5 cm compared to the detailed KENO results of: k eff = 1.1600 and 234.5 cm, again an excellent agreement. 5 refs

Assembly Discontinuity Factors for the Neutron Diffusion Equation discretized with the Finite Volume Method. Application to BWR

International Nuclear Information System (INIS)

Bernal, A.; Roman, J.E.; Miró, R.; Verdú, G.

2016-01-01

Highlights: • A method is proposed to solve the eigenvalue problem of the Neutron Diffusion Equation in BWR. • The Neutron Diffusion Equation is discretized with the Finite Volume Method. • The currents are calculated by using a polynomial expansion of the neutron flux. • The current continuity and boundary conditions are defined implicitly to reduce the size of the matrices. • Different structured and unstructured meshes were used to discretize the BWR. - Abstract: The neutron flux spatial distribution in Boiling Water Reactors (BWRs) can be calculated by means of the Neutron Diffusion Equation (NDE), which is a space- and time-dependent differential equation. In steady state conditions, the time derivative terms are zero and this equation is rewritten as an eigenvalue problem. In addition, the spatial partial derivatives terms are transformed into algebraic terms by discretizing the geometry and using numerical methods. As regards the geometrical discretization, BWRs are complex systems containing different components of different geometries and materials, but they are usually modelled as parallelepiped nodes each one containing only one homogenized material to simplify the solution of the NDE. There are several techniques to correct the homogenization in the node, but the most commonly used in BWRs is that based on Assembly Discontinuity Factors (ADFs). As regards numerical methods, the Finite Volume Method (FVM) is feasible and suitable to be applied to the NDE. In this paper, a FVM based on a polynomial expansion method has been used to obtain the matrices of the eigenvalue problem, assuring the accomplishment of the ADFs for a BWR. This eigenvalue problem has been solved by means of the SLEPc library.

Diffusion in membranes: Toward a two-dimensional diffusion map

Directory of Open Access Journals (Sweden)

Toppozini Laura

2015-01-01

Full Text Available For decades, quasi-elastic neutron scattering has been the prime tool for studying molecular diffusion in membranes over relevant nanometer distances. These experiments are essential to our current understanding of molecular dynamics of lipids, proteins and membrane-active molecules. Recently, we presented experimental evidence from X-ray diffraction and quasi-elastic neutron scattering demonstrating that ethanol enhances the permeability of membranes. At the QENS 2014/WINS 2014 conference we presented a novel technique to measure diffusion across membranes employing 2-dimensional quasi-elastic neutron scattering. We present results from our preliminary analysis of an experiment on the cold neutron multi-chopper spectrometer LET at ISIS, where we studied the self-diffusion of water molecules along lipid membranes and have the possibility of studying the diffusion in membranes. By preparing highly oriented membrane stacks and aligning them horizontally in the spectrometer, our aim is to distinguish between lateral and transmembrane diffusion. Diffusion may also be measured at different locations in the membranes, such as the water layer and the hydrocarbon membrane core. With a complete analysis of the data, 2-dimensional mapping will enable us to determine diffusion channels of water and ethanol molecules to quantitatively determine nanoscale membrane permeability.

Iterative method for obtaining the prompt and delayed alpha-modes of the diffusion equation

International Nuclear Information System (INIS)

Singh, K.P.; Degweker, S.B.; Modak, R.S.; Singh, Kanchhi

2011-01-01

Highlights: → A method for obtaining α-modes of the neutron diffusion equation has been developed. → The difference between the prompt and delayed modes is more pronounced for the higher modes. → Prompt and delayed modes differ more in reflector region. - Abstract: Higher modes of the neutron diffusion equation are required in some applications such as second order perturbation theory, and modal kinetics. In an earlier paper we had discussed a method for computing the α-modes of the diffusion equation. The discussion assumed that all neutrons are prompt. The present paper describes an extension of the method for finding the α-modes of diffusion equation with the inclusion of delayed neutrons. Such modes are particularly suitable for expanding the time dependent flux in a reactor for describing transients in a reactor. The method is illustrated by applying it to a three dimensional heavy water reactor model problem. The problem is solved in two and three neutron energy groups and with one and six delayed neutron groups. The results show that while the delayed α-modes are similar to λ-modes they are quite different from prompt modes. The difference gets progressively larger as we go to higher modes.

Study of accelerated diffusion in gold and aluminium under neutron irradiation

International Nuclear Information System (INIS)

Acker, Denis.

1977-09-01

The speed-up of diffusion under neutron irradiation was studied. The experiments concern the self-diffusion of gold as a function of temperature and the heterodiffusion of copper and gold in aluminium against flux and temperature. In each of these systems the coefficients measured were 10 6 times higher than the expected extra-irradiation values for a flux of 6.10 12 n/cm 2 /s and at a temperature 0.33 Tsub(f), Tsub(f) being the matting point of the matrix expressed in Kelvins. The results obtained can be explained satisfactorily by assuming that, under irradiation: the activation energy of the diffusion coefficient is equal to half the hole migration energy (corrected for the hole-impurity interaction terms in the case of heterodiffusion); the diffusion coefficient under irradiation varies with the square root of the flux; defect wells eliminate interstitials much more efficient by than holes. The first two points agree well with theoretical predictions if the holes and interstitials are assumed to disappear essentially by mutual recombination, whereas the third can be interpreted in terms of a low efficiency of wells for holes and by supposing that the interstitial elimination reaction is limited only by the diffusion rate of these interstitials [fr

Nuclear theory for fast neutron nuclear data evaluation

International Nuclear Information System (INIS)

1988-11-01

The proceedings contain all invited and contributed papers presented at the Advisory Group Meeting on Nuclear Theory for Fast Neutron Data Evaluation held in Beijing 12-16 October 1987, as well as the conclusions and recommendations and the Chairman's summary of the meeting. The meeting presentations have been divided into six sessions devoted to the following topics: introductory speech (1 paper), optical potential (9 papers), compound nuclear theory (10 papers), pre-compound nuclear theory (13 papers), isomeric cross-section (1 paper) and intercomparison of nuclear model computer codes (1 paper). A separate abstract was prepared for each of these papers. Refs, figs and tabs

NodHex3D: An application for solving the neutron diffusion equations in hexagonal-Z geometry and steady state

International Nuclear Information System (INIS)

Esquivel E, J.; Del Valle G, E.

2014-10-01

The system called NodHex3D is a graphical application that allows the solution of the neutron diffusion equation. The system considers fuel assemblies of hexagonal cross section. This application arose from the idea of expanding the development of neutron own codes, used primarily for academic purposes. The advantage associated with the use of NodHex3D, is that the kernel configuration and fuel batches is dynamically without affecting directly the base source code of the solution of the neutron diffusion equation. In addition to the kernel configuration to use, specify the values for the cross sections for each batch of fuel used, these values are: diffusion coefficient, removal cross section, absorption cross section, fission cross section and dispersion cross section. Important also, considering that the system is able to perform calculations for various energy groups. As evidence of the operation of NodHex3D, was proposed to model three-dimensional core of a nuclear reactor VVER-1000, based on the reference problem AER-FCM-101. The configuration of the reactor core consists of fuel assemblies (25 batches), composed of seven distinct materials, one of which reflector material, vacuum boundary conditions on the surface delimiting the reactor core. The diffusion equation for two energy groups solves, obtaining the value of the effective neutron multiplication factor. The obtained results are compared to those documented in the reference problem and by 3-DNT codes. (Author)

Extreme neutron stars from Extended Theories of Gravity

Energy Technology Data Exchange (ETDEWEB)

Astashenok, Artyom V. [I. Kant Baltic Federal University, Institute of Physics and Technology, Nevskogo st. 14, Kaliningrad, 236041 (Russian Federation); Capozziello, Salvatore [Dipartimento di Fisica, Università di Napoli ' ' Federico II' ' , Via Cinthia, 9, Napoli, I-80126 Italy (Italy); Odintsov, Sergei D., E-mail: artyom.art@gmail.com, E-mail: capozziello@na.infn.it, E-mail: odintsov@ieec.uab.es [Instituciò Catalana de Recerca i Estudis Avançats (ICREA), Barcelona (Spain)

2015-01-01

We discuss neutron stars with strong magnetic mean fields in the framework of Extended Theories of Gravity. In particular, we take into account models derived from f(R) and f(G) extensions of General Relativity where functions of the Ricci curvature invariant R and the Gauss-Bonnet invariant G are respectively considered. Dense matter in magnetic mean field, generated by magnetic properties of particles, is described by assuming a model with three meson fields and baryons octet. As result, the considerable increasing of maximal mass of neutron stars can be achieved by cubic corrections in f(R) gravity. In principle, massive stars with M > 4M{sub ☉} can be obtained. On the other hand, stable stars with high strangeness fraction (with central densities ρ{sub c} ∼ 1.5–2.0 GeV/fm{sup 3}) are possible considering quadratic corrections of f(G) gravity. The magnetic field strength in the star center is of order 6–8 × 10{sup 18} G. In general, we can say that other branches of massive neutron stars are possible considering the extra pressure contributions coming from gravity extensions. Such a feature can constitute both a probe for alternative theories and a way out to address anomalous self-gravitating compact systems.

A diffuse neutron scattering study of clustering kinetics in Cu-Ni alloys

International Nuclear Information System (INIS)

Vrijen, J.; Radelaar, S.; Schwahn, D.

1977-01-01

Diffuse scattering of thermal neutrons was used to investigate the kinetics of clustering in Cu-Ni alloys. In order to optimize the experimental conditions the isotopes 65 Cu and 62 Ni were alloyed. The time evolution of the diffuse scattered intensity at 400 0 C has been measured for eight Cu-Ni alloys, varying in composition between 30 and 80 at. pour cent Ni. The relaxation of the so called null matrix, containing 56.5 at. pour cent Ni has also been investigated at 320, 340, 425 and 450 0 C. Using Cook's model from all these measurements information has been deduced about diffusion at low temperatures and about thermodynamic properties of the Cu-Ni system. It turns out that Cook's model is not sufficiently detailed for an accurate description of the initial stages of these relaxations

Application of optimal interation strategies to diffusion theory calculations

International Nuclear Information System (INIS)

Jones, R.B.

1978-01-01

The geometric interpretation of optimal (minimum computational time) iteration strategies is applied to one- and two-group, two-dimensional diffusion-theory calculations. The method is a ''spectral/time balance'' technique which weighs the convergence enhancement of the inner iteration procedure with that of the outer iteration loop and the time required to reconstruct the source. The diffusion-theory option of the discrete-ordinates transport code DOT3.5 was altered to incorporate the theoretical inner/outer decision logic. For the two-dimensional configuration considered, the optimal strategies reduced the total number of iterations performed for a given error criterion

Application of diffusion theory to neutral atom transport in fusion plasmas

International Nuclear Information System (INIS)

Hasan, M.Z.; Conn, R.W.; Pomraning, G.C.

1986-05-01

It is found that energy dependent diffusion theory provides excellent accuracy in the modelling of transport of neutral atoms in fusion plasmas. Two reasons in particular explain the good accuracy. First, while the plasma is optically thick for low energy neutrals, it is optically thin for high energy neutrals and diffusion theory with Marshak boundary conditions gives accurate results for an optically thin medium even for small values of 'c', the ratio of the scattering to the total cross section. Second, the effective value of 'c' at low energy becomes very close to one due to the down-scattering via collisions of high energy neutrals. The first reason is proven both computationally and theoretically by solving the transport equation in a power series in 'c' and the diffusion equation with 'general' Marshak boundary conditions. The second reason is established numerically by comparing the results from a one-dimensional, general geometry, multigroup diffusion theory code, written for this purpose, with the results obtained using the transport code ANISN

Modified free volume theory of self-diffusion and molecular theory of shear viscosity of liquid carbon dioxide.

Science.gov (United States)

Nasrabad, Afshin Eskandari; Laghaei, Rozita; Eu, Byung Chan

2005-04-28

In previous work on the density fluctuation theory of transport coefficients of liquids, it was necessary to use empirical self-diffusion coefficients to calculate the transport coefficients (e.g., shear viscosity of carbon dioxide). In this work, the necessity of empirical input of the self-diffusion coefficients in the calculation of shear viscosity is removed, and the theory is thus made a self-contained molecular theory of transport coefficients of liquids, albeit it contains an empirical parameter in the subcritical regime. The required self-diffusion coefficients of liquid carbon dioxide are calculated by using the modified free volume theory for which the generic van der Waals equation of state and Monte Carlo simulations are combined to accurately compute the mean free volume by means of statistical mechanics. They have been computed as a function of density along four different isotherms and isobars. A Lennard-Jones site-site interaction potential was used to model the molecular carbon dioxide interaction. The density and temperature dependence of the theoretical self-diffusion coefficients are shown to be in excellent agreement with experimental data when the minimum critical free volume is identified with the molecular volume. The self-diffusion coefficients thus computed are then used to compute the density and temperature dependence of the shear viscosity of liquid carbon dioxide by employing the density fluctuation theory formula for shear viscosity as reported in an earlier paper (J. Chem. Phys. 2000, 112, 7118). The theoretical shear viscosity is shown to be robust and yields excellent density and temperature dependence for carbon dioxide. The pair correlation function appearing in the theory has been computed by Monte Carlo simulations.

Application of linear and higher perturbation theory in reactor physics

International Nuclear Information System (INIS)

Woerner, D.

1978-01-01

For small perturbations in the material composition of a reactor according to the first approximation of perturbation theory the eigenvalue perturbation is proportional to the perturbation of the system. This assumption is true for the neutron flux not influenced by the perturbance. The two-dimensional code LINESTO developed for such problems in this paper on the basis of diffusion theory determines the relative change of the multiplication constant. For perturbations varying the neutron flux in the space of energy and position the eigenvalue perturbation is also influenced by this changed neutron flux. In such cases linear perturbation theory yields larger errors. Starting from the methods of calculus of variations there is additionally developed in this paper a perturbation method of calculation permitting in a quick and simple manner to assess the influence of flux perturbation on the eigenvalue perturbation. While the source of perturbations is evaluated in isotropic approximation of diffusion theory the associated inhomogeneous equation may be used to determine the flux perturbation by means of diffusion or transport theory. Possibilities of application and limitations of this method are studied in further systematic investigations on local perturbations. It is shown that with the integrated code system developed in this paper a number of local perturbations may be checked requiring little computing time. With it flux perturbations in first approximation and perturbations of the multiplication constant in second approximation can be evaluated. (orig./RW) [de

Determination of the ion thermal diffusivity from neutron emission profiles in decay

International Nuclear Information System (INIS)

Sasao, M.; Adams, J.M.; Conroy, S.; Jarvis, O.N.; Marcus, F.B.; Sadler, G.; Belle, P. van

1994-01-01

Spatial profiles of the neutron emission from deuterium plasmas are routinely obtained at the Joint European Torus (JET) using the line-integrated signals measured with a multichannel instrument. It is shown that the manner in which these profiles relax following the termination of strong heating with neutral beam injection (NBI) permits the local thermal diffusivity (χ i ) to be obtained with an accuracy of about 20%. (author)

POW3D-Neutron diffusion module of the AUS system. A user's manual

International Nuclear Information System (INIS)

Harrington, B.V.; Pollard, J.P.; Barry, J.M.

1996-11-01

POW3D is a three-dimensional neutron diffusion module of the AUS modular neutronics code system. It performs eigenvalue, source of feedback-free kinetics calculations. The module includes general criticality search options and extensive editing facilities including perturbation calculations. Output options include flux or reaction rate plot files. The code permits selection from one of a variety of different solution methods (MINI, ICCG or SLOR) for inner iterations with region re balance to enhance convergence. A MINI accelerated Gauss-Siedel method is used for upscatter iterations with group rebalance to enhance a convergence. Chebyshev source extrapolation is applied for outer iterations. A detailed index is included

Parallel preconditioned conjugate gradient algorithm applied to neutron diffusion problem

International Nuclear Information System (INIS)

Majumdar, A.; Martin, W.R.

1992-01-01

Numerical solution of the neutron diffusion problem requires solving a linear system of equations such as Ax = b, where A is an n x n symmetric positive definite (SPD) matrix; x and b are vectors with n components. The preconditioned conjugate gradient (PCG) algorithm is an efficient iterative method for solving such a linear system of equations. In this paper, the authors describe the implementation of a parallel PCG algorithm on a shared memory machine (BBN TC2000) and on a distributed workstation (IBM RS6000) environment created by the parallel virtual machine parallelization software

Comparison of experimentally-inferred ion thermal diffusivities with neoclassical theory for neutral beam-heated discharges in the Doublet III tokamak

International Nuclear Information System (INIS)

Groebner, R.J.

1986-04-01

The study of ion transport in neutral beam-heated discharges in tokamaks is necessary to determine if neoclassical theory can reliably be used to predict the performance of future machines. Previous studies of ion tranport have generally been difficult due to the lack of information regarding the ion temperature profile. The standard procedure used to study ion transport has been to model the T/sub i/ profile with the assumption that the ion thermal diffusivity profile chi/sub i/(r) was equal to a multiplier times chi/sub i//sup neo/(r), the ion thermal diffusivity calculated from neoclassical theory. The multiplier was varied until the calculated T/sub i/ profile agreed with the available ion temperature data, usually T/sub i/(0) or the measured neutron rate. Values of the multiplier in the range of 1 to 10 have generally been obtained with few estimates of the uncertainties in these values. Furthermore, there have been few, if any, attempts to calculate chi/sub i/ by modeling the ion temperature profiles in other ways. As a result, the issue as to whether or not the ion transport in tokamaks is in agreement with neoclassical theory has not been definitively answered

High order backward discretization of the neutron diffusion equation

Energy Technology Data Exchange (ETDEWEB)

Ginestar, D.; Bru, R.; Marin, J. [Universidad Politecnica de Valencia (Spain). Departamento de Matematica Aplicada; Verdu, G.; Munoz-Cobo, J.L. [Universidad Politecnica de Valencia (Spain). Departamento de Ingenieria Quimica y Nuclear; Vidal, V. [Universidad Politecnica de Valencia (Spain). Departamento de Sistemas Informaticos y Computacion

1997-11-21

Fast codes capable of dealing with three-dimensional geometries, are needed to be able to simulate spatially complicated transients in a nuclear reactor. We propose a new discretization technique for the time integration of the neutron diffusion equation, based on the backward difference formulas for systems of stiff ordinary differential equations. This method needs to solve a system of linear equations for each integration step, and for this purpose, we have developed an iterative block algorithm combined with a variational acceleration technique. We tested the algorithm with two benchmark problems, and compared the results with those provided by other codes, concluding that the performance and overall agreement are very good. (author).

Homogenization Theory for the Prediction of Obstructed Solute Diffusivity in Macromolecular Solutions.

Science.gov (United States)

Donovan, Preston; Chehreghanianzabi, Yasaman; Rathinam, Muruhan; Zustiak, Silviya Petrova

2016-01-01

The study of diffusion in macromolecular solutions is important in many biomedical applications such as separations, drug delivery, and cell encapsulation, and key for many biological processes such as protein assembly and interstitial transport. Not surprisingly, multiple models for the a-priori prediction of diffusion in macromolecular environments have been proposed. However, most models include parameters that are not readily measurable, are specific to the polymer-solute-solvent system, or are fitted and do not have a physical meaning. Here, for the first time, we develop a homogenization theory framework for the prediction of effective solute diffusivity in macromolecular environments based on physical parameters that are easily measurable and not specific to the macromolecule-solute-solvent system. Homogenization theory is useful for situations where knowledge of fine-scale parameters is used to predict bulk system behavior. As a first approximation, we focus on a model where the solute is subjected to obstructed diffusion via stationary spherical obstacles. We find that the homogenization theory results agree well with computationally more expensive Monte Carlo simulations. Moreover, the homogenization theory agrees with effective diffusivities of a solute in dilute and semi-dilute polymer solutions measured using fluorescence correlation spectroscopy. Lastly, we provide a mathematical formula for the effective diffusivity in terms of a non-dimensional and easily measurable geometric system parameter.

Homogenization Theory for the Prediction of Obstructed Solute Diffusivity in Macromolecular Solutions.

Directory of Open Access Journals (Sweden)

Preston Donovan

Full Text Available The study of diffusion in macromolecular solutions is important in many biomedical applications such as separations, drug delivery, and cell encapsulation, and key for many biological processes such as protein assembly and interstitial transport. Not surprisingly, multiple models for the a-priori prediction of diffusion in macromolecular environments have been proposed. However, most models include parameters that are not readily measurable, are specific to the polymer-solute-solvent system, or are fitted and do not have a physical meaning. Here, for the first time, we develop a homogenization theory framework for the prediction of effective solute diffusivity in macromolecular environments based on physical parameters that are easily measurable and not specific to the macromolecule-solute-solvent system. Homogenization theory is useful for situations where knowledge of fine-scale parameters is used to predict bulk system behavior. As a first approximation, we focus on a model where the solute is subjected to obstructed diffusion via stationary spherical obstacles. We find that the homogenization theory results agree well with computationally more expensive Monte Carlo simulations. Moreover, the homogenization theory agrees with effective diffusivities of a solute in dilute and semi-dilute polymer solutions measured using fluorescence correlation spectroscopy. Lastly, we provide a mathematical formula for the effective diffusivity in terms of a non-dimensional and easily measurable geometric system parameter.

Computational modeling for the angular reconstruction of monoenergetic neutron flux in non-multiplying slabs using synthetic diffusion approximation

International Nuclear Information System (INIS)

Mansur, Ralph S.; Barros, Ricardo C.

2011-01-01

We describe a method to determine the neutron scalar flux in a slab using monoenergetic diffusion model. To achieve this goal we used three ingredients in the computational code that we developed on the Scilab platform: a spectral nodal method that generates numerical solution for the one-speed slab-geometry fixed source diffusion problem with no spatial truncation errors; a spatial reconstruction scheme to yield detailed profile of the coarse-mesh solution; and an angular reconstruction scheme to yield approximately the neutron angular flux profile at a given location of the slab migrating in a given direction. Numerical results are given to illustrate the efficiency of the offered code. (author)

Spin-polarized neutron matter at different orders of chiral effective field theory

OpenAIRE

Sammarruca, F.; Machleidt, R.; Kaiser, N.

2015-01-01

Spin-polarized neutron matter is studied using chiral two- and three-body forces. We focus, in particular, on predictions of the energy per particle in ferromagnetic neutron matter at different orders of chiral effective field theory and for different choices of the resolution scale. We discuss the convergence pattern of the predictions and their cutoff dependence. We explore to which extent fully polarized neutron matter behaves (nearly) like a free Fermi gas. We also consider the more gener...

Maximum neutron flux in thermal reactors

International Nuclear Information System (INIS)

Strugar, P.V.

1968-12-01

Direct approach to the problem is to calculate spatial distribution of fuel concentration if the reactor core directly using the condition of maximum neutron flux and comply with thermal limitations. This paper proved that the problem can be solved by applying the variational calculus, i.e. by using the maximum principle of Pontryagin. Mathematical model of reactor core is based on the two-group neutron diffusion theory with some simplifications which make it appropriate from maximum principle point of view. Here applied theory of maximum principle are suitable for application. The solution of optimum distribution of fuel concentration in the reactor core is obtained in explicit analytical form. The reactor critical dimensions are roots of a system of nonlinear equations and verification of optimum conditions can be done only for specific examples

A diffusivity model for predicting VOC diffusion in porous building materials based on fractal theory

International Nuclear Information System (INIS)

Liu, Yanfeng; Zhou, Xiaojun; Wang, Dengjia; Song, Cong; Liu, Jiaping

2015-01-01

Highlights: • Fractal theory is introduced into the prediction of VOC diffusion coefficient. • MSFC model of the diffusion coefficient is developed for porous building materials. • The MSFC model contains detailed pore structure parameters. • The accuracy of the MSFC model is verified by independent experiments. - Abstract: Most building materials are porous media, and the internal diffusion coefficients of such materials have an important influences on the emission characteristics of volatile organic compounds (VOCs). The pore structure of porous building materials has a significant impact on the diffusion coefficient. However, the complex structural characteristics bring great difficulties to the model development. The existing prediction models of the diffusion coefficient are flawed and need to be improved. Using scanning electron microscope (SEM) observations and mercury intrusion porosimetry (MIP) tests of typical porous building materials, this study developed a new diffusivity model: the multistage series-connection fractal capillary-bundle (MSFC) model. The model considers the variable-diameter capillaries formed by macropores connected in series as the main mass transfer paths, and the diameter distribution of the capillary bundles obeys a fractal power law in the cross section. In addition, the tortuosity of the macrocapillary segments with different diameters is obtained by the fractal theory. Mesopores serve as the connections between the macrocapillary segments rather than as the main mass transfer paths. The theoretical results obtained using the MSFC model yielded a highly accurate prediction of the diffusion coefficients and were in a good agreement with the VOC concentration measurements in the environmental test chamber.

Turbulent diffusion of chemically reacting flows: Theory and numerical simulations.

Science.gov (United States)

Elperin, T; Kleeorin, N; Liberman, M; Lipatnikov, A N; Rogachevskii, I; Yu, R

2017-11-01

The theory of turbulent diffusion of chemically reacting gaseous admixtures developed previously [T. Elperin et al., Phys. Rev. E 90, 053001 (2014)PLEEE81539-375510.1103/PhysRevE.90.053001] is generalized for large yet finite Reynolds numbers and the dependence of turbulent diffusion coefficient on two parameters, the Reynolds number and Damköhler number (which characterizes a ratio of turbulent and reaction time scales), is obtained. Three-dimensional direct numerical simulations (DNSs) of a finite-thickness reaction wave for the first-order chemical reactions propagating in forced, homogeneous, isotropic, and incompressible turbulence are performed to validate the theoretically predicted effect of chemical reactions on turbulent diffusion. It is shown that the obtained DNS results are in good agreement with the developed theory.

Determination of the ion thermal diffusivity from neutron emission profiles in decay

Energy Technology Data Exchange (ETDEWEB)

Sasao, M. (National Inst. for Fusion Science, Nagoya (Japan)); Adams, J.M. (AEA Industrial Technology, Harwell (United Kingdom)); Conroy, S.; Jarvis, O.N.; Marcus, F.B.; Sadler, G.; Belle, P. van (Commission of the European Communities, Abingdon (United Kingdom). JET Joint Undertaking)

1994-01-01

Spatial profiles of the neutron emission from deuterium plasmas are routinely obtained at the Joint European Torus (JET) using the line-integrated signals measured with a multichannel instrument. It is shown that the manner in which these profiles relax following the termination of strong heating with neutral beam injection (NBI) permits the local thermal diffusivity ([chi][sub i]) to be obtained with an accuracy of about 20%. (author).

Solution of the neutron diffusion equation at two groups of energy by method of triangular finite elements

International Nuclear Information System (INIS)

Correia Filho, A.

1981-04-01

The Neutron Diffusion Equation at two groups of energy is solved with the use of the Finite - Element Method with first order triangular elements. The program EFTDN (Triangular Finite Elements on Neutron Diffusion) was developed using the language FORTRAN IV. The discrete formulation of the Diffusion Equation is obtained with the application of the Galerkin's Method. In order to solve the eigenvalue - problem, the Method of the Power is applied and, with the purpose of the convergence of the results, Chebshev's polynomial expressions are applied. On the solution of the systems of equations Gauss' Method is applied, divided in two different parts: triangularization of the matrix of coeficients and retrosubstitution taking in account the sparsity of the system. Several test - problems are solved, among then two P.W.R. type reactors, the ZION-1 with 1300 MWe and the 2D-IAEA - Benchmark. Comparision of results with standard solutions show the validity of application of the EFM and precision of the results. (Author) [pt

Numeric algorithms for parallel processors computer architectures with applications to the few-groups neutron diffusion equations

International Nuclear Information System (INIS)

Zee, S.K.

1987-01-01

A numeric algorithm and an associated computer code were developed for the rapid solution of the finite-difference method representation of the few-group neutron-diffusion equations on parallel computers. Applications of the numeric algorithm on both SIMD (vector pipeline) and MIMD/SIMD (multi-CUP/vector pipeline) architectures were explored. The algorithm was successfully implemented in the two-group, 3-D neutron diffusion computer code named DIFPAR3D (DIFfusion PARallel 3-Dimension). Numerical-solution techniques used in the code include the Chebyshev polynomial acceleration technique in conjunction with the power method of outer iteration. For inner iterations, a parallel form of red-black (cyclic) line SOR with automated determination of group dependent relaxation factors and iteration numbers required to achieve specified inner iteration error tolerance is incorporated. The code employs a macroscopic depletion model with trace capability for selected fission products' transients and critical boron. In addition to this, moderator and fuel temperature feedback models are also incorporated into the DIFPAR3D code, for realistic simulation of power reactor cores. The physics models used were proven acceptable in separate benchmarking studies

Studies of magnetism with inelastic scattering of cold neutrons; Etudes de magnetisme realisees a l'aide de la diffusion inelastique de neutrons froids

Energy Technology Data Exchange (ETDEWEB)

Jacrot, B [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1964-07-01

Inelastic scattering of cold neutrons can be used to study some aspects of magnetism: spins waves, exchange integrals, vicinity of Curie point. After description of the experimental set-up, several experiments, in the fields mentioned above, are analysed. (author) [French] La technique de diffusion inelastique des neutrons froids est utilisee pour etudier certains aspects du magnetisme: ondes de spins, integrales d'echange, etude au voisinage du point de Curie, etc. Apres une description de l'appareillage, on analyse diverses experiences effectuees dans les domaines enumeres plus haut. (auteur)

The KASY synthesis programme for the approximative solution of the 3-dimensional neutron diffusion equation

International Nuclear Information System (INIS)

Buckel, G.; Wouters, R. de; Pilate, S.

1977-01-01

The synthesis code KASY for an approximate solution of the three-dimensional neutron diffusion equation is described; the state of the art as well as envisaged program extensions and the application to tasks from the field of reactor designing are dealt with. (RW) [de

New aspects in the implementation of the quasi-static method for the solution of neutron diffusion problems in the framework of a nodal method

International Nuclear Information System (INIS)

Caron, D.; Dulla, S.; Ravetto, P.

2016-01-01

Highlights: • The implementation of the quasi-static method in 3D nodal diffusion theory model in hexagonal-z geometry is described. • Different formulations of the quasi-static technique are discussed. • The results presented illustrate the features of the various formulations, highlighting advantages and drawbacks. • A novel adaptive procedure for the selection of the time interval between shape recalculations is presented. - Abstract: The ability to accurately model the dynamic behaviour of the neutron distribution in a nuclear system is a fundamental aspect of reactor design and safety assessment. Due to the heavy computational burden associated to the direct time inversion of the full model, the quasi-static method has become a standard approach to the numerical solution of the nuclear reactor dynamic equations on the full phase space. The present paper is opened by an introductory critical review of the basics of the quasi-static scheme for the general neutron kinetic problem. Afterwards, the implementation of the quasi-static method in the context of a three-dimensional nodal diffusion theory model in hexagonal-z geometry is described, including some peculiar aspects of the adjoint nodal equations and the explicit formulation of the quasi-static nodal equations. The presentation includes the discussion of different formulations of the quasi-static technique. The results presented illustrate the features of the various formulations, highlighting the corresponding advantages and drawbacks. An adaptive procedure for the selection of the time interval between shape recalculations is also presented, showing its usefulness in practical applications.

Investigation of isothermal water infiltration into fired clay brick by scattered neutrons

International Nuclear Information System (INIS)

El Abd, A.; Abdel-Monem, A.M.; Kansouh, W.A.

2012-01-01

A method based on neutron scattering was proposed to investigate isothermal water infiltration in porous media. Two different kinds of fired clay bricks were investigated. While the sample absorb water, scattered neutrons from the different wetted regions, along the flow direction were continuously recorded. The results were discussed in terms of the theory of water infiltration in unsaturated porous media as well as by an anomalous diffusion approach. It was shown that the infiltration process in the Canadian clay brick (CCB) is Fickian and the water diffusivity was analytically determined, while it is non-Fickian in the Egyptian clay brick (ECB). The infiltration process in ECB can be modeled as a two stage Fickian process, at the low and high absorption times. The anomalous diffusion approach failed to describe the diffusion process in the ECB at all water contents. (author)

Evaluation of diffusion coefficients in multicomponent mixtures by means of the fluctuation theory

DEFF Research Database (Denmark)

Shapiro, Alexander

2003-01-01

We derive general expressions for diffusion coefficients in multicomponent non-ideal gas or liquid mixtures. The derivation is based on the general statistical theory of fluctuations around an equilibrium state. The matrix of diffusion coefficients is expressed in terms of the equilibrium...... characteristics. We demonstrate on several examples that the developed theory is in agreement with the established experimental facts and dependencies for the diffusion coefficients. (C) 2002 Elsevier Science B.V. All rights reserved....

Derivation of Inter-Atomic Force Constants of Cu2O from Diffuse Neutron Scattering Measurement

Directory of Open Access Journals (Sweden)

T. Makhsun

2013-04-01

Full Text Available Neutron scattering intensity from Cu2O compound has been measured at 10 K and 295 K with High Resolution Powder Diffractometer at JRR-3 JAEA. The oscillatory diffuse scattering related to correlations among thermal displacements of atoms was observed at 295 K. The correlation parameters were determined from the observed diffuse scattering intensity at 10 and 295 K. The force constants between the neighboring atoms in Cu2O were estimated from the correlation parameters and compared to those of Ag2O

Application of diffusion theory to the transport of neutral particles in fusion plasmas

International Nuclear Information System (INIS)

Hasan, M.Z.

1985-01-01

It is shown that the widely held view that diffusion theory can not provide good accuracy for the transport of neutral particles in fusion plasmas is misplaced. In fact, it is shown that multigroup diffusion theory gives quite good accuracy as compared to the transport theory. The reasons for this are elaborated and some of the physical and theoretical reasons which make the multigroup diffusion theory provide good accuracy are explained. Energy dependence must be taken into consideration to obtain a realistic neutral atom distribution in fusion plasmas. There are two reasons for this; presence of either is enough to necessitate an energy dependent treatment. First, the plasma temperature varies spatially, and second, the ratio of charge-exchange to total plasma-neutral interaction cross section (c) is not close to one. A computer code to solve the one-dimensional multigroup diffusion theory in general geometry (slab, cylindrical and spherical) has been written for use on Cray computers, and its results are compared with those from the one-dimensional transport code ANISN to support the above finding. A fast, compact and versatile two-dimensional finite element multigroup diffusion theory code, FINAT, in X-Y and R-Z cylindrical/toroidal geometries has been written for use on CRAY computers. This code has been compared with the two dimensional transport code DOT-4.3. The accuracy is very good, and FENAT runs much faster compared even to DOT-4.3 which is a finite difference code

Study of water diffusion on single-supported bilayer lipid membranes by quasielastic neutron scattering

DEFF Research Database (Denmark)

Bai, M.; Miskowiec, A.; Hansen, F. Y.

2012-01-01

High-energy-resolution quasielastic neutron scattering has been used to elucidate the diffusion of water molecules in proximity to single bilayer lipid membranes supported on a silicon substrate. By varying sample temperature, level of hydration, and deuteration, we identify three different types...... of diffusive water motion: bulk-like, confined, and bound. The motion of bulk-like and confined water molecules is fast compared to those bound to the lipid head groups (7-10 H2O molecules per lipid), which move on the same nanosecond time scale as H atoms within the lipid molecules. Copyright (C) EPLA, 2012...

Blackness coefficients, effective diffusion parameters, and control rod worths for thermal reactors - Methods

Energy Technology Data Exchange (ETDEWEB)

Bretscher, M M [Argonne National Laboratory, Argonne, IL 60439 (United States)

1985-07-01

Simple diffusion theory cannot be used to evaluate control rod worths in thermal neutron reactors because of the strongly absorbing character of the control material. However, reliable control rod worths can be obtained within the framework of diffusion theory if the control material is characterized by a set of mesh-dependent effective diffusion parameters. For thin slab absorbers the effective diffusion parameters can be expressed as functions of a suitably-defined pair of 'blackness coefficients'. Methods for calculating these blackness coefficients in the P1, P3, and P5 approximations, with and without scattering, are presented. For control elements whose geometry does not permit a thin slab treatment, other methods are needed for determining the effective diffusion parameters. One such method, based on reaction rate ratios, is discussed. (author)

Diffusion of Hydrogen in the beta-Phase of Pd-H Studied by Small Energy Transfer Neutron Scattering

Energy Technology Data Exchange (ETDEWEB)

Nelin, G; Skoeld, K

1974-07-01

The diffusion of hydrogen in beta-PdH has been studied by quasielastic neutron scattering. It is shown that the diffusion occurs through jumps between adjacent octahedral interstitial sites. The observed integrated quasielastic intensities cannot be described by a simple Debye-Waller factor. The phase transition from the beta-phase to the alpha-phase has also been studied. No dramatic changes in the scattering patterns were observed. It is concluded that the diffusion mechanism is remarkably similar between the low concentration alpha-phase and the high concentration beta-phase

Neutron scattering for investigation into the connection between phonons and diffusion in metallic systems

International Nuclear Information System (INIS)

Herzig, C.

1995-01-01

For examining the connection between the diffusion systematics and the lattice dynamics of the body-centered cubic metals, the temperature dependence of the self-diffusion (radiotracer technique) and the phonon dispersion (neutron scattering) have been measured in selected systems. In continuation of previous studies, the goal of the examinations reported was to put the earlier developed phonon-related diffusion model on a broader experimental basis, in order to perform verifying analyses. The phonon dispersion of the group 5 metal Nb has been measured up to high temperatures. In contrast to the values measured for the group 4 (β-Zr) and group 6 (Cr) metals, the dispersion in Nb revealed an only very weak temperature dependence. The exceptional case of the bcc β-Tl has been examined by measuring the diffusion and the dispersion in the β-T 83 In 17 alloy. Significant deviations from the conditions in the bcc transition metals have been found. Self-diffusion has been measured for the first time in Ba and β-Sc. Their diffusion systematics correlate with electron configuration. The influence of the d-electron concentration on the diffusion systematics has been measured in Ti-Mo and Hf-Nb alloys, the results backing the predictions of the phonon-related diffusion model. (orig.) [de

Calculation of the Inelastic Scattering of Neutrons from Polyethylene and Water; Calcul de la diffusion inelastique des neutrons par le polyethylene et l'eau; Raschet neuprugogo rasseyaniya nejtronov poliehtilenom i vodoj; Calculo de la dispersion inelastica de neutrones por polietileno y agua

Energy Technology Data Exchange (ETDEWEB)

Goldman, D T; Federighi, F D [Knolls Atomic Power Laboratory, General Electric Company, Schenectady, NY (United States)

1963-01-15

A model for the calculation of the scattering of thermal neutrons from chemical system was proposed by Nelkin. This model considered the actual dynamics of the scattering system as composed of a set of oscillatory motions, each describable by a Hamiltonian which commuted with each of the others. It was then possible to express the differential scattering cross-section in closed form. This model has been used to calculate the scattering of neutrons by water. Some care must be taken in performing the numerical integration over angle and energy. The scattering model has been extended to the calculation of neutron scattering from polyethylene C{sub n}H{sub 2n}. Analogous levels of polyethylene can be noted at 0.089 eV, 0.182 eV, 0.354 eV, and 0.533 eV. The differential and total cross-sections have been calculated for the scattering and the latter has been seen to be in reasonable agreement with experiment at room temperature. Scattering kernels have been calculated for a number of temperatures and where possible the results have been compared with experiment. In addition, neutron flux spectra and diffusion lengths have been calculated using the equations of reactor physics. Comparison of these Results with experimental data indicates that such integral measurements are indicative of at least the gross features of the scattering system and should be analysed in conduction with the detailed differential cross-section results. (author) [French] Nelkin a propose un modele pour calculer la diffusion de neutrons thermiques dans des systemes chimiques. Dans ce mod and le on considere que la dynamique reelle du systeme de diffusion se compose d'un ensemble de mouvements oscillatoires, chaque mouvement pouvant 6tre decrit par un hamiltonien commutant avec chacun des autres. Il est alors possible d'exprimer la section efficace differentielle de diffusion sous une forme fermee. Les auteurs ont employe ce modele pour calculer la diffusion des neutrons par l'eau. Il faut prendre

Analysis of the HTTR with Monte-Carlo and diffusion theory. An IRI-ECN intercomparison

Energy Technology Data Exchange (ETDEWEB)

De Haas, J.B.M. [Nuclear Research and Consultancy Group NRG, Petten (Netherlands); Wallerbos, E.J.M. [Interfaculty Reactor Institute IRI, Delft University of Technology, Delft (Netherlands)

2000-09-01

In the framework of the IAEA Co-ordinated Research Program (CRP) 'Evaluation of HTGR Performance' for the start-up core physics benchmark of the High Temperature Engineering Test Reactor (HTTR) two-group cross section data for a fuel compact lattice and for a two-dimensional R-Z model have been generated for comparison purposes. For this comparison, 5.2% enriched uranium was selected. Furthermore, a simplified core configuration utilising only the selected type of fuel has been analysed with both the Monte Carlo code KENO and with the diffusion theory codes BOLD VENTURE and PANTHER. With a very detailed KENO model of this simplified core, k{sub eff} was calculated to be 1.1278{+-}0.0005. Homogenisation of the core region was seen to increase k{sub eff} by 0.0340 which can be attributed to streaming of neutrons in the detailed model. The difference in k{sub eff} between the homogenised models of KENO and BOLD VENTURE amounts then only,{delta}k =0.0025. The PANTHER result for this core is k{sub eff} = 1. 1251, which is in good agreement with the KENO result. The fully loaded core configuration, with a range of enrichments, has also been analysed with both KENO and BOLD VENTURE. In this case the homogenisation was seen to increase k{sub eff} by 0.0375 (streaming effect). In BOLD VENTURE the critical state could be reached by the insertion of the control rods through adding an effective {sup 10}B density over the insertion depth while the streaming of neutrons was accounted for by adjustment of the diffusion coefficient. The generation time and the effective fraction of delayed neutrons in the critical state have been calculated to be 1.11 ms and 0.705 %, respectively. This yields a prompt decay constant at critical of 6.9 s{sup -1}. The analysis with PANTHER resulted in a k{sub eff} =1.1595 and a critical control rod setting of 244.5 cm compared to the detailed KENO results of: k{sub eff} = 1.1600 and 234.5 cm, again an excellent agreement. 5 refs.

A Cold Neutron Monochromator and Scattering Apparatus; Monochromateur et appareillage pour la diffusion de neutrons lents; Monokhromator dlya ''kholodnykh'' nejtronov i pribor dlya rasseyaniya; Monocromador y aparato de dispersion para neutrones frios

Energy Technology Data Exchange (ETDEWEB)

Harris, D; Cocking, S J; Egelstaff, P A; Webb, F J [Nuclear Physics Division, Aere, Harwell, Didcot, Berks (United Kingdom)

1963-01-15

A narrow band of neutron wavelengths (4 A and greater) is selected from a collimated neutron beam obtained from the Dido reactor at Harwell. These neutrqps are scattered by various samples and the energy transfer of the scattered neutrons measured using time-of-flight techniques. The neutrons, moderated by a liquid hydrogen source in the reactor pass through first a liquid nitrogen- cooled filter, then a single crystal of bismuth and finally they are ''chopped'' by a magnesium-cadmium high- speed curved slot rotor. In this apparatus the wavelength spread of 0. 3 A at 4 . 1 A is determined primarily by the Be-Bi filter, while the time spread (8 {mu}s) is determined by the rotor. The monochromated neutron bursts from this rotor are scattered by a sample and detected in one of two counter arrays. When studying liquid or polycrystalline samples an array of six BF{sub 3}, counter assemblies (each 2 inches x 24 inches in area)are used covering scatter angles from 20{sup o} to 90{sup o}. This array is placed below the neutron beam. Above the line of the neutron beam is a second array consisting of three scintillators 2 inches in diameter, which is used for the study of single crystal samples. The output of each counter is fed into a tape recording system which has 500 time channels available for each counter. This apparatus has been used to study neutron scattering from several gaseous, liquid and crystalline samples and the most recent measurements are presented in other papers in these proceedings. [French] Les auteurs extraient une bande etroite de neutrons ( 4 A et plus) d'un faisceau collimate de neutrons produits par le reacteur Dido de Harwell. On fait diffuser ces neutrons au moyen de divers echantillons et on mesure le transfert d'energie des neutrons diffuses par la methode du temps de vol. Les neutrons ralentis par de l'hydrogene liquide place dans le reacteur passent d'abord dans un filtre refroidi a l'azote liquide, puis dans un monocristal de bismuth

Diffusion of Innovation Theory: A Bridge for the Research-Practice Gap in Counseling

Science.gov (United States)

Murray, Christine E.

2009-01-01

This article presents a diffusion of innovation theory-based framework for addressing the gap between research and practice in the counseling profession. The author describes the nature of the research-practice gap and presents an overview of diffusion of innovation theory. On the basis of the application of several major postulates of diffusion…

A New Method for Predicting the Penetration and Slowing-Down of Neutrons in Reactor Shields

Energy Technology Data Exchange (ETDEWEB)

Hjaerne, L; Leimdoerfer, M

1965-05-15

A new approach is presented in the formulation of removal-diffusion theory. The 'removal cross-section' is redefined and the slowing-down between the multigroup diffusion equations is treated with a complete energy transfer matrix rather than in an age theory approximation. The method, based on the new approach contains an adjustable parameter. Examples of neutron spectra and thermal flux penetrations are given in a number of differing shield configurations and the results compare favorably with experiments and Moments Method calculations.

A New Method for Predicting the Penetration and Slowing-Down of Neutrons in Reactor Shields

International Nuclear Information System (INIS)

Hjaerne, L.; Leimdoerfer, M.

1965-05-01

A new approach is presented in the formulation of removal-diffusion theory. The 'removal cross-section' is redefined and the slowing-down between the multigroup diffusion equations is treated with a complete energy transfer matrix rather than in an age theory approximation. The method, based on the new approach contains an adjustable parameter. Examples of neutron spectra and thermal flux penetrations are given in a number of differing shield configurations and the results compare favorably with experiments and Moments Method calculations

Shielding calculations for the design of neutron radiography facility around PARR

International Nuclear Information System (INIS)

Ashraf, M.M.; Khan, A.R.

1989-06-01

Shielding calculations for neutron radiography facility, proposed to be established around PARR have been carried out using two group diffusion theory and shielding formulae. Gamma radiation penetration calculations have been carried out using simple attenuation methods. The fabrication and installation of the neutron radiography facility would provide the basis for designing a better collimating system and would help establish under water radiography facility for the inspection of highly radioactive materials and components etc. (orig./A.B.)

New applications of neutron noise theory in power reactor physics

Energy Technology Data Exchange (ETDEWEB)

Arzhanov, Vasiliy

2000-04-01

The present thesis deals with neutron noise theory as applied to three comparatively different topics (or problems) in power reactor physics. Namely they are: theoretical investigation of the possibility to use a newly proposed current-flux (C/F) detector in Pressurized Water Reactors (PWRs) for the localisation of anomalies; both definition and studies on the point kinetic and adiabatic approximations for the relatively recently proposed Accelerator Driven Systems (ADS); development of the general theory of linear reactor kinetics and neutron noise in systems with varying size. One important practical problem is to detect and localise a vibrating control rod pin. The significance comes from the operational experience which indicates that individual pins can execute excessive mechanical vibrations that may lead to damage. Such mechanical vibrations induce neutron noise that can be detected. While the detection is relatively easy, the localisation of a vibrating control rod is much more complicated because only one measuring position is available and one needs to have at least three measured quantities. Therefore it has currently been proposed that the fluctuations of the neutron current vector, called the current noise, can be used in addition to the scalar noise in reactor diagnostic problems. The thesis investigates the possibility of the localization of a vibrating control rod pin in a PWR control assembly by using the scalar neutron noise and the 2-D radial current noise as measured at one central point in the control assembly. An explicit localisation technique is elaborated in which the searched position is determined as the absolute minimum of a minimisation function. The technique is investigated in numerical simulations. The results of the simulation tests show the potential applicability of the method. By design accelerator-driven systems would operate in a subcritical mode with a strong external source. This calls for a revision of many concepts and

New applications of neutron noise theory in power reactor physics

International Nuclear Information System (INIS)

Arzhanov, Vasiliy

2000-04-01

The present thesis deals with neutron noise theory as applied to three comparatively different topics (or problems) in power reactor physics. Namely they are: theoretical investigation of the possibility to use a newly proposed current-flux (C/F) detector in Pressurized Water Reactors (PWRs) for the localisation of anomalies; both definition and studies on the point kinetic and adiabatic approximations for the relatively recently proposed Accelerator Driven Systems (ADS); development of the general theory of linear reactor kinetics and neutron noise in systems with varying size. One important practical problem is to detect and localise a vibrating control rod pin. The significance comes from the operational experience which indicates that individual pins can execute excessive mechanical vibrations that may lead to damage. Such mechanical vibrations induce neutron noise that can be detected. While the detection is relatively easy, the localisation of a vibrating control rod is much more complicated because only one measuring position is available and one needs to have at least three measured quantities. Therefore it has currently been proposed that the fluctuations of the neutron current vector, called the current noise, can be used in addition to the scalar noise in reactor diagnostic problems. The thesis investigates the possibility of the localization of a vibrating control rod pin in a PWR control assembly by using the scalar neutron noise and the 2-D radial current noise as measured at one central point in the control assembly. An explicit localisation technique is elaborated in which the searched position is determined as the absolute minimum of a minimisation function. The technique is investigated in numerical simulations. The results of the simulation tests show the potential applicability of the method. By design accelerator-driven systems would operate in a subcritical mode with a strong external source. This calls for a revision of many concepts and

Diffuse neutron scattering study of metallic interstitial solid solutions

International Nuclear Information System (INIS)

Barberis, P.

1991-10-01

We studied two interstitial solid solutions (Ni-C(1at%) and Nb-O(2at%) and two stabilized zirconia (ZrO2-CaO(13.6mol%) and ZrO2-Y2O3(9.6mol%) by elastic diffuse neutron scattering. We used polarized neutron scattering in the case of the ferromagnetic Ni-based sample, in order to determine the magnetic perturbation induced by the C atoms. Measurements were made on single crystals in the Laboratoire Leon Brillouin (CEA-CNRS, Saclay, France). An original algorithm to deconvolve time-of-flight spectra improved the separation between elastically and inelastically scattered intensities. In the case of metallic solutions, we used a simple non-linear model, assuming that interstitials are isolated and located in octahedral sites. Results are: - in both compounds, nearest neighbours are widely displaced away from the interstitial, while next nearest neighbours come slightly closer. - the large magnetic perturbation induced by carbon in Nickel decreases with increasing distance on the three first neighbour shells and is in good agreement with the total magnetization variation. - no chemical order between solute atoms could be evidenced. Stabilized zirconia exhibit a strong correlation between chemical order and the large displacements around vacancies and dopants. (Author). 132 refs., 38 figs., 13 tabs

TVEDIM, 2-D Homogeneous and Inhomogeneous Neutron Diffusion for X-Y, R-Z, R-Theta Geometry

International Nuclear Information System (INIS)

Kristiansen, G.K.

1987-01-01

1 - Nature of physical problem solved: The two-dimensional neutron diffusion equation (x-y, r-z, or r-theta geometry is solved, either in the inhomogeneous (source calculation) or the homogeneous form (K eff calculation or absorber adjustment). The boundary conditions specify each group current as a linear homogeneous function of the group fluxes (gamma matrix concept). For each material, the fission matrix is assumed to by dyadic. 2 - Method of solution: Finite difference formulation (5 point scheme, mesh corner variant) is used. Solution technique: multi-line SOR. Eigenvalue estimate by neutron balance

Neutron diffusion approximation solution for the the three layer borehole cylindrical geometry. Pt. 1. Theoretical description

International Nuclear Information System (INIS)

Czubek, J.A.; Woznicka, U.

1997-01-01

A solution of the neutron diffusion equation is given for a three layer cylindrical coaxial geometry. The calculation is performed in two neutron-energy groups which distinguish the thermal and epithermal neutron fluxes in the media irradiated by the fast point neutron source. The aim of the calculation is to define the neutron slowing down and migration lengths which are observed at a given point of the system. Generally, the slowing down and migration lengths are defined for an infinite homogenous medium (irradiated by the point neutron source) as a quotient of the neutron flux moment of the (2n + 2)-order to the moment of the 2n-order. Czubek(1992) introduced in the same manner the apparent neutron slowing down length and the apparent migration length for a given multi-region cylindrical geometry. The solutions in the present paper are applied to the method of semi-empirical calibration of neutron well-logging tools. The three-region cylindrical geometry corresponds to the borehole of radius R 1 surrounded by the intermediate region (e.g. mud cake) of thickness (R 2 -R 1 ) and finally surrounded by the geological formation which spreads from R 2 up to infinity. The cylinders of an infinite length are considered. The paper gives detailed solutions for the 0-th, 2-nd and 4-th neutron moments of the neutron fluxes for each neutron energy group and in each cylindrical layer. A comprehensive list of the solutions for integrals containing Bessel functions or their derivatives, which are absent in common tables of integrals, is also included. (author)

Statistical fluctuations of the number of neutrons in a pile; Fluctuations statistiques du nombre de neutrons dans une pile

Energy Technology Data Exchange (ETDEWEB)

Raievski, V [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1958-07-01

The theory of the statistical fluctuations in a pile is extended to the space dependent case, and gives the fluctuations of the number of neutrons in a cell of the core or reflector of the pile. This number changes through elementary processes occurring at random, which are, capture, source, fission and scattering. Of all these processes, fission is the only one which changes more than one neutron at a time and so is responsible of the deviation of the fluctuations from a Poisson law. The importance of this deviation depends on the dimensions of the cell compared to the slowing down length. When the dimensions are small, the fluctuations close to a Poisson law. (author) [French] La theorie des fluctuations statistiques est etendue au cas local et donne les fluctuations du nombre de neutrons dans une cellule situee dans le coeur ou le reflecteur de la pile. Ce nombre evolue au cours du temps sous l'influence de phenomenes aleatoires qui sont la capture, la diffusion, les sources et les neutrons secondaires de fission. L'emission simultanee de plusieurs neutrons distingue ce phenomene des precedents qui n'affectent qu'un neutron individuellement. L'importance de ce phenomene sur la loi de fluctuation depend des dimensions de la cellule par rapport a la longueur de ralentissement. Quand ces dimensions sont petites, le caractere particulier de ce phenomene disparait. (auteur)

Synergism of the method of characteristic, R-functions and diffusion solution for accurate representation of 3D neutron interactions in research reactors using the AGENT code system

International Nuclear Information System (INIS)

Hursin, Mathieu; Xiao Shanjie; Jevremovic, Tatjana

2006-01-01

This paper summarizes the theoretical and numerical aspects of the AGENT code methodology accurately applied for detailed three-dimensional (3D) multigroup steady-state modeling of neutron interactions in complex heterogeneous reactor domains. For the first time we show the fine-mesh neutron scalar flux distribution in Purdue research reactor (that was built over forty years ago). The AGENT methodology is based on the unique combination of the three theories: the method of characteristics (MOC) used to simulate the neutron transport in two-dimensional (2D) whole core heterogeneous calculation, the theory of R-functions used as a mathematical tool to describe the true geometry and fuse with the MOC equations, and one-dimensional (1D) higher-order diffusion correction of 2D transport model to account for full 3D heterogeneous whole core representation. The synergism between the radial 2D transport and the 1D axial transport (to take into account the axial neutron interactions and leakage), called the 2D/1D method (used in DeCART and CHAPLET codes), provides a 3D computational solution. The unique synergism between the AGENT geometrical algorithm capable of modeling any current or future reactor core geometry and 3D neutron transport methodology is described in details. The 3D AGENT accuracy and its efficiency are demonstrated showing the eigenvalues, point-wise flux and reaction rate distributions in representative reactor geometries. The AGENT code, comprising this synergism, represents a building block of the computational system, called the virtual reactor. Its main purpose is to perform 'virtual' experiments and demonstrations of various mainly university research reactor experiments

Naturalness in an Effective Field Theory for Neutron Star Matter

International Nuclear Information System (INIS)

Razeira, Moises; Vasconcellos, Cesar A.Z.; Bodmann, Bardo E.J.; Coelho, Helio T.; Dillig, Manfred

2004-01-01

High density hadronic matter is studied in a generalized relativistic multi-baryon lagrangian density. By comparing the predictions of our model with estimates obtained within a phenomenological naive dimensional analysis based on the naturalness of the coefficients of the theory, we show that naturalness plays a major role in effective field theory and, in combination with experiment, could represent a relevant criterium to select a model among others in the description of global static properties of neutron stars

Putting atomic diffusion theory of magnetic ApBp stars to the test: evaluation of the predictions of time-dependent diffusion models

Science.gov (United States)

Kochukhov, O.; Ryabchikova, T. A.

2018-02-01

A series of recent theoretical atomic diffusion studies has address the challenging problem of predicting inhomogeneous vertical and horizontal chemical element distributions in the atmospheres of magnetic ApBp stars. Here we critically assess the most sophisticated of such diffusion models - based on a time-dependent treatment of the atomic diffusion in a magnetized stellar atmosphere - by direct comparison with observations as well by testing the widely used surface mapping tools with the spectral line profiles predicted by this theory. We show that the mean abundances of Fe and Cr are grossly underestimated by the time-dependent theoretical diffusion model, with discrepancies reaching a factor of 1000 for Cr. We also demonstrate that Doppler imaging inversion codes, based either on modelling of individual metal lines or line-averaged profiles simulated according to theoretical three-dimensional abundance distribution, are able to reconstruct correct horizontal chemical spot maps despite ignoring the vertical abundance variation. These numerical experiments justify a direct comparison of the empirical two-dimensional Doppler maps with theoretical diffusion calculations. This comparison is generally unfavourable for the current diffusion theory, as very few chemical elements are observed to form overabundance rings in the horizontal field regions as predicted by the theory and there are numerous examples of element accumulations in the vicinity of radial field zones, which cannot be explained by diffusion calculations.

Sensitivity analysis of the Galerkin finite element method neutron diffusion solver to the shape of the elements

Energy Technology Data Exchange (ETDEWEB)

Hosseini, Seyed Abolfaz [Dept. of Energy Engineering, Sharif University of Technology, Tehran (Iran, Islamic Republic of)

2017-02-15

The purpose of the present study is the presentation of the appropriate element and shape function in the solution of the neutron diffusion equation in two-dimensional (2D) geometries. To this end, the multigroup neutron diffusion equation is solved using the Galerkin finite element method in both rectangular and hexagonal reactor cores. The spatial discretization of the equation is performed using unstructured triangular and quadrilateral finite elements. Calculations are performed using both linear and quadratic approximations of shape function in the Galerkin finite element method, based on which results are compared. Using the power iteration method, the neutron flux distributions with the corresponding eigenvalue are obtained. The results are then validated against the valid results for IAEA-2D and BIBLIS-2D benchmark problems. To investigate the dependency of the results to the type and number of the elements, and shape function order, a sensitivity analysis of the calculations to the mentioned parameters is performed. It is shown that the triangular elements and second order of the shape function in each element give the best results in comparison to the other states.

Three dimensional neutronic/thermal-hydraulic coupled simulation of MSR in transient state condition

International Nuclear Information System (INIS)

Zhou, Jianjun; Zhang, Daling; Qiu, Suizheng; Su, Guanghui; Tian, Wenxi; Wu, Yingwei

2015-01-01

Highlights: • Developed a three dimensional neutronic/thermal-hydraulic coupled transient analysis code for MSR. • Investigated the neutron distribution and thermal-hydraulic characters of the core under transient condition. • Analyzed three different transient conditions of inlet temperature drop, reactivity jump and pump coastdown. - Abstract: MSR (molten salt reactor) use liquid molten salt as coolant and fuel solvent, which was the only one liquid reactor of six Generation IV reactor types. As a liquid reactor the physical property of reactor was significantly influenced by fuel salt flow and the conventional analysis methods applied in solid fuel reactors are not applicable for this type of reactors. The present work developed a three dimensional neutronic/thermal-hydraulic coupled code investigated the neutronics and thermo-hydraulics characteristics of the core in transient condition based on neutron diffusion theory and numerical heat transfer. The code consists of two group neutron diffusion equations for fast and thermal neutron fluxes and six group balance equations for delayed neutron precursors. The code was separately validated by neutron benchmark and flow and heat transfer benchmark. Three different transient conditions was analyzed with inlet temperature drop, reactivity jump and pump coastdown. The results provide some valuable information in design and research this kind of reactor

Three dimensional neutronic/thermal-hydraulic coupled simulation of MSR in transient state condition

Energy Technology Data Exchange (ETDEWEB)

Zhou, Jianjun [School of Nuclear Science and Technology, Xi’an Jiaotong University, Xianning Road, 28, Xi’an 710049, Shaanxi (China); College of Mechanical and Power Engineering, China Three Gorges University, No 8, Daxue road, Yichang, Hubei 443002 (China); Zhang, Daling, E-mail: dlzhang@mail.xjtu.edu.cn [School of Nuclear Science and Technology, Xi’an Jiaotong University, Xianning Road, 28, Xi’an 710049, Shaanxi (China); Qiu, Suizheng; Su, Guanghui; Tian, Wenxi; Wu, Yingwei [School of Nuclear Science and Technology, Xi’an Jiaotong University, Xianning Road, 28, Xi’an 710049, Shaanxi (China)

2015-02-15

Highlights: • Developed a three dimensional neutronic/thermal-hydraulic coupled transient analysis code for MSR. • Investigated the neutron distribution and thermal-hydraulic characters of the core under transient condition. • Analyzed three different transient conditions of inlet temperature drop, reactivity jump and pump coastdown. - Abstract: MSR (molten salt reactor) use liquid molten salt as coolant and fuel solvent, which was the only one liquid reactor of six Generation IV reactor types. As a liquid reactor the physical property of reactor was significantly influenced by fuel salt flow and the conventional analysis methods applied in solid fuel reactors are not applicable for this type of reactors. The present work developed a three dimensional neutronic/thermal-hydraulic coupled code investigated the neutronics and thermo-hydraulics characteristics of the core in transient condition based on neutron diffusion theory and numerical heat transfer. The code consists of two group neutron diffusion equations for fast and thermal neutron fluxes and six group balance equations for delayed neutron precursors. The code was separately validated by neutron benchmark and flow and heat transfer benchmark. Three different transient conditions was analyzed with inlet temperature drop, reactivity jump and pump coastdown. The results provide some valuable information in design and research this kind of reactor.

SYNTH-C, Steady-State and Time-Dependent 3-D Neutron Diffusion with Thermohydraulic Feedback

Energy Technology Data Exchange (ETDEWEB)

Brega, E [ENEL-CRTN, Bastioni di Porta Volta 10, Milan (Italy); Salina, E [A.R.S. Spa, Viale Maino 35, Milan (Italy)

1980-04-01

1 - Description of problem or function: SYNTH-C-STEADY and SYNTH-C- TRANS solve respectively the steady-state and time-dependent few- group neutron diffusion equations in three dimensions x,y,z in the presence of fuel temperature and thermal-hydraulic feedback. The neutron diffusion and delayed precursor equations are approximated by a space-time (z,t) synthesis method with axially discontinuous trial functions. Three thermal-hydraulic and fuel heat transfer models are available viz. COBRA-3C/MIT model, lumped parameter (WIGL) model and adiabatic fuel heat-up model. 2 - Method of solution: The steady-state and time-dependent synthesis equations are solved respectively by the Wielandt's power method and by the theta-difference method (in time), both coupled with a block factorization technique and double precision arithmetic. The thermal-hydraulic model equations are solved by fully implicit finite differences (WIGL) or explicit-implicit difference techniques with iterations (COBRA-EC/MIT). 3 - Restrictions on the complexity of the problem: Except for the few- group limitation, the programs have no other fixed limitation so the ability to run a problem depends only on the available computer storage.

Diffusion Coefficient Calculations With Low Order Legendre Polynomial and Chebyshev Polynomial Approximation for the Transport Equation in Spherical Geometry

International Nuclear Information System (INIS)

Yasa, F.; Anli, F.; Guengoer, S.

2007-01-01

We present analytical calculations of spherically symmetric radioactive transfer and neutron transport using a hypothesis of P1 and T1 low order polynomial approximation for diffusion coefficient D. Transport equation in spherical geometry is considered as the pseudo slab equation. The validity of polynomial expansionion in transport theory is investigated through a comparison with classic diffusion theory. It is found that for causes when the fluctuation of the scattering cross section dominates, the quantitative difference between the polynomial approximation and diffusion results was physically acceptable in general

Parallel computing for homogeneous diffusion and transport equations in neutronics

International Nuclear Information System (INIS)

Pinchedez, K.

1999-06-01

Parallel computing meets the ever-increasing requirements for neutronic computer code speed and accuracy. In this work, two different approaches have been considered. We first parallelized the sequential algorithm used by the neutronics code CRONOS developed at the French Atomic Energy Commission. The algorithm computes the dominant eigenvalue associated with PN simplified transport equations by a mixed finite element method. Several parallel algorithms have been developed on distributed memory machines. The performances of the parallel algorithms have been studied experimentally by implementation on a T3D Cray and theoretically by complexity models. A comparison of various parallel algorithms has confirmed the chosen implementations. We next applied a domain sub-division technique to the two-group diffusion Eigen problem. In the modal synthesis-based method, the global spectrum is determined from the partial spectra associated with sub-domains. Then the Eigen problem is expanded on a family composed, on the one hand, from eigenfunctions associated with the sub-domains and, on the other hand, from functions corresponding to the contribution from the interface between the sub-domains. For a 2-D homogeneous core, this modal method has been validated and its accuracy has been measured. (author)

Thermal neutron inelastic scattering and it's application to the material science

International Nuclear Information System (INIS)

Li Zhuqi

1986-01-01

A brief description of the elementary scattering theory of the interaction between the thermal neutrons and the condensed matter is given and the characteristics related to the experimental method of the thermal neutrons inelastic scattering is described. Expressions of the phonons dispersion, density of the phonon state and the self-diffusion coefficient at the some conditions are also introduced. Some examples of describing diagram of the phonon dispersion, density of the phonons state and selfdiffusion coefficient measured by different authors are given

Continuous neutron slowing down theory applied to resonances

International Nuclear Information System (INIS)

Segev, M.

1977-01-01

Neutronic formalisms that discretize the neutron slowing down equations in large numerical intervals currently account for the bulk effect of resonances in a given interval by the narrow resonance approximation (NRA). The NRA reduces the original problem to an efficient numerical formalism through two assumptions: resonance narrowness with respect to the scattering bands in the slowing down equations and resonance narrowness with respect to the numerical intervals. Resonances at low energies are narrow neither with respect to the slowing down ranges nor with respect to the numerical intervals, which are usually of a fixed lethargy width. Thus, there are resonances to which the NRA is not applicable. To stay away from the NRA, the continuous slowing down (CSD) theory of Stacey was invoked. The theory is based on a linear expansion in lethargy of the collision density in integrals of the slowing down equations and had notable success in various problems. Applying CSD theory to the assessment of bulk resonance effects raises the problem of obtaining efficient quadratures for integrals involved in the definition of the so-called ''moderating parameter.'' The problem was solved by two approximations: (a) the integrals were simplified through a rationale, such that the correct integrals were reproduced for very narrow or very wide resonances, and (b) the temperature-broadened resonant line shapes were replaced by nonbroadened line shapes to enable analytical integration. The replacement was made in such a way that the integrated capture and scattering probabilities in each resonance were preserved. The resulting formalism is more accurate than the narrow-resonance formalisms and is equally as efficient

New methods in linear transport theory. Part of a coordinated programme on methods in neutron transport theory

International Nuclear Information System (INIS)

Mika, J.

1975-09-01

Originally the work was oriented towards two main topics: a) difference and integral methods in neutron transport theory. Two computers were used for numerical calculations GIER and CYBER-72. During the first year the main effort was shifted towards basic theoretical investigations. At the first step the ANIS code was adopted and later modified to check various finite difference approaches against each other. Then the general finite element method and the singular perturbation method were developed. The analysis of singularities of the one-dimensional neutron transport equation in spherical geometry has been done and presented. Later the same analysis for the case of cylindrical symmetry has been carried out. The second and the third year programme included the following topics: 1) finite difference methods in stationary neutron transport theory; 2)mathematical fundamentals of approximate methods for solving the transport equation; 3) singular perturbation method for the time-dependent transport equation; 4) investigation of various iterative procedures in reactor calculations. This investigation will help to better understanding of the mathematical basis for existing and developed numerical methods resulting in more effective algorithms for reactor computer codes

Applicability of the diffusion and simplified P3 theories for BWR pin-by-pin core analysis

International Nuclear Information System (INIS)

Tada, Kenichi; Yamamoto, Akio; Kitamura, Yasunori; Yamane, Yoshihiro; Watanabe, Masato; Noda, Hiroshi

2007-01-01

The pin-by-pin fine mesh core calculation method is considered as a candidate of next-generation core calculation method for BWR. In this study, the diffusion and the simplified P 3 (SP 3 ) theories are applied to the pin-by-pin core analysis of BWR. Performances of the diffusion and the SP 3 theories for cell-homogeneous pin-by-pin fine mesh BWR core analysis are evaluated through comparison with cell-heterogeneous detailed transport calculation by the method of characteristics (MOC). In this study, two-dimensional, 2x2 multi-assemblies geometry is used to compare the prediction accuracies of the diffusion and the SP 3 theories. The 2x2 multi- assemblies geometry consists of two types of 9x9 UO 2 assembly that have two different enrichment splittings. To mitigate the cell-homogenization error, the SPH method is applied for the pin-by-pin fine mesh calculation. The SPH method is a technique that reproduces a result of heterogeneous calculation by that of homogeneous calculation. The calculation results indicated that diffusion theory shows larger discrepancy than that of SP 3 theory on pin-wise fission rates. Furthermore, the accuracy of the diffusion theory would not be sufficient for the pin-by-pin fine mesh calculation. In contrast to the diffusion theory, the SP 3 theory shows much better accuracy on pin wise fission rates. Therefore, if the SP 3 theory is applied, the accuracy of the pin-by-pin fine mesh BWR core analysis will be higher and will be sufficient for production calculation. (author)

Application of the evolution theory in modelling of innovation diffusion

Directory of Open Access Journals (Sweden)

Krstić Milan

2016-01-01

Full Text Available The theory of evolution has found numerous analogies and applications in other scientific disciplines apart from biology. In that sense, today the so-called 'memetic-evolution' has been widely accepted. Memes represent a complex adaptable system, where one 'meme' represents an evolutional cultural element, i.e. the smallest unit of information which can be identified and used in order to explain the evolution process. Among others, the field of innovations has proved itself to be a suitable area where the theory of evolution can also be successfully applied. In this work the authors have started from the assumption that it is also possible to apply the theory of evolution in the modelling of the process of innovation diffusion. Based on the conducted theoretical research, the authors conclude that the process of innovation diffusion in the interpretation of a 'meme' is actually the process of imitation of the 'meme' of innovation. Since during the process of their replication certain 'memes' show a bigger success compared to others, that eventually leads to their natural selection. For the survival of innovation 'memes', their manifestations are of key importance in the sense of their longevity, fruitfulness and faithful replicating. The results of the conducted research have categorically confirmed the assumption of the possibility of application of the evolution theory with the innovation diffusion with the help of innovation 'memes', which opens up the perspectives for some new researches on the subject.

Neutron diffusion approximation solution for the the three layer borehole cylindrical geometry. Pt. 1. Theoretical description

Energy Technology Data Exchange (ETDEWEB)

Czubek, J.A.; Woznicka, U. [The H. Niewodniczanski Inst. of Nuclear Physics, Cracow (Poland)

1997-12-31

A solution of the neutron diffusion equation is given for a three layer cylindrical coaxial geometry. The calculation is performed in two neutron-energy groups which distinguish the thermal and epithermal neutron fluxes in the media irradiated by the fast point neutron source. The aim of the calculation is to define the neutron slowing down and migration lengths which are observed at a given point of the system. Generally, the slowing down and migration lengths are defined for an infinite homogenous medium (irradiated by the point neutron source) as a quotient of the neutron flux moment of the (2n{sup +}2)-order to the moment of the 2n-order. Czubek(1992) introduced in the same manner the apparent neutron slowing down length and the apparent migration length for a given multi-region cylindrical geometry. The solutions in the present paper are applied to the method of semi-empirical calibration of neutron well-logging tools. The three-region cylindrical geometry corresponds to the borehole of radius R{sub 1} surrounded by the intermediate region (e.g. mud cake) of thickness (R{sub 2}-R{sub 1}) and finally surrounded by the geological formation which spreads from R{sub 2} up to infinity. The cylinders of an infinite length are considered. The paper gives detailed solutions for the 0-th, 2-nd and 4-th neutron moments of the neutron fluxes for each neutron energy group and in each cylindrical layer. A comprehensive list of the solutions for integrals containing Bessel functions or their derivatives, which are absent in common tables of integrals, is also included. (author) 6 refs, 2 figs

Solution to the Diffusion equation for multi groups in X Y geometry using Linear Perturbation theory

International Nuclear Information System (INIS)

Mugica R, C.A.

2004-01-01

Diverse methods exist to solve numerically the neutron diffusion equation for several energy groups in stationary state among those that highlight those of finite elements. In this work the numerical solution of this equation is presented using Raviart-Thomas nodal methods type finite element, the RT0 and RT1, in combination with iterative techniques that allow to obtain the approached solution in a quick form. Nevertheless the above mentioned, the precision of a method is intimately bound to the dimension of the approach space by cell, 5 for the case RT0 and 12 for the RT1, and/or to the mesh refinement, that makes the order of the problem of own value to solve to grow considerably. By this way if it wants to know an acceptable approach to the value of the effective multiplication factor of the system when this it has experimented a small perturbation it was appeal to the Linear perturbation theory with which is possible to determine it starting from the neutron flow and of the effective multiplication factor of the not perturbed case. Results are presented for a reference problem in which a perturbation is introduced in an assemble that simulates changes in the control bar. (Author)

On remarks by K. Guenther on the application of track theory to neutron irradiations

International Nuclear Information System (INIS)

Katz, R.

1976-01-01

The author is replying to criticisms of the application of track theory to neutron irradiation. (Guenther, K., 1976, Int. J. Radiat. Biol., vol. 30, 495). Guenther correctly pointed out that any success of the theory for high neutron energies depends on the neglect of the error made at the stopping end of the path of a secondary heavy ion in relation to the overall estimate of the damage produced by that ion. The identity, size and position within the nucleus of the sensitive element whose inactivation leads to cell-killing are all unknown, but any predictions made using the theory are still useful in that they should provoke further experimental investigations ascertaining the limits of the theory. The track theory has other problems at low particle velocities. Consideration is given to the justification for ignoring the error at the stopping end under various conditions. The extent to which the different errors and neglects of the theory may be self-compensating is not yet known. Even if the agreement in r.b.e.-dose relations between calculation from cell survival parameters and experiment for different tissues is fortuitous, the algorithm serves a useful purpose since r.b.e-dose relations can be calculated from a knowledge of the particle energy spectrum of the radiation. Radiotherapy can then be planned for fast neutrons, pions and ion beams, and radiation hazards evaluated in complex radiation environments. (U.K.)

Exact Markov chains versus diffusion theory for haploid random mating.

Science.gov (United States)

Tyvand, Peder A; Thorvaldsen, Steinar

2010-05-01

Exact discrete Markov chains are applied to the Wright-Fisher model and the Moran model of haploid random mating. Selection and mutations are neglected. At each discrete value of time t there is a given number n of diploid monoecious organisms. The evolution of the population distribution is given in diffusion variables, to compare the two models of random mating with their common diffusion limit. Only the Moran model converges uniformly to the diffusion limit near the boundary. The Wright-Fisher model allows the population size to change with the generations. Diffusion theory tends to under-predict the loss of genetic information when a population enters a bottleneck. 2010 Elsevier Inc. All rights reserved.

Explicit studies of the quantum theory of light interstitial diffusion

International Nuclear Information System (INIS)

Emin, D.; Baskes, M.I.; Wilson, W.D.

1978-01-01

The formalism associated with small-polaron diffusion in the high temperature semiclassical regime is generalized so as to transcend simplifications employed in developing the nonadiabatic theory. The diffusion constant is then calculated for simple models in which the metal atoms interact with each other and with the interstitial atom with two-body forces. Studies of these models not only confirm the necessity of generalizing the formalism but also yield diffusion constants whose magnitudes and temperature dependenes ar consistent with the general features of the existing data for the diffusion of hydrogen and its isotopes in bcc metals. The motion of a positive muon between interstitial positions of a metal is also investigated

Neutron techniques

International Nuclear Information System (INIS)

Charlton, J.S.

1986-01-01

The way in which neutrons interact with matter such as slowing-down, diffusion, neutron absorption and moderation are described. The use of neutron techniques in industry, in moisture gages, level and interface measurements, the detection of blockages, boron analysis in ore feedstock and industrial radiography are discussed. (author)

Performance of a parallel algorithm for solving the neutron diffusion equation on the hypercube

International Nuclear Information System (INIS)

Kirk, B.L.; Azmy, Y.Y.

1989-01-01

The one-group, steady state neutron diffusion equation in two- dimensional Cartesian geometry is solved using the nodal method technique. By decoupling sets of equations representing the neutron current continuity along the length of rows and columns of computational cells a new iterative algorithm is derived that is more suitable to solving large practical problems. This algorithm is highly parallelizable and is implemented on the Intel iPSC/2 hypercube in three versions which differ essentially in the total size of communicated data. Even though speedup was achieved, the efficiency is very low when many processors are used leading to the conclusion that the hypercube is not as well suited for this algorithm as shared memory machines. 10 refs., 1 fig., 3 tabs

Numerical solution of the equation of neutrons transport on plane geometry by analytical schemes using acceleration by synthetic diffusion

International Nuclear Information System (INIS)

Alonso-Vargas, G.

1991-01-01

A computer program has been developed which uses a technique of synthetic acceleration by diffusion by analytical schemes. Both in the diffusion equation as in that of transport, analytical schemes were used which allowed a substantial time saving in the number of iterations required by source iteration method to obtain the K e ff. The program developed ASD (Synthetic Diffusion Acceleration) by diffusion was written in FORTRAN and can be executed on a personal computer with a hard disc and mathematical O-processor. The program is unlimited as to the number of regions and energy groups. The results obtained by the ASD program for K e ff is nearly completely concordant with those of obtained utilizing the ANISN-PC code for different analytical type problems in this work. The ASD program allowed obtention of an approximate solution of the neutron transport equation with a relatively low number of internal reiterations with good precision. One of its applications would be in the direct determinations of axial distribution neutronic flow in a fuel assembly as well as in the obtention of the effective multiplication factor. (Author)

Diffusion of graphite. The effect of cylindrical canals; Longueur de diffusion du graphite effet des canaux cylindriques

Energy Technology Data Exchange (ETDEWEB)

Carle, R; Clouet d' Orval, C; Martelly, J; Mazancourt, T de; Sagot, M; Lattes, R; Teste du Bailler, A [Commissariat a l' Energie Atomique, Dir. Industrielle, Saclay (France). Centre d' Etudes Nucleaires; Robert, C [Ecole Normale Superieure, 75 - Paris (France)

1957-07-01

Experiments on thermal neutron diffusion in the graphite used as moderator in the pile G1 have been carried out. The object of these experiments is to determine: - the intrinsic quality of this graphite, characterised by its diffusion length L or its Laplacian 1/L{sup 2} - the effect of the canals, which modifies anisotropically the macroscopic diffusion equation and is characterized by two principal diffusion regions (or two principal Laplacian), valid respectively for the diffusion in the direction of the canals and in a perpendicular direction. In order to determine them two experiments are necessary, in which the second derivatives of the flux in relation to the space coordinates are very different. These experiments form the object of the first two parts. Part 1: Diffusion along the axis of a flux coming from the pile source, and limited radially by a quasi cylindrical screen of cadmium bars. This screen, or Faraday cage is designed to give to the thermal flux produced the same radius of extrapolation to zero as that of the pile source. The determination of L (with the graphite full) has been made under the same conditions. The measurements have been interpreted in two ways. The influence of the brackets holding the detectors is discussed. Part 2: Radial diffusion in the graphite surrounding the 'long' cylindrical pile. This is well described by a sum of Bessel functions. Part 3: Results (valid for d = 1.61 t = 17 deg. C). For the graphite without cavity L = 52.7 {+-} 0.4 cm. The effect of the canals on the diffusion area and its anisotropy are in excellent agreement with the theory of Behrens: L(parallel) = 64.6 cm and L(perpendicular) 62.2 cm. Appendix: Theory of the Faraday cage. (author) [French] Des experiences de diffusion des neutrons thermiques dans le graphite constituant le moderateur de la pile G1 ont ete effectuees. Elles ont pour objet de determiner: - la qualite intrinseque de ce graphite, caracterisee par sa longueur de diffusion L ou son

On the exact solution for the multi-group kinetic neutron diffusion equation in a rectangle

International Nuclear Information System (INIS)

Petersen, C.Z.; Vilhena, M.T.M.B. de; Bodmann, B.E.J.

2011-01-01

In this work we consider the two-group bi-dimensional kinetic neutron diffusion equation. The solution procedure formalism is general with respect to the number of energy groups, neutron precursor families and regions with different chemical compositions. The fast and thermal flux and the delayed neutron precursor yields are expanded in a truncated double series in terms of eigenfunctions that, upon insertion into the kinetic equation and upon taking moments, results in a first order linear differential matrix equation with source terms. We split the matrix appearing in the transformed problem into a sum of a diagonal matrix plus the matrix containing the remaining terms and recast the transformed problem into a form that can be solved in the spirit of Adomian's recursive decomposition formalism. Convergence of the solution is guaranteed by the Cardinal Interpolation Theorem. We give numerical simulations and comparisons with available results in the literature. (author)

BLINDAGE: A neutron and gamma-ray transport code for shieldings with the removal-diffusion technique coupled with the point-kernel technique

International Nuclear Information System (INIS)

Fanaro, L.C.C.B.

1984-01-01

It was developed the BLINDAGE computer code for the radiation transport (neutrons and gammas) calculation. The code uses the removal - diffusion method for neutron transport and point-kernel technique with buil-up factors for gamma-rays. The results obtained through BLINDAGE code are compared with those obtained with the ANISN and SABINE computer codes. (Author) [pt

Dual detector neutron lifetime log: theory and practical applications

International Nuclear Information System (INIS)

Serpas, C.J.; Wichmann, P.A.; Fertl, W.H.; DeVries, M.R.; Rndall, R.R.

1977-01-01

The Neutron Lifetime Log instrumentation has continued to evolve and now is equipped with dual detectors for increased ease in gas detection and also a ratio response for a simultaneous porosity determination. A good deal of experimentation was involved to minimize both lithology and salinity effects on the porosity indication. This paper contains a discussion of the theory and concepts related to the application of the Dual Detector Neutron Lifetime Log (DNLL). It is important to note that with these advances the recording of thermal neutron capture cross section (Σ) remains consistent with the past measurements of earlier generations of instruments as the most accurate determination of this parameter. A number of field examples of the newly logged results are shown. These field cases include Dual Detector NLL's run thru the drill strings of highly deviated holes when difficulties were encountered in getting conventional open hole logs to bottom, logs thru open perforations and hot radioactive zones, comparisons of the large and small diameter instruments, logs with anomalous fluids in the annulus, logs thru multiple casing strings, and a number of other examples

Vectorization of three-dimensional neutron diffusion code CITATION

International Nuclear Information System (INIS)

Harada, Hiroo; Ishiguro, Misako

1985-01-01

Three-dimensional multi-group neutron diffusion code CITATION has been widely used for reactor criticality calculations. The code is expected to be run at a high speed by using recent vector supercomputers, when it is appropriately vectorized. In this paper, vectorization methods and their effects are described for the CITATION code. Especially, calculation algorithms suited for vectorization of the inner-outer iterative calculations which spend most of the computing time are discussed. The SLOR method, which is used in the original CITATION code, and the SOR method, which is adopted in the revised code, are vectorized by odd-even mesh ordering. The vectorized CITATION code is executed on the FACOM VP-100 and VP-200 computers, and is found to run over six times faster than the original code for a practical-scale problem. The initial value of the relaxation factor and the number of inner-iterations given as input data are also investigated since the computing time depends on these values. (author)

Mothers "Google It Up:" Extending Communication Channel Behavior in Diffusion of Innovations Theory.

Science.gov (United States)

Sundstrom, Beth

2016-01-01

This study employed qualitative methods, conducting 44 in-depth interviews with biological mothers of newborns to understand women's perceptions and use of new media, mass media, and interpersonal communication channels in relation to health issues. Findings contribute to theoretical and practical understandings of the role of communication channels in diffusion of innovations theory. In particular, this study provides a foundation for the use of qualitative research to advance applications of diffusion of innovations theory. Results suggest that participants resisted mass media portrayals of women's health. When faced with a health question, participants uniformly started with the Internet to "Google it up." Findings suggest new media comprise a new communication channel with new rules, serving the functions of both personal and impersonal influence. In particular, pregnancy and the postpartum period emerged as a time when campaign planners can access women in new ways online. As a result, campaign planners could benefit from introducing new ideas online and capitalizing on the strength of weak ties favored in new media. Results expand the innovativeness/needs paradox in diffusion of innovations theory by elaborating on the role of new media to reach underserved populations. These findings provide an opportunity to better understand patient information seeking through the lens of diffusion of innovations theory.

A call for Return to Rogers' Innovation Diffusion Theory ...

African Journals Online (AJOL)

On organizational characteristics, it is postulated that each of organizational readiness for change, culture, size and leader's change management style is positively related to the adoption of innovations. Gaps in the studies reviewed are highlighted. Keywords: Innovation Diffusion Theory; Everett Rogers; Adoption.

Crystal structure and ion-diffusion pathway of inorganic materials through neutron diffraction

International Nuclear Information System (INIS)

Yashima, Masatomo

2012-01-01

The present brief review describes the application of neutron powder diffractometry and maximum-entropy method to the studies of crystal structure and diffusional pathways of mobile ions in ionic conducting ceramic materials. La 0.62 Li 0.16 TiO 3 and L i0.6 FePO 4 exhibit two- and one-dimensional networks of Li cation diffusional pathways, respectively. In the fluorite-structure ionic conductors such as celia solid solution Ce 0.93 Y 0.07 O 1.96 , bismuth oxide solid solution δ-Bi 1.4 Yb 0.6 O 3 and copper iodide CuI, a similar curved diffusion pathway along the directions is observed. In the cubic ABO 3 perovskite-type ionic conductor, lanthanum gallate solid solution, the mobile ions diffuse along a curved line keeping the interatomic distance between the B cation and O 2- anion. We have experimentally confirmed that the anisotropic thermal motions of the apex O2 atom and the interstitial O3 atoms are essential for the high oxygen permeability of the K 2 NiF 4 -type mixed conductor. Diffusion paths of proton are visualized along c axis in hexagonal hydroxyapatite. (author)

Neutron stars in relativistic mean field theory with isovector scalar meson

International Nuclear Information System (INIS)

Kubis, S.; Kutschera, M.; Stachniewicz, S.

1996-12-01

We study the equation of state (EOS) of neutron star matter in a relativistic mean field (RMF) theory with the isovector scalar mean field corresponding to the δ-meson [a 0 (980)]. A range of values of the δ-meson coupling compatible with the Bonn potentials is explored. Parameters of the model in the isovector sector are constrained to fit the nuclear symmetry energy, E s ∼ 30 MeV. We find that proton fraction of neutron star matter is higher in the presence of the δ-field whereas the energy per particle is lower. The EOS becomes slightly stiffer and the maximum mass of the neutron star increased with increasing δmeson coupling. The effect is stronger for soft EOS. (author). 7 refs, 6 figs, 1 tab

Neutron stars in relativistic mean field theory with isovector scalar meson

International Nuclear Information System (INIS)

Kubis, S.; Kutschera, M.; Stachniewicz, S.

1998-01-01

We study the equation of state (EOS) of β-stable dense matter and models of neutron stars in the relativistic mean field (RMF) theory with the isovector scalar mean field corresponding to the δ-meson (a 0 (980)). A range of values of the δ-meson coupling compatible with the Bonn potentials is explored. Parameters of the model in the isovector sector are constrained to fit the nuclear symmetry energy, E s ∼30 MeV. We find that the quantity most sensitive to the δ-meson coupling is the proton fraction of neutron star matter. It increases significantly in the presence of the δ-field. The energy per baryon also increases but the effect is smaller. The EOS becomes slightly stiffer and the maximum neutron star mass increases for stronger δ-meson coupling. (author)

Neutron stars in relativistic mean field theory with isovector scalar meson

Energy Technology Data Exchange (ETDEWEB)

Kubis, S.; Kutschera, M.; Stachniewicz, S. [Institute of Nuclear Physics, Cracow (Poland)

1996-12-01

We study the equation of state (EOS) of neutron star matter in a relativistic mean field (RMF) theory with the isovector scalar mean field corresponding to the {delta}-meson [a{sub 0}(980)]. A range of values of the {delta}-meson coupling compatible with the Bonn potentials is explored. Parameters of the model in the isovector sector are constrained to fit the nuclear symmetry energy, E{sub s} {approx} 30 MeV. We find that proton fraction of neutron star matter is higher in the presence of the {delta}-field whereas the energy per particle is lower. The EOS becomes slightly stiffer and the maximum mass of the neutron star increased with increasing {delta}meson coupling. The effect is stronger for soft EOS. (author). 7 refs, 6 figs, 1 tab.

Improvement of calculation method for temperature coefficient of HTTR by neutronics calculation code based on diffusion theory. Analysis for temperature coefficient by SRAC code system

International Nuclear Information System (INIS)

Goto, Minoru; Takamatsu, Kuniyoshi

2007-03-01

The HTTR temperature coefficients required for the core dynamics calculations had been calculated from the HTTR core calculation results by the diffusion code with which the corrections had been performed using the core calculation results by the Monte-Carlo code MVP. This calculation method for the temperature coefficients was considered to have some issues to be improved. Then, the calculation method was improved to obtain the temperature coefficients in which the corrections by the Monte-Carlo code were not required. Specifically, from the point of view of neutron spectrum calculated by lattice calculations, the lattice model was revised which had been used for the calculations of the temperature coefficients. The HTTR core calculations were performed by the diffusion code with the group constants which were generated by the lattice calculations with the improved lattice model. The core calculations and the lattice calculations were performed by the SRAC code system. The HTTR core dynamics calculation was performed with the temperature coefficient obtained from the core calculation results. In consequence, the core dynamics calculation result showed good agreement with the experimental data and the valid temperature coefficient could be calculated only by the diffusion code without the corrections by Monte-Carlo code. (author)

Analysis of mass incident diffusion in Weibo based on self-organization theory

Science.gov (United States)

Pan, Jun; Shen, Huizhang

2018-02-01

This study introduces some theories and methods of self-organization system to the research of the diffusion mechanism of mass incidents in Weibo (Chinese Twitter). Based on the analysis on massive Weibo data from Songjiang battery factory incident happened in 2013 and Jiiangsu Qidong OJI PAPER incident happened in 2012, we find out that diffusion system of mass incident in Weibo satisfies Power Law, Zipf's Law, 1/f noise and Self-similarity. It means this system is the self-organization criticality system and dissemination bursts can be understood as one kind of Self-organization behavior. As the consequence, self-organized criticality (SOC) theory can be used to explain the evolution of mass incident diffusion and people may come up with the right strategy to control such kind of diffusion if they can handle the key ingredients of Self-organization well. Such a study is of practical importance which can offer opportunities for policy makers to have good management on these events.

Field theory of absorbing phase transitions with a non-diffusive conserved field

International Nuclear Information System (INIS)

Pastor-Satorras, R.; Vespignani, A.

2000-04-01

We investigate the critical behavior of a reaction-diffusion system exhibiting a continuous absorbing-state phase transition. The reaction-diffusion system strictly conserves the total density of particles, represented as a non-diffusive conserved field, and allows an infinite number of absorbing configurations. Numerical results show that it belongs to a wide universality class that also includes stochastic sandpile models. We derive microscopically the field theory representing this universality class. (author)

Spallation neutrons pulsed sources

International Nuclear Information System (INIS)

Carpenter, J.

1996-01-01

This article describes the range of scientific applications which can use these pulsed neutrons sources: Studies on super fluids, measures to verify the crawling model for the polymers diffusion; these sources are also useful to study the neutron disintegration, the ultra cold neutrons. In certain applications which were not accessible by neutrons diffusion, for example, radiations damages, radionuclides production and activation analysis, the spallation sources find their use and their improvement will bring new possibilities. Among others contributions, one must notice the place at disposal of pulsed muons sources and neutrinos sources. (N.C.). 3 figs

Estimation of delayed neutron emission probability by using the gross theory of nuclear β-decay

International Nuclear Information System (INIS)

Tachibana, Takahiro

1999-01-01

The delayed neutron emission probabilities (P n -values) of fission products are necessary in the study of reactor physics; e.g. in the calculation of total delayed neutron yields and in the summation calculation of decay heat. In this report, the P n -values estimated by the gross theory for some fission products are compared with experiment, and it is found that, on the average, the semi-gross theory somewhat underestimates the experimental P n -values. A modification of the β-decay strength function is briefly discussed to get more reasonable P n -values. (author)

Thermal diffuse scattering in time-of-flight neutron diffraction studied on SBN single crystals

International Nuclear Information System (INIS)

Prokert, F.; Savenko, B.N.; Balagurov, A.M.

1994-01-01

At time-of-flight (TOF) diffractometer D N-2, installed at the pulsed reactor IBR-2 in Dubna, Sr x Ba 1-x Nb 2 O 6 mixed single crystals (SBN-x) of different compositions (0.50 < x< 0.75) were investigated between 15 and 773 K. The diffraction patterns were found to be strongly influenced by the thermal diffuse scattering (TDS). The appearance of the TDS from the long wavelength acoustic models of vibration in single crystals is characterized by the ratio of the velocity of sound to the velocity of neutron. Due to the nature of the TOF Laue diffraction technique used on D N-2, the TDS around Bragg peaks has rather a complex profile. An understanding of the TDS close to Bragg peaks is essential in allowing the extraction of the diffuse scattering occurring at the diffuse ferroelectric phase transition in SBN crystals. 11 refs.; 9 figs.; 1 tab. (author)

Dynamic theory of neutron diffraction from a moving grating

Energy Technology Data Exchange (ETDEWEB)

Bushuev, V. A., E-mail: vabushuev@yandex.ru [Moscow State University (Russian Federation); Frank, A. I.; Kulin, G. V. [Joint Institute for Nuclear Research (Russian Federation)

2016-01-15

A multiwave dynamic theory of diffraction of ultracold neutrons from a moving phase grating has been developed in the approximation of coupled slowly varying amplitudes of wavefunctions. The effect of the velocity, period, and height of grooves of the grating, as well as the spectral angular distribution of the intensity of incident neurons, on the discrete energy spectrum and the intensity of diffraction reflections of various orders has been analyzed.

Comparison of diffusion and transport theory analysis with experimental results in fast breeder test reactor

International Nuclear Information System (INIS)

Sathyabama, N.; Mohanakrishnan, P.; Lee, S.M.

1994-01-01

A systematic analysis has been performed by 3 dimensional diffusion and transport methods to calculate the measured control rod worths and subassembly wise power distribution in fast breeder test reactor. Geometry corrections (rectangular to hexagonal and diffusion to transport corrections are estimated for multiplication factors and control rod worths. Calculated control rod worths by diffusion and transport theory are nearly the same and 10% above measured values. Power distribution in the core periphery is over predicted (15%) by diffusion theory. But, this over prediction reduces to 8% by use of the S N method. (authors). 9 refs., 4 tabs., 3 fig

Doublet channel neutron-deuteron scattering in leading order effective field theory

OpenAIRE

B. BlankleiderFlinders U.; J. Gegelia(INFN)

2015-01-01

The doublet channel neutron-deuteron scattering amplitude is calculated in leading order effective field theory (EFT). It is shown that this amplitude does not depend on a constant contact interaction three-body force. Satisfactory agreement with available data is obtained when only two-body forces are included.

The neutron electric dipole moments as a test of the superweak interaction theory

CERN Document Server

Wolfenstein, Lincoln

1974-01-01

Theoretical calculations of the neutron electric dipole moment D/sub n / are reviewed for various theories of CP violation. It is shown that for the superweak interaction theory D/sub n/ is less than 10/sup -29/ e.cm in contrast to values of 10/sup -23/ to 10/sup -24/ predicted by many but not all milliweak theories. It is concluded that prospective measurements of D/sub n/ may provide decisive evidence against or significant evidence in favour of the superweak theory. (26 refs).

Diffusion theory and knowledge dissemination, utilization, and integration in public health.

Science.gov (United States)

Green, Lawrence W; Ottoson, Judith M; García, César; Hiatt, Robert A

2009-01-01

Legislators and their scientific beneficiaries express growing concerns that the fruits of their investment in health research are not reaching the public, policy makers, and practitioners with evidence-based practices. Practitioners and the public lament the lack of relevance and fit of evidence that reaches them and barriers to their implementation of it. Much has been written about this gap in medicine, much less in public health. We review the concepts that have guided or misguided public health in their attempts to bridge science and practice through dissemination and implementation. Beginning with diffusion theory, which inspired much of public health's work on dissemination, we compare diffusion, dissemination, and implementation with related notions that have served other fields in bridging science and practice. Finally, we suggest ways to blend diffusion with other theory and evidence in guiding a more decentralized approach to dissemination and implementation in public health, including changes in the ways we produce the science itself.

Neutron stars in relativistic mean field theory with isovector scalar meson

Energy Technology Data Exchange (ETDEWEB)

Kubis, S.; Kutschera, M.; Stachniewicz, S. [H. Niewodniczanski Institute of Nuclear Physics, Cracow (Poland)

1998-03-01

We study the equation of state (EOS) of {beta}-stable dense matter and models of neutron stars in the relativistic mean field (RMF) theory with the isovector scalar mean field corresponding to the {delta}-meson (a{sub 0}(980)). A range of values of the {delta}-meson coupling compatible with the Bonn potentials is explored. Parameters of the model in the isovector sector are constrained to fit the nuclear symmetry energy, E{sub s}{approx}30 MeV. We find that the quantity most sensitive to the {delta}-meson coupling is the proton fraction of neutron star matter. It increases significantly in the presence of the {delta}-field. The energy per baryon also increases but the effect is smaller. The EOS becomes slightly stiffer and the maximum neutron star mass increases for stronger {delta}-meson coupling. (author) 8 refs, 6 figs, 2 tabs

Asymmetric nuclear matter and neutron star properties within the extended Brueckner theory

Energy Technology Data Exchange (ETDEWEB)

Hassaneen, Khaled S.A. [Sohag University, Physics Department, Faculty of Science, Sohag (Egypt); Taif University, Physics Department, Faculty of Science, Taif (Saudi Arabia)

2017-01-15

Microscopically, the equation of state (EOS) and other properties of asymmetric nuclear matter at zero temperature have been investigated extensively by adopting the non-relativistic Brueckner-Hartree-Fock (BHF) and the extended BHF approaches by using the self-consistent Green's function approach or by including a phenomenological three-body force. Once three-body forces are introduced, the phenomenological saturation point is reproduced and the theory is applied to the study of neutron star properties. We can calculate the total mass and radius for neutron stars using various equations of state at high densities in β-equilibrium without hyperons. A comparison with other microscopic predictions based on non-relativistic and density-dependent relativistic mean-field calculations has been done. It is found that relativistic EOS yields however larger mass and radius for neutron star than predictions based on non-relativistic approaches. Also the three-body force plays a crucial role to deduce the theoretical value of the maximum mass of neutron stars in agreement with recent measurements of the neutron star mass. (orig.)

The use of steady state neutron flux measurement to determine the size of an invaded region following fluid injection

International Nuclear Information System (INIS)

Parsons, R.J.

1983-01-01

By using a combination of Monte-Carlo and diffusion theory techniques, the behaviour of the thermal neutron flux during fluid injection is studied. It is shown that the change in neutron flux induced by the fluid injection, is equal to the neutron flux due to a certain thermal neutron source distribution. Using this result, a method of estimating the size of an elliptical invaded region is given. This choice of region shape is not a necessity but a convenience and it is possible that the method may be generalised to include higher order shapes. (author)

First-principles investigation of neutron-irradiation-induced point defects in B4C, a neutron absorber for sodium-cooled fast nuclear reactors

Science.gov (United States)

You, Yan; Yoshida, Katsumi; Yano, Toyohiko

2018-05-01

Boron carbide (B4C) is a leading candidate neutron absorber material for sodium-cooled fast nuclear reactors owing to its excellent neutron-capture capability. The formation and migration energies of the neutron-irradiation-induced defects, including vacancies, neutron-capture reaction products, and knocked-out atoms were studied by density functional theory calculations. The vacancy-type defects tend to migrate to the C–B–C chains of B4C, which indicates that the icosahedral cage structures of B4C have strong resistance to neutron irradiation. We found that lithium and helium atoms had significantly lower migration barriers along the rhombohedral (111) plane of B4C than perpendicular to this plane. This implies that the helium and lithium interstitials tended to follow a two-dimensional diffusion regime in B4C at low temperatures which explains the formation of flat disk like helium bubbles experimentally observed in B4C pellets after neutron irradiation. The knocked-out atoms are considered to be annihilated by the recombination of the close pairs of self-interstitials and vacancies.

Introductory theory of neutron scattering

International Nuclear Information System (INIS)

Gunn, J.M.F.

1986-12-01

The paper comprises a set of six lecture notes which were delivered to the summer school on 'Neutron Scattering at a pulsed source', Rutherford Laboratory, United Kingdom, 1986. The lectures concern the physical principles of neutron scattering. The topics of the lectures include: diffraction, incoherent inelastic scattering, connection with the Schroedinger equation, magnetic scattering, coherent inelastic scattering, and surfaces and neutron optics. (UK)

Atomic diffusion theory challenging the Cahn-Hilliard method

International Nuclear Information System (INIS)

Nastar, M.

2014-01-01

Our development of the self-consistent mean-field (SCMF) kinetic theory for nonuniform alloys leads to the statement that kinetic correlations induced by the vacancy diffusion mechanism have a dramatic effect on nano-scale diffusion phenomena, leading to nonlinear features of the interdiffusion coefficients. Lattice rate equations of alloys including nonuniform gradients of chemical potential are derived within the Bragg-Williams statistical approximation and the third shell kinetic approximation of the SCMF theory. General driving forces including deviations of the free energy from a local equilibrium thermodynamic formulation are introduced. These deviations are related to the variation of vacancy motion due to the spatial variation of the alloy composition. During the characteristic time of atomic diffusion, multiple exchanges of the vacancy with the same atoms may happen, inducing atomic kinetic correlations that depend as well on the spatial variation of the alloy composition. As long as the diffusion driving forces are uniform, the rate equations are shown to obey in this form the Onsager formalism of thermodynamics of irreversible processes (TIP) and the TIP-based Cahn-Hilliard diffusion equation. If now the chemical potential gradients are not uniform, the continuous limit of the present SCMF kinetic equations does not coincide with the Cahn-Hilliard (CH) equation. In particular, the composition gradient and higher derivative terms depending on kinetic parameters add to the CH thermodynamic-based composition gradient term. Indeed, a diffusion equation written as a mobility multiplied by a thermodynamic formulation of the driving forces is shown to be inadequate. In the reciprocal space, the thermodynamic driving force has to be multiplied by a nonlinear function of the wave vector accounting for the variation of kinetic correlations with composition inhomogeneities. Analytical expressions of the effective interdiffusion coefficient are given for two limit

Determination of the response function for the Portsmouth Gaseous Diffusion Plant criticality accident alarm system neutron detectors

International Nuclear Information System (INIS)

Tayloe, R.W. Jr.; Brown, A.S.; Dobelbower, M.C.; Woollard, J.E.

1997-03-01

Neutron-sensitive radiation detectors are used in the Portsmouth Gaseous Diffusion Plant's (PORTS) criticality accident alarm system (CAAS). The CAAS is composed of numerous detectors, electronics, and logic units. It uses a telemetry system to sound building evacuation horns and to provide remote alarm status in a central control facility. The ANSI Standard for a CAAS uses a free-in-air dose rate to define the detection criteria for a minimum accident-of-concern. Previously, the free-in-air absorbed dose rate from neutrons was used for determining the areal coverge of criticality detection within PORTS buildings handling fissile materials. However, the free-in-air dose rate does not accurately reflect the response of the neutron detectors in use at PORTS. Because the cost of placing additional CAAS detectors in areas of questionable coverage (based on a free-in-air absorbed dose rate) is high, the actual response function for the CAAS neutron detectors was determined. This report, which is organized into three major sections, discusses how the actual response function for the PORTS CAAS neutron detectors was determined. The CAAS neutron detectors are described in Section 2. The model of the detector system developed to facilitate calculation of the response function is discussed in Section 3. The results of the calculations, including confirmatory measurements with neutron sources, are given in Section 4

Platoon Dispersion Analysis Based on Diffusion Theory

Directory of Open Access Journals (Sweden)

Badhrudeen Mohamed

2017-01-01

Full Text Available Urbanization and gro wing demand for travel, causes the traffic system to work ineffectively in most urban areas leadin g to traffic congestion. Many approaches have been adopted to address this problem, one among them being the signal co-ordination. This can be achieved if the platoon of vehicles that gets discharged at one signal gets green at consecutive signals with minimal delay. However, platoons tend to get dispersed as they travel and this dispersion phenomenon should be taken into account for effective signal coordination. Reported studies in this area are from the homogeneous and lane disciplined traffic conditions. This paper analyse the platoon dispersion characteristics under heterogeneous and lane-less traffic conditions. Out of the various modeling techniques reported, the approach based on diffusion theory is used in this study. The diffusion theory based models so far assumed thedata to follow normal distribution. However, in the present study, the data was found to follow lognormal distribution and hence the implementation was carried out using lognormal distribution. The parameters of lognormal distribution were calibrated for the study condition. For comparison purpose, normal distribution was also calibrated and the results were evaluated. It was foun d that model with log normal distribution performed better in all cases than the o ne with normal distribution.

Theory of the Influence of Phonon-Phonon and Electron-Phonon Interactions on the Scattering of Neutrons by Crystals; Theorie de l'influence des interactions phonon-phonon et electron-phonon sur la diffusion des neutrons par des cristaux; Teoriya vliyaniya vzaimodejstvij fonon-fonon iehlvktron-fonon na rasseyanie nejtronov kristalla-; Teoria de la influencia de las interacciones fonon-fonon y electron-fonon en la dispersion de neutrones por cristales

Energy Technology Data Exchange (ETDEWEB)

Kokkedee, J J.J. [Institute for Theoretical Physics of the University of Utrecht (Netherlands)

1963-01-15

interatomic or interionic distance in the crystal). Approximate calculations are performed to give some insight into the orders of magnitude of the effects under study. (author) [French] Comme le predit la theorie harmonique, le spectre de la diffusion inelastique coherente de neutrons par un monocristal non conducteur, pour un angle de diffusion donne, se compose d'une serie de pics de fonction delta, qui se superposent a un bruit de fond continu. Les pics correspondent a des phenomenes a un phonon, dans lesquels un phonon est absorbe ou emis par le neutron; le bruit de fond provient de phenomenes a plusieurs phonons. Lorsqu'il existe des forces anharmoniques (interaction phonon-phonon) les pics de fonction delta s'elargissent pour former des pics finis et leur frequence centrale est dephasee par rapport aux valeurs harmoniques. Dans le cas d'un metal il y a, en plus des interactions phonon-phonon, une interaction entre les phonons et les electrons de conduction, laquelle contribue a dephaser et elargir encore davantage les pics a un phonon. Continuant les travaux de Van Hove (qui avait considere le cas relativement simple d'un cristal non conducteur a l'etat fondamental, soit T = 0{sup o}K) l'auteut a etudie les deplacements et les largeurs des pics de diffusion resultant des interactions indiquees plus haut, a l'aide de la theorie de la perturbation a plusieurs particules, en ayant largement recours a la methode des diagrammes. Il admet, avant tout examen du probleme, que quelle que soit la force des interactions, la largeur de chaque pic est petite par rapport a la valeur de la frequence en son centres dans ces conditions seulement, on peut considerer que les pics sont bien definis par rapport au bruit de fond, si les calculs d'interaction sont pousses jusqu'aux ordres superieurs. On estime que cette hipothbse est realisee tant que les temperatures ne sont pas trop elevees et que les valeurs du vecteur d'onde des phonons ne sont pas trop considerables. La methode

Analysis of diffuse scattering in neutron powder diagrams. Application to glassy carbon

International Nuclear Information System (INIS)

Boysen, H.

1985-01-01

From the quantitative analysis of the diffuse scattered intensity in powder diagrams valuable information about the disorder in crystals may be obtained. According to the dimensionality of this disorder (0D, 1D, 2D or 3D corresponding to diffuse peaks, streaks, planes or volume in reciprocal space) a characteristic modulation of the background is observed, which is described by specific functions. These are derived by averaging the appropriate cross sections over all crystallite orientations in the powder and folding with the resolution function of the instrument. If proper account is taken of all proportionality factors different components of the background can be put on one relative scale. The results are applied to two samples of glassy carbon differing in their degree of disorder. The neutron powder patterns contain contributions from 0D (00l peaks due to the stacking of graphitic layers), 1D (hkzeta streaks caused by the random orientation of these layers) and 3D (incoherent scattering, averaged thermal diffuse scattering, multiple scattering). From the fit to the observed data various parameters of the disorder like domain sizes, strains, interlayer distances, amount of incorporated hydrogen, pore sizes etc. are determined. It is shown that the omission of resolution corrections leads to false parameters. (orig.)

A digital data acquisition system for a time of flight neutron diffuse scattering instrument

International Nuclear Information System (INIS)

Venegas, Rafael; Bacza, Lorena; Navarro, Gustavo

1998-01-01

Full text. We describe the design of a digital data acquisition system built for acquiring and storing the information produced by a neutron diffuse scattering apparatus. This instrument is based on the analysis of pulsed subthermal neutron which are scattered by a solid or liquid sample, measured as function of the scattered neutron wavelength and momentum direction. The time of flight neutron intensities on 14 different angular detector positions and two fission chambers must be analyzed simultaneously for each neutron burst. A PC controlled data acquisition board system was built based on two parallel multiscannning units, each with its own add-one counting unit, and a common base time generator. The unit plugs onto the ISA bus through an interface card. Two separate counting units were designed, to avoid possible access competition between low counting rate counters at off-axis positions and the higher rate frontal 0 deg and beam monitoring counters. the first unit contains logic for 14 independent and simultaneous multi scaling inputs, with 128 time channels and dwell time per channel of 5, 10 or 20 microseconds. Sweep trigger is synchronized with an electric signal from a coil sensing the rotor. The second unit contains logic for four additional multi scalers using the same external synchronizing signal, similar in all others details to the previously described multi scalers. Basic control routines for the acquisitions were written in C and a program for spectrum display and user interface was written in C ++ for a Windows 3.1 OS. A block diagram of the system is presented

Neutron matter at next-to-next-to-next-to-leading order in chiral effective field theory.

Science.gov (United States)

Tews, I; Krüger, T; Hebeler, K; Schwenk, A

2013-01-18

Neutron matter presents a unique system for chiral effective field theory because all many-body forces among neutrons are predicted to next-to-next-to-next-to-leading order (N(3)LO). We present the first complete N(3)LO calculation of the neutron matter energy. This includes the subleading three-nucleon forces for the first time and all leading four-nucleon forces. We find relatively large contributions from N(3)LO three-nucleon forces. Our results provide constraints for neutron-rich matter in astrophysics with controlled theoretical uncertainties.

Beta-decay rate and beta-delayed neutron emission probability of improved gross theory

Science.gov (United States)

Koura, Hiroyuki

2014-09-01

A theoretical study has been carried out on beta-decay rate and beta-delayed neutron emission probability. The gross theory of the beta decay is based on an idea of the sum rule of the beta-decay strength function, and has succeeded in describing beta-decay half-lives of nuclei overall nuclear mass region. The gross theory includes not only the allowed transition as the Fermi and the Gamow-Teller, but also the first-forbidden transition. In this work, some improvements are introduced as the nuclear shell correction on nuclear level densities and the nuclear deformation for nuclear strength functions, those effects were not included in the original gross theory. The shell energy and the nuclear deformation for unmeasured nuclei are adopted from the KTUY nuclear mass formula, which is based on the spherical-basis method. Considering the properties of the integrated Fermi function, we can roughly categorized energy region of excited-state of a daughter nucleus into three regions: a highly-excited energy region, which fully affect a delayed neutron probability, a middle energy region, which is estimated to contribute the decay heat, and a region neighboring the ground-state, which determines the beta-decay rate. Some results will be given in the presentation. A theoretical study has been carried out on beta-decay rate and beta-delayed neutron emission probability. The gross theory of the beta decay is based on an idea of the sum rule of the beta-decay strength function, and has succeeded in describing beta-decay half-lives of nuclei overall nuclear mass region. The gross theory includes not only the allowed transition as the Fermi and the Gamow-Teller, but also the first-forbidden transition. In this work, some improvements are introduced as the nuclear shell correction on nuclear level densities and the nuclear deformation for nuclear strength functions, those effects were not included in the original gross theory. The shell energy and the nuclear deformation for

Transport equivalent diffusion constants for reflector region in PWRs

International Nuclear Information System (INIS)

Tahara, Yoshihisa; Sekimoto, Hiroshi

2002-01-01

The diffusion-theory-based nodal method is widely used in PWR core designs for reason of its high computing speed in three-dimensional calculations. The baffle/reflector (B/R) constants used in nodal calculations are usually calculated based on a one-dimensional transport calculation. However, to achieve high accuracy of assembly power prediction, two-dimensional model is needed. For this reason, the method for calculating transport equivalent diffusion constants of reflector material was developed so that the neutron currents on the material boundaries could be calculated exactly in diffusion calculations. Two-dimensional B/R constants were calculated using the transport equivalent diffusion constants in the two-dimensional diffusion calculation whose geometry reflected the actual material configuration in the reflector region. The two-dimensional B/R constants enabled us to predict assembly power within an error of 1.5% at hot full power conditions. (author)

Iterative solutions of finite difference diffusion equations

International Nuclear Information System (INIS)

Menon, S.V.G.; Khandekar, D.C.; Trasi, M.S.

1981-01-01

The heterogeneous arrangement of materials and the three-dimensional character of the reactor physics problems encountered in the design and operation of nuclear reactors makes it necessary to use numerical methods for solution of the neutron diffusion equations which are based on the linear Boltzmann equation. The commonly used numerical method for this purpose is the finite difference method. It converts the diffusion equations to a system of algebraic equations. In practice, the size of this resulting algebraic system is so large that the iterative methods have to be used. Most frequently used iterative methods are discussed. They include : (1) basic iterative methods for one-group problems, (2) iterative methods for eigenvalue problems, and (3) iterative methods which use variable acceleration parameters. Application of Chebyshev theorem to iterative methods is discussed. The extension of the above iterative methods to multigroup neutron diffusion equations is also considered. These methods are applicable to elliptic boundary value problems in reactor design studies in particular, and to elliptic partial differential equations in general. Solution of sample problems is included to illustrate their applications. The subject matter is presented in as simple a manner as possible. However, a working knowledge of matrix theory is presupposed. (M.G.B.)

A transmission probability method for calculation of neutron flux distributions in hexagonal geometry

International Nuclear Information System (INIS)

Wasastjerna, F.; Lux, I.

1980-03-01

A transmission probability method implemented in the program TPHEX is described. This program was developed for the calculation of neutron flux distributions in hexagonal light water reactor fuel assemblies. The accuracy appears to be superior to diffusion theory, and the computation time is shorter than that of the collision probability method. (author)

On the Emergence and Diffusion of Technological Capabilities and the Theory of the MNC

DEFF Research Database (Denmark)

Blomkvist, Katarina; Kappen, Philip; Zander, Ivo

2015-01-01

This paper intersects extant theories of the MNC with empirically observed patterns in the intra-company emergence and diffusion of technological capabilities. It draws upon a database containing the complete patenting history of 24 Swedish multinationals over the 1890-2008 period, which allows...... as distinctive and differentiated diffusion patterns across headquarters, greenfield subsidiaries, and acquired units in the MNC group. We conclude that a theory of the MNC should recognize the shift towards more equal conditions for the generation of new technology within the multinational organization......, but that within this overall development some conspicuous inequalities in intra-company capability dif-fusion remain to be accounted for....

CARMEN-SYSTEM, Programs System for Thermal Neutron Diffusion and Burnup with Feedback

International Nuclear Information System (INIS)

Ahnert, Carol; Aragones, Jose M.

1983-01-01

1 - Description of problem or function: CARMEN is a system of programs developed for the neutronic calculation of PWR cycles. It includes the whole chain of analysis from cell calculations to core calculations with burnup. The core calculations are based on diffusion theory with cross sections depending on the relevant space-dependent feedback effects which are present at each moment along the cycles. The diffusion calculations are in one, two or three dimensions and in two energy groups. The feedback effects which are treated locally are: burnup, water density, power density and fission products. In order to study in detail these parameters the core should be divided into as many zones as different cross section sets are expected to be required in order to reproduce reality correctly. A relevant difference in any feedback parameter between zones produces different cross section sets for the corresponding zones. CARMEN is also capable to perform the following calculations: - Multiplication factor by burnup step with fixed boron concentration - Buckling and control rod insertion - Buckling search by burnup step - Boron search by burnup step - Control rod insertion search by burnup step. 2 - Method of solution: The cell code (LEOPARD-TRACA) generates the fuel assembly cross sections versus burnup. This is the basic library to be used in the CARMEN code proper. With a planar distribution guess for power density, water density and fluxes, the macroscopic cross sections by zone are calculated by CARMEN, and then a diffusion calculation is done in the whole geometry. With the distribution of power density, heat accumulated in the coolant and the thermal and fast fluxes determined in the diffusion calculation, CARMEN calculates the values of the most relevant parameters that influence the macroscopic cross sections by zone: burnup, water density, effective fuel temperature and fission product concentrations. If these parameters by zone are different from the reference

The velocity correlation function in cosmic-ray diffusion theory

International Nuclear Information System (INIS)

Forman, M.A.

1977-01-01

The concept of velocity correlation functions is introduced and applied to the calculation of cosmic ray spatial diffusion coefficients. It is assumed that the pitch angle scattering coefficient is already known from some other theory, and is reasonably well-behaved. Previous results for the coefficient for diffusion parallel to the mean field are recovered when the velocity-changing mechanism is artificially restricted to pitch angle scattering. The velocity correlation method is then applied to the more general case where there are fluctuations in the local mean field. It is found that the parallel diffusion coefficient is reduced in proportion to the amplitude of the field fluctuations, and that the ratio of the perpendicular to parallel diffusion coefficients cannot be greater than 2 >/B 0 2 . It is shown in the appendix that the Liouville form of the scattering equation implies that the Fokker-Planck coefficients (Δμ 2 )/Δt=2Dsub(μμ) and (Δμ)/Δt=deltaDsub(μμ)/deltaμ, and that all higher-order coefficients are identically zero. (Auth.)

Numerical Test of Analytical Theories for Perpendicular Diffusion in Small Kubo Number Turbulence

Energy Technology Data Exchange (ETDEWEB)

Heusen, M.; Shalchi, A., E-mail: husseinm@myumanitoba.ca, E-mail: andreasm4@yahoo.com [Department of Physics and Astronomy, University of Manitoba, Winnipeg, MB R3T 2N2 (Canada)

2017-04-20

In the literature, one can find various analytical theories for perpendicular diffusion of energetic particles interacting with magnetic turbulence. Besides quasi-linear theory, there are different versions of the nonlinear guiding center (NLGC) theory and the unified nonlinear transport (UNLT) theory. For turbulence with high Kubo numbers, such as two-dimensional turbulence or noisy reduced magnetohydrodynamic turbulence, the aforementioned nonlinear theories provide similar results. For slab and small Kubo number turbulence, however, this is not the case. In the current paper, we compare different linear and nonlinear theories with each other and test-particle simulations for a noisy slab model corresponding to small Kubo number turbulence. We show that UNLT theory agrees very well with all performed test-particle simulations. In the limit of long parallel mean free paths, the perpendicular mean free path approaches asymptotically the quasi-linear limit as predicted by the UNLT theory. For short parallel mean free paths we find a Rechester and Rosenbluth type of scaling as predicted by UNLT theory as well. The original NLGC theory disagrees with all performed simulations regardless what the parallel mean free path is. The random ballistic interpretation of the NLGC theory agrees much better with the simulations, but compared to UNLT theory the agreement is inferior. We conclude that for this type of small Kubo number turbulence, only the latter theory allows for an accurate description of perpendicular diffusion.

Numerical Test of Analytical Theories for Perpendicular Diffusion in Small Kubo Number Turbulence

International Nuclear Information System (INIS)

Heusen, M.; Shalchi, A.

2017-01-01

In the literature, one can find various analytical theories for perpendicular diffusion of energetic particles interacting with magnetic turbulence. Besides quasi-linear theory, there are different versions of the nonlinear guiding center (NLGC) theory and the unified nonlinear transport (UNLT) theory. For turbulence with high Kubo numbers, such as two-dimensional turbulence or noisy reduced magnetohydrodynamic turbulence, the aforementioned nonlinear theories provide similar results. For slab and small Kubo number turbulence, however, this is not the case. In the current paper, we compare different linear and nonlinear theories with each other and test-particle simulations for a noisy slab model corresponding to small Kubo number turbulence. We show that UNLT theory agrees very well with all performed test-particle simulations. In the limit of long parallel mean free paths, the perpendicular mean free path approaches asymptotically the quasi-linear limit as predicted by the UNLT theory. For short parallel mean free paths we find a Rechester and Rosenbluth type of scaling as predicted by UNLT theory as well. The original NLGC theory disagrees with all performed simulations regardless what the parallel mean free path is. The random ballistic interpretation of the NLGC theory agrees much better with the simulations, but compared to UNLT theory the agreement is inferior. We conclude that for this type of small Kubo number turbulence, only the latter theory allows for an accurate description of perpendicular diffusion.

A diffusivity model for predicting VOC diffusion in porous building materials based on fractal theory.

Science.gov (United States)

Liu, Yanfeng; Zhou, Xiaojun; Wang, Dengjia; Song, Cong; Liu, Jiaping

2015-12-15

Most building materials are porous media, and the internal diffusion coefficients of such materials have an important influences on the emission characteristics of volatile organic compounds (VOCs). The pore structure of porous building materials has a significant impact on the diffusion coefficient. However, the complex structural characteristics bring great difficulties to the model development. The existing prediction models of the diffusion coefficient are flawed and need to be improved. Using scanning electron microscope (SEM) observations and mercury intrusion porosimetry (MIP) tests of typical porous building materials, this study developed a new diffusivity model: the multistage series-connection fractal capillary-bundle (MSFC) model. The model considers the variable-diameter capillaries formed by macropores connected in series as the main mass transfer paths, and the diameter distribution of the capillary bundles obeys a fractal power law in the cross section. In addition, the tortuosity of the macrocapillary segments with different diameters is obtained by the fractal theory. Mesopores serve as the connections between the macrocapillary segments rather than as the main mass transfer paths. The theoretical results obtained using the MSFC model yielded a highly accurate prediction of the diffusion coefficients and were in a good agreement with the VOC concentration measurements in the environmental test chamber. Copyright © 2015 Elsevier B.V. All rights reserved.

Mode-coupling theory of self-diffusion in diblock copolymers. II. Model calculations and experimental comparisons

International Nuclear Information System (INIS)

Guenza, M.; Schweizer, K.S.

1998-01-01

The predictions of polymer-mode-coupling theory for self-diffusion in entangled structurally and interaction symmetric diblock copolymer fluids are illustrated by explicit numerical calculations. We find that retardation of translational motion emerges near and somewhat below the order endash disorder transition (ODT) in an approximately exponential and/or thermally activated manner. At fixed reduced temperature, suppression of diffusion is enhanced with increasing diblock molecular weight, compositional symmetry, and/or copolymer concentration. At very low temperatures, a new entropic-like regime of mobility suppression is predicted based on an isotropic supercooled liquid description of the copolymer structure. Preliminary generalization of the theory to treat diblock tracer diffusion is also presented. Quantitative applications to recent self and tracer diffusion measurements on compositionally symmetric polyolefin diblock materials have been carried out, and very good agreement between theory and experiment is found. Asymmetry in block local friction constants is predicted to significantly influence mobility suppression, with the largest effects occurring when the minority block is also the high friction species. New experiments to further test the predictions of the theory are suggested. copyright 1998 American Institute of Physics

Quantum Monte Carlo calculations with chiral effective field theory interactions

Energy Technology Data Exchange (ETDEWEB)

Tews, Ingo

2015-10-12

The neutron-matter equation of state connects several physical systems over a wide density range, from cold atomic gases in the unitary limit at low densities, to neutron-rich nuclei at intermediate densities, up to neutron stars which reach supranuclear densities in their core. An accurate description of the neutron-matter equation of state is therefore crucial to describe these systems. To calculate the neutron-matter equation of state reliably, precise many-body methods in combination with a systematic theory for nuclear forces are needed. Chiral effective field theory (EFT) is such a theory. It provides a systematic framework for the description of low-energy hadronic interactions and enables calculations with controlled theoretical uncertainties. Chiral EFT makes use of a momentum-space expansion of nuclear forces based on the symmetries of Quantum Chromodynamics, which is the fundamental theory of strong interactions. In chiral EFT, the description of nuclear forces can be systematically improved by going to higher orders in the chiral expansion. On the other hand, continuum Quantum Monte Carlo (QMC) methods are among the most precise many-body methods available to study strongly interacting systems at finite densities. They treat the Schroedinger equation as a diffusion equation in imaginary time and project out the ground-state wave function of the system starting from a trial wave function by propagating the system in imaginary time. To perform this propagation, continuum QMC methods require as input local interactions. However, chiral EFT, which is naturally formulated in momentum space, contains several sources of nonlocality. In this Thesis, we show how to construct local chiral two-nucleon (NN) and three-nucleon (3N) interactions and discuss results of first QMC calculations for pure neutron systems. We have performed systematic auxiliary-field diffusion Monte Carlo (AFDMC) calculations for neutron matter using local chiral NN interactions. By

Homogenisation of a Wigner-Seitz cell in two group diffusion theory

International Nuclear Information System (INIS)

Allen, F.R.

1968-02-01

Two group diffusion theory is used to develop a theory for the homogenisation of a Wigner-Seitz cell, neglecting azimuthal flux components of higher order than dipoles. An iterative method of solution is suggested for linkage with reactor calculations. The limiting theory for no cell leakage leads to cell edge flux normalisation of cell parameters, the current design method for SGHW reactor design calculations. Numerical solutions are presented for a cell-plus-environment model with monopoles only. The results demonstrate the exact theory in comparison with the approximate recipes of normalisation to cell edge, moderator average, or cell average flux levels. (author)

Defects and diffusion, theory and simulation an annual retrospective I

CERN Document Server

Fisher, David J

2009-01-01

This first volume, in a new series covering entirely general results in the fields of defects and diffusion, includes abstracts of papers which appeared between the beginning of 2008 and the end of October 2009 (journal availability permitting).This new series replaces the 'general' section which was previously part of each issue of the Metals, Ceramics and Semiconductor retrospective series. As well as 356 abstracts, the volume includes original papers on all of the usual material groups: ""Predicting Diffusion Coefficients from First Principles via Eyring's Reaction Rate Theory"" (Mantina, C

Continuous and discreet methods in the aggregation and des fuzzy stages of a diffuse controller of neutron power

International Nuclear Information System (INIS)

Najera H, M.C.; Benitez R, J.S.

2003-01-01

The results of a comparative study are presented of: to) A denominated diffuse controller 'exact', designed by means of an innovative method that determines analytically so much the group of exit resultant in the aggregation stage like the de fuzzy process, and b) a diffuse controller denominated 'discreet' based on the discretization of the variable of having left as much for the aggregation as for the de fuzzy. These stages incorporated to the control algorithms whose objective is the ascent and regulation of the neutron power, carrying out an analysis of its performance. (Author)

Fourier convergence analysis applied to neutron diffusion Eigenvalue problem

International Nuclear Information System (INIS)

Lee, Hyun Chul; Noh, Jae Man; Joo, Hyung Kook

2004-01-01

Fourier error analysis has been a standard technique for the stability and convergence analysis of linear and nonlinear iterative methods. Though the methods can be applied to Eigenvalue problems too, all the Fourier convergence analyses have been performed only for fixed source problems and a Fourier convergence analysis for Eigenvalue problem has never been reported. Lee et al proposed new 2-D/1-D coupling methods and they showed that the new ones are unconditionally stable while one of the two existing ones is unstable at a small mesh size and that the new ones are better than the existing ones in terms of the convergence rate. In this paper the convergence of method A in reference 4 for the diffusion Eigenvalue problem was analyzed by the Fourier analysis. The Fourier convergence analysis presented in this paper is the first one applied to a neutronics eigenvalue problem to the best of our knowledge

Theory of the Thermal Diffusion of Microgel Particles in Highly Compressed Suspensions

Science.gov (United States)

Sokoloff, Jeffrey; Maloney, Craig; Ciamarra, Massimo; Bi, Dapeng

One amazing property of microgel colloids is the ability of the particles to thermally diffuse, even when they are compressed to a volume well below their swollen state volume, despite the fact that they are surrounded by and pressed against other particles. A glass transition is expected to occur when the colloid is sufficiently compressed for diffusion to cease. It is proposed that the diffusion is due to the ability of the highly compressed particles to change shape with little cost in free energy. It will be shown that most of the free energy required to compress microgel particles is due to osmotic pressure resulting from either counterions or monomers inside of the gel, which depends on the particle's volume. There is still, however, a cost in free energy due to polymer elasticity when particles undergo the distortions necessary for them to move around each other as they diffuse through the compressed colloid, even if it occurs at constant volume. Using a scaling theory based on simple models for the linking of polymers belonging to the microgel particles, we examine the conditions under which the cost in free energy needed for a particle to diffuse is smaller than or comparable to thermal energy, which is a necessary condition for particle diffusion. Based on our scaling theory, we predict that thermally activated diffusion should be possible when the mean number of links along the axis along which a distortion occurs is much larger than N 1 / 5, where Nis the mean number of monomers in a polymer chain connecting two links in the gel.

Remarks on some rock neutron parameters

International Nuclear Information System (INIS)

Czubek, J.A.

1983-01-01

A method to calculate the thermal neutron parameters (absorption cross-section, diffusion coefficient and diffusion length) of rocks is given. It is based on a proper energy averaging of cross-sections for all rock matrix and rock saturating liquid constituents. Special emphasis is given to the presence of hydrogen. The diffusion lengths in different lithologies in the function of the variable rock porosity have been calculated. An influence of the thermal neutron spectrum on the shape of the porosity calibration curves for the dual spacing neutron method is shown. This influence has been estimated on two porosity units, on average. (author)

Describing function theory as applied to thermal and neutronic problems

International Nuclear Information System (INIS)

Nassersharif, B.

1983-01-01

Describing functions have traditionally been used to obtain the solutions of systems of ordinary differential equations. In this work the describing function concept has been extended to include nonlinear, distributed parameter partial differential equations. A three-stage solution algorithm is presented which can be applied to any nonlinear partial differential equation. Two generalized integral transforms were developed as the T-transform for the time domain and the B-transform for the spatial domain. The thermal diffusion describing function (TDDF) is developed for conduction of heat in solids and a general iterative solution along with convergence criteria is presented. The proposed solution method is used to solve the problem of heat transfer in nuclear fuel rods with annular fuel pellets. As a special instance the solid cylindrical fuel pellet is examined. A computer program is written which uses the describing function concept for computing fuel pin temperatures in the radial direction during reactor transients. The second problem investigated was the neutron diffusion equation which is intrinsically different from the first case. Although, for most situations, it can be treated as a linear differential equation, the describing function method is still applicable. A describing function solution is derived for two possible cases: constant diffusion coefficient and variable diffusion coefficient. Two classes of describing functions are defined for each case which portray the leakage and absorption phenomena. For the specific case of a slab reactor criticality problem the comparison between analytical and describing function solutions revealed an excellent agreement

On progress of the solution of the stationary 2-dimensional neutron diffusion equation: a polynomial approximation method with error analysis

International Nuclear Information System (INIS)

Ceolin, C.; Schramm, M.; Bodmann, B.E.J.; Vilhena, M.T.

2015-01-01

Recently the stationary neutron diffusion equation in heterogeneous rectangular geometry was solved by the expansion of the scalar fluxes in polynomials in terms of the spatial variables (x; y), considering the two-group energy model. The focus of the present discussion consists in the study of an error analysis of the aforementioned solution. More specifically we show how the spatial subdomain segmentation is related to the degree of the polynomial and the Lipschitz constant. This relation allows to solve the 2-D neutron diffusion problem for second degree polynomials in each subdomain. This solution is exact at the knots where the Lipschitz cone is centered. Moreover, the solution has an analytical representation in each subdomain with supremum and infimum functions that shows the convergence of the solution. We illustrate the analysis with a selection of numerical case studies. (author)

On progress of the solution of the stationary 2-dimensional neutron diffusion equation: a polynomial approximation method with error analysis

Energy Technology Data Exchange (ETDEWEB)

Ceolin, C., E-mail: celina.ceolin@gmail.com [Universidade Federal de Santa Maria (UFSM), Frederico Westphalen, RS (Brazil). Centro de Educacao Superior Norte; Schramm, M.; Bodmann, B.E.J.; Vilhena, M.T., E-mail: celina.ceolin@gmail.com [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica

2015-07-01

Recently the stationary neutron diffusion equation in heterogeneous rectangular geometry was solved by the expansion of the scalar fluxes in polynomials in terms of the spatial variables (x; y), considering the two-group energy model. The focus of the present discussion consists in the study of an error analysis of the aforementioned solution. More specifically we show how the spatial subdomain segmentation is related to the degree of the polynomial and the Lipschitz constant. This relation allows to solve the 2-D neutron diffusion problem for second degree polynomials in each subdomain. This solution is exact at the knots where the Lipschitz cone is centered. Moreover, the solution has an analytical representation in each subdomain with supremum and infimum functions that shows the convergence of the solution. We illustrate the analysis with a selection of numerical case studies. (author)

Solving the neutron diffusion equation on combinatorial geometry computational cells for reactor physics calculations

International Nuclear Information System (INIS)

Azmy, Y. Y.

2004-01-01

An approach is developed for solving the neutron diffusion equation on combinatorial geometry computational cells, that is computational cells composed by combinatorial operations involving simple-shaped component cells. The only constraint on the component cells from which the combinatorial cells are assembled is that they possess a legitimate discretization of the underlying diffusion equation. We use the Finite Difference (FD) approximation of the x, y-geometry diffusion equation in this work. Performing the same combinatorial operations involved in composing the combinatorial cell on these discrete-variable equations yields equations that employ new discrete variables defined only on the combinatorial cell's volume and faces. The only approximation involved in this process, beyond the truncation error committed in discretizing the diffusion equation over each component cell, is a consistent-order Legendre series expansion. Preliminary results for simple configurations establish the accuracy of the solution to the combinatorial geometry solution compared to straight FD as the system dimensions decrease. Furthermore numerical results validate the consistent Legendre-series expansion order by illustrating the second order accuracy of the combinatorial geometry solution, the same as standard FD. Nevertheless the magnitude of the error for the new approach is larger than FD's since it incorporates the additional truncated series approximation. (authors)

Study of the diffusion movements of water by quasi-elastic scattering of slow neutrons

International Nuclear Information System (INIS)

Yamazaki, Ione Makiko

1980-01-01

The diffusion movements of water at three different temperatures in the liquid state have been studied by slow neutron quasi-elastic scattering. The measurements have been performed using the IPEN Triple Axis Spectrometer. Broadening and integrated intensity of the quasi-elastic line have been determined for several momentum transfer (K) in the range 0,7627 ≤ K ≤ 2,993 A -1 . The broadening of the quasi-elastic peaks as function of momentum transfer (K) observed at various temperatures has been interpreted in terms of globular diffusion models. The results obtained at 30 deg C have been explained in a consistent way considering the translational and rotational globular diffusion movements. To describe the results obtained at 55 deg and 70 deg C only the translational globular diffusion model was sufficient. This analysis indicates the existence in water of globules with distance of the farest proton position to the center of gravity of the globule 4,5 A, corroborating the idea of quasi-crystalline structure for water. The Debye-Waller factor has been obtained through the analysis of the integrated intensity of quasi-elastic scattering peaks over the K 2 measured range. From this analysis an estimative of the mean square displacement was obtained. (author)

An integral equation arising in two group neutron transport theory

International Nuclear Information System (INIS)

Cassell, J S; Williams, M M R

2003-01-01

An integral equation describing the fuel distribution necessary to maintain a flat flux in a nuclear reactor in two group transport theory is reduced to the solution of a singular integral equation. The formalism developed enables the physical aspects of the problem to be better understood and its relationship with the corresponding diffusion theory model is highlighted. The integral equation is solved by reducing it to a non-singular Fredholm equation which is then evaluated numerically

HEXAGA-III-120, -30. Three dimensional multi-group neutron diffusion programmes for a uniform triangular mesh with arbitrary group scattering

International Nuclear Information System (INIS)

Woznicki, Z.I.

1983-07-01

This report presents the HEXAGA-III-programme solving multi-group time-independent real and/or adjoint neutron diffusion equations for three-dimensional-triangular-z-geometry. The method of solution is based on the AGA two-sweep iterative method belonging to the family of factorization techniques. An arbitrary neutron scattering model is permitted. The report written for users provides the description of the programme input and output and the use of HEXAGA-III is illustrated by a sample reactor problem. (orig.) [de

Lithium diffusion in polyether ether ketone and polyimide stimulated by in situ electron irradiation and studied by the neutron depth profiling method

Science.gov (United States)

Vacik, J.; Hnatowicz, V.; Attar, F. M. D.; Mathakari, N. L.; Dahiwale, S. S.; Dhole, S. D.; Bhoraskar, V. N.

2014-10-01

Diffusion of lithium from a LiCl aqueous solution into polyether ether ketone (PEEK) and polyimide (PI) assisted by in situ irradiation with 6.5 MeV electrons was studied by the neutron depth profiling method. The number of the Li atoms was found to be roughly proportional to the diffusion time. Regardless of the diffusion time, the measured depth profiles in PEEK exhibit a nearly exponential form, indicating achievement of a steady-state phase of a diffusion-reaction process specified in the text. The form of the profiles in PI is more complex and it depends strongly on the diffusion time. For the longer diffusion time, the profile consists of near-surface bell-shaped part due to Fickian-like diffusion and deeper exponential part.

UN Method For The Critical Slab Problem In One-Speed Neutron Transport Theory

International Nuclear Information System (INIS)

Oeztuerk, Hakan; Guengoer, Sueleyman

2008-01-01

The Chebyshev polynomial approximation (U N method) is used to solve the critical slab problem in one-speed neutron transport theory using Marshak boundary condition. The isotropic scattering kernel with the combination of forward and backward scattering is chosen for the neutrons in a uniform finite slab. Numerical results obtained by the U N method are presented in the tables together with the results obtained by the well-known P N method for comparison. It is shown that the method converges rapidly with its easily executable equations.

Discrete nodal integral transport-theory method for multidimensional reactor physics and shielding calculations

International Nuclear Information System (INIS)

Lawrence, R.D.; Dorning, J.J.

1980-01-01

A coarse-mesh discrete nodal integral transport theory method has been developed for the efficient numerical solution of multidimensional transport problems of interest in reactor physics and shielding applications. The method, which is the discrete transport theory analogue and logical extension of the nodal Green's function method previously developed for multidimensional neutron diffusion problems, utilizes the same transverse integration procedure to reduce the multidimensional equations to coupled one-dimensional equations. This is followed by the conversion of the differential equations to local, one-dimensional, in-node integral equations by integrating back along neutron flight paths. One-dimensional and two-dimensional transport theory test problems have been systematically studied to verify the superior computational efficiency of the new method

Conjugate Gradient like methods and their application to fixed source neutron diffusion problems

International Nuclear Information System (INIS)

Suetomi, Eiichi; Sekimoto, Hiroshi

1989-01-01

This paper presents a number of fast iterative methods for solving systems of linear equations appearing in fixed source problems for neutron diffusion. We employed the conjugate gradient and conjugate residual methods. In order to accelerate the conjugate residual method, we proposed the conjugate residual squared method by transforming the residual polynomial of the conjugate residual method. Since the convergence of these methods depends on the spectrum of coefficient matrix, we employed the incomplete Choleski (IC) factorization and the modified IC (MIC) factorization as preconditioners. These methods were applied to some neutron diffusion problems and compared with the successive overrelaxation (SOR) method. The results of these numerical experiments showed superior convergence characteristics of the conjugate gradient like method with MIC factorization to the SOR method, especially for a problem involving void region. The CPU time of the MICCG, MICCR and MICCRS methods showed no great difference. In order to vectorize the conjugate gradient like methods based on (M)IC factorization, the hyperplane method was used and implemented on the vector computers, the HITAC S-820/80 and ETA10-E (one processor mode). Significant decrease of the CPU times was observed on the S-820/80. Since the scaled conjugate gradient (SCG) method can be vectorized with no manipulation, it was also compared with the above methods. It turned out the SCG method was the fastest with respect to the CPU times on the ETA10-E. These results suggest that one should implement suitable algorithm for different vector computers. (author)

Scattering of Neutrons by Liquid Bromine; Diffusion des neutrons par le brome liquide; R; Dispersion de neutrones por bromo liquido

Energy Technology Data Exchange (ETDEWEB)

Coote, G E; Haywood, B C [Atomic Energy of Canada Ltd., Chalk River, Ontario (Canada)

1963-01-15

Neutrons of 0.037 eV and 0.0088 eV were scattered from a thin sample of liquid bromine at room temperature, and the energy distributions of the scattered neutrons measured at angles from 10{sup o} to 160{sup o} by the time-of-flight method. The angular distribution confirms the results of a previous study by Caglioti. Spectra were expressed in the form of the ''scattering law'' S({alpha},{beta}) of Egelstaff and analysed to derive the generalized frequency distribution p({beta}) of atomic motions in the liquid. The function p({beta}) has a broad smooth peak centred at {beta}{approx}0.3, and shows no evidence for discrete levels in the measured range 0<{beta}< 0.8: the general shape of the curve supports the 'quasi-crystalline' picture of the liquid. Difficulty in the absolute normalization of p({beta}) is discussed. (author) [French] Des neutrons de 0,037 eV et 0,0088 eV ont ete dissuses par un echantillon mince de brome liquide a la temperature ambiante; on a mesure, par la methode du temps de vol, les distributions d'energies des neutrons diffuses, pour des angles compris entre 10{sup o} et 160{sup o}. La distribution angulaire confirme les resultats d'une etude anterieure faite par Caglioti. Les spectres ont ete exprimes d'apres la ''loi de dispersion'' S({alpha},{beta}) d'Egelstaff et analyses pour determiner la distribution generalisee des frequences p({beta}) des mouvements atomiques dans le liquide. La fonction p({beta}) comporte un pic large et a faible pente dont le centre est a {beta} {approx} 0,3 et ne presente aucune indication de niveaux discrets dans la gamme mesuree 0 < {beta} < 0,8; la forme generale de la courbe confirme l'image ''quasi cristalline'' du liquide. Les auteurs examinent les difficultes qui s'opposent a la normalisation absolue de p({beta}). (author) [Spanish] Los autores han estudiado la dispersion de neutrones de 0,037 eV y 0,0088 eV en una muestra de bromo liquido de espesor reducido, a temperatura ambiente. La distribucion

Literature survey of matrix diffusion theory and of experiments and data including natural analogues

International Nuclear Information System (INIS)

Ohlsson, Yvonne; Neretnieks, I.

1995-08-01

Diffusion theory in general and matrix diffusion in particular has been outlined, and experimental work has been reviewed. Literature diffusion data has been systematized in the form of tables and data has been compared and discussed. Strong indications of surface diffusion and anion exclusion have been found, and natural analogue studies and in-situ experiments suggest pore connectivity in the scale of meters. Matrix diffusion, however, mostly seem to be confined to zones of higher porosity extending only a few centimeters into the rock. Surface coating material do not seem to hinder sorption or diffusion into the rock. 54 refs, 18 tabs

A coupled deformation-diffusion theory for fluid-saturated porous solids