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
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
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
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)
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
International Nuclear Information System (INIS)
Kirk, B.L.; Azmy, Y.Y.
1992-01-01
In this paper the one-group, steady-state neutron diffusion equation in two-dimensional Cartesian geometry is solved using the nodal integral method. The discrete variable equations comprise loosely coupled sets of equations representing the nodal balance of neutrons, as well as neutron current continuity along rows or columns of computational cells. An iterative algorithm that is more suitable for solving large problems concurrently is derived based on the decomposition of the spatial domain and is accelerated using successive overrelaxation. This algorithm is very well suited for parallel computers, especially since the spatial domain decomposition occurs naturally, so that the number of iterations required for convergence does not depend on the number of processors participating in the calculation. Implementation of the authors' algorithm on the Intel iPSC/2 hypercube and Sequent Balance 8000 parallel computer is presented, and measured speedup and efficiency for test problems are reported. The results suggest that the efficiency of the hypercube quickly deteriorates when many processors are used, while the Sequent Balance retains very high efficiency for a comparable number of participating processors. This leads to the conjecture that message-passing parallel computers are not as well suited for this algorithm as shared-memory machines
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)
Applying the response matrix method for solving coupled neutron diffusion and transport problems
International Nuclear Information System (INIS)
Sibiya, G.S.
1980-01-01
The numerical determination of the flux and power distribution in the design of large power reactors is quite a time-consuming procedure if the space under consideration is to be subdivided into very fine weshes. Many computing methods applied in reactor physics (such as the finite-difference method) require considerable computing time. In this thesis it is shown that the response matrix method can be successfully used as an alternative approach to solving the two-dimension diffusion equation. Furthermore it is shown that sufficient accuracy of the method is achieved by assuming a linear space dependence of the neutron currents on the boundaries of the geometries defined for the given space. (orig.) [de
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)
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)
International Nuclear Information System (INIS)
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 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
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.
International Nuclear Information System (INIS)
Vondy, D.R.; Fowler, T.B.; Cunningham, G.W.
1975-10-01
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 1 ) in up to three-dimensional geometry is described. A variety of types of problems may be solved: the usual eigenvalue problem, a direct criticality search on the buckling, on a reciprocal velocity absorber (prompt mode), or on nuclide concentrations, or an indirect criticality search on nuclide concentrations, or on dimensions. First-order perturbation analysis capability is available at the macroscopic cross section level
Energy Technology Data Exchange (ETDEWEB)
Verdu, G.; Miro, R. [Departamento de Ingenieria Quimica y Nuclear, Universidad Politecnica de Valencia, Valencia (Spain); Ginestar, D. [Departamento de Matematica Aplicada, Universidad Politecnica de Valencia, Valencia (Spain); Vidal, V. [Departamento de Sistemas Informaticos y Computacion, Universidad Politecnica de Valencia, Valencia (Spain)
1999-05-01
To calculate the neutronic steady state of a nuclear power reactor core and its subcritical modes, it is necessary to solve a partial eigenvalue problem. In this paper, an implicit restarted Arnoldi method is presented as an advantageous alternative to classical methods as the Power Iteration method and the Subspace Iteration method. The efficiency of these methods, has been compared calculating the dominant Lambda modes of several configurations of the Three Mile Island reactor core.
EDEF: a program for solving the neutron diffusion equation using microcomputers
International Nuclear Information System (INIS)
Fernandes, A.; Maiorino, J.R.
1990-01-01
This work presents the development of a program to solve the two-group two-dimensional diffusion equation (with a buckling option to simulate axial leakage) applying the finite element method. It has been developed to microcomputers compatibles to the IBM-PC. Among the facilities of the program, we can mention the simplicity to represent two-dimensional complex domains, the input through a pre-processor and the output in which the fluxes are presented graphically. The program also calculates the multiplication factor, the peaking factor and the power distribution. (author) [pt
International Nuclear Information System (INIS)
Azmy, Y.Y.; Kirk, B.L.
1990-01-01
Modern parallel computer architectures offer an enormous potential for reducing CPU and wall-clock execution times of large-scale computations commonly performed in various applications in science and engineering. Recently, several authors have reported their efforts in developing and implementing parallel algorithms for solving the neutron diffusion equation on a variety of shared- and distributed-memory parallel computers. Testing of these algorithms for a variety of two- and three-dimensional meshes showed significant speedup of the computation. Even for very large problems (i.e., three-dimensional fine meshes) executed concurrently on a few nodes in serial (nonvector) mode, however, the measured computational efficiency is very low (40 to 86%). In this paper, the authors present a highly efficient (∼85 to 99.9%) algorithm for solving the two-dimensional nodal diffusion equations on the Sequent Balance 8000 parallel computer. Also presented is a model for the performance, represented by the efficiency, as a function of problem size and the number of participating processors. The model is validated through several tests and then extrapolated to larger problems and more processors to predict the performance of the algorithm in more computationally demanding situations
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)
International Nuclear Information System (INIS)
Andrushevskii, N.M.; Shchedrin, B.M.; Simonov, V.I.
2004-01-01
New algorithms for solving the atomic structure of equivalent nanodimensional clusters of the same orientations randomly distributed over the initial single crystal (crystal matrix) have been suggested. A cluster is a compact group of substitutional, interstitial or other atoms displaced from their positions in the crystal matrix. The structure is solved based on X-ray or neutron diffuse scattering data obtained from such objects. The use of the mathematical apparatus of Fourier transformations of finite functions showed that the appropriate sampling of the intensities of continuous diffuse scattering allows one to synthesize multiperiodic difference Patterson functions that reveal the systems of the interatomic vectors of an individual cluster. The suggested algorithms are tested on a model one-dimensional structure
Final report [on solving the multigroup diffusion equations
International Nuclear Information System (INIS)
Birkhoff, G.
1975-01-01
Progress achieved in the development of variational methods for solving the multigroup neutron diffusion equations is described. An appraisal is made of the extent to which improved variational methods could advantageously replace difference methods currently used
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
International Nuclear Information System (INIS)
Putney, J.M.
1983-05-01
The characteristics of a simple parallel micro-processor (PMP) are reviewed and its software requirements discussed. One of the more immediate applications is the multi-spatial simulation of a nuclear reactor station. This is of particular interest because 3D reactor simulation might then be possible as part of operating procedure for PFR and CDFR. A major part of a multi-spatial reactor simulator is the solution of the neutron diffusion equation. A procedure is described for solving the equation on a PMP, which is applied to the nodal expansion method with modifications to the nodal expansion codes RECNEC and HEXNEC. Estimations of the micro-processor requirements for the simulation of both PFR and CDFR are given. (U.K.)
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
The magnetic diffusion of neutrons; La diffusion magnetique des neutrons
Energy Technology Data Exchange (ETDEWEB)
Koehler, W C [Commissariat a l' Energie Atomique, Saclay (France).Centre d' Etudes Nucleaires
1959-07-01
The purpose of this report is to examine briefly the diffusion of neutrons by substances, particularly by crystals containing permanent atomic or ionic magnetic moments. In other words we shall deal with ferromagnetic, antiferromagnetic, ferrimagnetic or paramagnetic crystals, but first it is necessary to touch on nuclear diffusion of neutrons. We shall start with the interaction of the neutron with a single diffusion centre; the results will then be applied to the magnetic interactions of the neutron with the satellite electrons of the atom; finally we shall discuss the diffusion of neutrons by crystals. (author) [French] Le but de ce rapport est d'examiner, brievement, la diffusion des neutrons par les substances, et surtout, par des cristaux qui contiennent des moments magnetiques atomiques ou ioniques permanents. C'est-a-dire que nous nous interesserons aux cristaux ferromagnetiques, antiferromagnetiques, ferrimagnetiques ou paramagnetiques; il nous faut cependant rappeler d'abord la diffusion nucleaire des neutrons. Nous commencerons par l'interaction du neutron avec un seul centre diffuseur; puis les resultats seront appliques aux interactions magnetiques du neutron avec les electrons satellites de l'atome; enfin nous discuterons la diffusion des neutrons par les cristaux. (auteur)
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.)
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.
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)
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)
Solving crystal structures from neutron diffraction data
International Nuclear Information System (INIS)
Wilson, C.C.
1987-07-01
In order to pursue crystal structure determination using neutron diffraction data, and given the wide experience available of solving structures using X-ray data, the codes used in X-ray structural analysis should be adapted to the different requirements of a neutron experiment. Modifications have been made to a direct methods program MITHRIL and to a Patterson methods program PATMET to incorporate into these the features of neutron rather than X-ray diffraction. While to date these modifications have been fairly straightforward and many sophistications remain to be exploited, results obtained from the neutron versions of both programs are promising. (author)
Galerkin method for solving diffusion equations
International Nuclear Information System (INIS)
Tsapelkin, E.S.
1975-01-01
A programme for the solution of the three-dimensional two-group multizone neutron diffusion problem in (x, y, z)-geometry is described. The programme XYZ-5 gives the currents of both groups, the effective neutron multiplication coefficient and several integral properties of the reactor. The solution was found with the Galerkin method using speciallly constructed and chosen coordinate functions. The programme is written in ALGOL-60 and consists of 5 parts. Its text is given
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.
Energy Technology Data Exchange (ETDEWEB)
Esquivel E, J. [ININ, Carretera Mexico-Toluca s/n, 52750 Ocoyoacac, Estado de Mexico (Mexico); Del Valle G, E., E-mail: jaime.esquivel@inin.gob.mx [IPN, Escuela Superior de Fisica y Matematicas, Av. IPN s/n, Edificio 9, Col. San Pedro Zacatenco, 07738 Mexico D. F. (Mexico)
2014-10-15
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)
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
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)
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
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
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
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
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
Solving the uncommon reactor core neutronics problems
International Nuclear Information System (INIS)
Vondy, D.R.; Fowler, T.B.
1980-01-01
The common reactor core neutronics problems have fundamental neutron space, energy spectrum solutions. Typically the most positive eigenvalue is associated with an all-positive flux for the pseudo-steady-state condition (k/sub eff/), or the critical state is to be effected by selective adjustment of some variable such as the fuel concentration. With sophistication in reactor analysis has come the demand for solutions of other, uncommon neutronics problems. Importance functionss are needed for sensitivity and uncertainty analyses, as for ratios of intergral reaction rates such as the fuel conversion (breeding) ratio. The dominant higher harmonic solution is needed in stability analysis. Typically the desired neutronics solution must contain negative values to qualify as a higher harmonic or to satisfy a fixed source containing negative values. Both regular and adjoint solutions are of interest as are special integrals of the solutions to support analysis
Solving the equation of neutron transport
International Nuclear Information System (INIS)
Nasfi, Rim
2009-01-01
This work is devoted to the study of some numerical methods of resolution of the problem of transport of the neutrons. We started by introducing the equation integro-differential transport of the neutrons. Then we applied the finite element method traditional for stationary and nonstationary linear problems in 2D. A great part is reserved for the presentation of the mixed numerical diagram and mixed hybrid with two types of uniform grids: triangular and rectangular. Thereafter we treated some numerical examples by implementations in Matlab in order to test the convergence of each method. To finish, we had results of simulation by the Monte Carlo method on a problem of two-dimensional transport with an aim of comparing them with the results resulting from the finite element method mixed hybrids. Some remarks and prospects conclude this work.
A method for solving neutron transport equation
International Nuclear Information System (INIS)
Dimitrijevic, Z.
1993-01-01
The procedure for solving the transport equation by directly integrating for case one-dimensional uniform multigroup medium is shown. The solution is expressed in terms of linear combination of function H n (x,μ), and the coefficient is determined from given conditions. The solution is applied for homogeneous slab of critical thickness. (author)
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
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).
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
Finite element method for solving neutron transport problems
International Nuclear Information System (INIS)
Ferguson, J.M.; Greenbaum, A.
1984-01-01
A finite element method is introduced for solving the neutron transport equations. Our method falls into the category of Petrov-Galerkin solution, since the trial space differs from the test space. The close relationship between this method and the discrete ordinate method is discussed, and the methods are compared for simple test problems
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)
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 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).
Neutron diffusion: connection with the theory of browniam motion
International Nuclear Information System (INIS)
Dellagi, Mohamed
1977-01-01
The displacement of the neutron projection on an axis Ox and its density of probability are introduced instead of describing the diffusion theory with neutron density, as is usual. If the point source O is isotropic and neutron monoenergetic, the brownian particle described by Langevin's equation and neutron have the same time correlation of velocity [fr
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)
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
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
Deterministic methods to solve the integral transport equation in neutronic
International Nuclear Information System (INIS)
Warin, X.
1993-11-01
We present a synthesis of the methods used to solve the integral transport equation in neutronic. This formulation is above all used to compute solutions in 2D in heterogeneous assemblies. Three kinds of methods are described: - the collision probability method; - the interface current method; - the current coupling collision probability method. These methods don't seem to be the most effective in 3D. (author). 9 figs
Guiding brine shrimp through mazes by solving reaction diffusion equations
Singal, Krishma; Fenton, Flavio
Excitable systems driven by reaction diffusion equations have been shown to not only find solutions to mazes but to also to find the shortest path between the beginning and the end of the maze. In this talk we describe how we can use the Fitzhugh-Nagumo model, a generic model for excitable media, to solve a maze by varying the basin of attraction of its two fixed points. We demonstrate how two dimensional mazes are solved numerically using a Java Applet and then accelerated to run in real time by using graphic processors (GPUs). An application of this work is shown by guiding phototactic brine shrimp through a maze solved by the algorithm. Once the path is obtained, an Arduino directs the shrimp through the maze using lights from LEDs placed at the floor of the Maze. This method running in real time could be eventually used for guiding robots and cars through traffic.
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.
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)
Adjacent-cell Preconditioners for solving optically thick neutron transport problems
International Nuclear Information System (INIS)
Azmy, Y.Y.
1994-01-01
We develop, analyze, and test a new acceleration scheme for neutron transport methods, the Adjacent-cell Preconditioner (AP) that is particularly suited for solving optically thick problems. Our method goes beyond Diffusion Synthetic Acceleration (DSA) methods in that it's spectral radius vanishes with increasing cell thickness. In particular, for the ID case the AP method converges immediately, i.e. in one iteration, to 10 -4 pointwise relative criterion in problems with dominant cell size of 10 mfp or thicker. Also the AP has a simple formalism and is cell-centered hence, multidimensional and high order extensions are easier to develop, and more efficient to implement
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.)
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)
Current trends in methods for neutron diffusion calculations
International Nuclear Information System (INIS)
Adams, C.H.
1977-01-01
Current work and trends in the application of neutron diffusion theory to reactor design and analysis are reviewed. Specific topics covered include finite-difference methods, synthesis methods, nodal calculations, finite-elements and perturbation theory
Numerical method for solving integral equations of neutron transport. II
International Nuclear Information System (INIS)
Loyalka, S.K.; Tsai, R.W.
1975-01-01
In a recent paper it was pointed out that the weakly singular integral equations of neutron transport can be quite conveniently solved by a method based on subtraction of singularity. This previous paper was devoted entirely to the consideration of simple one-dimensional isotropic-scattering and one-group problems. The present paper constitutes interesting extensions of the previous work in that in addition to a typical two-group anisotropic-scattering albedo problem in the slab geometry, the method is also applied to an isotropic-scattering problem in the x-y geometry. These results are compared with discrete S/sub N/ (ANISN or TWOTRAN-II) results, and for the problems considered here, the proposed method is found to be quite effective. Thus, the method appears to hold considerable potential for future applications. (auth)
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
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)
International Nuclear Information System (INIS)
Halilou, A.; Lounici, A.
1981-01-01
The subject is divided in two parts: In the first part a nodal method has been worked out to solve the steady state multigroup diffusion equation. This method belongs to the same set of nodal methods currently used to calculate the exact fission powers and neutron fluxes in a very short computing time. It has been tested on a two dimensional idealized reactors. The effective multiplication factor and the fission powers for each fuel element have been calculated. The second part consists in studying and mastering the multigroup diffusion code DAHRA - a reduced version of DIANE - a two dimensional code using finite difference method
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)
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)
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
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.
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
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
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
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)
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)
Cooperative learning of neutron diffusion and transport theories
International Nuclear Information System (INIS)
Robinson, Michael A.
1999-01-01
A cooperative group instructional strategy is being used to teach a unit on neutron transport and diffusion theory in a first-year-graduate level, Reactor Theory course that was formerly presented in the traditional lecture/discussion style. Students are divided into groups of two or three for the duration of the unit. Class meetings are divided into traditional lecture/discussion segments punctuated by cooperative group exercises. The group exercises were designed to require the students to elaborate, summarize, or practice the material presented in the lecture/discussion segments. Both positive interdependence and individual accountability are fostered by adjusting individual grades on the unit exam by a factor dependent upon group achievement. Group collaboration was also encouraged on homework assignments by assigning each group a single grade on each assignment. The results of the unit exam have been above average in the two classes in which the cooperative group method was employed. In particular, the problem solving ability of the students has shown particular improvement. Further,the students felt that the cooperative group format was both more educationally effective and more enjoyable than the lecture/discussion format
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.
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
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
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
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)
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
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.)
Energy Technology Data Exchange (ETDEWEB)
Fletcher, J K
1973-05-01
CTD is a computer program written in Fortran 4 to solve the multi-group diffusion theory equations in X, Y, Z and triangular Z geometries. A power print- out neutron balance and breeding gain are also produced. 4 references. (auth)
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.
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.
An inherently parallel method for solving discretized diffusion equations
International Nuclear Information System (INIS)
Eccleston, B.R.; Palmer, T.S.
1999-01-01
A Monte Carlo approach to solving linear systems of equations is being investigated in the context of the solution of discretized diffusion equations. While the technique was originally devised decades ago, changes in computer architectures (namely, massively parallel machines) have driven the authors to revisit this technique. There are a number of potential advantages to this approach: (1) Analog Monte Carlo techniques are inherently parallel; this is not necessarily true to today's more advanced linear equation solvers (multigrid, conjugate gradient, etc.); (2) Some forms of this technique are adaptive in that they allow the user to specify locations in the problem where resolution is of particular importance and to concentrate the work at those locations; and (3) These techniques permit the solution of very large systems of equations in that matrix elements need not be stored. The user could trade calculational speed for storage if elements of the matrix are calculated on the fly. The goal of this study is to compare the parallel performance of Monte Carlo linear solvers to that of a more traditional parallelized linear solver. The authors observe the linear speedup that they expect from the Monte Carlo algorithm, given that there is no domain decomposition to cause significant communication overhead. Overall, PETSc outperforms the Monte Carlo solver for the test problem. The PETSc parallel performance improves with larger numbers of unknowns for a given number of processors. Parallel performance of the Monte Carlo technique is independent of the size of the matrix and the number of processes. They are investigating modifications to the scheme to accommodate matrix problems with positive off-diagonal elements. They are also currently coding an on-the-fly version of the algorithm to investigate the solution of very large linear systems
Generalized diffusion theory for calculating the neutron transport scalar flux
International Nuclear Information System (INIS)
Alcouffe, R.E.
1975-01-01
A generalization of the neutron diffusion equation is introduced, the solution of which is an accurate approximation to the transport scalar flux. In this generalization the auxiliary transport calculations of the system of interest are utilized to compute an accurate, pointwise diffusion coefficient. A procedure is specified to generate and improve this auxiliary information in a systematic way, leading to improvement in the calculated diffusion scalar flux. This improvement is shown to be contingent upon satisfying the condition of positive calculated-diffusion coefficients, and an algorithm that ensures this positivity is presented. The generalized diffusion theory is also shown to be compatible with conventional diffusion theory in the sense that the same methods and codes can be used to calculate a solution for both. The accuracy of the method compared to reference S/sub N/ transport calculations is demonstrated for a wide variety of examples. (U.S.)
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)
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...
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
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.)
An extension of diffusion theory for thermal neutrons near boundaries
International Nuclear Information System (INIS)
Alvarez Rivas, J. L.
1963-01-01
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 PIGC P/928 (1995), ANL-5872 (1959), DEGR 319 (D) (1961). This model could be extended also to plane geometry. (Author) 19 refs
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)
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
Application of Trotter approximation for solving time dependent neutron transport equation
International Nuclear Information System (INIS)
Stancic, V.
1987-01-01
A method is proposed to solve multigroup time dependent neutron transport equation with arbitrary scattering anisotropy. The recurrence relation thus obtained is simple, numerically stable and especially suitable for treatment of complicated geometries. (author)
Diffusion theory model for optimization calculations of cold neutron sources
International Nuclear Information System (INIS)
Azmy, Y.Y.
1987-01-01
Cold neutron sources are becoming increasingly important and common experimental facilities made available at many research reactors around the world due to the high utility of cold neutrons in scattering experiments. The authors describe a simple two-group diffusion model of an infinite slab LD 2 cold source. The simplicity of the model permits to obtain an analytical solution from which one can deduce the reason for the optimum thickness based solely on diffusion-type phenomena. Also, a second more sophisticated model is described and the results compared to a deterministic transport calculation. The good (particularly qualitative) agreement between the results suggests that diffusion theory methods can be used in parametric and optimization studies to avoid the generally more expensive transport calculations
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
Finite element method for neutron diffusion problems in hexagonal geometry
International Nuclear Information System (INIS)
Wei, T.Y.C.; Hansen, K.F.
1975-06-01
The use of the finite element method for solving two-dimensional static neutron diffusion problems in hexagonal reactor configurations is considered. It is investigated as a possible alternative to the low-order finite difference method. Various piecewise polynomial spaces are examined for their use in hexagonal problems. The central questions which arise in the design of these spaces are the degree of incompleteness permissible and the advantages of using a low-order space fine-mesh approach over that of a high-order space coarse-mesh one. There is also the question of the degree of smoothness required. Two schemes for the construction of spaces are described and a number of specific spaces, constructed with the questions outlined above in mind, are presented. They range from a complete non-Lagrangian, non-Hermite quadratic space to an incomplete ninth order space. Results are presented for two-dimensional problems typical of a small high temperature gas-cooled reactor. From the results it is concluded that the space used should at least include the complete linear one. Complete spaces are to be preferred to totally incomplete ones. Once function continuity is imposed any additional degree of smoothness is of secondary importance. For flux shapes typical of the small high temperature gas-cooled reactor the linear space fine-mesh alternative is to be preferred to the perturbation quadratic space coarse-mesh one and the low-order finite difference method is to be preferred over both finite element schemes
FMCEIR: a Monte Carlo program for solving the stationary neutron and gamma transport equation
International Nuclear Information System (INIS)
Taormina, A.
1978-05-01
FMCEIR is a three-dimensional Monte Carlo program for solving the stationary neutron and gamma transport equation. It is used to study the problem of neutron and gamma streaming in the GCFR and HHT reactor channels. (G.T.H.)
VARI-QUIR-3, 2-D Multigroup Steady-State Neutron Diffusion in X-Y R-Z or R-Theta Geometry
International Nuclear Information System (INIS)
Collier, George
1984-01-01
1 - Nature of physical problem solved: The steady-state, multigroup, two-dimensional neutron diffusion equations are solved in x-y, r-z, and r-theta geometry. 2 - Method of solution: A Gauss-Seidel type of solution with inner and outer iterations is used. The source is held constant during the inner iterations
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.
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)
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
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.
RDANN a new methodology to solve the neutron spectra unfolding problem
International Nuclear Information System (INIS)
Ortiz R, J.M.; Martinez B, M.R.; Vega C, H.R.
2006-01-01
The optimization processes known as Taguchi method and DOE methodology are applied to the design, training and testing of Artificial Neural Networks in the neutron spectrometry field, which offer potential benefits in the evaluation of the behavior of the net as well as the ability to examine the interaction of the weights and neurons inside the same one. In this work, the Robust Design of Artificial Neural Networks methodology is used to solve the neutron spectra unfolding problem, designing, training and testing an ANN using a set of 187 neutron spectra compiled by the International Atomic Energy Agency, to obtain the better neutron spectra unfolded from the Bonner spheres spectrometer's count rates. (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
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.)
HEXAN - a hexagonal nodal code for solving the diffusion equation
International Nuclear Information System (INIS)
Makai, M.
1982-07-01
This report describes the theory of and provides a user's manual for the HEXAN program, which is a nodal program for the solution of the few-group diffusion equation in hexagonal geometry. Based upon symmetry considerations, the theory provides an analytical solution in a homogeneous node. WWER and HTGR test problem solutions are presented. The equivalence of the finite-difference scheme and the response matrix method is proven. The properties of a symmetric node's response matrix are investigated. (author)
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)
A symmetrized quasi-diffusion method for solving multidimensional transport problems
International Nuclear Information System (INIS)
Miften, M.M.; Larsen, E.W.
1992-01-01
In this paper, the authors propose a 'symmetrized' QD (SQD) method in which the non-self-adjoint QD diffusion problem is replaced by two self-adjoint diffusion problems. These problems are more easily discretized and more efficiently solved than in the standard QD method. They also give SQD calculational results for transport problems in x-y geometry
Nodal approximations of varying order by energy group for solving the diffusion equation
International Nuclear Information System (INIS)
Broda, J.T.
1992-02-01
The neutron flux across the nuclear reactor core is of interest to reactor designers and others. The diffusion equation, an integro-differential equation in space and energy, is commonly used to determine the flux level. However, the solution of a simplified version of this equation when automated is very time consuming. Since the flux level changes with time, in general, this calculation must be made repeatedly. Therefore solution techniques that speed the calculation while maintaining accuracy are desirable. One factor that contributes to the solution time is the spatial flux shape approximation used. It is common practice to use the same order flux shape approximation in each energy group even though this method may not be the most efficient. The one-dimensional, two-energy group diffusion equation was solved, for the node average flux and core k-effective, using two sets of spatial shape approximations for each of three reactor types. A fourth-order approximation in both energy groups forms the first set of approximations used. The second set used combines a second-order approximation with a fourth-order approximation in energy group two. Comparison of the results from the two approximation sets show that the use of a different order spatial flux shape approximation results in considerable loss in accuracy for the pressurized water reactor modeled. However, the loss in accuracy is small for the heavy water and graphite reactors modeled. The use of different order approximations in each energy group produces mixed results. Further investigation into the accuracy and computing time is required before any quantitative advantage of the use of the second-order approximation in energy group one and the fourth-order approximation in energy group two can be determined
Energy Technology Data Exchange (ETDEWEB)
Pop-Jordanov, J P [Institute of Nuclear Sciences Boris Kidric, Vinca, Beograd (Yugoslavia)
1963-12-15
A method for calculating of neutron termalization in heterogeneous rector core was developed. It is more precise than the diffusion method but more complcated. Concerning accuracy it is comparable to non-diffusion methods. Sonce the approach was analytical need for powerful computer is avoided and the description of physical phenomena is more transparent. Convergence is satsfactory. Constraints of the proposed method are: low neutron absorption in the moderator, negligible slowing down in the fuel, and big lattice pitch. The method is applicable for heavy water and graphite moderator systems. Based on the application of this method, procedures were developed for calculating thermal utilzation and neutron temperature. Since 1/v dependence of cross sections is not estimated this metof could be used for long-term reactivity changes.
D-Iteration: diffusion approach for solving PageRank
Hong, Dohy; Huynh, The Dang; Mathieu, Fabien
2015-01-01
In this paper we present a new method that can accelerate the computation of the PageRank importance vector. Our method, called D-Iteration (DI), is based on the decomposition of the matrix-vector product that can be seen as a fluid diffusion model and is potentially adapted to asynchronous implementation. We give theoretical results about the convergence of our algorithm and we show through experimentations on a real Web graph that DI can improve the computation efficiency compared to other ...
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
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)
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)
From baking a cake to solving the diffusion equation
Olszewski, Edward A.
2006-06-01
We explain how modifying a cake recipe by changing either the dimensions of the cake or the amount of cake batter alters the baking time. We restrict our consideration to the génoise and obtain a semiempirical relation for the baking time as a function of oven temperature, initial temperature of the cake batter, and dimensions of the unbaked cake. The relation, which is based on the diffusion equation, has three parameters whose values are estimated from data obtained by baking cakes in cylindrical pans of various diameters. The relation takes into account the evaporation of moisture at the top surface of the cake, which is the dominant factor affecting the baking time of a cake.
Linear extended neutron diffusion theory for semi-in finites homogeneous means
International Nuclear Information System (INIS)
Vazquez R, R.; Vazquez R, A.; Espinosa P, G.
2009-10-01
Originally developed for heterogeneous means, the linear extended neutron diffusion theory is applied to the limit case of monoenergetic neutron diffusion in a semi-infinite homogeneous mean with a neutron source, located in the coordinate origin situated in the frontier of dispersive material. The monoenergetic neutron diffusion is studied taking into account the spatial deviations in the neutron flux to the interfacial current caused by the neutron source, as well as the influence of the spatial deviations in the absorption rate. The developed pattern is an unidimensional model for an energy group obtained of application of volumetric average diffusion equation in the moderator. The obtained results are compared against the classic diffusion theory and qualitatively against the neutron transport theory. (Author)
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
International Nuclear Information System (INIS)
Kim, Kyung-O; Jeong, Hae Sun; Jo, Daeseong
2017-01-01
Hermite-type collocation method) in order to solve this problem. On the basis of these results, it is expected that the mesh-free method including the RPIM can be sufficiently employed in numerical analysis for the multi-group neutron-diffusion equation and can be considered as an alternative numerical approach to overcome the drawbacks of existing nodal methods.
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)
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)
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
FEMB, 2-D Homogeneous Neutron Diffusion in X-Y Geometry with Keff Calculation, Dyadic Fission Matrix
International Nuclear Information System (INIS)
Misfeldt, I.B.
1987-01-01
1 - Nature of physical problem solved: The two-dimensional neutron diffusion equation (xy geometry) is solved in the homogeneous form (K eff calculation). 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 be dyadic. 2 - Method of solution: Finite element formulation with Lagrange type elements. Solution technique: SOR with extrapolation. 3 - Restrictions on the complexity of the problem: Maximum order of the Lagrange elements is 6
Contribution to solving the problem of neutron thermalization in heterogeneous reactor
International Nuclear Information System (INIS)
Pop-Jordanov, J. P.
1963-12-01
A method for calculating of neutron termalization in heterogeneous rector core was developed. It is more precise than the diffusion method but more complcated. Concerning accuracy it is comparable to non-diffusion methods. Sonce the approach was analytical need for powerful computer is avoided and the description of physical phenomena is more transparent. Convergence is satsfactory. Constraints of the proposed method are: low neutron absorption in the moderator, negligible slowing down in the fuel, and big lattice pitch. The method is applicable for heavy water and graphite moderator systems. Based on the application of this method, procedures were developed for calculating thermal utilzation and neutron temperature. Since 1/v dependence of cross sections is not estimated this metof could be used for long-term reactivity changes
RDANN a new methodology to solve the neutron spectra unfolding problem
Energy Technology Data Exchange (ETDEWEB)
Ortiz R, J.M.; Martinez B, M.R.; Vega C, H.R. [UAZ, Av. Ramon Lopez Velarde No. 801, 98000 Zacatecas (Mexico)
2006-07-01
The optimization processes known as Taguchi method and DOE methodology are applied to the design, training and testing of Artificial Neural Networks in the neutron spectrometry field, which offer potential benefits in the evaluation of the behavior of the net as well as the ability to examine the interaction of the weights and neurons inside the same one. In this work, the Robust Design of Artificial Neural Networks methodology is used to solve the neutron spectra unfolding problem, designing, training and testing an ANN using a set of 187 neutron spectra compiled by the International Atomic Energy Agency, to obtain the better neutron spectra unfolded from the Bonner spheres spectrometer's count rates. (Author)
The Multigroup Neutron Diffusion Equations/1 Space Dimension
Energy Technology Data Exchange (ETDEWEB)
Linde, Sven
1960-06-15
A description is given of a program for the Ferranti Mercury computer which solves the one-dimensional multigroup diffusion equations in plane, cylindrical or spherical geometry, and also approximates automatically a two-dimensional solution by separating the space variables. In section A the method of calculation is outlined and the preparation of data for two group problems is described. The spatial separation of two-dimensional equations is considered in section B. Section C covers the multigroup equations. These parts are self contained and include all information required for the use of the program. Details of the numerical methods are given in section D. Three sample problems are solved in section E. Punching and operating instructions are given in an appendix.
The Multigroup Neutron Diffusion Equations/1 Space Dimension
International Nuclear Information System (INIS)
Linde, Sven
1960-06-01
A description is given of a program for the Ferranti Mercury computer which solves the one-dimensional multigroup diffusion equations in plane, cylindrical or spherical geometry, and also approximates automatically a two-dimensional solution by separating the space variables. In section A the method of calculation is outlined and the preparation of data for two group problems is described. The spatial separation of two-dimensional equations is considered in section B. Section C covers the multigroup equations. These parts are self contained and include all information required for the use of the program. Details of the numerical methods are given in section D. Three sample problems are solved in section E. Punching and operating instructions are given in an appendix
Development of neutron diffuse scattering analysis code by thin film and multilayer film
International Nuclear Information System (INIS)
Soyama, Kazuhiko
2004-01-01
To research surface structure of thin film and multilayer film by neutron, a neutron diffuse scattering analysis code using DWBA (Distorted-Wave Bron Approximation) principle was developed. Subjects using this code contain the surface and interface properties of solid/solid, solid/liquid, liquid/liquid and gas/liquid, and metal, magnetism and polymer thin film and biomembran. The roughness of surface and interface of substance shows fractal self-similarity and its analytical model is based on DWBA theory by Sinha. The surface and interface properties by diffuse scattering are investigated on the basis of the theoretical model. The calculation values are proved to be agreed with the experimental values. On neutron diffuse scattering by thin film, roughness of surface of thin film, correlation function, neutron propagation by thin film, diffuse scattering by DWBA theory, measurement model, SDIFFF (neutron diffuse scattering analysis program by thin film) and simulation results are explained. On neutron diffuse scattering by multilayer film, roughness of multilayer film, principle of diffuse scattering, measurement method and simulation examples by MDIFF (neutron diffuse scattering analysis program by multilayer film) are explained. (S.Y.)To research surface structure of thin film and multilayer film by neutron, a neutron diffuse scattering analysis code using DWBA (Distorted-Wave Bron Approximation) principle was developed. Subjects using this code contain the surface and interface properties of solid/solid, solid/liquid, liquid/liquid and gas/liquid, and metal, magnetism and polymer thin film and biomembran. The roughness of surface and interface of substance shows fractal self-similarity and its analytical model is based on DWBA theory by Sinha. The surface and interface properties by diffuse scattering are investigated on the basis of the theoretical model. The calculation values are proved to be agreed with the experimental values. On neutron diffuse scattering
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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
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)
Group theoretic approach for solving the problem of diffusion of a drug through a thin membrane
Abd-El-Malek, Mina B.; Kassem, Magda M.; Meky, Mohammed L. M.
2002-03-01
The transformation group theoretic approach is applied to study the diffusion process of a drug through a skin-like membrane which tends to partially absorb the drug. Two cases are considered for the diffusion coefficient. The application of one parameter group reduces the number of independent variables by one, and consequently the partial differential equation governing the diffusion process with the boundary and initial conditions is transformed into an ordinary differential equation with the corresponding conditions. The obtained differential equation is solved numerically using the shooting method, and the results are illustrated graphically and in tables.
Local Fractional Series Expansion Method for Solving Wave and Diffusion Equations on Cantor Sets
Directory of Open Access Journals (Sweden)
Ai-Min Yang
2013-01-01
Full Text Available We proposed a local fractional series expansion method to solve the wave and diffusion equations on Cantor sets. Some examples are given to illustrate the efficiency and accuracy of the proposed method to obtain analytical solutions to differential equations within the local fractional derivatives.
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)
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
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
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)
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
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.
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)
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
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
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.
International Nuclear Information System (INIS)
Itagaki, Masafumi; Sahashi, Naoki.
1996-01-01
The multiple reciprocity method (MRM) in conjunction with the boundary element method has been employed to solve one-group eigenvalue problems described by the three-dimensional (3-D) neutron diffusion equation. The domain integral related to the fission source is transformed into a series of boundary-only integrals, with the aid of the higher order fundamental solutions based on the spherical and the modified spherical Bessel functions. Since each degree of the higher order fundamental solutions in the 3-D cases has a singularity of order (1/r), the above series of boundary integrals requires additional terms which do not appear in the 2-D MRM formulation. The critical eigenvalue itself can be also described using only boundary integrals. Test calculations show that Wielandt's spectral shift technique guarantees rapid and stable convergence of 3-D MRM computations. (author)
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.
Energy Technology Data Exchange (ETDEWEB)
Tumelero, Fernanda; Petersen, Claudio Zen; Goncalves, Glenio Aguiar [Universidade Federal de Pelotas, Capao do Leao, RS (Brazil). Programa de Pos Graduacao em Modelagem Matematica; Schramm, Marcelo [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica
2016-12-15
In this work, we report a solution to solve the Neutron Point Kinetics Equations applying the Polynomial Approach Method. The main idea is to expand the neutron density and delayed neutron precursors as a power series considering the reactivity as an arbitrary function of the time in a relatively short time interval around an ordinary point. In the first interval one applies the initial conditions and the analytical continuation is used to determine the solutions of the next intervals. A genuine error control is developed based on an analogy with the Rest Theorem. For illustration, we also report simulations for different approaches types (linear, quadratic and cubic). The results obtained by numerical simulations for linear approximation are compared with results in the literature.
Boundary element methods applied to two-dimensional neutron diffusion problems
International Nuclear Information System (INIS)
Itagaki, Masafumi
1985-01-01
The Boundary element method (BEM) has been applied to two-dimensional neutron diffusion problems. The boundary integral equation and its discretized form have been derived. Some numerical techniques have been developed, which can be applied to critical and fixed-source problems including multi-region ones. Two types of test programs have been developed according to whether the 'zero-determinant search' or the 'source iteration' technique is adopted for criticality search. Both programs require only the fluxes and currents on boundaries as the unknown variables. The former allows a reduction in computing time and memory in comparison with the finite element method (FEM). The latter is not always efficient in terms of computing time due to the domain integral related to the inhomogeneous source term; however, this domain integral can be replaced by the equivalent boundary integral for a region with a non-multiplying medium or with a uniform source, resulting in a significant reduction in computing time. The BEM, as well as the FEM, is well suited for solving irregular geometrical problems for which the finite difference method (FDM) is unsuited. The BEM also solves problems with infinite domains, which cannot be solved by the ordinary FEM and FDM. Some simple test calculations are made to compare the BEM with the FEM and FDM, and discussions are made concerning the relative merits of the BEM and problems requiring future solution. (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)
3-D anisotropic neutron diffusion in optically thick media with optically thin channels
International Nuclear Information System (INIS)
Trahan, Travis J.; Larsen, Edward W.
2011-01-01
Standard neutron diffusion theory accurately approximates the neutron transport process for optically thick, scattering-dominated systems in which the angular neutron flux is a weak (nearly linear) function of angle. Therefore, standard diffusion theory is not directly applicable for Very High Temperature Reactor (VHTR) cores, which contain numerous narrow, axially-oriented, nearly-voided coolant channels. However, we have derived a new, accurate diffusion equation for such problems, which contains nonstandard anisotropic diffusion coefficients near and within the channels, but which reduces to the standard diffusion approximation away from the channels. The new diffusion approximation significantly improves the accuracy of VHTR diffusion simulations, while having lower computational cost than higher-order transport methods. (author)
Agarwal, P.; El-Sayed, A. A.
2018-06-01
In this paper, a new numerical technique for solving the fractional order diffusion equation is introduced. This technique basically depends on the Non-Standard finite difference method (NSFD) and Chebyshev collocation method, where the fractional derivatives are described in terms of the Caputo sense. The Chebyshev collocation method with the (NSFD) method is used to convert the problem into a system of algebraic equations. These equations solved numerically using Newton's iteration method. The applicability, reliability, and efficiency of the presented technique are demonstrated through some given numerical examples.
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.
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)
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)
Splitting Method for Solving the Coarse-Mesh Discretized Low-Order Quasi-Diffusion Equations
International Nuclear Information System (INIS)
Hiruta, Hikaru; Anistratov, Dmitriy Y.; Adams, Marvin L.
2005-01-01
In this paper, the development is presented of a splitting method that can efficiently solve coarse-mesh discretized low-order quasi-diffusion (LOQD) equations. The LOQD problem can reproduce exactly the transport scalar flux and current. To solve the LOQD equations efficiently, a splitting method is proposed. The presented method splits the LOQD problem into two parts: (a) the D problem that captures a significant part of the transport solution in the central parts of assemblies and can be reduced to a diffusion-type equation and (b) the Q problem that accounts for the complicated behavior of the transport solution near assembly boundaries. Independent coarse-mesh discretizations are applied: the D problem equations are approximated by means of a finite element method, whereas the Q problem equations are discretized using a finite volume method. Numerical results demonstrate the efficiency of the methodology presented. This methodology can be used to modify existing diffusion codes for full-core calculations (which already solve a version of the D problem) to account for transport effects
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.
Parareal in time 3D numerical solver for the LWR Benchmark neutron diffusion transient model
Energy Technology Data Exchange (ETDEWEB)
Baudron, Anne-Marie, E-mail: anne-marie.baudron@cea.fr [Laboratoire de Recherche Conventionné MANON, CEA/DEN/DANS/DM2S and UPMC-CNRS/LJLL (France); CEA-DRN/DMT/SERMA, CEN-Saclay, 91191 Gif sur Yvette Cedex (France); Lautard, Jean-Jacques, E-mail: jean-jacques.lautard@cea.fr [Laboratoire de Recherche Conventionné MANON, CEA/DEN/DANS/DM2S and UPMC-CNRS/LJLL (France); CEA-DRN/DMT/SERMA, CEN-Saclay, 91191 Gif sur Yvette Cedex (France); Maday, Yvon, E-mail: maday@ann.jussieu.fr [Sorbonne Universités, UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions and Institut Universitaire de France, F-75005, Paris (France); Laboratoire de Recherche Conventionné MANON, CEA/DEN/DANS/DM2S and UPMC-CNRS/LJLL (France); Brown Univ, Division of Applied Maths, Providence, RI (United States); Riahi, Mohamed Kamel, E-mail: riahi@cmap.polytechnique.fr [Laboratoire de Recherche Conventionné MANON, CEA/DEN/DANS/DM2S and UPMC-CNRS/LJLL (France); CMAP, Inria-Saclay and X-Ecole Polytechnique, Route de Saclay, 91128 Palaiseau Cedex (France); Salomon, Julien, E-mail: salomon@ceremade.dauphine.fr [CEREMADE, Univ Paris-Dauphine, Pl. du Mal. de Lattre de Tassigny, F-75016, Paris (France)
2014-12-15
In this paper we present a time-parallel algorithm for the 3D neutrons calculation of a transient model in a nuclear reactor core. The neutrons calculation consists in numerically solving the time dependent diffusion approximation equation, which is a simplified transport equation. The numerical resolution is done with finite elements method based on a tetrahedral meshing of the computational domain, representing the reactor core, and time discretization is achieved using a θ-scheme. The transient model presents moving control rods during the time of the reaction. Therefore, cross-sections (piecewise constants) are taken into account by interpolations with respect to the velocity of the control rods. The parallelism across the time is achieved by an adequate use of the parareal in time algorithm to the handled problem. This parallel method is a predictor corrector scheme that iteratively combines the use of two kinds of numerical propagators, one coarse and one fine. Our method is made efficient by means of a coarse solver defined with large time step and fixed position control rods model, while the fine propagator is assumed to be a high order numerical approximation of the full model. The parallel implementation of our method provides a good scalability of the algorithm. Numerical results show the efficiency of the parareal method on large light water reactor transient model corresponding to the Langenbuch–Maurer–Werner benchmark.
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)
International Nuclear Information System (INIS)
Bosevski, T.
1971-01-01
The polynomial interpolation of neutron flux between the chosen space and energy variables enabled transformation of the integral transport equation into a system of linear equations with constant coefficients. Solutions of this system are the needed values of flux for chosen values of space and energy variables. The proposed improved method for solving the neutron transport problem including the mathematical formalism is simple and efficient since the number of needed input data is decreased both in treating the spatial and energy variables. Mathematical method based on this approach gives more stable solutions with significantly decreased probability of numerical errors. Computer code based on the proposed method was used for calculations of one heavy water and one light water reactor cell, and the results were compared to results of other very precise calculations. The proposed method was better concerning convergence rate, decreased computing time and needed computer memory. Discretization of variables enabled direct comparison of theoretical and experimental results
Fast resolution of the neutron diffusion equation through public domain Ode codes
Energy Technology Data Exchange (ETDEWEB)
Garcia, V.M.; Vidal, V.; Garayoa, J. [Universidad Politecnica de Valencia, Departamento de Sistemas Informaticos, Valencia (Spain); Verdu, G. [Universidad Politecnica de Valencia, Departamento de Ingenieria Quimica y Nuclear, Valencia (Spain); Gomez, R. [I.E.S. de Tavernes Blanques, Valencia (Spain)
2003-07-01
The time-dependent neutron diffusion equation is a partial differential equation with source terms. The resolution method usually includes discretizing the spatial domain, obtaining a large system of linear, stiff ordinary differential equations (ODEs), whose resolution is computationally very expensive. Some standard techniques use a fixed time step to solve the ODE system. This can result in errors (if the time step is too large) or in long computing times (if the time step is too little). To speed up the resolution method, two well-known public domain codes have been selected: DASPK and FCVODE that are powerful codes for the resolution of large systems of stiff ODEs. These codes can estimate the error after each time step, and, depending on this estimation can decide which is the new time step and, possibly, which is the integration method to be used in the next step. With these mechanisms, it is possible to keep the overall error below the chosen tolerances, and, when the system behaves smoothly, to take large time steps increasing the execution speed. In this paper we address the use of the public domain codes DASPK and FCVODE for the resolution of the time-dependent neutron diffusion equation. The efficiency of these codes depends largely on the preconditioning of the big systems of linear equations that must be solved. Several pre-conditioners have been programmed and tested; it was found that the multigrid method is the best of the pre-conditioners tested. Also, it has been found that DASPK has performed better than FCVODE, being more robust for our problem.We can conclude that the use of specialized codes for solving large systems of ODEs can reduce drastically the computational work needed for the solution; and combining them with appropriate pre-conditioners, the reduction can be still more important. It has other crucial advantages, since it allows the user to specify the allowed error, which cannot be done in fixed step implementations; this, of course
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.
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 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)
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)
Comparison of two Ssub(infinity) methods for solving the neutron transport equation
International Nuclear Information System (INIS)
Mennig, J.; Brandt, D.; Haelg, W.
1978-01-01
A semianalytic method (S 0 sub(infinity)) is presented for solving the monoenergetic multi-region transport equation. This method is compared with results from S 1 sub(infinity)-theory given in the literature. Application of S 1 sub(infinity)-theory to reactor shields may lead to negative neutron fluxes and to flux oscillations. These unphysical effects are completely avoided by the new method. Numerical results demonstrate the limitations of S 1 sub(infinity) and confirm the numerical stability of (S 0 sub(infinity)). (Auth.)
International Nuclear Information System (INIS)
Zalan, T.A.
1988-01-01
Multi-energy-group neutron diffusion theory is used to numerically evaluate the utility of two different dual-detector neutron porosity logging devices, a 14 MeV (accelerator) neutron source - epithermal neutron detector device and a 4 MeV neutron source - capture gamma-ray detector device, relative to the traditional 4 MeV neutron source - thermal neutron detector device. Fast and epithermal neutron diffusion parameters are calculated using Monte Carlo - derived neutron flux distributions. Thermal parameters are calculated from tabulated cross sections. An existing analytical method to describe the transport of gamma-rays through common earth materials is modified in order to accommodate the modeling of the 4 MeV neutron - capture gamma-ray device. The 14 MeV neutron - epithermal neutron device is found to be less sensitive to porosity than the 4 MeV neutron - capture gamma-ray device, which in turn is found to be less sensitive to porosity than the traditional 4 MeV neutron - thermal neutron device. Salinity effects are found to be comparable for the 4 MeV neutron - capture gamma-ray and 4 MeV neutron - thermal neutron devices. The 4 MeV neutron capture gamma-ray measurement is found to be deepest investigating
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 ...
Albedo-adjusted fast-neutron diffusion coefficients in reactor reflectors
International Nuclear Information System (INIS)
Terney, W.B.
1975-01-01
In the newer, larger pressurized-water reactor cores, the calculated power distributions are fairly sensitive to the number of neutron groups used and to the treatment of the reflector cross sections. Comparisons between transport and diffusion calculations show that the latter substantially underpredict the reflector albedos in the fast (top) group and that the power distribution is shifted toward the core center when compared to 4-group transport theory results. When the fast-neutron diffusion coefficients are altered to make the transport- and diffusion-theory albedos agree, the power distributions are also brought into agreement. An expression for the fast-neutron diffusion coefficients in reflector regions has been derived such that the diffusion calculation reproduces the albedo obtained from a transport solution. In addition, a correction factor for mesh effects applicable to coarse mesh problems is presented. The use of the formalism gives the correct albedos and improved power distributions. (U.S.)
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
International Nuclear Information System (INIS)
Potemki, Valeri G.; Borisevich, Valentine D.; Yupatov, Sergei V.
1996-01-01
This paper describes the the next evolution step in development of the direct method for solving systems of Nonlinear Algebraic Equations (SNAE). These equations arise from the finite difference approximation of original nonlinear partial differential equations (PDE). This method has been extended on the SNAE with three variables. The solving SNAE bases on Reiterating General Singular Value Decomposition of rectangular matrix pencils (RGSVD-algorithm). In contrast to the computer algebra algorithm in integer arithmetic based on the reduction to the Groebner's basis that algorithm is working in floating point arithmetic and realizes the reduction to the Kronecker's form. The possibilities of the method are illustrated on the example of solving the one-dimensional diffusion equation for 3-component model isotope mixture in a ga centrifuge. The implicit scheme for the finite difference equations without simplifying the nonlinear properties of the original equations is realized. The technique offered provides convergence to the solution for the single run. The Toolbox SNAE is developed in the framework of the high performance numeric computation and visualization software MATLAB. It includes more than 30 modules in MATLAB language for solving SNAE with two and three variables. (author)
International Nuclear Information System (INIS)
Grimstone, M.J.
1978-06-01
The WRS Modular Programming System has been developed as a means by which programmes may be more efficiently constructed, maintained and modified. In this system a module is a self-contained unit typically composed of one or more Fortran routines, and a programme is constructed from a number of such modules. This report describes one WRS module, the function of which is to solve a set of multigroup diffusion equations for a system represented in one-dimensional plane, cylindrical or spherical geometry. The information given in this manual is of use both to the programmer wishing to incorporate the module in a programme, and to the user of such a programme. (author)
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...
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.)
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)
Energy Technology Data Exchange (ETDEWEB)
Ceolin, Celina; Schramm, Marcelo; Bodmann, Bardo Ernst Josef; Vilhena, Marco Tullio Mena Barreto de [Universidade Federal do Rio Grande do Sul, Porto Alegre (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica; Bogado Leite, Sergio de Queiroz [Comissao Nacional de Energia Nuclear, Rio de Janeiro (Brazil)
2014-11-15
In this work the authors solved the steady state neutron diffusion equation for a multi-layer slab assuming the multi-group energy model. The method to solve the equation system is based on an expansion in Taylor Series resulting in an analytical expression. The results obtained can be used as initial condition for neutron space kinetics problems. The neutron scalar flux was expanded in a power series, and the coefficients were found by using the ordinary differential equation and the boundary and interface conditions. The effective multiplication factor k was evaluated using the power method. We divided the domain into several slabs to guarantee the convergence with a low truncation order. We present the formalism together with some numerical simulations.
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.
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
International Nuclear Information System (INIS)
Coulomb, F.
1989-06-01
The aim of this work is to study methods for solving the diffusion equation, based on a primal or mixed-dual finite elements discretization and well suited for use on multiprocessors computers; domain decomposition methods are the subject of the main part of this study, the linear systems being solved by the block-Jacobi method. The origin of the diffusion equation is explained in short, and various variational formulations are reminded. A survey of iterative methods is given. The elemination of the flux or current is treated in the case of a mixed method. Numerical tests are performed on two examples of reactors, in order to compare mixed elements and Lagrange elements. A theoretical study of domain decomposition is led in the case of Lagrange finite elements, and convergence conditions for the block-Jacobi method are derived; the dissection decomposition is previously the purpose of a particular numerical analysis. In the case of mixed-dual finite elements, a study is led on examples and is confirmed by numerical tests performed for the dissection decomposition; furthermore, after being justified, decompositions along axes of symmetry are numerically tested. In the case of a decomposition into two subdomains, the dissection decomposition and the decomposition with an integrated interface are compared. Alternative directions methods are defined; the convergence of those relative to Lagrange elements is shown; in the case of mixed elements, convergence conditions are found [fr
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
Directory of Open Access Journals (Sweden)
Inci Cilingir Sungu
2015-01-01
Full Text Available A new application of the hybrid generalized differential transform and finite difference method is proposed by solving time fractional nonlinear reaction-diffusion equations. This method is a combination of the multi-time-stepping temporal generalized differential transform and the spatial finite difference methods. The procedure first converts the time-evolutionary equations into Poisson equations which are then solved using the central difference method. The temporal differential transform method as used in the paper takes care of stability and the finite difference method on the resulting equation results in a system of diagonally dominant linear algebraic equations. The Gauss-Seidel iterative procedure then used to solve the linear system thus has assured convergence. To have optimized convergence rate, numerical experiments were done by using a combination of factors involving multi-time-stepping, spatial step size, and degree of the polynomial fit in time. It is shown that the hybrid technique is reliable, accurate, and easy to apply.
Energy Technology Data Exchange (ETDEWEB)
Ryu, Eun Hyun; Song, Yong Mann; Park, Joo Hwan [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2013-05-15
If time-dependent equation is solved with the FEM, the limitation of the input geometry will disappear. It has often been pointed out that the numerical methods implemented in the RFSP code are not state-of-the-art. Although an acceleration method such as the Coarse Mesh Finite Difference (CMFD) for Finite Difference Method (FDM) does not exist for the FEM, one should keep in mind that the number of time steps for the transient simulation is not large. The rigorous formulation in this study will richen the theoretical basis of the FEM and lead to an extension of the dynamics code to deal with a more complicated problem. In this study, the formulation for the 1-D, 1-G Time Dependent Neutron Diffusion Equation (TDNDE) without consideration of the delay neutron will first be done. A problem including one multiplying medium will be solved. Also several conclusions from a comparison between the numerical and analytic solutions, a comparison between solutions with various element orders, and a comparison between solutions with different time differencing will be made to be certain about the formulation and FEM solution. By investigating various cases with different values of albedo, theta, and the order of elements, it can be concluded that the finite element solution is agree well with the analytic solution. The higher the element order used, the higher the accuracy improvements are obtained.
Energy Technology Data Exchange (ETDEWEB)
Liu Guoming [Department of Nuclear Engineering, Xi' an Jiaotong University, Xi' an, Shaanxi 710049 (China)], E-mail: gmliusy@gmail.com; Wu Hongchun; Cao Liangzhi [Department of Nuclear Engineering, Xi' an Jiaotong University, Xi' an, Shaanxi 710049 (China)
2008-09-15
This paper presents a transmission probability method (TPM) to solve the neutron transport equation in three-dimensional triangular-z geometry. The source within the mesh is assumed to be spatially uniform and isotropic. At the mesh surface, the constant and the simplified P{sub 1} approximation are invoked for the anisotropic angular flux distribution. Based on this model, a code TPMTDT is encoded. It was verified by three 3D Takeda benchmark problems, in which the first two problems are in XYZ geometry and the last one is in hexagonal-z geometry, and an unstructured geometry problem. The results of the present method agree well with those of Monte-Carlo calculation method and Spherical Harmonics (P{sub N}) method.
Abdelsalhin, Tiziano; Maselli, Andrea; Ferrari, Valeria
2018-04-01
The LIGO/Virgo Collaboration has recently announced the direct detection of gravitational waves emitted in the coalescence of a neutron star binary. This discovery allows, for the first time, to set new constraints on the behavior of matter at supranuclear density, complementary with those coming from astrophysical observations in the electromagnetic band. In this paper we demonstrate the feasibility of using gravitational signals to solve the relativistic inverse stellar problem, i.e., to reconstruct the parameters of the equation of state (EoS) from measurements of the stellar mass and tidal Love number. We perform Bayesian inference of mock data, based on different models of the star internal composition, modeled through piecewise polytropes. Our analysis shows that the detection of a small number of sources by a network of advanced interferometers would allow to put accurate bounds on the EoS parameters, and to perform a model selection among the realistic equations of state proposed in the literature.
Iterative Two- and One-Dimensional Methods for Three-Dimensional Neutron Diffusion Calculations
International Nuclear Information System (INIS)
Lee, Hyun Chul; Lee, Deokjung; Downar, Thomas J.
2005-01-01
Two methods are proposed for solving the three-dimensional neutron diffusion equation by iterating between solutions of the two-dimensional (2-D) radial and one-dimensional (1-D) axial solutions. In the first method, the 2-D/1-D equations are coupled using a current correction factor (CCF) with the average fluxes of the lower and upper planes and the axial net currents at the plane interfaces. In the second method, an analytic expression for the axial net currents at the interface of the planes is used for planar coupling. A comparison of the new methods is made with two previously proposed methods, which use interface net currents and partial currents for planar coupling. A Fourier convergence analysis of the four methods was performed, and results indicate that the two new methods have at least three advantages over the previous methods. First, the new methods are unconditionally stable, whereas the net current method diverges for small axial mesh size. Second, the new methods provide better convergence performance than the other methods in the range of practical mesh sizes. Third, the spectral radii of the new methods asymptotically approach zero as the mesh size increases, while the spectral radius of the partial current method approaches a nonzero value as the mesh size increases. Of the two new methods proposed here, the analytic method provides a smaller spectral radius than the CCF method, but the CCF method has several advantages over the analytic method in practical applications
Coarse-grain parallel solution of few-group neutron diffusion equations
International Nuclear Information System (INIS)
Sarsour, H.N.; Turinsky, P.J.
1991-01-01
The authors present a parallel numerical algorithm for the solution of the finite difference representation of the few-group neutron diffusion equations. The targeted architectures are multiprocessor computers with shared memory like the Cray Y-MP and the IBM 3090/VF, where coarse granularity is important for minimizing overhead. Most of the work done in the past, which attempts to exploit concurrence, has concentrated on the inner iterations of the standard outer-inner iterative strategy. This produces very fine granularity. To coarsen granularity, the authors introduce parallelism at the nested outer-inner level. The problem's spatial domain was partitioned into contiguous subregions and assigned a processor to solve for each subregion independent of all other subregions, hence, processors; i.e., each subregion is treated as a reactor core with imposed boundary conditions. Since those boundary conditions on interior surfaces, referred to as internal boundary conditions (IBCs), are not known, a third iterative level, the recomposition iterations, is introduced to communicate results between subregions
Three-dimensional h-adaptivity for the multigroup neutron diffusion equations
Wang, Yaqi
2009-04-01
Adaptive mesh refinement (AMR) has been shown to allow solving partial differential equations to significantly higher accuracy at reduced numerical cost. This paper presents a state-of-the-art AMR algorithm applied to the multigroup neutron diffusion equation for reactor applications. In order to follow the physics closely, energy group-dependent meshes are employed. We present a novel algorithm for assembling the terms coupling shape functions from different meshes and show how it can be made efficient by deriving all meshes from a common coarse mesh by hierarchic refinement. Our methods are formulated using conforming finite elements of any order, for any number of energy groups. The spatial error distribution is assessed with a generalization of an error estimator originally derived for the Poisson equation. Our implementation of this algorithm is based on the widely used Open Source adaptive finite element library deal.II and is made available as part of this library\\'s extensively documented tutorial. We illustrate our methods with results for 2-D and 3-D reactor simulations using 2 and 7 energy groups, and using conforming finite elements of polynomial degree up to 6. © 2008 Elsevier Ltd. All rights reserved.
Nodal integral method for the neutron diffusion equation in cylindrical geometry
International Nuclear Information System (INIS)
Azmy, Y.Y.
1987-01-01
The nodal methodology is based on retaining a higher a higher degree of analyticity in the process of deriving the discrete-variable equations compared to conventional numerical methods. As a result, extensive numerical testing of nodal methods developed for a wide variety of partial differential equations and comparison of the results to conventional methods have established the superior accuracy of nodal methods on coarse meshes. Moreover, these tests have shown that nodal methods are more computationally efficient than finite difference and finite-element methods in the sense that they require shorter CPU times to achieve comparable accuracy in the solutions. However, nodal formalisms and the final discrete-variable equations they produce are, in general, more complicated than their conventional counterparts. This, together with anticipated difficulties in applying the transverse-averaging procedure in curvilinear coordinates, has limited the applications of nodal methods, so far, to Cartesian geometry, and with additional approximations to hexagonal geometry. In this paper the authors report recent progress in deriving and numerically implementing a nodal integral method (NIM) for solving the neutron diffusion equation in cylindrical r-z geometry. Also, presented are comparisons of numerical solutions to two test problems with those obtained by the Exterminator-2 code, which indicate the superior accuracy of the nodal integral method solutions on much coarser meshes
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)
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.)
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
Two-dimensional finite element neutron diffusion analysis using hierarchic shape functions
International Nuclear Information System (INIS)
Carpenter, D.C.
1997-01-01
Recent advances have been made in the use of p-type finite element method (FEM) for structural and fluid dynamics problems that hold promise for reactor physics problems. These advances include using hierarchic shape functions, element-by-element iterative solvers and more powerful mapping techniques. Use of the hierarchic shape functions allows greater flexibility and efficiency in implementing energy-dependent flux expansions and incorporating localized refinement of the solution space. The irregular matrices generated by the p-type FEM can be solved efficiently using element-by-element conjugate gradient iterative solvers. These solvers do not require storage of either the global or local stiffness matrices and can be highly vectorized. Mapping techniques based on blending function interpolation allow exact representation of curved boundaries using coarse element grids. These features were implemented in a developmental two-dimensional neutron diffusion program based on the use of hierarchic shape functions (FEM2DH). Several aspects in the effective use of p-type analysis were explored. Two choices of elemental preconditioning were examined--the proper selection of the polynomial shape functions and the proper number of functions to use. Of the five shape function polynomials tested, the integral Legendre functions were the most effective. The serendipity set of functions is preferable over the full tensor product set. Two global preconditioners were also examined--simple diagonal and incomplete Cholesky. The full effectiveness of the finite element methodology was demonstrated on a two-region, two-group cylindrical problem but solved in the x-y coordinate space, using a non-structured element grid. The exact, analytic eigenvalue solution was achieved with FEM2DH using various combinations of element grids and flux expansions
Vectorized and multitasked solution of the few-group neutron diffusion equations
International Nuclear Information System (INIS)
Zee, S.K.; Turinsky, P.J.; Shayer, Z.
1989-01-01
A numerical algorithm with parallelism was used to solve the two-group, multidimensional neutron diffusion equations on computers characterized by shared memory, vector pipeline, and multi-CPU architecture features. Specifically, solutions were obtained on the Cray X/MP-48, the IBM-3090 with vector facilities, and the FPS-164. The material-centered mesh finite difference method approximation and outer-inner iteration method were employed. Parallelism was introduced in the inner iterations using the cyclic line successive overrelaxation iterative method and solving in parallel across lines. The outer iterations were completed using the Chebyshev semi-iterative method that allows parallelism to be introduced in both space and energy groups. For the three-dimensional model, power, soluble boron, and transient fission product feedbacks were included. Concentrating on the pressurized water reactor (PWR), the thermal-hydraulic calculation of moderator density assumed single-phase flow and a closed flow channel, allowing parallelism to be introduced in the solution across the radial plane. Using a pinwise detail, quarter-core model of a typical PWR in cycle 1, for the two-dimensional model without feedback the measured million floating point operations per second (MFLOPS)/vector speedups were 83/11.7. 18/2.2, and 2.4/5.6 on the Cray, IBM, and FPS without multitasking, respectively. Lower performance was observed with a coarser mesh, i.e., shorter vector length, due to vector pipeline start-up. For an 18 x 18 x 30 (x-y-z) three-dimensional model with feedback of the same core, MFLOPS/vector speedups of --61/6.7 and an execution time of 0.8 CPU seconds on the Cray without multitasking were measured. Finally, using two CPUs and the vector pipelines of the Cray, a multitasking efficiency of 81% was noted for the three-dimensional model
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
Pulsed neutron determination of anisotropic diffusion constants in multi-layered slabs
International Nuclear Information System (INIS)
Sri Ram, K.
1978-01-01
Anisotropic neutron diffusion parameters for graphite and plexiglas slab assemblies were calculated using one-dimensional discrete ordinates code ANISN, and also Case's eigenfunction expansion technique as suggested by Leonard. These calculated values were checked with the pulsed neutron experimental results as well as simple diffusion theory calculations of Spinrad. Relatively little experimental work has been done with heterogeneous assemblies which do not contain voids. The present comparison shows that the experimental results agree well with transport theory calculations. It appears from the results and inter-comparison of this work in simple geometries, that the pulsed neutron method can yield accurate experimental anisotropic diffusion constants, and can therefore be applied to more complicated geometries which may be difficult to calculate. (author)
Analysis and development of spatial hp-refinement methods for solving the neutron transport equation
International Nuclear Information System (INIS)
Fournier, D.
2011-01-01
The different neutronic parameters have to be calculated with a higher accuracy in order to design the 4. generation reactor cores. As memory storage and computation time are limited, adaptive methods are a solution to solve the neutron transport equation. The neutronic flux, solution of this equation, depends on the energy, angle and space. The different variables are successively discretized. The energy with a multigroup approach, considering the different quantities to be constant on each group, the angle by a collocation method called SN approximation. Once the energy and angle variable are discretized, a system of spatially-dependent hyperbolic equations has to be solved. Discontinuous finite elements are used to make possible the development of hp-refinement methods. Thus, the accuracy of the solution can be improved by spatial refinement (h-refinement), consisting into subdividing a cell into sub-cells, or by order refinement (p-refinement), by increasing the order of the polynomial basis. In this thesis, the properties of this methods are analyzed showing the importance of the regularity of the solution to choose the type of refinement. Thus, two error estimators are used to lead the refinement process. Whereas the first one requires high regularity hypothesis (analytical solution), the second one supposes only the minimal hypothesis required for the solution to exist. The comparison of both estimators is done on benchmarks where the analytic solution is known by the method of manufactured solutions. Thus, the behaviour of the solution as a regard of the regularity can be studied. It leads to a hp-refinement method using the two estimators. Then, a comparison is done with other existing methods on simplified but also realistic benchmarks coming from nuclear cores. These adaptive methods considerably reduces the computational cost and memory footprint. To further improve these two points, an approach with energy-dependent meshes is proposed. Actually, as the
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
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)
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)
On an adaptive time stepping strategy for solving nonlinear diffusion equations
International Nuclear Information System (INIS)
Chen, K.; Baines, M.J.; Sweby, P.K.
1993-01-01
A new time step selection procedure is proposed for solving non- linear diffusion equations. It has been implemented in the ASWR finite element code of Lorenz and Svoboda [10] for 2D semiconductor process modelling diffusion equations. The strategy is based on equi-distributing the local truncation errors of the numerical scheme. The use of B-splines for interpolation (as well as for the trial space) results in a banded and diagonally dominant matrix. The approximate inverse of such a matrix can be provided to a high degree of accuracy by another banded matrix, which in turn can be used to work out the approximate finite difference scheme corresponding to the ASWR finite element method, and further to calculate estimates of the local truncation errors of the numerical scheme. Numerical experiments on six full simulation problems arising in semiconductor process modelling have been carried out. Results show that our proposed strategy is more efficient and better conserves the total mass. 18 refs., 6 figs., 2 tabs
Neutron diffusion in spheroidal, bispherical, and toroidal systems
International Nuclear Information System (INIS)
Williams, M.M.R.
1986-01-01
The neutron flux has been studied around absorbing bodies of spheroidal, bispherical, and toroidal shapes in an infinite nonabsorbing medium. Exact solutions have been obtained by using effective boundary conditions at the surfaces of the absorbing bodies. The problems considered are as follows: 1. Neutron flux and current distributions around prolate and oblate spheroids. It is shown that an equivalent sphere approximation can lead to accurate values for the rate of absorption. 2. Neutron flux and current in a bispherical system of unequal spheres. Three separate situations arise here: (a) two absorbing spheres, (b) two spherical sources, and (c) one spherical source and one absorbing sphere. It is shown how the absorption rate in the two spheres depends on their separation. 3. Neutron flux and current in a toroidal system: (a) an absorbing toroid and (b) a toroidal source. The latter case simulates the flux distribution from a thermonuclear reactor vessel. Finally, a brief description of how these techniques can be extended to multiregion problems is given
International Nuclear Information System (INIS)
Matausek, M.
1972-01-01
A new proposed method for solving the space-energy dependent spherical harmonics equations represents a methodological contribution to neutron transport theory. The proposed method was applied for solving the problem of spec-energy transport of fast and resonance neutrons in multi-zone, cylindrical y symmetric infinite reactor cell and is related to previously developed procedure for treating the thermal energy region. The advantages of this method are as follows: a unique algorithm was obtained for detailed determination of spatial and energy distribution of neutrons (from thermal to fast) in the reactor cell; these detailed distributions enable more precise calculations of criticality conditions, obtaining adequate multigroup data and better interpretation of experimental data; computing time is rather short
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)
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
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
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)
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)
International Nuclear Information System (INIS)
Turinsky, P.J.; Al-Chalabi, R.M.K.; Engrand, P.; Sarsour, H.N.; Faure, F.X.; Guo, W.
1994-06-01
NESTLE is a FORTRAN77 code that solves the few-group neutron diffusion equation utilizing the Nodal Expansion Method (NEM). NESTLE can solve the eigenvalue (criticality); eigenvalue adjoint; external fixed-source steady-state; or external fixed-source. or eigenvalue initiated transient problems. The code name NESTLE originates from the multi-problem solution capability, abbreviating Nodal Eigenvalue, Steady-state, Transient, Le core Evaluator. The eigenvalue problem allows criticality searches to be completed, and the external fixed-source steady-state problem can search to achieve a specified power level. Transient problems model delayed neutrons via precursor groups. Several core properties can be input as time dependent. Two or four energy groups can be utilized, with all energy groups being thermal groups (i.e. upscatter exits) if desired. Core geometries modelled include Cartesian and Hexagonal. Three, two and one dimensional models can be utilized with various symmetries. The non-linear iterative strategy associated with the NEM method is employed. An advantage of the non-linear iterative strategy is that NSTLE can be utilized to solve either the nodal or Finite Difference Method representation of the few-group neutron diffusion equation
International Nuclear Information System (INIS)
Hall, S.K.; Eaton, M.D.; Williams, M.M.R.
2012-01-01
Highlights: ► Isogeometric analysis used to obtain solutions to the neutron diffusion equation. ► Exact geometry captured for a circular fuel pin within a square moderator. ► Comparisons are made between the finite element method and isogeometric analysis. ► Error and observed order of convergence found using an analytic solution. -- Abstract: In this paper the neutron diffusion equation is solved using Isogeometric Analysis (IGA), which is an attempt to generalise Finite Element Analysis (FEA) to include exact geometries. In contrast to FEA, the basis functions are rational functions instead of polynomials. These rational functions, called non-uniform rational B-splines, are used to capture both the geometry and approximate the solution. The method of manufactured solutions is used to verify a MatLab implementation of IGA, which is then applied to a pincell problem. This is a circular uranium fuel pin within a square block of graphite moderator. A new method is used to compute an analytic solution to a simplified version of this problem, and is then used to observe the order of convergence of the numerical scheme. Comparisons are made against quadratic finite elements for the pincell problem, and it is found that the disadvantage factor computed using IGA is less accurate. This is due to a cancellation of errors in the FEA solution. A modified pincell problem with vacuum boundary conditions is then considered. IGA is shown to outperform FEA in this situation.
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
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
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
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.
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)
International Nuclear Information System (INIS)
Ceolin, Celina
2010-01-01
The objective of this work is to obtain an analytical solution of the neutron diffusion kinetic equation in one-dimensional cartesian geometry, to monoenergetic and multigroup problems. These equations are of the type stiff, due to large differences in the orders of magnitude of the time scales of the physical phenomena involved, which make them difficult to solve. The basic idea of the proposed method is applying the spectral expansion in the scalar flux and in the precursor concentration, taking moments and solving the resulting matrix problem by the Laplace transform technique. Bearing in mind that the equation for the precursor concentration is a first order linear differential equation in the time variable, to enable the application of the spectral method we introduce a fictitious diffusion term multiplied by a positive value which tends to zero. This procedure opened the possibility to find an analytical solution to the problem studied. We report numerical simulations and analysis of the results obtained with the precision controlled by the truncation order of the series. (author)
Diffusive instability of a kaon condensate in neutron star matter
International Nuclear Information System (INIS)
Kubis, Sebastian
2004-01-01
The beta equilibrated dense matter with kaon condensate is analyzed with respect to extended stability conditions, including charge fluctuations. This kind of the diffusive instability appeared to be common property in the kaon condensation case. Results for three different nuclear models are presented
ADI as a preconditioning for solving the convection-diffusion equation
International Nuclear Information System (INIS)
Chin, R.C.Y.; Manteuffel, T.A.; De Pillis, J.
1984-01-01
The authors examine a splitting of the operator obtained from a steady convection-diffusion equation with variable coefficients in which the convection term dominates. The operator is split into a dominant and subdominant parts consistent with the inherent directional property of the partial differential equation. The equations involving the dominant parts should be easily solved. The authors accelerate the convergence of this splitting or the outer iteration by a Chebyshev semi-iterative method. When the dominant part has constant coefficients, it can be easily solved using alternating direction implicit (ADI) methods. This is called the inner iteration. The optimal parameters for a stationary two-parameter ADI method are obtained when the eigenvalues become complex. This corresponds to either the horizontal or the vertical half-grid Reynolds number larger than unity. The Chebyshev semi-iterative method is used to accelerate the convergence of the inner ADI iteration. A two-fold increase in speed is obtained when the ADI iteration matrix has real eigenvalues, and the increase is less significant when the eigenvalues are complex. If either the horizontal or the vertical half-grid Reynolds number is equal to one, the spectral radius of the optimal ADI iterative matrix is zero. However, a high degree of nilpotency impairs rapid convergence. This problem is removed by introducing a more implicit iterative method called ADI/Gauss-Seidel (ADI/GS). ADI/GS resolves the nilpotency and, thus, converges more rapidly for half-grid Reynolds number near 1. Finally, these methods are compared with several well-known schemes on test problems. 23 references, 5 figures
On the adequacy of message-passing parallel supercomputers for solving neutron transport problems
International Nuclear Information System (INIS)
Azmy, Y.Y.
1990-01-01
A coarse-grained, static-scheduling parallelization of the standard iterative scheme used for solving the discrete-ordinates approximation of the neutron transport equation is described. The parallel algorithm is based on a decomposition of the angular domain along the discrete ordinates, thus naturally producing a set of completely uncoupled systems of equations in each iteration. Implementation of the parallel code on Intcl's iPSC/2 hypercube, and solutions to test problems are presented as evidence of the high speedup and efficiency of the parallel code. The performance of the parallel code on the iPSC/2 is analyzed, and a model for the CPU time as a function of the problem size (order of angular quadrature) and the number of participating processors is developed and validated against measured CPU times. The performance model is used to speculate on the potential of massively parallel computers for significantly speeding up real-life transport calculations at acceptable efficiencies. We conclude that parallel computers with a few hundred processors are capable of producing large speedups at very high efficiencies in very large three-dimensional problems. 10 refs., 8 figs
Diffusion of water adsorbed in hydrotalcite: neutron scattering Study
Energy Technology Data Exchange (ETDEWEB)
Mitra, S [Solid State Physics Division, Bhabha Atomic Research Centre, Mumbai (India); Pramanik, A [Unilever Research India, Bangalore 500 066 (India); Chakrabarty, D [Godrej Sara Lee Limited, Research and Development Centre, Mumbai 400 079 (India); Juranyi, F [Laboratory for Neutron Scattering, ETHZ and PSI, CH-5232 Villigen PSI (Switzerland); Gautam, S [Solid State Physics Division, Bhabha Atomic Research Centre, Mumbai (India); Mukhopadhyay, R [Solid State Physics Division, Bhabha Atomic Research Centre, Mumbai (India)
2007-12-15
Layered double hydroxides (LDH) are a class of ionic lamellar solids with positively charged layers of two kinds of metallic cations and exchangeable hydrated anions. Quasi-elastic neutron scattering (QENS) measurements are performed in this type of LDH structured hydrated hydrotalcite sample to study the dynamical behaviour of the water in geometric confinement within the layers. Dynamical parameters correspond to the confined water molecules revealed that depending on the amount of excess water present, behaves differently and approaches bulk values at high concentration. Both translational and rotational dynamical parameters showed that at very low concentration of excess water, water molecules are attached to the surfaces and show the confinement effect.
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)
Sun, HongGuang; Liu, Xiaoting; Zhang, Yong; Pang, Guofei; Garrard, Rhiannon
2017-09-01
Fractional-order diffusion equations (FDEs) extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media. Real-world diffusion can be multi-dimensional, requiring efficient numerical solvers that can handle long-term memory embedded in mass transport. To address this challenge, a semi-discrete Kansa method is developed to approximate the two-dimensional spatiotemporal FDE, where the Kansa approach first discretizes the FDE, then the Gauss-Jacobi quadrature rule solves the corresponding matrix, and finally the Mittag-Leffler function provides an analytical solution for the resultant time-fractional ordinary differential equation. Numerical experiments are then conducted to check how the accuracy and convergence rate of the numerical solution are affected by the distribution mode and number of spatial discretization nodes. Applications further show that the numerical method can efficiently solve two-dimensional spatiotemporal FDE models with either a continuous or discrete mixing measure. Hence this study provides an efficient and fast computational method for modeling super-diffusive, sub-diffusive, and mixed diffusive processes in large, two-dimensional domains with irregular shapes.
Convergence properties of iterative algorithms for solving the nodal diffusion equations
International Nuclear Information System (INIS)
Azmy, Y.Y.; Kirk, B.L.
1990-01-01
We drive the five point form of the nodal diffusion equations in two-dimensional Cartesian geometry and develop three iterative schemes to solve the discrete-variable equations: the unaccelerated, partial Successive Over Relaxation (SOR), and the full SOR methods. By decomposing the iteration error into its Fourier modes, we determine the spectral radius of each method for infinite medium, uniform model problems, and for the unaccelerated and partial SOR methods for finite medium, uniform model problems. Also for the two variants of the SOR method we determine the optimal relaxation factor that results in the smallest number of iterations required for convergence. Our results indicate that the number of iterations for the unaccelerated and partial SOR methods is second order in the number of nodes per dimension, while, for the full SOR this behavior is first order, resulting in much faster convergence for very large problems. We successfully verify the results of the spectral analysis against those of numerical experiments, and we show that for the full SOR method the linear dependence of the number of iterations on the number of nodes per dimension is relatively insensitive to the value of the relaxation parameter, and that it remains linear even for heterogenous problems. 14 refs., 1 fig
Solving the radiation diffusion and energy balance equations using pseudo-transient continuation
International Nuclear Information System (INIS)
Shestakov, A.I.; Greenough, J.A.; Howell, L.H.
2005-01-01
We develop a scheme for the system coupling the radiation diffusion and matter energy balance equations. The method is based on fully implicit, first-order, backward Euler differencing; Picard-Newton iterations solve the nonlinear system. We show that iterating on the radiation energy density and the emission source is more robust. Since the Picard-Newton scheme may not converge for all initial conditions and time steps, pseudo-transient continuation (Ψtc) is introduced. The combined Ψtc-Picard-Newton scheme is analyzed. We derive conditions on the Ψtc parameter that guarantee physically meaningful iterates, e.g., positive energies. Successive Ψtc iterates are bounded and the radiation energy density and emission source tend to equilibrate. The scheme is incorporated into a multiply dimensioned, massively parallel, Eulerian, radiation-hydrodynamic computer program with automatic mesh refinement (AMR). Three examples are presented that exemplify the scheme's performance. (1) The Pomraning test problem that models radiation flow into cold matter. (2) A similar, but more realistic problem simulating the propagation of an ionization front into tenuous hydrogen gas with a Saha model for the equation-of-state. (3) A 2D axisymmetric (R,Z) simulation with real materials featuring jetting, radiatively driven, interacting shocks
Iterative schemes for obtaining dominant alpha-modes of the neutron diffusion equation
International Nuclear Information System (INIS)
Singh, K.P.; Modak, R.S.; Degweker, S.B.; Singh, Kanchhi
2009-01-01
Two new methods of obtaining dominant prompt alpha-modes (sometimes referred to as time-eigenfunctions) of the multigroup neutron diffusion equation are discussed. In the first of these, we initially compute the dominant K-eigenfunctions and K-eigenvalues (denoted by λ 1 , λ 2 , λ 3 ...λ 1 being equal to the K eff ) for the given nuclear reactor model, by existing method based on sub-space iteration (SSI) which is an improved version of power iteration method. Subsequently, a uniformly distributed (positive or negative) 1/v absorber of sufficient concentration is added so as to make a particular eigenvalue λ i equal to unity. This gives ith alpha-mode. This procedure is repeated to find all the required alpha-modes. In the second method, we solve the alpha-eigenvalue problem directly by SSI method. This is clearly possible for a sub-critical reactor for which the inverse of the dominant alpha-eigenvalues are also the largest in magnitude as required by the SSI method. Here, the procedure is made applicable even to a super-critical reactor by making the reactor model sub-critical by the addition of a 1/v absorber. Results of these calculations for a 3-D two group PHWR test-case are given. These results are validated against the results as obtained by a completely different approach based on Orthomin(1) algorithm published earlier. The direct method based on the sub-space iteration strategy is found to be a simple and reliable method for obtaining any number of alpha-modes. Also comments have been made on the relationship between fundamental α and k values.
International Nuclear Information System (INIS)
Tittle, C.W.
1992-01-01
Diffusion theory has been successfully used to model the effect of fluid invasion into the formation for neutron porosity logs and for the gamma-gamma density log. The purpose of this paper is to present results of computations using a five-group time-dependent diffusion code on invasion effects for the pulsed neutron thermal decay time log. Previous invasion studies by the author involved the use of a three-dimensional three-group steady-state diffusion theory to model the dual-detector thermal neutron porosity log and the gamma-gamma density log. The five-group time-dependent code MGNDE (Multi-Group Neutron Diffusion Equation) used in this work was written by Ferguson. It has been successfully used to compute the intrinsic formation life-time correction for pulsed neutron thermal decay time logs. This application involves the effect of fluid invasion into the formation
Neutrons in a highly diffusive medium a new propulsion tool for deep space exploration?
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...
Energy Technology Data Exchange (ETDEWEB)
Mousavi Shirazi, Seyed Alireza [Islamic Azad Univ. (I.A.U.), Dept. of Physics, Tehran (Iran, Islamic Republic of)
2015-07-15
In this symbolic investigation, a cylindrical cell in a LWR, which consists of one fuel pin and moderator (water), is considered. The width of this cylindrical cell is divided into 100 equal units. Since the neutron flux in a cylindrical fuel pin is resulting from the diffusion equation: -(1)/(r)(d)/(dr)Dr(d)/(dr)φ(r) + Σ{sub a}φ(r) = S(r), the amount of fast neutron fluxes are obtained on the basis of the numeric solution of this equation, and the applied boundary conditions are considered: φ'(0) = φ'(1) = 0. This differential equation is solved by the tridiagonal method for variant enrichments of uranium. Neutron fluxes are obtained in variant radii of fuel pin and moderator and are finally compared with each other. There are some interesting outcomes resulting from this investigation. It can be inferred that because of the fuel enrichment increment, the fast neutron flux increases significantly at the centre of core, while many of the fast neutrons produced are absorbed after entering the water region, moderation of lots of them causes the reduced neutron flux to get improved in this region.
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
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)
International Nuclear Information System (INIS)
Zhang, M.; Takeda, M.; Nakajima, H.
2006-01-01
Laboratory diffusion testing as well as batch experiments are well established and widely adopted techniques for characterizing the diffusive and adsorptive properties of geological, geotechnical, and synthetic materials in both scientific and applied fields, including geological disposal of radioactive waste. Although several types of diffusion test, such as the through- diffusion test, in-diffusion test, out-diffusion test, and column test, are currently available, different methods may have different advantages and disadvantages. In addition, traditional methods may have limitations, such as the need for relatively long test times, cumbersome test procedures, and the possibility of errors due to differences between analytical assumptions and actual test conditions. Furthermore, traditional batch experiments using mineral powders are known to overestimate the sorption coefficient. In part 1 of this report, we present a brief overview of laboratory diffusion and batch experiments. The advantages, disadvantages, limitations, and/or potential problems associated with individual tests were compared and summarized. This comprehensive report will provide practical references for reviewing the results obtained from relevant experiments, especially from the viewpoint of regulation. To solve and/or eliminate the potential problems associated with conventional methods, and to obtain the diffusion coefficient and rock capacity factor from a laboratory test both rapidly and accurately, part 2 of this study discusses possible strategies involving the development of rigorous solutions to some relevant test methods, and sensitivity analyses for the related tests that may be helpful to judge the accuracy of the two parameters to be determined from individual tests. (authors)
Energy Technology Data Exchange (ETDEWEB)
Azmy, Yousry
2014-06-10
We employ the Integral Transport Matrix Method (ITMM) as the kernel of new parallel solution methods for the discrete ordinates approximation of the within-group neutron transport equation. The ITMM abandons the repetitive mesh sweeps of the traditional source iterations (SI) scheme in favor of constructing stored operators that account for the direct coupling factors among all the cells' fluxes and between the cells' and boundary surfaces' fluxes. The main goals of this work are to develop the algorithms that construct these operators and employ them in the solution process, determine the most suitable way to parallelize the entire procedure, and evaluate the behavior and parallel performance of the developed methods with increasing number of processes, P. The fastest observed parallel solution method, Parallel Gauss-Seidel (PGS), was used in a weak scaling comparison with the PARTISN transport code, which uses the source iteration (SI) scheme parallelized with the Koch-baker-Alcouffe (KBA) method. Compared to the state-of-the-art SI-KBA with diffusion synthetic acceleration (DSA), this new method- even without acceleration/preconditioning-is completitive for optically thick problems as P is increased to the tens of thousands range. For the most optically thick cells tested, PGS reduced execution time by an approximate factor of three for problems with more than 130 million computational cells on P = 32,768. Moreover, the SI-DSA execution times's trend rises generally more steeply with increasing P than the PGS trend. Furthermore, the PGS method outperforms SI for the periodic heterogeneous layers (PHL) configuration problems. The PGS method outperforms SI and SI-DSA on as few as P = 16 for PHL problems and reduces execution time by a factor of ten or more for all problems considered with more than 2 million computational cells on P = 4.096.
A fast nodal neutron diffusion method for cartesian geometry
International Nuclear Information System (INIS)
Makai, M.; Maeder, C.
1983-01-01
A numerical method based on an analytical solution to the three-dimensional two-group diffusion equation has been derived assuming that the flux is a sum of the functions of one variable. In each mesh the incoming currents are used as boundary conditions. The final equations for the average flux and the outgoing currents are of the response matrix type. The method is presented in a form that can be extended to the general multigroup case. In the SEXI computer program developed on the basis of this method, the response matrix elements are recalculated in each outer iteration to minimize the data transfer between disk storage and central memory. The efficiency of the method is demonstrated for a light water reactor (LWR) benchmark problem. The SEXI program has been incorporated into the LWR simulator SILWER code as a possible option
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
International Nuclear Information System (INIS)
Kirk, B.L.; Azmy, Y.
1994-01-01
A modified scheme is developed for solving the two-dimensional nodal diffusion equations on distributed memory computers. The scheme is aimed at minimizing the volume of communication among processors while maximizing the tasks in parallel. Results show a significant improvement in parallel efficiency on the Intel iPSC/860 hypercube compared to previous algorithms
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.)
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
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...
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
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
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
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).
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)
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
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
Energy Technology Data Exchange (ETDEWEB)
Stancic, V [Institut za nuklearne nauke Boris Kidric, Vinca, Beograd (Yugoslavia)
1987-07-01
A method is proposed to solve multigroup time dependent neutron transport equation with arbitrary scattering anisotropy. The recurrence relation thus obtained is simple, numerically stable and especially suitable for treatment of complicated geometries. (author)
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)
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.
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
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)
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
Directory of Open Access Journals (Sweden)
Shahid Hasnain
2017-07-01
Full Text Available This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.
Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman
2017-07-01
This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.
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)
Energy Technology Data Exchange (ETDEWEB)
Petersen, Claudio Z. [Universidade Federal de Pelotas, Capao do Leao (Brazil). Programa de Pos Graduacao em Modelagem Matematica; Bodmann, Bardo E.J.; Vilhena, Marco T. [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Programa de Pos-graduacao em Engenharia Mecanica; Barros, Ricardo C. [Universidade do Estado do Rio de Janeiro, Nova Friburgo, RJ (Brazil). Inst. Politecnico
2014-12-15
In the present work we solve in analytical representation the three dimensional neutron kinetic diffusion problem in rectangular Cartesian geometry for homogeneous and bounded domains for any number of energy groups and precursor concentrations. The solution in analytical representation is constructed using a hierarchical procedure, i.e. the original problem is reduced to a problem previously solved by the authors making use of a combination of the spectral method and a recursive decomposition approach. Time dependent absorption cross sections of the thermal energy group are considered with step, ramp and Chebyshev polynomial variations. For these three cases, we present numerical results and discuss convergence properties and compare our results to those available in the literature.
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.
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
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.
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
Tayebi, A.; Shekari, Y.; Heydari, M. H.
2017-07-01
Several physical phenomena such as transformation of pollutants, energy, particles and many others can be described by the well-known convection-diffusion equation which is a combination of the diffusion and advection equations. In this paper, this equation is generalized with the concept of variable-order fractional derivatives. The generalized equation is called variable-order time fractional advection-diffusion equation (V-OTFA-DE). An accurate and robust meshless method based on the moving least squares (MLS) approximation and the finite difference scheme is proposed for its numerical solution on two-dimensional (2-D) arbitrary domains. In the time domain, the finite difference technique with a θ-weighted scheme and in the space domain, the MLS approximation are employed to obtain appropriate semi-discrete solutions. Since the newly developed method is a meshless approach, it does not require any background mesh structure to obtain semi-discrete solutions of the problem under consideration, and the numerical solutions are constructed entirely based on a set of scattered nodes. The proposed method is validated in solving three different examples including two benchmark problems and an applied problem of pollutant distribution in the atmosphere. In all such cases, the obtained results show that the proposed method is very accurate and robust. Moreover, a remarkable property so-called positive scheme for the proposed method is observed in solving concentration transport phenomena.
International Nuclear Information System (INIS)
Ezaki, Masahiro; Mitake, Susumu; Ozawa, Tamotsu
1979-06-01
The SCOTCH program solves the one-dimensional (R or Z), two-group reactor kinetics equations with multi-channel temperature transients and fluid dynamics. Sub-program SCOTCH-RX simulates the space-time neutron diffusion in radial direction, and sub-program SCOTCH-AX simulates the same in axial direction. The program has about 8,000 steps of FORTRAN statement and requires about 102 kilo-words of computer memory. (author)
Neutron and Proton Diffusion in Fusion Reactions for the Synthesis of Superheavy Nuclei
International Nuclear Information System (INIS)
Ming-Hui, Huang; Zai-Guo, Gan; Zhao-Qing, Feng; Xiao-Hong, Zhou; Jun-Qing, Li
2008-01-01
The restriction of the one dimensional (1D) master equation (ME) with the mass number of the projectile-like fragment as a variable is studied, and a two-dimensional (2D) master equation with the neutron and proton numbers as independent variables is set up, and solved numerically. Our study showed that the 2D ME can describe the fusion process well in all projectile-target combinations. Therefore the possible channels to synthesize super-heavy nuclei can be studied correctly in wider possibilities. The available condition for employing 1D ME is pointed out
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
NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION.
Liu, F; Meerschaert, M M; McGough, R J; Zhuang, P; Liu, Q
2013-03-01
In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.
NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION
Liu, F.; Meerschaert, M.M.; McGough, R.J.; Zhuang, P.; Liu, Q.
2013-01-01
In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and technique...
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....
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.)
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
International Nuclear Information System (INIS)
Carmo, E.G.D. do; Galeao, A.C.N.R.
1986-01-01
A new method specially designed to solve highly convective transport problems is proposed. Using a variational approach it is shown that this weighted residual method belongs to a class of Petrov-Galerkin's approximation. Some examples are presented in order to demonstrate the adequacy of this method in predicting internal or external boundary layers. (Author) [pt
Boudin , Laurent; Mathiaud , Julien
2012-01-01
In this work, we discuss some numerical properties of the viscous numerical scheme introduced in [Boudin, Mathiaud, NMPDE 2012] to solve the one-dimensional pressureless gases system, and study in particular, from a computational viewpoint, its asymptotic behavior when the viscosity parameter used in the scheme becomes smaller.
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)
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)
A new integral method for solving the point reactor neutron kinetics equations
International Nuclear Information System (INIS)
Li Haofeng; Chen Wenzhen; Luo Lei; Zhu Qian
2009-01-01
A numerical integral method that efficiently provides the solution of the point kinetics equations by using the better basis function (BBF) for the approximation of the neutron density in one time step integrations is described and investigated. The approach is based on an exact analytic integration of the neutron density equation, where the stiffness of the equations is overcome by the fully implicit formulation. The procedure is tested by using a variety of reactivity functions, including step reactivity insertion, ramp input and oscillatory reactivity changes. The solution of the better basis function method is compared to other analytical and numerical solutions of the point reactor kinetics equations. The results show that selecting a better basis function can improve the efficiency and accuracy of this integral method. The better basis function method can be used in real time forecasting for power reactors in order to prevent reactivity accidents.
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.)
Homotopy decomposition method for solving one-dimensional time-fractional diffusion equation
Abuasad, Salah; Hashim, Ishak
2018-04-01
In this paper, we present the homotopy decomposition method with a modified definition of beta fractional derivative for the first time to find exact solution of one-dimensional time-fractional diffusion equation. In this method, the solution takes the form of a convergent series with easily computable terms. The exact solution obtained by the proposed method is compared with the exact solution obtained by using fractional variational homotopy perturbation iteration method via a modified Riemann-Liouville derivative.
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.
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
International Nuclear Information System (INIS)
Magat, Ph.
1997-04-01
Today neutron transport in PWR's core is routinely computed through the transport-diffusion(2 groups) scheme. This method gives satisfactory results for reactors operating in normal conditions but the 2 group diffusion approximation is unable to take into account interface effects or anisotropy. The improvement of this scheme is logically possible through the use of a simplified P N method (SP N ) for the modeling of the core. The comparison between S N calculations and SP N calculations shows an excellent agreement on eigenvalues as well as on power maps. We can notice that: -) it is no use extending the development beyond P 3 , there is no effect; -) the P 1 development is adequate; and -) the P 0 development is totally inappropriate. Calculations performed on the N4 core of the Chooz power plant have enabled us to compare diffusion operators with transport operators (SP 1 , SP 3 , SP 5 and SP 7 ). These calculations show that the implementation of the SP N method is feasible but the extra-costs in computation times and memory are important. We recommend: SP 5 P 1 calculations for heterogeneous 2-dimension geometry and SP 3 P 1 calculations for the homogeneous 3-dimension geometry. (A.C.)
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)
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)
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.)
International Nuclear Information System (INIS)
Petersen, Claudio Zen; Vilhena, Marco T.; Barros, Ricardo C.
2009-01-01
In this paper the application of the Laplace transform method is described in order to determine the energy-dependent albedo matrix that is used in the boundary conditions multigroup neutron diffusion eigenvalue problems in slab geometry for nuclear reactor global calculations. In slab geometry, the diffusion albedo substitutes without approximation the baffle-reflector system around the active domain. Numerical results to typical test problems are shown to illustrate the accuracy and the efficiency of the Chebysheff acceleration scheme. (orig.)
Genetic algorithms - A new technique for solving the neutron spectrum unfolding problem
International Nuclear Information System (INIS)
Freeman, David W.; Edwards, D. Ray; Bolon, Albert E.
1999-01-01
A new technique utilizing genetic algorithms has been applied to the Bonner sphere neutron spectrum unfolding problem. Genetic algorithms are part of a relatively new field of 'evolutionary' solution techniques that mimic living systems with computer-simulated 'chromosome' solutions. Solutions mate and mutate to create better solutions. Several benchmark problems, considered representative of radiation protection environments, have been evaluated using the newly developed UMRGA code which implements the genetic algorithm unfolding technique. The results are compared with results from other well-established unfolding codes. The genetic algorithm technique works remarkably well and produces solutions with relatively high spectral qualities. UMRGA appears to be a superior technique in the absence of a priori data - it does not rely on 'lucky' guesses of input spectra. Calculated personnel doses associated with the unfolded spectra match benchmark values within a few percent
The Nodal Polynomial Expansion method to solve the multigroup diffusion equations
International Nuclear Information System (INIS)
Ribeiro, R.D.M.
1983-03-01
The methodology of the solutions of the multigroup diffusion equations and uses the Nodal Polynomial Expansion Method is covered. The EPON code was developed based upon the above mentioned method for stationary state, rectangular geometry, one-dimensional or two-dimensional and for one or two energy groups. Then, one can study some effects such as the influence of the baffle on the thermal flux by calculating the flux and power distribution in nuclear reactors. Furthermore, a comparative study with other programs which use Finite Difference (CITATION and PDQ5) and Finite Element (CHD and FEMB) Methods was undertaken. As a result, the coherence, feasibility, speed and accuracy of the methodology used were demonstrated. (Author) [pt
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.
TRITON, 3-D Multi-Region Neutron Diffusion Burnup with Criticality Search
International Nuclear Information System (INIS)
1974-01-01
1 - Nature of physical problem solved: TRITON is a multigroup diffusion depletion program in three dimensions (x,y,z). In addition to the straight K eff calculation, three types of criticality searches are possible - diluted control isotope search, region-wise smeared control isotope search, region-wise smeared control isotope search, region-wise smeared control isotope boundary search (the control isotope can be smeared over one region or over a group of regions called a control bank). The depletion equations are solved region-wise. More than one microscopic cross section library can be used in the various regions of the reactor. The same is true for self-shielding factors. Such sets of data can be changed at pre-determined time steps. 2 - Method of solution: The mathematical model employed for the solution of the finite difference equations, which is derived from a seven-point approximation of diffusion equations, is an on-line Chebyshev semi- iterative method. 3 - Restrictions on the complexity of the problem: Maximum number of: library sets: 1; self-shielding sets: 10; compositions: 100; self-shielding coefficients: 6000; groups: 10; fuel isotopes: 30; fission products: 29; isotopes: 50; burnable isotopes: 40; control banks: 100; mesh points: 15000; regions: 400; time steps: 100; control areas: 100; small time steps: 200; elements in the control list: 400; x planes: 100; y planes: 100; z planes: 100
International Nuclear Information System (INIS)
Filio Lopez, Carlos.
1979-01-01
A calculation program (URA 6.F4) was elaborated on FORTRAN IV language, that through finite differences solves the unidimensional scalar Helmholtz equation, assuming only one energy group, in spherical cylindrical or plane geometry. The purpose is the determination of the flow distribution in a reactor of spherical cylindrical or plane geometry and the critical dimensions. Feeding as entrance datas to the program the geometry, diffusion coefficients and macroscopic transversals cross sections of absorption and fission for each region. The differential diffusion equation is converted with its boundary conditions, to one system of homogeneous algebraic linear equations using the box integration technique. The investigation on criticality is converted then in a succession of eigenvalue problems for the critical eigenvalue. In general, only is necessary to solve the first eigenvalue and its corresponding eigenvector, employing the power method. The obtained results by the program for the critical dimensions of the clean reactors are admissible, the existing error as respect to the analytic is less of 0.5%; by the analysed reactors of three regions, the relative error with respect to the semianalytic result is less of 0.2%. With this program is possible to obtain one quantitative description of one reactor if the transversal sections that appears in the monoenergetic model are adequatedly averaged by the energy group used. (author)
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)
Solution of two group neutron diffusion equation by using homotopy analysis method
International Nuclear Information System (INIS)
Cavdar, S.
2010-01-01
The Homotopy Analysis Method (HAM), proposed in 1992 by Shi Jun Liao and has been developed since then, is based on differential geometry as well as homotopy which is a fundamental concept in topology. It has proved to be useful for obtaining series solutions of many such problems involving algebraic, linear/non-linear, ordinary/partial differential equations, differential-integral equations, differential-difference equations, and coupled equations of them. Briefly, through HAM, it is possible to construct a continuous mapping of an initial guess approximation to the exact solution of the equation of concern. An auxiliary linear operator is chosen to construct such kind of a continuous mapping and an auxiliary parameter is used to ensure the convergence of series solution. We present the solutions of two-group neutron diffusion equation through HAM in this work. We also compare the results with that obtained by other well-known solution analytical and numeric methods.
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
Use of diffusion bonded SS-Al composite material in the development of neutron detectors
International Nuclear Information System (INIS)
Alex, Mary; Prasad, K.R.; Pappachan, A.L.; Grover, A.K.; Krishnan, J.; Derose, D.J.; Bhanumurthy, K.; Kale, G.B.
2005-01-01
The present paper describes the development of a SS-Al composite plate in-house at BARC by diffusion bonding technique. Details of the several tests carried out on the composite material and the use of the plate in the development of a boron lined neutron chamber for Dhruva reactor control instrumentation has been described. The bonded sample has withstood tensile strength test, leak test and thermal cycling test and the leak rate was observed to be less than 3 x 10 -10 stdcc/sec. The chamber with the composite material has been installed in Dhruva Basket C location and connected to the log rate safety channel. It has been working successfully for the past two years. The use of SS-Al composite material has improved the reliability and long-term performance of the detector. (author)
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
Determination of the ion thermal diffusivity from neutron emission profiles in decay
International Nuclear Information System (INIS)
Sasao, M.; Adam, J.M.; Conroy, S.; Jarvis, O.N.; Marcus, F.B.; Sadler, G.; Belle, P. van
1992-01-01
Spatial profiles of neutron emission are routinely obtained at the Joint European Torus (JET) from line-integrated emissivities measured with a multi-channel instrument. It is shown that the manner in which the emission profiles relax following 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%. The radial profiles of χ i for small minor radius (r/a 2 /s for H-mode plasmas with plasma current I p = 3.1 MA and toroidal field B T = 2.3T. The experimental value of χ i is smallest for Z eff = 2.2 and increases weakly with increasing Z eff . The experimental results disagree by two orders of magnitude with predictions from an ion temperature gradient driven turbulence model. (author) 6 refs., 3 figs
Adam, A. M. A.; Bashier, E. B. M.; Hashim, M. H. A.; Patidar, K. C.
2017-07-01
In this work, we design and analyze a fitted numerical method to solve a reaction-diffusion model with time delay, namely, a delayed version of a population model which is an extension of the logistic growth (LG) equation for a food-limited population proposed by Smith [F.E. Smith, Population dynamics in Daphnia magna and a new model for population growth, Ecology 44 (1963) 651-663]. Seeing that the analytical solution (in closed form) is hard to obtain, we seek for a robust numerical method. The method consists of a Fourier-pseudospectral semi-discretization in space and a fitted operator implicit-explicit scheme in temporal direction. The proposed method is analyzed for convergence and we found that it is unconditionally stable. Illustrative numerical results will be presented at the conference.
The limitation and modification of flux-limited diffusion theory
International Nuclear Information System (INIS)
Liu Chengan; Huang Wenkai
1986-01-01
The limitation of various typical flux-limited diffusion theory and advantages of asymptotic diffusion theory with time absorption constant are analyzed and compared. The conclusions are as following: Though the flux-limited problem in neutron diffusion theory are theoretically solved by derived flux-limited diffusion equation, it's going too far to limit flux due to the inappropriate assumption in deriving flux-limited diffusion equation. The asymptotic diffusion theory with time absorption constant has eliminated the above-mentioned limitation, and it is more accurate than flux-limited diffusion theory in describing neutron transport problem
Hamming method for solving the delayed neutron precursor concentration for reactivity calculation
International Nuclear Information System (INIS)
Díaz, Daniel Suescún; Ospina, Juan Felipe Flórez; Sarasty, Jesús Andrés Rodríguez
2012-01-01
Highlights: ► We present a new formulation to calculate the reactivity using the Hamming method. ► This method shows better accuracy than existing methods for reactivity calculation. ► The reactivity is calculated without limitation of the nuclear power form. ► The method can be implemented in reactivity meters with time step of up to 0.1 s. - Abstract: We propose a new method for numerically solving the inverse point kinetic equation for a nuclear reactor using the Hamming method, without requiring the nuclear power history and without using the Laplace transform. This new method converges with accuracy of order h 5 , where h is the step in the computation time. The procedure is validated for different forms of the nuclear power and with different time steps. The results indicate that this method has a better accuracy and lower computational effort compared with other conventional methods that use the nuclear power history.
Energy Technology Data Exchange (ETDEWEB)
Wu Hongchun [Nuclear Engineering Department, Xi' an Jiaotong University, Xi' an 710049, Shaanxi (China)]. E-mail: hongchun@mail.xjtu.edu.cn; Liu Pingping [Nuclear Engineering Department, Xi' an Jiaotong University, Xi' an 710049, Shaanxi (China); Zhou Yongqiang [Nuclear Engineering Department, Xi' an Jiaotong University, Xi' an 710049, Shaanxi (China); Cao Liangzhi [Nuclear Engineering Department, Xi' an Jiaotong University, Xi' an 710049, Shaanxi (China)
2007-01-15
In the advanced reactor, the fuel assembly or core with unstructured geometry is frequently used and for calculating its fuel assembly, the transmission probability method (TPM) has been used widely. However, the rectangle or hexagon meshes are mainly used in the TPM codes for the normal core structure. The triangle meshes are most useful for expressing the complicated unstructured geometry. Even though finite element method and Monte Carlo method is very good at solving unstructured geometry problem, they are very time consuming. So we developed the TPM code based on the triangle meshes. The TPM code based on the triangle meshes was applied to the hybrid fuel geometry, and compared with the results of the MCNP code and other codes. The results of comparison were consistent with each other. The TPM with triangle meshes would thus be expected to be able to apply to the two-dimensional arbitrary fuel assembly.
International Nuclear Information System (INIS)
Cvikl, B.; Dahlborg, U.; Calvo-Dahlborg, M.
1999-01-01
Based upon the model of particles diffusion within the sphere of partially absorbing boundaries, the possibilities of the detection, by the incoherent cold neutron scattering method, of particle precipitation on the boundary walls, has been investigated. The calculated scattering law as a function of the boundary absorption properties exhibits distinct characteristic which might, under favorable conditions, make such an experimental attempt feasible.(author)
International Nuclear Information System (INIS)
Modak, R.S.; Sahni, D.C.
1996-01-01
Some simple reciprocity-like relations that exist in multi-group neutron diffusion and transport theory over bare homogeneous regions are presented. These relations do not involve the adjoint solutions and are directly related to numerical schemes based on an explicit evaluation of the fission matrix. (author)
A method of precise profile analysis of diffuse scattering for the KENS pulsed neutrons
International Nuclear Information System (INIS)
Todate, Y.; Fukumura, T.; Fukazawa, H.
2001-01-01
An outline of our profile analysis method, which is now of practical use for the asymmetric KENS pulsed thermal neutrons, are presented. The analysis of the diffuse scattering from a single crystal of D 2 O is shown as an example. The pulse shape function is based on the Ikeda-Carpenter function adjusted for the KENS neutron pulses. The convoluted intensity is calculated by a Monte-Carlo method and the precision of the calculation is controlled. Fitting parameters in the model cross section can be determined by the built-in nonlinear least square fitting procedure. Because this method is the natural extension of the procedure conventionally used for the triple-axis data, it is easy to apply with generality and versatility. Most importantly, furthermore, this method has capability of precise correction of the time shift of the observed peak position which is inevitably caused in the case of highly asymmetric pulses and broad scattering function. It will be pointed out that the accurate determination of true time-of-flight is important especially in the single crystal inelastic experiments. (author)
International Nuclear Information System (INIS)
Ching, J.; Oblow, E.M.; Goldstein, H.
1976-01-01
An algebraic equivalence between the point-energy and multigroup forms of the Boltzmann transport equation is demonstrated that allows the development of a discrete energy, discrete ordinates method for the solution of radiation transport problems. In the discrete energy method, the group averaging required in the cross-section processing for multigroup calculations is replaced by a faster numerical quadrature scheme capable of generating transfer cross sections describing all the physical processes of interest on a fine point-energy grid. Test calculations in which the discrete energy method is compared with the multigroup method show that, for the same energy grid, the discrete energy method is much faster, although somewhat less accurate, than the multigroup method. However, the accuracy of the discrete energy method increases rapidly as the spacing between energy grid points is decreased, approaching that of multigroup calculations. For problems requiring great detail in the energy spectrum, the discrete energy method is therefore expected to be far more economical than the multigroup technique for equivalent accuracy solutions. This advantage of the point method is demonstrated by application to the study of neutron transport in a thick iron slab
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
International Nuclear Information System (INIS)
Schaefer, A.
1979-02-01
A new code for efficient solution of the multidimensional stationary multi-group, diffusion equation, to be used within a HTGR-code model, is presented. The approximation and iteration methods are described. Spacial approximation is based on the QUABOX-coarse-mesh method, but iteration methods are different from QUABOX to give linear dependence of computation time on the number of energy groups. Results for various multidimensional multi-group problems, among them the THTR pebble bed reactor are analyzed. It is shown, that computational labor for a 3D-case is reduced by about a factor 30 in comparison with conventional finite-difference-methods. Thus 3D-full-core calculations appear to be feasible for large HTGR's. (orig.) [de
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
International Nuclear Information System (INIS)
Chang, Jonghwa
2014-01-01
Today, we can use a computer cluster consist of a few hundreds CPUs with reasonable budget. Such computer system enables us to do detailed modeling of reactor core. The detailed modeling will improve the safety and the economics of a nuclear reactor by eliminating un-necessary conservatism or missing consideration. To take advantage of such a cluster computer, efficient parallel algorithms must be developed. Mechanical structure analysis community has studied the domain decomposition method to solve the stress-strain equation using the finite element methods. One of the most successful domain decomposition method in terms of robustness is FETI-DP. We have modified the original FETI-DP to solve the eigenvalue problem for the multi-group diffusion problem in previous study. In this study, we report the result of recent modification to handle the three-dimensional subdomain partitioning, and the sub-domain multi-group problem. Modified FETI-DP algorithm has been successfully applied for the eigenvalue problem of multi-group neutron diffusion equation. The overall CPU time is decreasing as number of sub-domains (partitions) is increasing. However, there may be a limit in decrement due to increment of the number of primal points will increase the CPU time spent by the solution of the global equation. Even distribution of computational load (criterion a) is important to achieve fast computation. The subdomain partition can be effectively performed using suitable graph theory partition package such as MeTIS
Energy Technology Data Exchange (ETDEWEB)
Chang, Jonghwa [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2014-10-15
Today, we can use a computer cluster consist of a few hundreds CPUs with reasonable budget. Such computer system enables us to do detailed modeling of reactor core. The detailed modeling will improve the safety and the economics of a nuclear reactor by eliminating un-necessary conservatism or missing consideration. To take advantage of such a cluster computer, efficient parallel algorithms must be developed. Mechanical structure analysis community has studied the domain decomposition method to solve the stress-strain equation using the finite element methods. One of the most successful domain decomposition method in terms of robustness is FETI-DP. We have modified the original FETI-DP to solve the eigenvalue problem for the multi-group diffusion problem in previous study. In this study, we report the result of recent modification to handle the three-dimensional subdomain partitioning, and the sub-domain multi-group problem. Modified FETI-DP algorithm has been successfully applied for the eigenvalue problem of multi-group neutron diffusion equation. The overall CPU time is decreasing as number of sub-domains (partitions) is increasing. However, there may be a limit in decrement due to increment of the number of primal points will increase the CPU time spent by the solution of the global equation. Even distribution of computational load (criterion a) is important to achieve fast computation. The subdomain partition can be effectively performed using suitable graph theory partition package such as MeTIS.
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
Water diffusion through compacted clays analyzed by neutron scattering and tracer experiments
International Nuclear Information System (INIS)
Gonzalez Sanchez, F.
2007-11-01
/cm 3 , in order to reduce the pore sizes and to better study the dynamic properties of water close to the water-clay interface. We compared the water dynamics in fully hydrated compacted clays, at two significantly different time-space scales, in an attempt to distinguish the relevant features of the water transport. A fundamental microscopic investigation, tracing down to the atomic level was carried out, by neutron scattering, using time-of-flight and backscattering techniques. A classical macroscopic study was performed by using tracer through-diffusion methods. At the macroscopic level (time/spatial scale of about hours/mm to cm) the water diffusion depends strongly on the clay pore size and arrangement of the particles. However, at the microscopic level (time/spatial scale of about ten to hundred picosecond/10 -8 cm) the diffusion is governed by the local environment, which concerns to cations and clay surfaces and less to the particle arrangement. For a further understanding of this local environment, the water diffusion in clays was also measured at different hydration states, to vary the fraction of interlayer or external layer water, as compared to free pore water. The large difference in the diffusion paths of the two selected techniques makes a direct comparison of water diffusivities impossible. Therefore, two possibilities were established: An indirect comparison by connecting the results for diffusion coefficient at the two different scales through pure geometrical and electrostatic factors; and a direct comparison through the activation energy E a which was estimated from the dependence of the diffusion coefficients on the temperature. In contrast to the macroscopic diffusion coefficients, the activation energy is probably less influenced by geometrical factors and more by microscopic interactions, and thus could possibly be directly compared at the two different scales. The research was accomplished by a detailed characterization of the clay samples
Water diffusion through compacted clays analyzed by neutron scattering and tracer experiments
Energy Technology Data Exchange (ETDEWEB)
Gonzalez Sanchez, F
2007-11-15
/cm{sup 3}, in order to reduce the pore sizes and to better study the dynamic properties of water close to the water-clay interface. We compared the water dynamics in fully hydrated compacted clays, at two significantly different time-space scales, in an attempt to distinguish the relevant features of the water transport. A fundamental microscopic investigation, tracing down to the atomic level was carried out, by neutron scattering, using time-of-flight and backscattering techniques. A classical macroscopic study was performed by using tracer through-diffusion methods. At the macroscopic level (time/spatial scale of about hours/mm to cm) the water diffusion depends strongly on the clay pore size and arrangement of the particles. However, at the microscopic level (time/spatial scale of about ten to hundred picosecond/10{sup -8} cm) the diffusion is governed by the local environment, which concerns to cations and clay surfaces and less to the particle arrangement. For a further understanding of this local environment, the water diffusion in clays was also measured at different hydration states, to vary the fraction of interlayer or external layer water, as compared to free pore water. The large difference in the diffusion paths of the two selected techniques makes a direct comparison of water diffusivities impossible. Therefore, two possibilities were established: An indirect comparison by connecting the results for diffusion coefficient at the two different scales through pure geometrical and electrostatic factors; and a direct comparison through the activation energy E{sub a} which was estimated from the dependence of the diffusion coefficients on the temperature. In contrast to the macroscopic diffusion coefficients, the activation energy is probably less influenced by geometrical factors and more by microscopic interactions, and thus could possibly be directly compared at the two different scales. The research was accomplished by a detailed characterization of the clay
International Nuclear Information System (INIS)
Couto, Nozimar do
2003-01-01
Diffusion theory is traditionally applied to nuclear reactor global calculations. Based on the good results generated by the one-dimensional spectral nodal diffusion (SND) method for benchmark problems, we offer the SND method for nuclear reactor global calculations in X,Y geometry. In this method, the continuity equation and Flick law are transverse integrated in each spatial direction leading to a system of two 'one-dimensional' equations coupled by the transverse leakage terms. We then apply the SND method to numerically solve this system with constant approximations for the transverse leakage terms. We perform a spectral analysis to determine the local general solution of each 'one-dimensional' nodal equation with flat approximation for the transverse leakages. We used special auxiliary equations with parameters that are to be determined in order to preserve the analytical general solutions in the numerical algorithm. By considering continuity conditions at the node interfaces and appropriate boundary conditions, we obtain a solvable system of discretized equations involving the node-edge average scalar fluxes at each estimate of the dominant eigenvalue (k eff ) in the outer power iterations. As we considered approximations to the transverse leakages, the SND method is not free of spatial truncation errors. Nevertheless, it generated good results for the typical model problems that we considered. (author)
International Nuclear Information System (INIS)
Fournier, D.; Le Tellier, R.; Suteau, C.; Herbin, R.
2011-01-01
The solution of the time-independent neutron transport equation in a deterministic way invariably consists in the successive discretization of the three variables: energy, angle and space. In the SNATCH solver used in this study, the energy and the angle are respectively discretized with a multigroup approach and the discrete ordinate method. A set of spatial coupled transport equations is obtained and solved using the Discontinuous Galerkin Finite Element Method (DGFEM). Within this method, the spatial domain is decomposed into elements and the solution is approximated by a hierarchical polynomial basis in each one. This approach is time and memory consuming when the mesh becomes fine or the basis order high. To improve the computational time and the memory footprint, adaptive algorithms are proposed. These algorithms are based on an error estimation in each cell. If the error is important in a given region, the mesh has to be refined (h−refinement) or the polynomial basis order increased (p−refinement). This paper is related to the choice between the two types of refinement. Two ways to estimate the error are compared on different benchmarks. Analyzing the differences, a hp−refinement method is proposed and tested. (author)
International Nuclear Information System (INIS)
Ozgener, B.; Azgener, H.A.
1991-01-01
In finite element formulations for the solution of the within-group neutron diffusion equation, two different treatments are possible for the group source term: the consistent source approximation (CSA) and the lumped source approximation (LSA). CSA results in intra-group scattering and fission matrices which have the same nondiagonal structure as the global coefficient matrix. This situation might be regarded as a disadvantage, compared to the conventional (i.e. finite difference) methods where the intra-group scattering and fission matrices are diagonal. To overcome this disadvantage, LSA could be used to diagonalize these matrices. LSA is akin to the lumped mass approximation of continuum mechanics. We concentrate on two different aspects of the source approximations. Although it has been reported that LSA does not modify the asymptotic h 2 convergence behaviour for linear elements, the effect of LSA on convergence of higher degree elements has not been investigated. Thus, we would be interested in determining, p, the asymptotic order of convergence, in: Δk |k eff (analytical) -k eff (finite element)| = Ch p (1) for finite element approximations of varying degree (N) with both of the source approximations. Since (1) is valid in the asymptotic limit, we must use ultra-fine meshes and quadruple precision arithmetic. For our order of convergence study, we used infinite cylindrical geometry with azimuthal symmetry. Hence, the effects of singularities remain uninvestigated. The second aspect we dwell on is the performance of LSA in bilinear 3-D finite element calculations, compared to CSA. LSA has been used quite extensively in 1- and 2-D even-parity transport and diffusion calculations. In this work, we will try to assess the relative merits of LSA and CSA in 3-D problems. (author)
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
International Nuclear Information System (INIS)
Kubaschewski, O.
1983-01-01
The diffusion rate values of titanium, its compounds and alloys are summarized and tabulated. The individual chemical diffusion coefficients and self-diffusion coefficients of certain isotopes are given. Experimental methods are listed which were used for the determination of diffusion coefficients. Some values have been taken over from other studies. Also given are graphs showing the temperature dependences of diffusion and changes in the diffusion coefficient with concentration changes
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)
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
International Nuclear Information System (INIS)
Priem, Thierry
1988-01-01
Short-range order in non-stoichiometric transition metal carbides and nitrides (TiN 0.82 , TiC 0.64 , TiC 0.76 , NbC 0.73 and NbC 0.83 ) was investigated by thermal neutron diffuse scattering on G4-4 (L.L.B - Saclay) and D10 (I.L.L. Grenoble) spectrometers. From experimental measurements, we have found that metalloid vacancies (carbon or nitrogen) prefer the f.c.c. third neighbour positions. Ordering interaction energies were calculated within the Ising model framework by three approximations: mean field (Clapp and Moss formula), Monte-Carlo simulation, Cluster variation Method. The energies obtained by the two latter methods are very close, and in qualitative agreement with theoretical values calculated from the band structure. Theoretical phase diagrams were calculated from these ordering energies for TiN x and TiC x ; three ordered structures were predicted, corresponding to compositions Ti 6 N 5 Ti 2 C and Ti 3 C 2 . On the other hand, atomic displacements are induced by vacancies. The metal first neighbours were found to move away from a vacancy, whereas the second neighbours move close to it. Near neighbour atomic displacements were theoretically determined by the lattice statics formalism with results in good agreement with experiment. (author) [fr
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)); Adam, 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)
1992-01-01
Spatial profiles of neutron emission are routinely obtained at the Joint European Torus (JET) from line-integrated emissivities measured with a multi-channel instrument. It is shown that the manner in which the emission profiles relax following 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%. The radial profiles of [chi][sub i] for small minor radius (r/a < 0.6) were found to be flat and to take values between 0.3 and 1.1 m[sup 2]/s for H-mode plasmas with plasma current I[sub p] = 3.1 MA and toroidal field B[sub T] = 2.3T. The experimental value of [chi][sub i] is smallest for Z[sub eff] = 2.2 and increases weakly with increasing Z[sub eff]. The experimental results disagree by two orders of magnitude with predictions from an ion temperature gradient driven turbulence model. (author) 6 refs., 3 figs.
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
Can a large neutron excess help solve the baryon loading problem in gamma-Ray burst fireballs?
Fuller; Pruet; Abazajian
2000-09-25
We point out that the baryon loading problem in gamma-ray burst (GRB) models can be ameliorated if a significant fraction of the baryons which inertially confine the fireball is converted to neutrons. A high neutron fraction can result in a reduced transfer of energy from relativistic light particles in the fireball to baryons. The energy needed to produce the required relativistic flow in the GRB is consequently reduced, in some cases by orders of magnitude. A high neutron-to-proton ratio has been calculated in neutron star-merger fireball environments. Significant neutron excess also could occur near compact objects with high neutrino fluxes.
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.
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
Energy Technology Data Exchange (ETDEWEB)
Nguyen-Ngoc, H [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1969-07-01
In order to reduce computing time, two and three-dimensional multigroup neutron diffusion equations in cylindrical, rectangular (X, Y), (X, Y, Z) and hexagonal geometries are solved by the method of synthesis using an appropriate variational principle (stationary principle). The basic idea is to reduce the number of independent variables by constructing two or three-dimensional solutions from solutions of fewer variables, hence the name 'synthesis method'. Whatever the geometry, we are led to solve a system of ordinary differential equations with matrix coefficients to which one can apply well-known numerical methods: CHEBYSHEV's polynomial method, Gaussian elimination. Numerical results furnished by synthesis programs written for the IBM 7094, the IBM 360-75 and the CDC 6600 computers, are confronted with those which are given by programs employing the classical finite difference method. [French] En vue de reduire le-temps de calcul, les equations de diffusion neutronique, multigroupe, a deux et trois dimensions d'espace dans les geometries cylindrique, rectangulaire (X, Y), (X, Y, Z) et hexagonale sont resolues par la methode de synthese utilisant un principe variationnel approprie (principe stationnaire). L'idee consiste a reduire le nombre de variables independantes par construction d'une solution bi ou tridimensionnelle au moyen de solutions dependant d'un nombre inferieur de variables, d'ou le nom de la methode. Dans tous les cas de geometrie, nous sommes conduits a resoudre un systeme d'equations differentielles a coefficients matriciels auquel peuvent s'appliquer les methodes numeriques courantes; methode polynomiale de TCHEBYCHEFF et methode d'elimination de GAUSS. Les resultats numeriques obtenus par nos codes de synthese programmes sur IBM 7094, IBM 360-75 et CDC 6600, sont confrontes avec ceux que fournissent les programmes adoptant la methode classique des differences finies. (auteur)
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)
Energy Technology Data Exchange (ETDEWEB)
Raievski, V; Horowitz, J [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1955-07-01
The further method is the outcome of a technique used in the study of neutrons in scattering and slowing-down environment. In this technique, we replace the constant sources used in the classic experiences by modulated sources with a variable frequency. The object of this article is to describe the extension of the method for the mean free path for transport of thermal neutrons and also to indicate the possible applications for other sizes, as the slowing length, or the absolute value of the cross-section of the boron. (M.B.) [French] La methode qui va etre decrite est l'aboutissement d'une technique utilisee dans l'etude des milieux ou diffusent et se ralentissent des neutrons. Dans cette technique, on remplace les sources constantes utilisees dans les experiences classiques par des sources modulees, a frequence variable. L'objet de cet article est de decrire l'extension de la methode a la mesure du libre parcours moyen de transport des neutrons thermiques et egalement d'indiquer les applications possibles a la mesure d'autres grandeurs, telles que la longueur de ralentissement, ou la valeur absolue de la section de capture du bore. (M.B.)
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
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
International Nuclear Information System (INIS)
Cacuci, D.G.; Univ. of Karlsruhe; Kiefhaber, E.; Stehle, B.
1998-01-01
The explicit solution developed by Cacuci for the multigroup neutron diffusion equation at interior corners in two-dimensional two-region domains has been applied to the SNR-300 fast reactor prototype design to obtain the exact behavior of the multigroup fluxes at and around typical corners arising between absorber/fuel and follower/fuel assemblies. The calculations have been performed in hexagonal geometry using four energy groups, and the results clearly show that the multigroup fluxes are finite but not analytical at interior corners. In particular, already the first-order spatial derivatives of the multigroup fluxes become unbounded at the corners between follower and fuel assemblies. These results highlight the need to treat properly the influence of corners, both for the direct calculation and for the reconstruction of pointwise neutron flux and power distributions in heterogeneous reactor cores
International Nuclear Information System (INIS)
Costa, Danilo Leite
2013-01-01
This work aims to present a study about the power distribution behavior in a PWR type reactor, considering both intensity and migration of power peaks due to insertion of control rods into the core. Employing the multidimensional steady-state neutron diffusion equation in order to simulate the neutron flux, and using the Finite Difference Method. Furthermore, based on the axial power distribution on the largest heat flux rod, is carried out thermal analysis of this rod and associated coolant channel. For this purpose is employed the FueLRod 3 D code, it uses the Finite Element Method to model the fuel rod and the associated coolant channel, allowing the thermohydraulics simulation of a single rod discretized in three dimensions, considering the heat flux from the pellet, crossing the gap and the cladding until it reaches the coolant. (author)
Energy Technology Data Exchange (ETDEWEB)
Golikov, V V; Shapiro, F L; Shkatula, A; Yanik, E A [Ob' edinennyj institut yadernykh issledovanij, Dubna, Union of Soviet Socialist Republics (Russian Federation)
1963-01-15
Using the pulsed fut reactor in the Joint Institute for Nuclear Research, an installation was set up to investigate the spectrometry of cold neutrons. The moderator, adjoining the reactor reflector, and the beryllium filter were at the temperature of liquid nitrogen. The scatterer, located at a distance of about 0. 6 m from the moderator, was irradiated by flashes of cold neutrons, whose duration was determined by the lifetime of the neutrons in the moderator and the dispersion of the times-of-flight over a distance of 0. 6 m. The frequency of the flashes was 8/s. The steep beryllium edge of the spectrum, lying around 200 {mu}s, was used for spectrometry in the quasi-elastic range. The energy of the scattered neutrons was determined by the time-of-flight over the distance between scatterer and detector, which was about 10-40 m. ZnS + 10{sub 2}{sup 10} O{sub 3} scintillation detectors with surfaces of 300 and 2 000 cm{sup 2} were used and the efficiency, for fast neutrons, was about 60%. (author) [French] A l'aide du reacteur a flux pulse de neutrons rapides de l'Institut unifie de recherches nucleaires, les auteurs ont mis au point une installation pour la spectrometrie des neutrons thermiques. Le ralentisseur contigu au reflecteur du reacteur et le filtre deberyllium sont maintenus a la temperature de l'azote liquide. Le diffuseur, place a environ 60 cm du ralentisseur, est irradie par une bouffee de neutrons thermiques dont la duree est determinee par la vie moyenne des neutrons dans le ralentisseur et par l'etalement des temps de vol necessaires pour parcourir la distance de 60 cm. La frequence des bouffees est de 8/s. Pour la spectrometrie dans la region quasi-elastique, on utilise la bande en bordure du spectre qui correspond au beryllium et s'etale sur environ 200 {mu}s. L'energie des neutrons diffuses est determinee par la duree du parcours entre le diffuseur et le detecteur. Les auteurs ont utilise des detecteurs a scintillation a ZnS + 10{sub 2}{sup 10} O
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
DEFF Research Database (Denmark)
Hansen, Flemming Yssing; Criswell, L.; Fuhrmann, D
2004-01-01
Molecular dynamics simulations of a tetracosane (n-C24H50) monolayer adsorbed on a graphite basal-plane surface show that there are diffusive motions associated with the creation and annihilation of gauche defects occurring on a time scale of similar to0.1-4 ns. We present evidence...... that these relatively slow motions are observable by high-energy-resolution quasielastic neutron scattering (QNS) thus demonstrating QNS as a technique, complementary to nuclear magnetic resonance, for studying conformational dynamics on a nanosecond time scale in molecular monolayers....
Schaefer, P W
2000-10-01
This article addresses syndromes that clinically and/or radiologically resemble acute stroke. These syndromes generally fall into four categories. (1) Patients with acute neurological deficits with nonischemic lesions and no acute abnormality on diffusion-weighted images. These patients may have peripheral vertigo, migraines, seizures, dementia, functional disorders, amyloid angiopathy, or metabolic disorders. When these patients present, we can confidently predict that they are not undergoing infarction. (2) Patients with ischemic lesions with reversible clinical deficits. Nearly 50% of patients with transient ischemic attacks have lesions with restricted diffusion. Patients with transient global amnesia may have punctate lesions with restricted diffusion in the medial hippocampus, parahippocampal gyms, and corpus callosum. (3) Vasogenic edema syndromes that may mimic acute infarction clinically and on conventional imaging. These include eclampsia/hypertensive encephalopathy, other posterior leukoencephalopathies, human immunodeficiency virus encephalopathy, hyperperfusion syndrome following carotid endarterectomy, venous sinus thrombosis, acute demyelination, and neoplasm. These syndromes demonstrate elevated diffusion rather than the restricted diffusion associated with acute ischemic stroke. (4) Entities in which restricted diffusion may resemble acute infarction. These include pyogenic infections, herpes virus encephalitis, Creutzfeldt-Jakob disease, diffuse axonal injury, tumors with dense cell packing, and rare acute demyelinative lesions.
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
Neutron Diffusion in a Space Lattice of Fissionable and Absorbing Materials
Feynman, R. P.; Welton, T. A.
1946-08-27
Methods are developed for estimating the effect on a critical assembly of fabricating it as a lattice rather than in the more simply interpreted homogeneous manner. An idealized case is discussed supposing an infinite medium in which fission, elastic scattering and absorption can occur, neutrons of only one velocity present, and the neutron m.f.p. independent of position and equal to unity with the unit of length used.
Boron Neutron Capture Therapy activity of diffused tumors at TRIGA Mark II in Pavia
Energy Technology Data Exchange (ETDEWEB)
Bortolussi, S.; Stella, S.; De Bari, A.; Altieri, S. [Department of Nuclear and Theoretical Physics, University of Pavia, Pavia (Italy)]|[National Institute of Nuclear Physics (INFN), Pavia (Italy); Bruschi, P.; Bakeine, J.G. [Department of Nuclear and Theoretical Physics, University of Pavia, Pavia (Italy); Clerici, A.; Ferrari, C.; Zonta, C.; Zonta, A. [Department of Surgery, University of Pavia, Pavia (Italy); Nano, R. [Department of Animal Biology, University of Pavia, Pavia (Italy)
2008-10-29
The Boron neutron Capture Therapy research in Pavia has a long tradition: it begun more than 20 years ago at the TRIGA Mark II reactor of the University. A technique for the treatment of the hepatic metastases was developed, consisting in explanting the liver treated with {sup 10}B, irradiating it in the thermal column of the reactor, and re-implanting the organ in the patient. In the last years, the possibility of applying BNCT to the lung tumours using epithermal collimated neutron beams and without explanting the organ, is being explored. The principal obtained results of the BNCT research will be presented, with particular emphasis on the following aspects: a) the project of a new thermal column configuration to make the thermal neutron flux more uniform inside the explanted liver, b) the Monte Carlo study by means of the MCNP code of the thermal neutron flux distribution inside a patient's thorax irradiated with epithermal neutrons, and c) the measurement of the boron concentration in tissues by (n,{alpha}) spectroscopy and neutron autoradiography. (authors)
Boron Neutron Capture Therapy activity of diffused tumors at TRIGA Mark II in Pavia
International Nuclear Information System (INIS)
Bortolussi, S.; Stella, S.; De Bari, A.; Altieri, S.; Bruschi, P.; Bakeine, J.G.; Clerici, A.; Ferrari, C.; Zonta, C.; Zonta, A.; Nano, R.
2008-01-01
The Boron neutron Capture Therapy research in Pavia has a long tradition: it begun more than 20 years ago at the TRIGA Mark II reactor of the University. A technique for the treatment of the hepatic metastases was developed, consisting in explanting the liver treated with 10 B, irradiating it in the thermal column of the reactor, and re-implanting the organ in the patient. In the last years, the possibility of applying BNCT to the lung tumours using epithermal collimated neutron beams and without explanting the organ, is being explored. The principal obtained results of the BNCT research will be presented, with particular emphasis on the following aspects: a) the project of a new thermal column configuration to make the thermal neutron flux more uniform inside the explanted liver, b) the Monte Carlo study by means of the MCNP code of the thermal neutron flux distribution inside a patient's thorax irradiated with epithermal neutrons, and c) the measurement of the boron concentration in tissues by (n,α) spectroscopy and neutron autoradiography. (authors)
Energy Technology Data Exchange (ETDEWEB)
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)
International Nuclear Information System (INIS)
Tsuji, Masashi; Chiba, Gou
2000-01-01
A hierarchical domain decomposition boundary element method (HDD-BEM) for solving the multiregion neutron diffusion equation (NDE) has been fully parallelized, both for numerical computations and for data communications, to accomplish a high parallel efficiency on distributed memory message passing parallel computers. Data exchanges between node processors that are repeated during iteration processes of HDD-BEM are implemented, without any intervention of the host processor that was used to supervise parallel processing in the conventional parallelized HDD-BEM (P-HDD-BEM). Thus, the parallel processing can be executed with only cooperative operations of node processors. The communication overhead was even the dominant time consuming part in the conventional P-HDD-BEM, and the parallelization efficiency decreased steeply with the increase of the number of processors. With the parallel data communication, the efficiency is affected only by the number of boundary elements assigned to decomposed subregions, and the communication overhead can be drastically reduced. This feature can be particularly advantageous in the analysis of three-dimensional problems where a large number of processors are required. The proposed P-HDD-BEM offers a promising solution to the deterioration problem of parallel efficiency and opens a new path to parallel computations of NDEs on distributed memory message passing parallel computers. (author)
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
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
International Nuclear Information System (INIS)
Nemkovski, K; Ioffe, A; Su, Y; Babcock, E; Schweika, W; Brückel, Th
2017-01-01
We present the concept and the results of the simulations of a new polarizer for the diffuse neutron scattering spectrometer DNS at MLZ. The concept of the polarizer is based on the idea of a bender made from the stack of the silicon wafers with a double-side supermirror polarizing coating and absorbing spacers in between. Owing to its compact design, such a system provides more free space for the arrangement of other instrument components. To reduce activation of the polarizer in the high intensity neutron beam of the DNS spectrometer we plan to use the Fe/Si supermirrors instead of currently used FeCoV/Ti:N ones. Using the VITESS simulation package we have performed simulations for horizontally focusing polarizing benders with different geometries in the combination with the double-focusing crystal monochromator of DNS. Neutron transmission and polarization efficiency as well as the effects of the focusing for convergent conventional C-benders and S-benders have been analyzed both for wedge-like and plane-parallel convergent geometries of the channels. The results of these simulations and the advantages/disadvantages of the various configurations are discussed. (paper)
Nemkovski, K.; Ioffe, A.; Su, Y.; Babcock, E.; Schweika, W.; Brückel, Th
2017-06-01
We present the concept and the results of the simulations of a new polarizer for the diffuse neutron scattering spectrometer DNS at MLZ. The concept of the polarizer is based on the idea of a bender made from the stack of the silicon wafers with a double-side supermirror polarizing coating and absorbing spacers in between. Owing to its compact design, such a system provides more free space for the arrangement of other instrument components. To reduce activation of the polarizer in the high intensity neutron beam of the DNS spectrometer we plan to use the Fe/Si supermirrors instead of currently used FeCoV/Ti:N ones. Using the VITESS simulation package we have performed simulations for horizontally focusing polarizing benders with different geometries in the combination with the double-focusing crystal monochromator of DNS. Neutron transmission and polarization efficiency as well as the effects of the focusing for convergent conventional C-benders and S-benders have been analyzed both for wedge-like and plane-parallel convergent geometries of the channels. The results of these simulations and the advantages/disadvantages of the various configurations are discussed.
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.
Energy Technology Data Exchange (ETDEWEB)
Askew, J R; Brissenden, R J [Technical Assessments and Services Division, Atomic Energy Establishment, Winfrith, Dorchester, Dorset (United Kingdom)
1963-08-15
This report gives an account of the DSN method for simulating neutron transport, together with methods of solution developed to deal with problems in the physics of thermal reactors, for which previously available computer programmes were unsatisfactory. The methods described are those incorporated in the programmes WINFRITH DSN written in FORTRAN language for the IBM 7090 and STRETCH computers. (author)
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
International Nuclear Information System (INIS)
Jagannathan, V.
1985-01-01
A modular computer code system called FEMSYN has been developed to solve the multigroup diffusion theory equations. The various methods that are incorporated in FEMSYN are (i) finite difference method (FDM) (ii) finite element method (FEM) and (iii) single channel flux synthesis method (SCFS). These methods are described in detail in parts II, III and IV of the present report. In this report, a comparison of the accuracy and the speed of different methods of solution for some benchmark problems are reported. The input preparation and listing of sample input and output are included in the Appendices. The code FEMSYN has been used to solve a wide variety of reactor core problems. It can be used for both LWR and PHWR applications. (author)
Directory of Open Access Journals (Sweden)
Mohammad Siddique
2010-08-01
Full Text Available Parabolic partial differential equations with nonlocal boundary conditions arise in modeling of a wide range of important application areas such as chemical diffusion, thermoelasticity, heat conduction process, control theory and medicine science. In this paper, we present the implementation of positivity- preserving Padé numerical schemes to the two-dimensional diffusion equation with nonlocal time dependent boundary condition. We successfully implemented these numerical schemes for both Homogeneous and Inhomogeneous cases. The numerical results show that these Padé approximation based numerical schemes are quite accurate and easily implemented.
ARGO, 1-D Neutron Diffusion in Slab, Cylindrical, Spherical Geometry from JAERI Fast-Set, ABBN, RCBN
International Nuclear Information System (INIS)
Ikawa, Koji
1971-01-01
1 - Nature of physical problem solved: ARGO is a one-dimensional (slab, cylinder or sphere), multigroup diffusion code for use in fast reactor criticality and kinetic parameter analysis. Three cross section sets, i.e., JAERI-Fast-Set, ABBN-Set and RCBN-Set, of 25 groups are prepared for the code as its library tapes. 2 - Method of solution: Eigenvalues are computed by ordinary source-iteration techniques with ordinary acceleration methods for convergence. 3 - Restrictions on the complexity of the problem: Sphere geometry
Energy Technology Data Exchange (ETDEWEB)
Ott, F
1998-11-26
Theoretical (Zeeman energy effects) and experimental (beam polarisation problems) progress have been made in the understanding of polarized neutron reflectivity with polarisation analysis. It has been shown that modelization and numerical simulations makes it possible to avoid to have to systematically measure a full set of reflectivity curves for each field and temperature condition. It has been possible to determine a magnetic profile as a function of the field in a magnetic bilayer system by using only a few points in the reciprocal space. This technique allows to considerable reduce the experiment time. In single nickel layer systems, we have shown that it is possible to induce magnetic rotation inhomogeneities when these systems are subjects to deformation strains. The effect are related to magneto-elastic constants gradients. In trilayer systems, with a ME constant modulation, we have been able to induce large magnetic rotation gradients. A new magneto-optic technique to measure the magnetization direction without rotating the magnetic field has been developed. The field of neutron reflectivity has been extended to off-specular studies. It has been possible to account quantitatively of the off-specular diffusion on 2-D model systems (prepared by optical lithography). This new technique should make it possible in the future to determine magnetic structures with a in-depth as well as lateral resolution. (author)
Directory of Open Access Journals (Sweden)
Md. Nur Alam
2016-06-01
Full Text Available In this article, we apply the exp(-Φ(ξ-expansion method to construct many families of exact solutions of nonlinear evolution equations (NLEEs via the nonlinear diffusive predator–prey system and the Bogoyavlenskii equations. These equations can be transformed to nonlinear ordinary differential equations. As a result, some new exact solutions are obtained through the hyperbolic function, the trigonometric function, the exponential functions and the rational forms. If the parameters take specific values, then the solitary waves are derived from the traveling waves. Also, we draw 2D and 3D graphics of exact solutions for the special diffusive predator–prey system and the Bogoyavlenskii equations by the help of programming language Maple.
3-D Deep Penetration Neutron Imaging of Thick Absorgin and Diffusive Objects Using Transport Theory
Energy Technology Data Exchange (ETDEWEB)
Ragusa, Jean; Bangerth, Wolfgang
2011-08-01
here explores the inverse problem of optical tomography applied to heterogeneous domains. The neutral particle transport equation was used as the forward model for how neutral particles stream through and interact within these heterogeneous domains. A constrained optimization technique that uses Newtons method served as the basis of the inverse problem. Optical tomography aims at reconstructing the material properties using (a) illuminating sources and (b) detector readings. However, accurate simulations for radiation transport require that the particle (gamma and/or neutron) energy be appropriate discretize in the multigroup approximation. This, in turns, yields optical tomography problems where the number of unknowns grows (1) about quadratically with respect to the number of energy groups, G, (notably to reconstruct the scattering matrix) and (2) linearly with respect to the number of unknown material regions. As pointed out, a promising approach could rely on algorithms to appropriately select a material type per material zone rather than G2 values. This approach, though promising, still requires further investigation: (a) when switching from cross-section values unknowns to material type indices (discrete integer unknowns), integer programming techniques are needed since derivative information is no longer available; and (b) the issue of selecting the initial material zoning remains. The work reported here proposes an approach to solve the latter item, whereby a material zoning is proposed using one-group or few-groups transport approximations. The capabilities and limitations of the presented method were explored; they are briefly summarized next and later described in fuller details in the Appendices. The major factors that influenced the ability of the optimization method to reconstruct the cross sections of these domains included the locations of the sources used to illuminate the domains, the number of separate experiments used in the reconstruction, the
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
experiments, which are sensitive mainly to P{sub 0} scattering. In particular one may test the P{sub 1} scattering kernel appropriate to a given molecular model. Third, the transport cross-section may be calculated directly from the experiments for use in multigroup reactor analysis. (author) [French] On mesure par les methodes du temps de vol les sections efficaces differentielles de diffusion simple (d{sigma}/d {Omega}) pour les ralentisseurs usuels. On utilise des neutrons thermiques produits par une source puisee intense (accelerateur lineaire de la General Atomic) avec un parcours de vol de 12 m a l'extremite duquel est place un echantillon mince du ralentisseur a l*etude. En outre, on a egalement prevu un petit parcours de vol terminal pour les neutrons diffuses, entre l'echantillon et plusieurs detecteurs de neutrons entierement absorbants. Cette methode permet de mesurer simultanement la distribution angulaire de diffusion pour plus de 50 energies des neutrons incidents. Les intensites sont-elevees, le bruit de fond est faible et bien defini et on peut proceder a des mesures rapides pour tous les angles de diffusion compris entre 10 et 155 degres. Les auteurs presentent des mesures de la section efficace differentielle de diffusion pour le vanadium, H{sub 2}O, D{sub 2}O et ZrH. On a etudie le vanadium pour controler le dispositif experimental. On a fait des mesures avec H{sub 2}O pour diverses epaisseurs et orientations des echantillons en vue de les comparer aux calculs fondes sur divers modeles de diffusion par l'hydrogene lie et aux resultats obtenus par Springer et Reinsch. Toutes les mesures experimentales ont ete corrigees pour tenir compte des effets importants de la diffusion multiple dans les echantillons. Pour l'instant, on n'a pas observe experimentalement la variation accusee que fait prevoir le modele de diffusion de Nelkin lorsque l'energie des neutrons est d'environ 0,06 eV; ceci est du au fait que l'hypothese du rotateur unique inhibe a 0,06 eV n'a pas
Energy Technology Data Exchange (ETDEWEB)
Bally, D; Tarina, V; Todireanu, S [Institute of Atomic Physics, Bucharest (Romania)
1963-01-15
The angular distribution of 1.61 A wavelength neutrons scattered from hydrogen and ethylene has been measured. For ethylene the pressure was varied from 15 to 60 atm and for hydrogen from 60 to 110 atm. The investigated angular range was between 5''o and 90{sup o}. The experimental results obtained have been compared with the differential cross-section calculated using the Krieger-Nelkin formulae. (author) [French] Les auteurs ont mesure la distribution angulaire des neutrons ayant une longueur d'onde de 1,61 A diffuses par de l'hydrogene et par l'ethylene. Ils ont fait varier la pression de l'ethylene de 15 a 60 atm et celle de l'hydrogene de 60 a 110 atm. Le domaine angulaire etudie etait compris entre 5{sup o} et 90{sup o}. Les resultats des experiences ont ete compares aux sections efficaces differentielles calculees au moyen des formules de Krieger-Nelkin. (author) [Spanish] Los autores han medido la distribucion angular de neutrones de longitud de onda igual a 1,61 A, despersados por hidrogeno y etileno. En el caso del etileno, la presion vario de 15 a 60 atm y en el del higrogeno, de 60 a 110 atm. Los autores han explorado angulos comprendidos entre 5{sup o} y 90{sup o}. comparan los resultados experimentales obtenidos con el valor de la seccion eficaz diferencial calculado con ayuda de las formulas de Kriger-Nelkin. (author)
Neutron-proton elastic diffusion study at low transfer between 400-1000 MeV
International Nuclear Information System (INIS)
Wellers, F.
1986-01-01
This thesis presents the first complete results of forward differential cross-section, over the entire range of the intermediate energies, in the neutron-proton system. The neutron beam is produced with the synchrotron Saturne II, using the reaction of deuteron break-up, which gives it a relatively high intensity and a small energy dispersion. The experimental apparatus is a drift ionization chamber, IKAR, filled with high pressure gas which plays the double role of target and detector of the recoil proton. The use of a neutral beam requires new procedures in the analysis, more elaborate than in the case of charged projectiles, where scattered particles were detected in coincidence in wire chambers. The results are then normalized and discussed, using a phenomenological parametrization, and integrated in a continuously energy-dependent phase-shifts analysis. An entirely analytic Glauber calculation allows us to estimate the validity of the normalization method [fr
International Nuclear Information System (INIS)
Schuerrer, F.
1980-01-01
For characterizing heterogene configurations of pebble-bed reactors the fine structure of the flux distribution as well as the determination of the macroscopic neutronphysical quantities are of interest. When calculating system parameters of Wigner-Seitz-cells the usual codes for neutron spectra calculation always neglect the modulation of the neutron flux by the influence of neighbouring spheres. To judge the error arising from that procedure it is necessary to determinate the flux distribution in the surrounding of a spherical fuel element. In the present paper an approximation method to calculate the flux distribution in the two-sphere model is developed. This method is based on the exactly solvable problem of the flux determination of a point source of neutrons in an infinite medium, which contains a spherical perturbation zone eccentric to the point source. An iteration method allows by superposing secondary fields and alternately satisfying the conditions of continuity on the surface of each of the two fuel elements to advance to continually improving approximations. (orig.) 891 RW/orig. 892 CKA [de
International Nuclear Information System (INIS)
Volino, F.
1976-01-01
After a short review of the main concepts concerning the neutron and its interaction with matter, the authors focus their attention on the study of molecular systems by means of neutron scattering. Instead of reviewing the subject yet again, they limit themselves to the new kind of work which can be done now, with the combined help of high flux reactors and novel instruments. As examples, a few experiments performed at the Institut Laue-Langevin in Grenoble are described: a neutron diffraction study of liquid acetonitrile using a powder diffractometer installed at the hot source; three high-resolution quasi-elastic studies of molecular motions - in an organic solid, (PAA), an organic liquid (C 3 H 6 ) and a liquid crystal (TBBA) - made by combining measurements with high and ultra-high energy resolution spectrometers installed at the cold source. The concept of elastic incoherent structure factor (EISF) is extensively used for the analysis. Finally some prospects on possible future developments are presented. (orig./HK) [de
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)
Energy Technology Data Exchange (ETDEWEB)
Sagot, M; Tellier, H [Commissariat a l' Energie Atomique. Centre d' Etudes Nucleaires de Saclay, 91 - Gif-sur-Yvette (France)
1963-07-01
The diffusion coefficient, cooling coefficient, and anisotropy of graphite were determined to be (2.19 {+-} 0.03) x 10{sup 5} cm{sup 2} sec{sup -1}, (37.9 {+-} 4) x 10{sup 5} cm{sup 4} sec{sup -1}, and 1.017 {+-} 0.008, respectively. The range of geometrical buckling was from 7 to 155 m{sup -2}. The values obtained are compared with published values. (authors) [French] Un programme experimental utilisant la methode de la source pulsee de neutrons a ete realise sur le graphite. La gamme des laplaciens couverte est de 7 m{sup -2} a 155 m{sup -2}. Les resultats en sont presentes dans ce rapport: - coefficient de diffusion D{sub 0} = (2,19 {+-} 0,03) x 10{sup 5} cm{sup 2} s{sup -1} - coefficient de refroidissement C = (37,9 {+-} 4) x 10{sup 5} cm{sup 4} s{sup -1} - anisotropie du graphite (D parall./D perp.) = 1,017 {+-} 0,008. Ils sont compares aux valeurs deja publiees. (auteurs)
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)
International Nuclear Information System (INIS)
Kumar, V.; Sahni, D.C.
1983-01-01
In this paper, the authors present the mathematical techniques that were developed for solving the integral transport equation for the criticality of a homogeneous cylinder of finite height with general anisotropic scattering. They present the integral transport equations for the Fourier transformed spherical harmonic moments of the angular flux. These moments are also represented by a series of products of spherical Bessel functions. The criticality problem is, then, posed by the matrix eigenvalue problem whose eigenvector is composed of the expansion coefficients mentioned above. An methodology of calculating the general matrix element is discussed by using the recursion relations derived in this paper. Finally, for the one-group criticality of finite cylinders, the benchmark results are generated when scattering is linearly anisotropic. Also, these benchmarks are solved and compared with the S/sub N/ method of TWOTRAN
Czech Academy of Sciences Publication Activity Database
Vacík, Jiří; Hnatowicz, Vladimír; Attar, F. M. D.; Mathakari, N. L.; Dahiwale, S. S.; Dhole, S. D.; Bhoraskar, V. N.
2014-01-01
Roč. 169, č. 10 (2014), s. 885-891 ISSN 1042-0150 R&D Projects: GA ČR(CZ) GBP108/12/G108; GA MŠk(XE) LM2011019 Institutional support: RVO:61389005 Keywords : diffusion * lithium * neutron depth profiling * polymers Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders Impact factor: 0.513, year: 2014
International Nuclear Information System (INIS)
Silva A, L.; Del Valle G, E.
2012-10-01
This work shows an application of the program COMSOL Multi physics Ver. 4.2a in the solution of the neutron diffusion equations for several energy groups in nuclear reactors whose core is formed by assemblies of hexagonal transversal cut as is the cas of fast reactors. A reference problem of 4 energy groups is described of which takes the cross sections which are processed by means of a program that prepares the definition of the constants utilized in COMSOL for the generic partial differential equations that this uses. The considered solution domain is the sixth part of the core which is applied frontier conditions of reflection and incoming flux zero. The discretization mesh is elaborated in automatic way by COMSOL and the solution method is one of finite elements of Lagrange grade two. The reference problem is known as the Knk with and without control rod which led to propose the calculation of the effective multiplication factor in function of the control rod fraction from a value 0 (completely inserted control rod) until the value 1 (completely extracted control rod). Besides this the reactivity was determined as well as the change of this in function of control rod fraction. The neutrons scalar flux for each energy group with and without control rod is proportioned. The reported results show a behavior similar to the one reported in other works but using the discreet ordinates S 2 approximation. (Author)
Welland, M. J.; Tenuta, E.; Prudil, A. A.
2017-06-01
This article describes a phase-field model for an isothermal multicomponent, multiphase system which avoids implicit interfacial energy contributions by starting from a grand potential formulation. A method is developed for incorporating arbitrary forms of the equilibrium thermodynamic potentials in all phases to determine an explicit relationship between chemical potentials and species concentrations. The model incorporates variable densities between adjacent phases, defect migration, and dependence of internal pressure on object dimensions ranging from the macro- to nanoscale. A demonstrative simulation of an overpressurized nanoscopic intragranular bubble in nuclear fuel migrating to a grain boundary under kinetically limited vacancy diffusion is shown.
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
Three-dimensional h-adaptivity for the multigroup neutron diffusion equations
Wang, Yaqi; Bangerth, Wolfgang; Ragusa, Jean
2009-01-01
diffusion equation for reactor applications. In order to follow the physics closely, energy group-dependent meshes are employed. We present a novel algorithm for assembling the terms coupling shape functions from different meshes and show how it can be made
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: a code to solve one-, two-, and three-dimensional finite-difference diffusion theory problems
International Nuclear Information System (INIS)
Derstine, K.L.
1984-04-01
The mathematical development and numerical solution of the finite-difference equations are summarized. The report provides a guide for user application and details the programming structure of DIF3D. Guidelines are included for implementing the DIF3D export package on several large scale computers. Optimized iteration methods for the solution of large-scale fast-reactor finite-difference diffusion theory calculations are presented, along with their theoretical basis. The computational and data management considerations that went into their formulation are discussed. The methods utilized include a variant of the Chebyshev acceleration technique applied to the outer fission source iterations and an optimized block successive overrelaxation method for the within-group iterations. A nodal solution option intended for analysis of LMFBR designs in two- and three-dimensional hexagonal geometries is incorporated in the DIF3D package and is documented in a companion report, ANL-83-1
Development and verification of the neutron diffusion solver for the GeN-Foam multi-physics platform
International Nuclear Information System (INIS)
Fiorina, Carlo; Kerkar, Nordine; Mikityuk, Konstantin; Rubiolo, Pablo; Pautz, Andreas
2016-01-01
Highlights: • Development and verification of a neutron diffusion solver based on OpenFOAM. • Integration in the GeN-Foam multi-physics platform. • Implementation and verification of acceleration techniques. • Implementation of isotropic discontinuity factors. • Automatic adjustment of discontinuity factors. - Abstract: The Laboratory for Reactor Physics and Systems Behaviour at the PSI and the EPFL has been developing in recent years a new code system for reactor analysis based on OpenFOAM®. The objective is to supplement available legacy codes with a modern tool featuring state-of-the-art characteristics in terms of scalability, programming approach and flexibility. As part of this project, a new solver has been developed for the eigenvalue and transient solution of multi-group diffusion equations. Several features distinguish the developed solver from other available codes, in particular: object oriented programming to ease code modification and maintenance; modern parallel computing capabilities; use of general unstructured meshes; possibility of mesh deformation; cell-wise parametrization of cross-sections; and arbitrary energy group structure. In addition, the solver is integrated into the GeN-Foam multi-physics solver. The general features of the solver and its integration with GeN-Foam have already been presented in previous publications. The present paper describes the diffusion solver in more details and provides an overview of new features recently implemented, including the use of acceleration techniques and discontinuity factors. In addition, a code verification is performed through a comparison with Monte Carlo results for both a thermal and a fast reactor system.
Measurement of Diffusion Parameters and of Anisotropy of Graphite with a Pulsed Source of Neutrons
International Nuclear Information System (INIS)
Sagot, M.; Tellier, H.
1963-01-01
The diffusion coefficient, cooling coefficient, and anisotropy of graphite were determined to be (2.19 ± 0.03) x 10 5 cm 2 sec -1 , (37.9 ± 4) x 10 5 cm 4 sec -1 , and 1.017 ± 0.008, respectively. The range of geometrical buckling was from 7 to 155 m -2 . The values obtained are compared with published values. (authors) [fr
International Nuclear Information System (INIS)
Mallick, Ritam
2011-01-01
The Rankine-Hugoniot condition has been solved to study phase transition in an astrophysical scenario mainly in the case of phase transition from a neutron star (NS) to a quark star (QS). The equations of state and temperature play a huge role in determining the nature of the front propagation, which brings about the phase transition in a NS. The shock jump conditions can be solved analytically, but the situation changes drastically by the inclusion of the magnetic field. High magnetic fields, which are always associated with a NS play a huge role in determining the structure and evolution of a NS. So, a magnetic field has been introduced in the shock jump condition in the de Hoffmann-Teller frame. The modified conservation condition for the perpendicular and oblique shocks is obtained in this frame. Numerical solution of the perpendicular shock has been obtained, which shows considerable deviation from the nonmagnetic case. The results show that the magnetic field helps in shock generation. It also indirectly hints at the instability of the matter and thereby the NS for very high magnetic field, implying that NSs can only support a magnetic field of some finite strength.
International Nuclear Information System (INIS)
Jagannathan, V.
1985-01-01
For solving the multigroup diffusion theory equations in 3-D problems in which the material properties are uniform in large segments of axial direction, the synthesis method is known to give fairly accurate results, at very low computational cost. In the code system FEMSYN, the single channel continuous flux synthesis option has been incorporated. One can generate the radial trail functions by either finite difference method (FDM) or finite element method (FEM). The axial mixing functions can also be found by either FDM or FEM. Use of FEM for both radial and axial directions is found to reduce the calculation time considerably. One can determine eigenvalue, 3-D flux and power distributions with FEMSYN. In this report, a detailed discription of the synthesis module SYNTHD is given. (author)
Energy Technology Data Exchange (ETDEWEB)
Tetsu, Hiroyuki; Nakamoto, Taishi, E-mail: h.tetsu@geo.titech.ac.jp [Earth and Planetary Sciences, Tokyo Institute of Technology, Tokyo 152-8551 (Japan)
2016-03-15
Radiation is an important process of energy transport, a force, and a basis for synthetic observations, so radiation hydrodynamics (RHD) calculations have occupied an important place in astrophysics. However, although the progress in computational technology is remarkable, their high numerical cost is still a persistent problem. In this work, we compare the following schemes used to solve the nonlinear simultaneous equations of an RHD algorithm with the flux-limited diffusion approximation: the Newton–Raphson (NR) method, operator splitting, and linearization (LIN), from the perspective of the computational cost involved. For operator splitting, in addition to the traditional simple operator splitting (SOS) scheme, we examined the scheme developed by Douglas and Rachford (DROS). We solve three test problems (the thermal relaxation mode, the relaxation and the propagation of linear waves, and radiating shock) using these schemes and then compare their dependence on the time step size. As a result, we find the conditions of the time step size necessary for adopting each scheme. The LIN scheme is superior to other schemes if the ratio of radiation pressure to gas pressure is sufficiently low. On the other hand, DROS can be the most efficient scheme if the ratio is high. Although the NR scheme can be adopted independently of the regime, especially in a problem that involves optically thin regions, the convergence tends to be worse. In all cases, SOS is not practical.
Energy Technology Data Exchange (ETDEWEB)
Tardy-Joubert, P [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1966-03-01
The cascade induced in protective screens by a 3 GeV proton beam has been studied using activation detectors; the results have been compared with the cosmic neutron spectrum in the atmosphere. A study of the secondary neutron spectrum has made, it possible to obtain the distribution of the dose and to determine the maximum permissible fluxes expressed in terms of the energy, taking into account all the daughter products present. The dose calculated has been checked experimentally. The proportion of cascade neutrons has been studied using the idea of an imaginary source. The parameters which have to be introduced into the general equations to take into account scattering in the the air have been determined. (author) [French] La cascade induite dans les ecrans de protection par un faisceau de protons de 3 GeV a ete etudiee au moyen de detecteurs a activation et la comparaison a ete faite avec le spectre des neutrons cosmiques dans l'atmosphere. L'etude du spectre des neutrons secondaires a permis de preciser la distribution de la dose et de determiner les flux maximaux admissibles qui sont exprimes en fonction de l'energie, en tenant compte de l'ensemble des descendants presents. La dose calculee a ete verifiee experimentalement. La propagation des neutrons de cascade a ete etudiee en introduisant la notion de source fictive. Les parametres a introduire dans les equations generales pour rendre compte de la diffusion dans l'air ont ete determines. (auteur)
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
Energy Technology Data Exchange (ETDEWEB)
Abramson - Szteinsznaider, D [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1961-07-01
- The aim of this work is to see if this reaction occurs only by compound nucleus formation or involves some contribution of direct interaction. In the first case, the angular distribution of inelastic neutrons is symmetric about 90 degree. In the second case, this distribution must be asymmetric and must change slowly with energy of incident neutrons. The neutrons corresponding at the excitation of a given level of the residual nucleus are selected by their coincidence with the {gamma} rays of deexcitation of this level. From the results of our measurements on iron, iodine and bismuth and of other laboratories on different elements, we can conclude that generally, the inelastic scattering of neutrons of some MeV occurs only by compound nucleus. (author) [French] - Le but de ce travail est de determiner si cette reaction s'effectue uniquement par passage par un noyau compose ou fait intervenir un processus d'interaction directe. Dans le premier cas, la distribution angulaire des neutrons inelastiques est symetrique par rapport a 90 degree. Dans le deuxieme cas, cette distribution doit etre asymetrique et doit varier lentement avec l'energie des neutrons incidents. Les neutrons correspondant a l'excitation d'un niveau determine du residuel sont selectionnes par leur cofncidence avec les rayonnements {gamma} de desexcitation de ce niveau. D'apres les resultats de nos mesures sur le fer, l'iode et le bismuth et de celles des autres laboratoires sur differents elements, nous pouvons conclure que, en general, la diffusion inelastique des neutrons de quelques MeV s'effectue uniquement par noyau compose. (auteur)
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)
Deuterium short-range order in Pd0.975Ag0.025D0.685 by diffuse neutron scattering
DEFF Research Database (Denmark)
Blaschko, O.; Klemencic, R.; Fratzl, P.
1983-01-01
By diffuse neutron scattering the D short-range order in a Pd0.975Ag0.025D0.685 crystal was investigated at 50 and 70K. The results are compared with the D ordering in the PdDx system previously investigated, and it is shown that the isointensity contours around the (1/2,1,0) point are similar...
International Nuclear Information System (INIS)
Pugliesi, R.
1983-01-01
The hydrogen diffusion in the storage material Ti sub(0.8) Zr sub(0.2)CrMnH 3 has been studied in the temperature range of 260 to 360K, by means of the quasi-elastic neutron scattering technique. The experimental measurements have been performed using a high resolution backscattering spectrometer. The half widths at half maximum of the quasi-elastic line have been determined for momentum transfers in the range 0.24 to 1.85 A -1 . The data, corrected for multiple scattering effect, have been analysed in term of simple diffusion and jump diffusion models. From the diffusion coefficients determined at different temperatures, the following Arrhenius equation was obtained: D= (3+-1) x 10 -8 m 2 /s exp [-(220+-20 meV/kT] yielding a diffusion coefficient at room temperature of 6.0 x 10 -12 m 2 /s. This comparatively fast hydrogen diffusion is not the rate determining step in the absorption and desorption kinetics. The results at large momentum transfers show evidence for the existence of more than one component in the quasi-elastic spectra. This fact has been explained considering the diffusion governed by the existence of energetically different interstitial sites and by blocking effects due to the high hydrogen concentration. (Author) [pt
Energy Technology Data Exchange (ETDEWEB)
Morgenstern, J [Commissariat a l' Energie Atomique, 91 - Saclay (France). Centre d' Etudes Nucleaires
1968-09-01
The strength functions S{sub 0} and S{sub 1}, and the scattering length R' are studied. The values of S{sub 0}, S{sub 1} and R' are obtained by shape analysis of the individual resonances observed in total neutron cross-section measurements. These measurements were performed at the Saclay 45 MeV linac by the time of flight method. The best resolution achieved was equal to 0.19 ns/m. We have particularly studied the nuclei around number of mass A = 50, 90, 140 and 200. The experimental values of S{sub 0}, S{sub 1} and R' are compared with optical model calculations. A fairly good agreement is obtained using an optical potential with surface absorption. (author) [French] Nous etudions les fonctions densite S{sub 0} et S{sub 1} ainsi que le rayon de diffusion R'. Les valeurs de S{sub 0}, S{sub 1} et R' sont determinees a partir de l'analyse de forme des resonances individuelles observees lors de la mesure de la section efficace neutronique totale. Cette mesure a ete faite aupres de l'accelerateur lineaire d'electrons de 45 MeV de Saclay par la methode du temps de vol. La meilleure resolution atteinte etait egale a 0.19 ns/m. Nous avons particulierement etudie les noyaux situes vers les nombres de masse A 50, 90, 140 et 200. Nous comparons ensuite les valeurs experimentales de S{sub 0}, S{sub 1} et R' a differents calculs de modele optique. Un bon accord est obtenu avec un potentiel optique a absorption de surface. (auteur)
Energy Technology Data Exchange (ETDEWEB)
Morgenstern, J. [Commissariat a l' Energie Atomique, 91 - Saclay (France). Centre d' Etudes Nucleaires
1968-09-01
The strength functions S{sub 0} and S{sub 1}, and the scattering length R' are studied. The values of S{sub 0}, S{sub 1} and R' are obtained by shape analysis of the individual resonances observed in total neutron cross-section measurements. These measurements were performed at the Saclay 45 MeV linac by the time of flight method. The best resolution achieved was equal to 0.19 ns/m. We have particularly studied the nuclei around number of mass A = 50, 90, 140 and 200. The experimental values of S{sub 0}, S{sub 1} and R' are compared with optical model calculations. A fairly good agreement is obtained using an optical potential with surface absorption. (author) [French] Nous etudions les fonctions densite S{sub 0} et S{sub 1} ainsi que le rayon de diffusion R'. Les valeurs de S{sub 0}, S{sub 1} et R' sont determinees a partir de l'analyse de forme des resonances individuelles observees lors de la mesure de la section efficace neutronique totale. Cette mesure a ete faite aupres de l'accelerateur lineaire d'electrons de 45 MeV de Saclay par la methode du temps de vol. La meilleure resolution atteinte etait egale a 0.19 ns/m. Nous avons particulierement etudie les noyaux situes vers les nombres de masse A 50, 90, 140 et 200. Nous comparons ensuite les valeurs experimentales de S{sub 0}, S{sub 1} et R' a differents calculs de modele optique. Un bon accord est obtenu avec un potentiel optique a absorption de surface. (auteur)
RASH D - A mercury programme for neutron shielding calculations
International Nuclear Information System (INIS)
Bendall, D.E.
1962-08-01
An improved version of an earlier neutron shielding programme (RASH B) is described. The new programme is also written in Mercury Autocode and solves a set of multigroup diffusion equations in one dimension. It differs from RASH B in that distributed source terms may be introduced into all the groups if required. Some other improvements are also included. (author)
Energy Technology Data Exchange (ETDEWEB)
Fernandez, B [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1963-07-01
A calculation for double scattering and absorption corrections in fast neutron scattering experiments using Monte-Carlo method is given. Application to cylindrical target is presented in FORTRAN symbolic language. (author) [French] Un calcul des corrections de double diffusion et d'absorption dans les experiences de diffusion de neutrons rapides par la methode de Monte-Carlo est presente. L'application au cas d'une cible cylindrique est traitee en langage symbolique FORTRAN. (auteur)
Energy Technology Data Exchange (ETDEWEB)
Joshi, B. V.; Nargundkar, V. R.; Subbarao, K. [Atomic Energy Establishment Trombay, Bombay (India)
1965-08-15
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: {lambda}{sub 0} = absorption constant = 156.02 {+-} 4.37 s{sup -1} D = diffusion coefficient = (1.3334 {+-} 0.0128) x 10{sup 5} cm{sup 2}/s C = diffusion cooling constant = (-4.8758 {+-} 0.5846) x 10{sup 5} cm{sup 4}/s. The effect of neglecting the contribution of the B{sup 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) [French] Les auteurs decrivent l'emploi de la methode des neutrons puises pour la determination precise des parametres de diffusion des ralentisseurs. Ils ont calculi ceux de la glucine par cette methode. Des deuterons puises au moyen d'un accelerateur a cascade produisaient les bouffees de neutrons par la reaction Be (d, n). Le detecteur etait constitue par un compteur proportionnel au BF{sub 3} enrichi. En choisissant convenablement
Energy Technology Data Exchange (ETDEWEB)
Singwi, K S; Sjolander, A; Rahman, A [Argonne National Laboratory, Argonne, IL (United States)
1963-01-15
An important question which arises in connection with slow neutron scattering by liquids is: does there exist a frequency spectrum tor liquids analogous to that in solids? The answer to this question is given by showing that the width function {gamma}(t) of the Gaussian space-time self-correlation function G{sub s}(r,t) can be expressed, by using the frequency spectrum of the velocity auto-correlation function, in a form which is formally identical with that of a harmonic solid. Thus a knowledge of the frequency spectrum of the velocity auto-correlation function should enable one to calculate slow neutron scattering by liquids as has been emphasized by Egelstaff and co-workers. Using a stochastic model of a liquid, the frequency spectrum f({omega}) of the velocity auto-correlation function is calculated for water at 300{sup o}K and for liquid lead at 620{sup o}K. In the case of water a maximum in f({omega}) corresponding to {Dirac_h} 75{sup o}K is predicted. For lead the maximum also occurs at nearly the same {omega}-value. There also occurs a minimum in f({omega})in both cases. Larsson and Dahlborg have observed a maximum in f({omega}) at the above predicted {omega}-value. A recent observation in liquid lead of Cotter et al. probably confirms our prediction too. (author) [French] Dans le domaine de la diffusion des neutrons lents par des liquides une question importante se pose: existe-t-il un spectre de frequences pour les liquides analogue au spectre pour les solides? On peut repondre d cette quesnon en montrant que la fonction de largeur {gamma}(t) de la fonction gaussienne spatio-temporelle d'auto-correlation G{sub s}(r,t) peut etre exprimee, en employant le spectre de frequences de la fonction d'auto-correlation des vitesses, sous uune forme qui presente le membe aspect formel que celle d'un solide harmonique. par consequent, la connaissance du spectre de frequences de la fonction d'auto-correlation des vitesses devrait permettre de calculer la diffusion des
Energy Technology Data Exchange (ETDEWEB)
Costa, Danilo Leite
2013-07-01
This work aims to present a study about the power distribution behavior in a PWR type reactor, considering both intensity and migration of power peaks due to insertion of control rods into the core. Employing the multidimensional steady-state neutron diffusion equation in order to simulate the neutron flux, and using the Finite Difference Method. Furthermore, based on the axial power distribution on the largest heat flux rod, is carried out thermal analysis of this rod and associated coolant channel. For this purpose is employed the FueLRod{sub 3}D code, it uses the Finite Element Method to model the fuel rod and the associated coolant channel, allowing the thermohydraulics simulation of a single rod discretized in three dimensions, considering the heat flux from the pellet, crossing the gap and the cladding until it reaches the coolant. (author)
International Nuclear Information System (INIS)
Fernandes, A.
1991-01-01
A method to solve three dimensional neutron transport equation and it is based on the original work suggested by J.K. Fletcher (42, 43). The angular dependence of the flux is approximated by associated Legendre functions and the finite element method is applied to the space components is presented. When the angular flux, the scattering cross section and the neutrons source are expanded in associated Legendre functions, the first order neutron transport equation is reduced to a coupled set of second order diffusion like equations. These equations are solved in an iterative way by the finite element method to the moments. (author)
International Nuclear Information System (INIS)
Owens, A.J.
1977-01-01
The effects of non-field-aligned diffusion (i.e., terms in the diffusion tensor proportional to the antisymmetric coefficient kappa/sub A/) on the observed day-to-day deviation of the diffusive diurnal anisotropy from the daily average magnetic field direction are considered. Using reasonable parameters for the diffusion of cosmic rays in interplanetary space, I show that these terms give a natural explanation for the angular difference between the anisotropy and field directions during normal quiet interplanetary epochs
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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)
International Nuclear Information System (INIS)
Tasaki, Yutaka; Ichikawa, Yasushi; Kobo, Norio; Shinohara, Kazuhiko; Boillat, Pierre; Kramer, Denis; Scherer, Gunther G.; Lehmann, Eberhard H.
2008-01-01
The mass transfer characteristics of gas diffusion layer (GDL) are closely related to cell performance in PEFC. In this study, In situ diagnostic of water distribution in thickness direction of MEA by Neutron Imaging has been carried out for three MEAs with different GDLs on cathode side as well as I-V characteristics. It was confirmed that this method is useful for analyzing water distribution in thickness direction of MEA. The relationship between I-V characteristics and liquid water distribution has been studied. (author)
International Nuclear Information System (INIS)
Woznicki, Z.
1979-06-01
This report presents the AGA two-sweep iterative methods belonging to the family of factorization techniques in their practical application in the HEXAGA-II two-dimensional programme to obtain the numerical solution to the multi-group, time-independent, (real and/or adjoint) neutron diffusion equations for a fine uniform triangular mesh. An arbitrary group scattering model is permitted. The report written for the users provides the description of input and output. The use of HEXAGA-II is illustrated by two sample reactor problems. (orig.) [de
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Fournier, D.
2011-10-10
The different neutronic parameters have to be calculated with a higher accuracy in order to design the 4. generation reactor cores. As memory storage and computation time are limited, adaptive methods are a solution to solve the neutron transport equation. The neutronic flux, solution of this equation, depends on the energy, angle and space. The different variables are successively discretized. The energy with a multigroup approach, considering the different quantities to be constant on each group, the angle by a collocation method called SN approximation. Once the energy and angle variable are discretized, a system of spatially-dependent hyperbolic equations has to be solved. Discontinuous finite elements are used to make possible the development of hp-refinement methods. Thus, the accuracy of the solution can be improved by spatial refinement (h-refinement), consisting into subdividing a cell into sub-cells, or by order refinement (p-refinement), by increasing the order of the polynomial basis. In this thesis, the properties of this methods are analyzed showing the importance of the regularity of the solution to choose the type of refinement. Thus, two error estimators are used to lead the refinement process. Whereas the first one requires high regularity hypothesis (analytical solution), the second one supposes only the minimal hypothesis required for the solution to exist. The comparison of both estimators is done on benchmarks where the analytic solution is known by the method of manufactured solutions. Thus, the behaviour of the solution as a regard of the regularity can be studied. It leads to a hp-refinement method using the two estimators. Then, a comparison is done with other existing methods on simplified but also realistic benchmarks coming from nuclear cores. These adaptive methods considerably reduces the computational cost and memory footprint. To further improve these two points, an approach with energy-dependent meshes is proposed. Actually, as the
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
Poulsen, H. F.; Andersen, N. H.; Lebech, B.
1991-02-01
We report experimental results of twin-domain size and bulk oxygen in-diffusion kinetics of YBa 2Cu 3O 6+ x, which supplement a previous and simultaneous study of the structural phase diagram and oxygen equilibrium partial pressure. Analysis of neutron powder diffraction peak broadening show features which are identified to result from temperature independent twin-domain formation in to different orthorhombic phases with domain sizes and 250 and 350Å, respectively. The oxygen in-diffusion flow shows simple relaxation type behaviour J=J 0 exp( {-t}/{τ}) despite a rather broad particle size distribution. At higher temperatures, τ is activated with activation energies 0.55 and 0.25 eV in the tetragonal and orthorhombic phases, respectively. Comparison between twin-domain sizes and bulk oxygen in-diffusion time constants indicates that the twin-domain boundaries may contribute to the effective bulk oxygen in-diffusion. All our results may be interpreted in terms of the 2D ASYNNNI model description of the oxygen basal plane ordering, and they suggest that recent first principles interaction parameters should be modified.
Salles, Fabrice; Jobic, Hervé; Devic, Thomas; Llewellyn, Philip L; Serre, Christian; Férey, Gérard; Maurin, Guillaume
2010-01-26
Quasi-elastic neutron scattering measurements are combined with molecular dynamics simulations to determine the self-diffusivity, corrected diffusivity, and transport diffusivity of CO(2) in the metal-organic framework MIL-47(V) (MIL = Materials Institut Lavoisier) over a wide range of loading. The force field used for describing the host/guest interactions is first validated on the thermodynamics of the MIL-47(V)/CO(2) system, prior to being transferred to the investigations of the dynamics. A decreasing profile is then deduced for D(s) and D(o) whereas D(t) presents a non monotonous evolution with a slight decrease at low loading followed by a sharp increase at higher loading. Such decrease of D(t) which has never been evidenced in any microporous systems comes from the atypical evolution of the thermodynamic correction factor that reaches values below 1 at low loading. This implies that, due to intermolecular interactions, the CO(2) molecules in MIL-47(V) do not behave like an ideal gas. Further, molecular simulations enabled us to elucidate unambiguously a 3D diffusion mechanism within the pores of MIL-47(V).
Reim, J. D.; Rosén, E.; Zaharko, O.; Mostovoy, M.; Robert, J.; Valldor, M.; Schweika, W.
2018-04-01
The hexagonal swedenborgite, CaBaCo2Fe2O7 , is a chiral frustrated antiferromagnet, in which magnetic ions form alternating kagome and triangular layers. We observe a long-range √{3 }×√{3 } antiferromagnetic order setting in below TN=160 K by neutron diffraction on single crystals of CaBaCo2Fe2O7 . Both magnetization and polarized neutron single crystal diffraction measurements show that close to TN spins lie predominantly in the a b plane, while upon cooling the spin structure becomes increasingly canted due to Dzyaloshinskii-Moriya interactions. The ordered structure can be described and refined within the magnetic space group P 31 m' . Diffuse scattering between the magnetic peaks reveals that the spin order is partial. Monte Carlo simulations based on a Heisenberg model with two nearest-neighbor exchange interactions show a similar diffuse scattering and coexistence of the √{3 }×√{3 } order with disorder. The coexistence can be explained by the freedom to vary spins without affecting the long-range order, which gives rise to ground-state degeneracy. Polarization analysis of the magnetic peaks indicates the presence of long-period cycloidal spin correlations resulting from the broken inversion symmetry of the lattice, in agreement with our symmetry analysis.
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
International Nuclear Information System (INIS)
Ondis, L.A. II; Tyburski, L.J.; Moskowitz, B.S.
2000-01-01
The RCP01 Monte Carlo program is used to analyze many geometries of interest in nuclear design and analysis of light water moderated reactors such as the core in its pressure vessel with complex piping arrangement, fuel storage arrays, shipping and container arrangements, and neutron detector configurations. Written in FORTRAN and in use on a variety of computers, it is capable of estimating steady state neutron or photon reaction rates and neutron multiplication factors. The energy range covered in neutron calculations is that relevant to the fission process and subsequent slowing-down and thermalization, i.e., 20 MeV to 0 eV. The same energy range is covered for photon calculations
Energy Technology Data Exchange (ETDEWEB)
Ondis, L.A., II; Tyburski, L.J.; Moskowitz, B.S.
2000-03-01
The RCP01 Monte Carlo program is used to analyze many geometries of interest in nuclear design and analysis of light water moderated reactors such as the core in its pressure vessel with complex piping arrangement, fuel storage arrays, shipping and container arrangements, and neutron detector configurations. Written in FORTRAN and in use on a variety of computers, it is capable of estimating steady state neutron or photon reaction rates and neutron multiplication factors. The energy range covered in neutron calculations is that relevant to the fission process and subsequent slowing-down and thermalization, i.e., 20 MeV to 0 eV. The same energy range is covered for photon calculations.
Zanotti, J.-M.
2005-11-01
Le présent document ne se veut pas un article de revue mais plutôt un élément d'initiation à une technique encore marginale en Biologie. Le lecteur est supposé être un non spécialiste de la diffusion de neutrons poursuivant une thématique à connotation biologique ou biophysique mettant en jeu des phénomènes dynamiques. En raison de la forte section de diffusion incohérente de l'atome d'hydrogène et de l'abondance de cet élément dans les protéines, la diffusion incohérente inélastique de neutrons est une technique irremplaçable pour sonder la dynamique interne des macromolécules biologiques. Après un rappel succinct des éléments théoriques de base, nous décrivons le fonctionnement de différents types de spectromètres inélastiques par temps de vol sur source continue ou pulsée et discutons leurs mérites respectifs. Les deux alternatives utilisées pour décrire la dynamique des protéines sont abordées: (i)l'une en termes de physique statistique, issue de la physique des verres, (ii) la seconde est une interprétation mécanistique. Nous montrons dans ce cas, comment mettre à profit les complémentarités de domaines en vecteur de diffusion et de résolution en énergie de différents spectromètres inélastiques de neutrons (temps de vol, backscattering et spin-écho) pour accéder, à l'aide d'un modèle physique simple, à la dynamique des protéines sur une échelle de temps allant d'une fraction de picoseconde à quelques nanosecondes.
International Nuclear Information System (INIS)
Hussein, H.M.; Sakr, A.M.; Amin, E.H.
2011-01-01
The objective of this paper is to assess the suitability and the accuracy of the deterministic diffusion method for the neutronic calculations of the TRIGA type research reactors in proposed condensed energy spectra of five and seven groups with one and three thermal groups respectively, using the calculational line: WIMSD-IAEA-69 nuclear data library/ WIMSD-5B lattice and cell calculations code/ CITVAP v3.1 core calculations code. Firstly, The assessment goes through analyzing the integral parameters - k e ff, ρ 238 , σ 235 , σ 238 , and C * - of the TRX and BAPL benchmark lattices and comparison with experimental and previous reference results using other ENDLs at the full energy spectra, which show good agreement with the references at both spectra. Secondly, evaluation of the 3D nuclear characteristics of three different cores of the TRR-1/M1 TRIGA Mark- III Thai research reactor, using the CITVAP v3.1 code and macroscopic cross-section libraries generated using the WIMSD-5B code at the proposed energy spectra separately. The results include the excess reactivities and the worth of control rods, which were compared with previous Monte Carlo results and experimental values, that show good agreement with the references at both energy spectra, albeit better accuracies are shown with the five groups spectrum. The results also includes neutron flux distributions which are settled for future comparisons with other calculational techniques, even, they are comparable to reactors and fuels of the same type. The study reflects the adequacy of using the pre-stated calculational line at the condensed energy spectra for evaluation of the neutronic parameters of the TRIGA type reactors, and future comparisons of the un-benchmarked results could assure this result for wider range of neutronics or safety-related parameters
Boron Neutron Capture Therapy at the TRIGA Mark II of Pavia, Italy - The BNCT of the diffuse tumours
Energy Technology Data Exchange (ETDEWEB)
Altieri, S.; Bortolussi, S.; Stella, S.; Bruschi, P.; Gadan, M.A. [University of Pavia (Italy); INFN - National Institute for Nuclear Physics, of Pavia (Italy)
2008-10-29
The selectivity based on the B distribution rather than on the irradiation field makes Boron neutron Capture Therapy (BNCT) a valid option for the treatment of the disseminated tumours. As the range of the high LET particles is shorter than a cell diameter, the normal cells around the tumour are not damaged by the reactions occurring in the tumoral cells. PAVIA 2001: first treatment of multiple hepatic metastases from colon ca by BNCT and auto-transplantation technique: TAOrMINA project. The liver was extracted after BPA infusion, irradiated in the Thermal Column of the Pavia TRIGA Mark II reactor, and re-implanted in the patient. Two patients were treated, demonstrating the feasibility of the therapy and the efficacy in destroying the tumoral nodules sparing the healthy tissues. In the last years, the possibility of applying BNCT to the lung tumours using epithermal collimated neutron beams and without explanting the organ, is being explored. The principal obtained results of the BNCT research are presented, with particular emphasis on the following aspects: a) the project of a new thermal column configuration to make the thermal neutron flux more uniform inside the explanted liver, b) the Monte Carlo study by means of the MCNP code of the thermal neutron flux distribution inside a patient's thorax irradiated with epithermal neutrons, and c) the measurement of the boron concentration in tissues by (n,{alpha}) spectroscopy and neutron autoradiography. The dose distribution in the thorax are simulated using MCNP and the anthropomorphic model ADAM. To have a good thermal flux distribution inside the lung epithermal neutrons must be used, which thermalize crossing the first tissue layers. Thermal neutrons do not penetrate and the obtained uniformity is poor. In the future, the construction of a PGNAA facility using a horizontal channel of the TRIGA Mark II is planned. With this method the B concentration can be measured also in liquid samples (blood, urine) and
Energy Technology Data Exchange (ETDEWEB)
Rojas R, E.; Benitez R, J. S. [Instituto Tecnologico de Toluca, Division de Estudios de Posgrado e Investigacion, Av. Tecnologico s/n, Ex-Rancho La Virgen, 50140 Metepec, Estado de Mexico (Mexico); Segovia de los Rios, J. A.; Rivero G, T. [ININ, Gerencia de Ciencias Aplicadas, Carretera Mexico-Toluca s/n, 52750 Ocoyoacac, Estado de Mexico (Mexico)], e-mail: jorge.benitez@inin.gob.mx
2009-10-15
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)
Solutions of Boltzmann`s Equation for Mono-energetic Neutrons in an Infinite Homogeneous Medium
Wigner, E. P.
1943-11-30
Boltzman's equation is solved for the case of monoenergetic neutrons created by a plane or point source in an infinite medium which has spherically symmetric scattering. The customary solution of the diffusion equation appears to be multiplied by a constant factor which is smaller than 1. In addition to this term the total neutron density contains another term which is important in the neighborhood of the source. It varies as 1/r{sup 2} in the neighborhood of a point source. (auth)
Energy Technology Data Exchange (ETDEWEB)
Hlinka, J
1995-06-27
The aim of this work is to study the betaine calcium chloride dihydrate (BCCD) lattice dynamics by neutrons inelastic and coherent scattering. In the first part are summarized the main properties of the BCCD as they are determined in some previous experimental works. It has been more particularly emphasized on the structural and dynamical properties of this compound. The theoretical concepts used in incommensurate dielectric materials physics are given in the second part. They are at first introduced generally and then applied to BCCD. In the third part is described the experimental method used in this work : the neutrons inelastic scattering. The experimental results on the BCCD normal phase dynamics are then presented. These results and their interpretation allow to build up a semi-microscopic model introduced in the fifth part. The incommensurate lattice dynamics (at 20 K under the transition temperature towards the modulated phase) is studied in the last part. It has been shown that new aspects in relation to the previous works appear in BCCD. (O.L.). 121 refs., 25 figs., 5 tabs.
International Nuclear Information System (INIS)
Dubcova, Lenka; Solin, Pavel; Hansen, Glen; Park, HyeongKae
2011-01-01
Multiphysics solution challenges are legion within the field of nuclear reactor design and analysis. One major issue concerns the coupling between heat and neutron flow (neutronics) within the reactor assembly. These phenomena are usually very tightly interdependent, as large amounts of heat are quickly produced with an increase in fission events within the fuel, which raises the temperature that affects the neutron cross section of the fuel. Furthermore, there typically is a large diversity of time and spatial scales between mathematical models of heat and neutronics. Indeed, the different spatial resolution requirements often lead to the use of very different meshes for the two phenomena. As the equations are coupled, one must take care in exchanging solution data between them, or significant error can be introduced into the coupled problem. We propose a novel approach to the discretization of the coupled problem on different meshes based on an adaptive multimesh higher-order finite element method (hp-FEM), and compare it to popular interpolation and projection methods. We show that the multimesh hp-FEM method is significantly more accurate than the interpolation and projection approaches considered in this study.
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)
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)
Energy Technology Data Exchange (ETDEWEB)
Jacsot, B; Netter, F [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires; Galula, M [Centre National de la Recherche Scientifique (CNRS), 91 - Gif-sur-Yvette (France)
1955-07-01
The time-of-flight spectrometers is constituted of a mechanic swivel obturator which absorbs neutrons until energies above 1 KeV, a mechanic filter which allow to retain only high wave length components and a delayed pulses selector with 100 channels. Its main application field is the thermic region where it allowed to measure the inelastic scattering of neutrons using various materials as H{sub 2}O, D{sub 2}O, Be, BeO, etc... (M.P.)
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
International Nuclear Information System (INIS)
Ikeda, Hideaki; Takeda, Toshikazu
2001-01-01
A space/time nodal diffusion code based on the nodal expansion method (NEM), EPISODE, was developed in order to evaluate transient neutron behavior in light water reactor cores. The present code employs the improved quasistatic (IQS) method for spatial neutron kinetics, and neutron flux distribution is numerically obtained by solving the neutron diffusion equation with the nonlinear iteration scheme to achieve fast computation. A predictor-corrector (PC) method developed in the present study enabled to apply a coarse time mesh to the transient spatial neutron calculation than that applicable in the conventional IQS model, which improved computational efficiency further. Its computational advantage was demonstrated by applying to the numerical benchmark problems that simulate reactivity-initiated events, showing reduction of computational times up to a factor of three than the conventional IQS. The thermohydraulics model was also incorporated in EPISODE, and the capability of realistic reactivity event analyses was verified using the SPERT-III/E-Core experimental data. (author)
International Nuclear Information System (INIS)
Takeshi, Y.; Keisuke, K.
1983-01-01
The multigroup neutron diffusion equation for two-dimensional triangular geometry is solved by the finite Fourier transformation method. Using the zero-th-order equation of the integral equation derived by this method, simple algebraic expressions for the flux are derived and solved by the alternating direction implicit method. In sample calculations for a benchmark problem of a fast breeder reactor, it is shown that the present method gives good results with fewer mesh points than the usual finite difference method
Energy Technology Data Exchange (ETDEWEB)
Chang, Jonghwa [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2014-05-15
Parallelization of Monte Carlo simulation is widely adpoted. There are also several parallel algorithms developed for the SN transport theory using the parallel wave sweeping algorithm and for the CPM using parallel ray tracing. For practical purpose of reactor physics application, the thermal feedback and burnup effects on the multigroup cross section should be considered. In this respect, the domain decomposition method(DDM) is suitable for distributing the expensive cross section calculation work. Parallel transport code and diffusion code based on the Raviart-Thomas mixed finite element method was developed. However most of the developed methods rely on the heuristic convergence of flux and current at the domain interfaces. Convergence was not attained in some cases. Mechanical stress computation community has also work on the DDM to solve the stress-strain equation using the finite element methods. The most successful domain decomposition method in terms of robustness is FETI-DP. We have modified the original FETI-DP to solve the eigenvalue problem for the multigroup diffusion problem in this study.
International Nuclear Information System (INIS)
Ragusa, Jean; Bangerth, Wolfgang
2011-01-01
here explores the inverse problem of optical tomography applied to heterogeneous domains. The neutral particle transport equation was used as the forward model for how neutral particles stream through and interact within these heterogeneous domains. A constrained optimization technique that uses Newtons method served as the basis of the inverse problem. Optical tomography aims at reconstructing the material properties using (a) illuminating sources and (b) detector readings. However, accurate simulations for radiation transport require that the particle (gamma and/or neutron) energy be appropriate discretize in the multigroup approximation. This, in turns, yields optical tomography problems where the number of unknowns grows (1) about quadratically with respect to the number of energy groups, G, (notably to reconstruct the scattering matrix) and (2) linearly with respect to the number of unknown material regions. As pointed out, a promising approach could rely on algorithms to appropriately select a material type per material zone rather than G2 values. This approach, though promising, still requires further investigation: (a) when switching from cross-section values unknowns to material type indices (discrete integer unknowns), integer programming techniques are needed since derivative information is no longer available; and (b) the issue of selecting the initial material zoning remains. The work reported here proposes an approach to solve the latter item, whereby a material zoning is proposed using one-group or few-groups transport approximations. The capabilities and limitations of the presented method were explored; they are briefly summarized next and later described in fuller details in the Appendices. The major factors that influenced the ability of the optimization method to reconstruct the cross sections of these domains included the locations of the sources used to illuminate the domains, the number of separate experiments used in the reconstruction, the
Energy Technology Data Exchange (ETDEWEB)
Silva A, L.; Del Valle G, E., E-mail: evalle@ipn.mx [IPN, Escuela Superior de Fisica y Matematicas, Av. IPN s/n, Col. San Pedro Zacatenco, 07738 Mexico D. F. (Mexico)
2012-10-15
This work shows an application of the program COMSOL Multi physics Ver. 4.2a in the solution of the neutron diffusion equations for several energy groups in nuclear reactors whose core is formed by assemblies of hexagonal transversal cut as is the cas of fast reactors. A reference problem of 4 energy groups is described of which takes the cross sections which are processed by means of a program that prepares the definition of the constants utilized in COMSOL for the generic partial differential equations that this uses. The considered solution domain is the sixth part of the core which is applied frontier conditions of reflection and incoming flux zero. The discretization mesh is elaborated in automatic way by COMSOL and the solution method is one of finite elements of Lagrange grade two. The reference problem is known as the Knk with and without control rod which led to propose the calculation of the effective multiplication factor in function of the control rod fraction from a value 0 (completely inserted control rod) until the value 1 (completely extracted control rod). Besides this the reactivity was determined as well as the change of this in function of control rod fraction. The neutrons scalar flux for each energy group with and without control rod is proportioned. The reported results show a behavior similar to the one reported in other works but using the discreet ordinates S{sub 2} approximation. (Author)
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.
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
International Nuclear Information System (INIS)
Esquivel E, J.; Alonso V, G.; Del Valle G, E.
2015-09-01
The solution of the neutron diffusion equation either for reactors in steady state or time dependent, is obtained through approximations generated by implementing of nodal methods such as RTN-0 (Raviart-Thomas-Nedelec of zero index), which is used in this study. Since the nodal methods are applied in quadrangular geometries, in this paper a technique in which the hexagonal geometry through the transfinite interpolation of Gordon-Hall becomes the appropriate geometry to make use of the nodal method RTN-0 is presented. As a result, a computer program was developed, whereby is possible to obtain among other results the neutron multiplication effective factor (k eff ), and the distribution of radial and/or axial power. To verify the operation of the code, was applied to three benchmark problems: in the first two reactors VVER and FBR, results k eff and power distribution are obtained, considering the steady state case of reactor; while the third problem a type VVER is analyzed, in its case dependent of time, which qualitative results are presented on the behavior of the reactor power. (Author)
Energy Technology Data Exchange (ETDEWEB)
Dolling, G. [Chalk River Nuclear Laboratories, Chalk River, ON (Canada)
1965-04-15
The normal modes of vibration of the pure semiconductors germanium and silicon have been extensively studied by means of coherent one-phonon scattering of slow neutrons from single-crystal specimens. The present paper describes similar experiments performed (i) on germanium heavily doped ({approx}0.1%) with (a) arsenic and (b) gallium, and also (ii) on silicon doped with phosphorus. In each case, control experiments were carried out on high- purity crystals. All measurements were performed with the triple-axis crystal spectrometer at Chalk River Nuclear Laboratories. The elastic constant C{sub 44} for germanium is known to be appreciably dependent on the dopant concentration, and so certain transverse acoustic (TA) modes of long wavelength were studied to see if such effects persisted into the dispersive region. Other TA modes whose frequencies could be measured with high precision were also studied in both materials to check as sensitively as possible for small effects which might be ascribed to the existence of excess electrons or holes. A particularly careful study was made of modes having the following wave vectors (aq/2{pi}, where a is the cubic unit cell side): (i) in germanium, (1,0,0), (ii) in silicon, (0.85, 0.85, 0) and (0.3, 0, 0). Such normal modes might be expected to show anomalous behaviour in the n-type crystals, since inter-valley scattering of electrons between adjacent conduction band minima would require their co-operation in order to conserve ''crystal momentum''. The results in all cases were negative, i. e. no differences in phonon frequencies or energy widths between pure and doped specimens were observed, within the experimental accuracy. In the most favourable cases, this (relative) accuracy is about 0.5% in frequency, rising to 2.0% for certain longitudinal optic modes in silicon. (author) [French] L'auteur a etudie, a l'aide d'experiences de diffusion coherente (a un phonon) de neutrons lents par des monocristaux, les modes normaux de
International Nuclear Information System (INIS)
Desai, B.R.; Xu, G.
1990-01-01
Based on the idea that electromagnetism is responsible for mass differences within isotopic multiplets (e.g., pointlike neutron and proton or u and d quarks), we generalize an SU(2)xU(1) model in a toy field theory of vectors to a supersymmetric model and investigate the finite mass difference within the isotopic doublet. It is found that under soft-supersymmetry breaking, a positive n-p mass difference can be obtained under reasonable assumptions for the parameters involved
International Nuclear Information System (INIS)
Narain, Rajendra
1995-01-01
Using the concept of Very Intense Continuous High Flux Pulsed Reactor to obtain a rotating high flux pulse in an annular core an analytical treatment for the quasi-static solution with a moving reflector is presented. Under quasi-static situation, time averaged values for important parameters like multiplication factor, flux, leakage do not change with time. As a result the instantaneous solution can be considered to be separable in time and space after correcting for the coordinates for the motion of the pulser. The space behaviour of the pulser is considered as exp(-αx 2 ). Movement of delayed neutron precursors is also taken into account. (author). 4 refs
Parand, K.; Nikarya, M.
2017-11-01
In this paper a novel method will be introduced to solve a nonlinear partial differential equation (PDE). In the proposed method, we use the spectral collocation method based on Bessel functions of the first kind and the Jacobian free Newton-generalized minimum residual (JFNGMRes) method with adaptive preconditioner. In this work a nonlinear PDE has been converted to a nonlinear system of algebraic equations using the collocation method based on Bessel functions without any linearization, discretization or getting the help of any other methods. Finally, by using JFNGMRes, the solution of the nonlinear algebraic system is achieved. To illustrate the reliability and efficiency of the proposed method, we solve some examples of the famous Fisher equation. We compare our results with other methods.
Influence of the external neutron sources in the criticality prediction using 1/M curve
Energy Technology Data Exchange (ETDEWEB)
Pereira, Valmir [COPPE/UFRJ, Programa de Engenharia Nuclear, Caixa Postal 68509, 21941-972 Rio de Janeiro (Brazil); Carvalho da Silva, Fernando [COPPE/UFRJ, Programa de Engenharia Nuclear, Caixa Postal 68509, 21941-972 Rio de Janeiro (Brazil); Martinez, Aquilino Senra [COPPE/UFRJ, Programa de Engenharia Nuclear, Caixa Postal 68509, 21941-972 Rio de Janeiro (Brazil)]. E-mail: aquilino@lmp.ufrj.br
2005-11-15
The influence of external neutron sources in the process to obtain the criticality condition is estimated. To reach this objective, the three-dimensional neutron diffusion equation in two groups of energy is solved, for a subcritical PWR reactor core with external neutron sources. The results are compared with the solution of the corresponding problem without external neutron sources, that is an eigenvalue problem. The method developed for this purposes it makes use of both the nodal method (for calculation of the neutron flux) and the finite differences method (for calculation of the adjoint flux). A coarse mesh finite difference method was developed for the adjoint flux calculation, which uses the output of the nodal expansion method. The results regarding the influence of the external neutron source presence for attaining criticality have shown that far from criticality it is necessary to calculate the reactivity values of the system.
Influence of the external neutron sources in the criticality prediction using 1/M curve
International Nuclear Information System (INIS)
Pereira, Valmir; Carvalho da Silva, Fernando; Martinez, Aquilino Senra
2005-01-01
The influence of external neutron sources in the process to obtain the criticality condition is estimated. To reach this objective, the three-dimensional neutron diffusion equation in two groups of energy is solved, for a subcritical PWR reactor core with external neutron sources. The results are compared with the solution of the corresponding problem without external neutron sources, that is an eigenvalue problem. The method developed for this purposes it makes use of both the nodal method (for calculation of the neutron flux) and the finite differences method (for calculation of the adjoint flux). A coarse mesh finite difference method was developed for the adjoint flux calculation, which uses the output of the nodal expansion method. The results regarding the influence of the external neutron source presence for attaining criticality have shown that far from criticality it is necessary to calculate the reactivity values of the system
International Nuclear Information System (INIS)
Polivanskij, V.P.
1989-01-01
The method to solve two-dimensional equations of neutron transport using 4P 0 -approximation is presented. Previously such approach was efficiently used for the solution of one-dimensional problems. New an attempt is made to apply the approach to solution of two-dimensional problems. Algorithm of the solution is given, as well as results of test neutron-physical calculations. A considerable as compared with diffusion approximation is shown. 11 refs
International Nuclear Information System (INIS)
Buckler, A.N.
1978-10-01
The report describes the theoretical basis of the methods that have been developed for correlating measurements of spatially distributed quantities taken on the reactor with the lattice constants in the diffusion equations. The method can be used with any thermal reactor system of current interest, but the first application is to provide a replacement for the SAMSON code for Winfrith SGHW studies, where the measurements of interest are channel powers. (author)
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
SLAROM, Neutron Flux Distribution and Spectra in Lattice Cell
International Nuclear Information System (INIS)
Nakagawa, M.; Tsuchihashi, K.
2002-01-01
1 - Description of program or function: SLAROM solves the neutron integral transport equations to determine flux distribution and spectra in a lattice and calculates cell averaged effective cross sections. 2 - Method of solution: Collision probability method for cell calculation and 1D diffusion for core calculation. 3 - Restrictions on the complexity of the problem: Variable dimensions are used throughout the program so that computer core requirements depend on a variety of program parameters
Neutronic design of a 22 MW MTR type nuclear research reactor
International Nuclear Information System (INIS)
Khamis, I.; Khattab, K.; Soleman, I.; Ghazi, N.
2006-12-01
The neutronic design calculations of a 22 MW MTR type nuclear research reactor are conducted in this project. This reactor type is selected by the Arab Atomic Energy Commission in a cooperated project. The design calculations are conducted in two methods: The deterministic method, solving the neutron transport and diffusion equations using the WIMSD4 and the CITATION codes, and the probabilistic method using the MCNP code. Good agreements are noticed between the results of the multiplication factor and the neutron flux distribution which prove the accuracy of our models using the two methods. (author)
Neutronic design of a 22 MW MTR type nuclear research reactor
International Nuclear Information System (INIS)
Khamis, I.; Khattab, K.; Soleman, I.; Ghazi, N.
2008-01-01
The neutronic design calculations of a 22 MW MTR type nuclear research reactor are conducted in this project. This reactor type is selected by the Arab Atomic Energy Commission in a cooperated project. The design calculations are conducted in two methods: The deterministic method, solving the neutron transport and diffusion equations using the WIMSD4 and the CITATION codes, and the probabilistic method using the MCNP code. Good agreements are noticed between the results of the multiplication factor and the neutron flux distribution which prove the accuracy of our models using the two methods. (authors)
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.)
Isotopic neutron sources for neutron activation analysis
International Nuclear Information System (INIS)
Hoste, J.
1988-06-01
This User's Manual is an attempt to provide for teaching and training purposes, a series of well thought out demonstrative experiments in neutron activation analysis based on the utilization of an isotopic neutron source. In some cases, these ideas can be applied to solve practical analytical problems. 19 refs, figs and tabs
Energy Technology Data Exchange (ETDEWEB)
Couto, Nozimar do
2003-07-01
Diffusion theory is traditionally applied to nuclear reactor global calculations. Based on the good results generated by the one-dimensional spectral nodal diffusion (SND) method for benchmark problems, we offer the SND method for nuclear reactor global calculations in X,Y geometry. In this method, the continuity equation and Flick law are transverse integrated in each spatial direction leading to a system of two 'one-dimensional' equations coupled by the transverse leakage terms. We then apply the SND method to numerically solve this system with constant approximations for the transverse leakage terms. We perform a spectral analysis to determine the local general solution of each 'one-dimensional' nodal equation with flat approximation for the transverse leakages. We used special auxiliary equations with parameters that are to be determined in order to preserve the analytical general solutions in the numerical algorithm. By considering continuity conditions at the node interfaces and appropriate boundary conditions, we obtain a solvable system of discretized equations involving the node-edge average scalar fluxes at each estimate of the dominant eigenvalue (k{sub eff}) in the outer power iterations. As we considered approximations to the transverse leakages, the SND method is not free of spatial truncation errors. Nevertheless, it generated good results for the typical model problems that we considered. (author)
Energy Technology Data Exchange (ETDEWEB)
Couto, Nozimar do
2003-07-01
Diffusion theory is traditionally applied to nuclear reactor global calculations. Based on the good results generated by the one-dimensional spectral nodal diffusion (SND) method for benchmark problems, we offer the SND method for nuclear reactor global calculations in X,Y geometry. In this method, the continuity equation and Flick law are transverse integrated in each spatial direction leading to a system of two 'one-dimensional' equations coupled by the transverse leakage terms. We then apply the SND method to numerically solve this system with constant approximations for the transverse leakage terms. We perform a spectral analysis to determine the local general solution of each 'one-dimensional' nodal equation with flat approximation for the transverse leakages. We used special auxiliary equations with parameters that are to be determined in order to preserve the analytical general solutions in the numerical algorithm. By considering continuity conditions at the node interfaces and appropriate boundary conditions, we obtain a solvable system of discretized equations involving the node-edge average scalar fluxes at each estimate of the dominant eigenvalue (k{sub eff}) in the outer power iterations. As we considered approximations to the transverse leakages, the SND method is not free of spatial truncation errors. Nevertheless, it generated good results for the typical model problems that we considered. (author)
International Nuclear Information System (INIS)
Mesot, J.
1992-11-01
Superconductivity in the cuprates is believed to be controlled by the density of mobile charges in the CuO 2 planes. In particular, the charge transfer process from the chains to the planes seems to play an important role. Consequently, it is crucial to observe directly the influence of different types of perturbations on the electronic structure of these compounds. The crystal field (CF) spectroscopy of the rare earth allows us to make these observations, since in the perovskite-type compounds YBa 2 Cu 3 O x (123) and YBa 2 Cu 4 O 8 (1248) the replacement of the Y ions by most of the magnetic rare-earth (R) ions does not have a detrimental effect on the superconductivity. The (2J+1)-fold degeneracy of the ground-state J-multiplet of the R ions will be partially lifted under the action of the CF potential created by the neighbouring atoms. By means of inelastic neutron scattering experiments it is possible to observe directly the transitions between the CF states. This means that we can obtain useful information on both the structural and the charge distribution parameters in the vicinity of the R ion. In the 123 and 1248 systems, the R ions are sandwiched between two CuO 2 planes, thus the CF interaction at the R sites constitutes an ideal probe of the local symmetry and charge distribution of the superconducting planes. In the first part of this work, we discuss the importance of the intermediate coupling and J mixing effects on the determination of the CF parameters of the 123 compounds. In order to quantify the charge transfer process from the chains to the planes, we performed a detailed analysis of the CF of Er 3+ in the 123 and 248 compounds under the following conditions: oxygen deficiency, Zn and Ni doping of the Cu sites, external pressure and fast neutron irradiation. In parallel, we present conclusions obtained from diffraction experiments. (author) figs., tabs., 113 refs
Energy Technology Data Exchange (ETDEWEB)
Bakeine, G.J. [Department of Clinical Medicine and Neurology, Cattinara Hospital, University of Trieste (Italy)], E-mail: jamesbakeine1@yahoo.com; Di Salvo, M. [Department of Nuclear and Theoretical Physics, University of Pavia, Via Bassi 6, Pavia (Italy); Bortolussi, S.; Stella, S. [Department of Nuclear and Theoretical Physics, University of Pavia, Via Bassi 6, Pavia (Italy); National Institute of Nuclear Physics (INFN) Section of Pavia, Via Bassi 6, Pavia (Italy); Bruschi, P. [Department of Nuclear and Theoretical Physics, University of Pavia, Via Bassi 6, Pavia (Italy); Bertolotti, A.; Nano, R. [Department of Animal Biology University of Pavia, Piazza Botta, Pavia (Italy); Clerici, A.; Ferrari, C.; Zonta, C. [Department of Surgery University of Pavia, Piazza Botta, Pavia (Italy); Marchetti, A. [Scientific Research Office, Fondazione San Matteo University Policlinic, Pavia (Italy); Altieri, S. [Department of Nuclear and Theoretical Physics, University of Pavia, Via Bassi 6, Pavia (Italy); National Institute of Nuclear Physics (INFN) Section of Pavia, Via Bassi 6, Pavia (Italy)
2009-07-15
In order for boron neutron capture therapy (BNCT) to be eligible for application in lung tumour disease, three fundamental criteria must be fulfilled: there must be selective uptake of boron in the tumour cells with respect to surrounding healthy tissue, biological effectiveness of the radiation therapy and minimal damage or collateral effects of the irradiation on the surrounding tissues. In this study, we evaluated the biological effectiveness of BNCT by in vitro irradiation of rat colon-carcinoma cells previously incubated in boron-enriched medium. One part of these cells was re-cultured in vitro while the other was inoculated via the inferior vena cava to induce pulmonary metastases in a rat model. We observed a post-irradiation in vitro cell viability of 0.05% after 8 days of cell culture. At 4 months follow-up, all animal subjects in the treatment group that received irradiated boron-containing cells were alive. No animal survived beyond 1 month in the control group that received non-treated cells (p<0.001 Kaplan-Meier). These preliminary findings strongly suggest that BNCT has a significant lethal effect on tumour cells and post irradiation surviving cells lose their malignant capabilities in vivo. This radio-therapeutic potential warrants the investigation of in vivo BNCT for lung tumour metastases.
International Nuclear Information System (INIS)
Bakeine, G.J.; Di Salvo, M.; Bortolussi, S.; Stella, S.; Bruschi, P.; Bertolotti, A.; Nano, R.; Clerici, A.; Ferrari, C.; Zonta, C.; Marchetti, A.; Altieri, S.
2009-01-01
In order for boron neutron capture therapy (BNCT) to be eligible for application in lung tumour disease, three fundamental criteria must be fulfilled: there must be selective uptake of boron in the tumour cells with respect to surrounding healthy tissue, biological effectiveness of the radiation therapy and minimal damage or collateral effects of the irradiation on the surrounding tissues. In this study, we evaluated the biological effectiveness of BNCT by in vitro irradiation of rat colon-carcinoma cells previously incubated in boron-enriched medium. One part of these cells was re-cultured in vitro while the other was inoculated via the inferior vena cava to induce pulmonary metastases in a rat model. We observed a post-irradiation in vitro cell viability of 0.05% after 8 days of cell culture. At 4 months follow-up, all animal subjects in the treatment group that received irradiated boron-containing cells were alive. No animal survived beyond 1 month in the control group that received non-treated cells (p<0.001 Kaplan-Meier). These preliminary findings strongly suggest that BNCT has a significant lethal effect on tumour cells and post irradiation surviving cells lose their malignant capabilities in vivo. This radio-therapeutic potential warrants the investigation of in vivo BNCT for lung tumour metastases.
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
Energy Technology Data Exchange (ETDEWEB)
Bal, G. [Departement MMN, Service IMA, Direction des Etudes et Recherches, Electricite de France (EDF), 92 - Clamart (France)
1995-10-01
Neutron transport in nuclear reactors is quite well modelled by the linear Boltzmann transport equation. Its solution is relatively easy, but unfortunately too expensive to achieve whole core computations. Thus, we have to simplify it, for example by homogenizing some physical characteristics. However, the solution may then be inaccurate. Moreover, in strongly homogeneous areas, the error may be too big. Then we would like to deal with such an inconvenient by solving the equation accurately on this area, but more coarsely away from it, so that the computation is not too expensive. This problem is the subject of a thesis. We present here some results obtained for slab geometry. The couplings between the fine and coarse discretization regions could be conceived in a number of approaches. Here, we only deal with the coupling at crossing the interface between two sub-domains. In the first section, we present the coupling of discrete ordinate methods for solving the homogeneous, isotropic and mono-kinetic equation. Coupling operators are defined and shown to be optimal. The second and the third sections are devoted to an extension of the previous results when the equation is non-homogeneous, anisotropic and multigroup (under some restrictive assumptions). Some numerical results are given in the case of isotropic and mono-kinetic equations. (author) 15 refs.
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.
FINELM: a multigroup finite element diffusion code
International Nuclear Information System (INIS)
Higgs, C.E.; Davierwalla, D.M.
1981-06-01
FINELM is a FORTRAN IV program to solve the Neutron Diffusion Equation in X-Y, R-Z, R-theta, X-Y-Z and R-theta-Z geometries using the method of Finite Elements. Lagrangian elements of linear or higher degree to approximate the spacial flux distribution have been provided. The method of dissections, coarse mesh rebalancing and Chebyshev acceleration techniques are available. Simple user defined input is achieved through extensive input subroutines. The input preparation is described followed by a program structure description. Sample test cases are provided. (Auth.)
Energy Technology Data Exchange (ETDEWEB)
Najera H, M.C.; Benitez R, J.S. [ININ, 52045 Ocoyoacac, Estado de Mexico (Mexico)
2003-07-01
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)
Multi-level nonlinear diffusion acceleration method for multigroup transport k-Eigenvalue problems
International Nuclear Information System (INIS)
Anistratov, Dmitriy Y.
2011-01-01
The nonlinear diffusion acceleration (NDA) method is an efficient and flexible transport iterative scheme for solving reactor-physics problems. This paper presents a fast iterative algorithm for solving multigroup neutron transport eigenvalue problems in 1D slab geometry. The proposed method is defined by a multi-level system of equations that includes multigroup and effective one-group low-order NDA equations. The Eigenvalue is evaluated in the exact projected solution space of smallest dimensionality, namely, by solving the effective one- group eigenvalue transport problem. Numerical results that illustrate performance of the new algorithm are demonstrated. (author)
Zapata, M. A. Uh; Van Bang, D. Pham; Nguyen, K. D.
2016-05-01
This paper presents a parallel algorithm for the finite-volume discretisation of the Poisson equation on three-dimensional arbitrary geometries. The proposed method is formulated by using a 2D horizontal block domain decomposition and interprocessor data communication techniques with message passing interface. The horizontal unstructured-grid cells are reordered according to the neighbouring relations and decomposed into blocks using a load-balanced distribution to give all processors an equal amount of elements. In this algorithm, two parallel successive over-relaxation methods are presented: a multi-colour ordering technique for unstructured grids based on distributed memory and a block method using reordering index following similar ideas of the partitioning for structured grids. In all cases, the parallel algorithms are implemented with a combination of an acceleration iterative solver. This solver is based on a parabolic-diffusion equation introduced to obtain faster solutions of the linear systems arising from the discretisation. Numerical results are given to evaluate the performances of the methods showing speedups better than linear.
Directory of Open Access Journals (Sweden)
Gratien Jean-Marc
2017-03-01
Full Text Available Nowadays, some frameworks like Arcane and Dune offer a number of advanced tools to deal with the complexity related to parallelism, meshes and linear solvers. However, they do not handle the high level complexity related to discretization methods and physical models. Generative programming and Domain Specific Languages (DSL are key technologies allowing to write code with a high level expressive language and take advantage of the efficiency of generated code with low level services. DSL may be embedded in host languages like Python or C++. Such languages, named in that case Domain Specific Embedded Languages (DSEL, are applied for instance in frameworks like Fenics or Feel++ which are dedicated to the domain of Finite Element (FE methods and Galerkin methods. ArcFVDSL is a DSEL developed on top of the Arcane framework, aiming to implement various lowest order methods (Finite-Volume (FV, Mimetic Finite Difference (MFD, Mixed Hybrid Finite Volume (MHFV, etc. for diffusive problems on general meshes. In this paper, we present various implementations of different complex academic problems. We focus on the capability of the language to allow the description and the resolution of these problems with several lowest-order methods. We illustrate the benefits of such technology combined to runtime system tools like Heterogeneous Abstract RunTime System (HARTS and its ability to handle seamlessly new heterogeneous architectures with multi-core processors enhanced by General Purpose computing on Graphics Processing Units (GP-GPU. We present the performance results of each implementation on different kinds of heterogeneous hardware architecture.
Energy Technology Data Exchange (ETDEWEB)
Perrin, P [Commisariat a l' Energie Atomique, Grenoble (France). Centre d' Etudes Nucleaires
1963-07-15
Experimental measurements of 14 MeV fast neutrons scattering by {sup 12}C by time-flight spectrometer, with a 1.7 n. sec over-all resolution. The excitation of the 7.65 MeV level is observed. (author) [French] Etude experimentate de la diffusion par {sup 12}C des neutrons rapides de 14 MeV a l'aide d'un spectrometre de resolution totale de 17 n/s. Observation de l'excitation du niveau 0+ de 7,65 MeV. (auteur)
Lattice cell diffusion coefficients. Definitions and comparisons
International Nuclear Information System (INIS)
Hughes, R.P.
1980-01-01
Definitions of equivalent diffusion coefficients for regular lattices of heterogeneous cells have been given by several authors. The paper begins by reviewing these different definitions and the unification of their derivation. This unification makes clear how accurately each definition (together with appropriate cross-section definitions to preserve the eigenvalue) represents the individual reaction rates within the cell. The approach can be extended to include asymmetric cells and whereas before, the buckling describing the macroscopic flux shape was real, here it is found to be complex. A neutron ''drift'' coefficient as well as a diffusion coefficient is necessary to produce the macroscopic flux shape. The numerical calculation of the various different diffusion coefficients requires the solutions of equations similar to the ordinary transport equation for an infinite lattice. Traditional reactor physics codes are not sufficiently flexible to solve these equations in general. However, calculations in certain simple cases are presented and the theoretical results quantified. In difficult geometries, Monte Carlo techniques can be used to calculate an effective diffusion coefficient. These methods relate to those already described provided that correlation effects between different generations of neutrons are included. Again, these effects are quantified in certain simple cases. (author)
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)
A matrix formalism to solve interface condition equations in a reactor system
Energy Technology Data Exchange (ETDEWEB)
Matausek, M V [Boris Kidric Institute of Nuclear Sciences Vinca, Beograd (Yugoslavia)
1970-05-15
When a nuclear reactor or a reactor lattice cell is treated by an approximate procedure to solve the neutron transport equation, as the last computational step often appears a problem of solving systems of algebraic equations stating the interface and boundary conditions for the neutron flux moments. These systems have usually the coefficient matrices of the block-bi diagonal type, containing thus a large number of zero elements. In the present report it is shown how such a system can be solved efficiently accounting for all the zero elements both in the coefficient matrix and in the free term vector. The procedure is presented here for the case of multigroup P{sub 3} calculation of neutron flux distribution in a cylindrical reactor lattice cell. Compared with the standard gaussian elimination method, this procedure is more advantageous both in respect to the number of operations needed to solve a given problem and in respect to the computer memory storage requirements. A similar formalism can also be applied for other approximate methods, for instance for multigroup diffusion treatment of a multi zone reactor. (author)
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.)
Energy Technology Data Exchange (ETDEWEB)
Magat, Ph
1997-04-01
Today neutron transport in PWR's core is routinely computed through the transport-diffusion(2 groups) scheme. This method gives satisfactory results for reactors operating in normal conditions but the 2 group diffusion approximation is unable to take into account interface effects or anisotropy. The improvement of this scheme is logically possible through the use of a simplified P{sub N} method (SP{sub N}) for the modeling of the core. The comparison between S{sub N} calculations and SP{sub N} calculations shows an excellent agreement on eigenvalues as well as on power maps. We can notice that: -) it is no use extending the development beyond P{sub 3}, there is no effect; -) the P{sub 1} development is adequate; and -) the P{sub 0} development is totally inappropriate. Calculations performed on the N4 core of the Chooz power plant have enabled us to compare diffusion operators with transport operators (SP{sub 1}, SP{sub 3}, SP{sub 5} and SP{sub 7}). These calculations show that the implementation of the SP{sub N} method is feasible but the extra-costs in computation times and memory are important. We recommend: SP{sub 5}P{sub 1} calculations for heterogeneous 2-dimension geometry and SP{sub 3}P{sub 1} calculations for the homogeneous 3-dimension geometry. (A.C.)
Energy Technology Data Exchange (ETDEWEB)
Magat, Ph
1997-04-01
Today neutron transport in PWR's core is routinely computed through the transport-diffusion(2 groups) scheme. This method gives satisfactory results for reactors operating in normal conditions but the 2 group diffusion approximation is unable to take into account interface effects or anisotropy. The improvement of this scheme is logically possible through the use of a simplified P{sub N} method (SP{sub N}) for the modeling of the core. The comparison between S{sub N} calculations and SP{sub N} calculations shows an excellent agreement on eigenvalues as well as on power maps. We can notice that: -) it is no use extending the development beyond P{sub 3}, there is no effect; -) the P{sub 1} development is adequate; and -) the P{sub 0} development is totally inappropriate. Calculations performed on the N4 core of the Chooz power plant have enabled us to compare diffusion operators with transport operators (SP{sub 1}, SP{sub 3}, SP{sub 5} and SP{sub 7}). These calculations show that the implementation of the SP{sub N} method is feasible but the extra-costs in computation times and memory are important. We recommend: SP{sub 5}P{sub 1} calculations for heterogeneous 2-dimension geometry and SP{sub 3}P{sub 1} calculations for the homogeneous 3-dimension geometry. (A.C.)
International Nuclear Information System (INIS)
Irvine, J.M.
1978-01-01
The subject is covered in chapters entitled: introduction (resume of stellar evolution, gross characteristics of neutron stars); pulsars (pulsar characteristics, pulsars as neutron stars); neutron star temperatures (neutron star cooling, superfluidity and superconductivity in neutron stars); the exterior of neutron stars (the magnetosphere, the neutron star 'atmosphere', pulses); neutron star structure; neutron star equations of state. (U.K.)
Diffusion Under Geometrical Constraint
Ogawa, Naohisa
2014-01-01
Here we discus the diffusion of particles in a curved tube. This kind of transport phenomenon is observed in biological cells and porous media. To solve such a problem, we discuss the three dimensional diffusion equation with a confining wall forming a thinner tube. We find that the curvature appears in a effective diffusion coefficient for such a quasi-one-dimensional system. As an application to higher dimensional case, we discuss the diffusion in a curved surface with ...
Energy Technology Data Exchange (ETDEWEB)
Otnes, K; Palevsky, H [Brookhaven National Laboratory, Upton, NY (United States)
1963-01-15
A new chopper apparatus for use at the Brookhaven High Flux Beam Reactor is now under construction. It is a three-element phased rotof system. The rotors are 80 cm in diameter, run at a maximum speed of 15000 rev/min, and are designed to give three neutron bursts of monochromatic neutrons per revolution. Two rotors spin about a horizontal axis whereas the third operates vertically. The system can be operated with either one, two or three of the chopper elements, depending on the type of measurement that is completed. For inelastic measurements where the neutron gains energy, a double rotor system will be most useful. For this configuration the burst time and wave length spread (full widths at 1/2 maximum) will be 16 {mu}s and 0.16 A for 4 A incident neutrons, and the intensity at the sample (4 x 1.6 cm) will be 2 x 10{sup 6} n/s. For quasi-elastic and elastic neutron measurements the three-rotor configuration will be best suited. The corresponding burst time and wave length spread can be as small as 8 {mu}s and 0.04 A giving an intensity of 10{sup 4} n/s on a sample of (4 X 0.8 c m ), The wave length and time resolution are adjustable between the above two limits in such a way as to obtain the maximum neutron intensity for a given experiment. (author) [French] Un nouveau selecteur destine au reacteur a haut flux de Brookhaven est actuellement en construction. Il s'agit d'un dispositif a trois rotors dephasables. Les rotors ont un diametre de 80 cm, tournent a une vitesse maximum de 15 000 tours pat minute et sont concus de maniere a fournir trois bouffees de neutrons monochromatiques a chaque tour. Deux rotors tournent autour d'un axe horizontal, le troisieme, autour d'un axe vertical. Le dispositif peut fonctionner avec un, deux ou trois elements, selon le type de mesure que l'on se propose de faire. Pour les mesures de diffusion inelastique ou les neutrons gagnent de l'energie, un dispositif a deux rotors sera tres utile. Pour cette configuation, la duree et la
Overview of the history of neutronics computations
International Nuclear Information System (INIS)
Gelbard, E.M.
1992-01-01
This paper provides some background and perspective on the history of neutronics computations. The author started his carerr at Bettis Atomic Power Laboratory (BAPL) in 1954. At that time, computers were primitive and unfamiliar to most of us. Bettis did own an IBM Card Programmed Computer, which, as its name suggested, had a punched-card memory, and some of the industry's first cross-section preparation codes (the early MUFTs) were written for this machine by Ben Mount. There was also at BAPL another digital machine, which spewed output everywhere on punched tape. But the laboratory's most powerful machine was an analog computer that solved two-group diffusion equations in two dimensions. An excellent physicist of that period argued that analog machines were the wave of the future because digital computers could never solve the diffusion equation in two dimensions. At the time, this seemed like a very reasonable prediction; yet it was not very long before Bettis was renting time on UNIVACs all over the country precisely to solve the two-dimensional diffusion equation. Since then, we have learned that it is always risky to predict future trends in the computer industry
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
Exchange bias studied with polarized neutron reflectivity
International Nuclear Information System (INIS)
Velthuis, S. G. E. te
2000-01-01
The role of Polarized Neutron Reflectivity (PNR) for studying natural and synthetic exchange biased systems is illustrated. For a partially oxidized thin film of Co, cycling of the magnetic field causes a considerable reduction of the bias, which the onset of diffuse neutron scattering shows to be due to the loosening of the ferromagnetic domains. On the other hand, PNR measurements of a model exchange bias junction consisting of an n-layered Fe/Cr antiferromagnetic (AF) superlattice coupled with an m-layered Fe/Cr ferromagnetic (F) superlattice confirm the predicted collinear magnetization in the two superlattices. The two magnetized states of the F (along or opposite to the bias field) differ only in the relative orientation of the F and adjacent AF layer. The possibility of reading clearly the magnetic state at the interface pinpoints the commanding role that PNR is having in solving this intriguing problem
A multi-group neutron noise simulator for fast reactors
International Nuclear Information System (INIS)
Tran, Hoai Nam; Zylbersztejn, Florian; Demazière, Christophe; Jammes, Christian; Filliatre, Philippe
2013-01-01
Highlights: • The development of a neutron noise simulator for fast reactors. • The noise equation is solved fully in a frequency-domain. • A good agreement with ERANOS on the static calculations. • Noise calculations induced by a localized perturbation of absorption cross section. - Abstract: A neutron noise simulator has been developed for fast reactors based on diffusion theory with multi-energy groups and several groups of delayed neutron precursors. The tool is expected to be applicable for core monitoring of fast reactors and also for other reactor types with hexagonal fuel assemblies. The noise sources are modeled through small stationary fluctuations of macroscopic cross sections, and the induced first order noise is solved fully in the frequency domain. Numerical algorithms are implemented for solving both the static and noise equations using finite differences for spatial discretization, where a hexagonal assembly is radially divided into finer triangular meshes. A coarse mesh finite difference (CMFD) acceleration has been used for accelerating the convergence of both the static and noise calculations. Numerical calculations have been performed for the ESFR core with 33 energy groups and 8 groups of delayed neutron precursors using the cross section data generated by the ERANOS code. The results of the static state have been compared with those obtained using ERANOS. The results show an adequate agreement between the two calculations. Noise calculations for the ESFR core have also been performed and demonstrated with an assumption of the perturbation of the absorption cross section located at the central fuel ring
CYLFUX, Fast Reactor Reactivity Transients Simulation in LWR by 2-D 2 Group Diffusion
International Nuclear Information System (INIS)
Schmidt, A.
1973-01-01
1 - Nature of physical problem solved: A 2-dimensional calculation of the 2-group, space-dependent neutron diffusion equations is performed in r-z geometry using an arbitrary number of groups of delayed neutron precursors. The program is designed to simulate fast reactivity excursions in light water reactors taking into account Doppler feedback via adiabatic heatup of fuel. Axial motions of control rods may be considered including scram action on option. 2 - Method of solution: The differential equations are solved at each time step by an explicit finite difference method using two time levels. The stationary distributions are obtained by using the same algorithm. 3 - Restrictions on the complexity of the problem: No restriction to the number of space points and delayed neutron energy groups besides the computer size
A modular spherical harmonics approach to the neutron transport equation
International Nuclear Information System (INIS)
Inanc, F.; Rohach, A.F.
1989-01-01
A modular nodal method was developed for solving the neutron transport equation in 2-D xy coordinates. The spherical harmonic expansion was used for approximating the second-order even-parity form of the neutron transport equation. The boundary conditions of the spherical harmonics approximation were derived in a form to have forms analogous to the partial currents in the neutron diffusion equation. Relations were developed for generating both the second-order spherical harmonic equations and the boundary conditions in an automated computational algorithm. Nodes using different orders of the spherical harmonics approximation to the transport equation were interfaced through mixed-type boundary conditions. The determination of spherical harmonic orders implemented in the nodes were determined by the scheme in an automated manner. Results of the method compared favorably to benchmark problems. (author)
Intense fusion neutron sources
International Nuclear Information System (INIS)
Kuteev, B. V.; Goncharov, P. R.; Sergeev, V. Yu.; Khripunov, V. I.
2010-01-01
The review describes physical principles underlying efficient production of free neutrons, up-to-date possibilities and prospects of creating fission and fusion neutron sources with intensities of 10 15 -10 21 neutrons/s, and schemes of production and application of neutrons in fusion-fission hybrid systems. The physical processes and parameters of high-temperature plasmas are considered at which optimal conditions for producing the largest number of fusion neutrons in systems with magnetic and inertial plasma confinement are achieved. The proposed plasma methods for neutron production are compared with other methods based on fusion reactions in nonplasma media, fission reactions, spallation, and muon catalysis. At present, intense neutron fluxes are mainly used in nanotechnology, biotechnology, material science, and military and fundamental research. In the near future (10-20 years), it will be possible to apply high-power neutron sources in fusion-fission hybrid systems for producing hydrogen, electric power, and technological heat, as well as for manufacturing synthetic nuclear fuel and closing the nuclear fuel cycle. Neutron sources with intensities approaching 10 20 neutrons/s may radically change the structure of power industry and considerably influence the fundamental and applied science and innovation technologies. Along with utilizing the energy produced in fusion reactions, the achievement of such high neutron intensities may stimulate wide application of subcritical fast nuclear reactors controlled by neutron sources. Superpower neutron sources will allow one to solve many problems of neutron diagnostics, monitor nano-and biological objects, and carry out radiation testing and modification of volumetric properties of materials at the industrial level. Such sources will considerably (up to 100 times) improve the accuracy of neutron physics experiments and will provide a better understanding of the structure of matter, including that of the neutron itself.
Intense fusion neutron sources
Kuteev, B. V.; Goncharov, P. R.; Sergeev, V. Yu.; Khripunov, V. I.
2010-04-01
The review describes physical principles underlying efficient production of free neutrons, up-to-date possibilities and prospects of creating fission and fusion neutron sources with intensities of 1015-1021 neutrons/s, and schemes of production and application of neutrons in fusion-fission hybrid systems. The physical processes and parameters of high-temperature plasmas are considered at which optimal conditions for producing the largest number of fusion neutrons in systems with magnetic and inertial plasma confinement are achieved. The proposed plasma methods for neutron production are compared with other methods based on fusion reactions in nonplasma media, fission reactions, spallation, and muon catalysis. At present, intense neutron fluxes are mainly used in nanotechnology, biotechnology, material science, and military and fundamental research. In the near future (10-20 years), it will be possible to apply high-power neutron sources in fusion-fission hybrid systems for producing hydrogen, electric power, and technological heat, as well as for manufacturing synthetic nuclear fuel and closing the nuclear fuel cycle. Neutron sources with intensities approaching 1020 neutrons/s may radically change the structure of power industry and considerably influence the fundamental and applied science and innovation technologies. Along with utilizing the energy produced in fusion reactions, the achievement of such high neutron intensities may stimulate wide application of subcritical fast nuclear reactors controlled by neutron sources. Superpower neutron sources will allow one to solve many problems of neutron diagnostics, monitor nano-and biological objects, and carry out radiation testing and modification of volumetric properties of materials at the industrial level. Such sources will considerably (up to 100 times) improve the accuracy of neutron physics experiments and will provide a better understanding of the structure of matter, including that of the neutron itself.
Energy Technology Data Exchange (ETDEWEB)
Harris, D; Duffil, C [Atomic Energy of Canada Ltd., Chalk River, Ontario (Canada); Wraight, L A [Aere, Harwell, Didcot, Berks (United Kingdom)
1963-01-15
Scintillation counters discussed in this paper are of two types : (i) UP or B{sub 2}O{sub 3} fixed with zinc sulphide in varving composition, (ii) Li containing glasses of varying composition. The ideal composition of each rype for neutron scattering experiments and their relative sensitivity tae neutrons and {gamma}-rays are considered. The ZnS type can be used with a {gamma}-ray pulse shape discriminator and practical experience of its use in a multi-counter time-of-flight experiment is described. The Li glass has higher {gamma}-background but also higher neutron efficiency. Performance figures of a scintillator containing 25% by wt. Li{sub 2}O and 1 mm thick will be given. (author) [French] Les compteurs a scintillations etudies sont de deux types : i) LiF ou B{sub 2}O{sub 3} fixe par du sulfure de zinc en composition variable, ii) verres contenant du lithium en composition variable. Les auteurs examinent la composition ideale de chaque type de compteur pour les experiences de diffusion de neutrons, ainsi que leur sinsibilite rrelative aux neutrons et aux rayons gamma. On peut utiliser le compteur a ZnS avec un discriminates de forme pour rayons gamma; les auteurs decrivent l'experience qu'ils ont de son emploi dans une experience de temps de vol a plusieurs compteurs. Le compteur verre-Li a un mouvement propre plus eleve pour les rayons gamma mais une meilleure efficacite vis-a-vis des neutrons. Les auteurs donnent quelques chiffres concernant le fonctionnement d'un scintillateur contenant 25% en poids de Li{sub 2}O et ayant une epaisseur de un millimetre. (author) [Spanish] Los contadores de centelleo examinados en esta memoria son de dos tipos : a) de LiF o B{sub 2}O{sub 3} mezclado con sulfuro de cinc en proporciones variables; b) de vidrios litiados de diversas composiciones. Los autores estudian la composicion ideal de cada tipo para experimentos de dispersion neutronica, asi como su sensibilidad relativa a los neutrones y a los rayos gamma. El tio de Zn
Neutron logging reliability techniques and apparatus
International Nuclear Information System (INIS)
Johnstone, C.W.
1975-01-01
Apparatus and methods for verifying the validity of data derived at least in part by neutron logging of earth formations, and, where indicated, for affording neutron diffusion-corrected values of such data, are disclosed. (WHK)
Energy Technology Data Exchange (ETDEWEB)
Candelore, N R; Gast, R C; Ondis, II, L A
1978-08-01
The RCP01 Monte Carlo program for the CDC-7600 and CDC-6600 performs fixed source or eigenfunction neutron reaction rate calculations, or photon reaction rate calculations, for complex geometries. The photon calculations may be linked to the neutron reaction rate calculations. For neutron calculations, the full energy range is treated as required for neutron birth by the fission process and the subsequent neutron slowing down and thermalization, i.e., 10 MeV to 0 eV; for photon calculations the same energy range is treated. The detailed cross sections required for the neutron or photon collision processes are provided by RCPL1. This report provides details of the various types of neutron and photon starts and collisions, the common geometry tracking, and the input required. 37 figures, 1 table.
International Nuclear Information System (INIS)
Woznicki, Z.
1976-05-01
This report presents the AGA two-sweep iterative methods belonging to the family of factorization techniques in their practical application in the HEXAGA-II two-dimensional programme to obtain the numerical solution to the multi-group, time-independent, (real and/or adjoint) neutron diffusion equations for a fine uniform triangular mesh. An arbitrary group scattering model is permitted. The report written for the users provides the description of input and output. The use of HEXAGA-II is illustrated by two sample reactor problems. (orig.) [de
Diffusion in Coulomb crystals.
Hughto, J; Schneider, A S; Horowitz, C J; Berry, D K
2011-07-01
Diffusion in Coulomb crystals can be important for the structure of neutron star crusts. We determine diffusion constants D from molecular dynamics simulations. We find that D for Coulomb crystals with relatively soft-core 1/r interactions may be larger than D for Lennard-Jones or other solids with harder-core interactions. Diffusion, for simulations of nearly perfect body-centered-cubic lattices, involves the exchange of ions in ringlike configurations. Here ions "hop" in unison without the formation of long lived vacancies. Diffusion, for imperfect crystals, involves the motion of defects. Finally, we find that diffusion, for an amorphous system rapidly quenched from Coulomb parameter Γ=175 to Coulomb parameters up to Γ=1750, is fast enough that the system starts to crystalize during long simulation runs. These results strongly suggest that Coulomb solids in cold white dwarf stars, and the crust of neutron stars, will be crystalline and not amorphous.
Investigating The Integral Control Rod Worth Of The Miniature Neutron Source Reactor MNSR
International Nuclear Information System (INIS)
Nguyen Hoang Hai; Do Quang Binh
2011-01-01
Determining control rod characteristics is an essential problem of nuclear reactor analysis. In this research, the integral control rod worth of the miniature neutron source reactor MNSR is investigated. Some other parameters of the nuclear reactor, such as core excess reactivity, shut down margin, are also calculated. Group constants for all reactor components are generated by the WIMSD code and then are used in the CITATION code to solve the neutron diffusion equations. The maximum relative error of the calculated results compared with the measurement data is about 3.5%. (author)
Solving quantum riddles with neutron scattering
Energy Technology Data Exchange (ETDEWEB)
Fobes, David M. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Janoschek, Marc [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-05-16
Quantum materials exhibit a rich landscape of highly-degenerate quantum states that are widely regarded to hold vast potential for future applications, ranging from power management and transmission, to platforms for quantum computation, to novel versatile sensors and electronics. A key to realizing the promise of future applications is to identify the fundamental energy scales that control the emergence of such quantum states and their properties.
Multi-level methods for solving multigroup transport eigenvalue problems in 1D slab geometry
International Nuclear Information System (INIS)
Anistratov, D. Y.; Gol'din, V. Y.
2009-01-01
A methodology for solving eigenvalue problems for the multigroup neutron transport equation in 1D slab geometry is presented. In this paper we formulate and compare different variants of nonlinear multi-level iteration methods. They are defined by means of multigroup and effective one-group low-order quasi diffusion (LOQD) equations. We analyze the effects of utilization of the effective one-group LOQD problem for estimating the eigenvalue. We present numerical results to demonstrate the performance of the iteration algorithms in different types of reactor-physics problems. (authors)
Directory of Open Access Journals (Sweden)
Espinat D.
2006-11-01
Full Text Available Les techniques de diffusion, des rayons X, des neutrons et de la lumière, jouent un rôle très important pour la compréhension des milieux colloïdaux. Peu d'articles de la littérature s'attachent à présenter conjointement les trois méthodes. Nous avons, dans la première partie de cet article, détaillé les principes théoriques en insistent tout particulièrement sur les spécificités de chacune. Après les rappels concernant la diffusion par les systèmes dilués, nous nous sommes intéressés aux systèmes concentrés pour lesquels les entités diffusantes sont en interaction. Les milieux dispersés montrent souvent une certaine polydispersité que l'on cherche à mesurer; les techniques de diffusion permettent cette mesure. Nous terminerons cette revue par une description des appareillages utilisés. La deuxième partie de cet article concernera une large illustration des possibilités de ces méthodes d'analyse à l'étude des systèmes colloïdaux, sur la base de travaux effectués à I'IFP (Institut Français du Pétrole ou dans de nombreux laboratoires de recherche extérieurs. This article aims to describe X-ray, neutron and light scattering techniques with emphasis on their specific nature and their scope of application. Indeed, whereas light diffusion has been used for a long time in research laboratories, in particular for characterizing polymers in solution, small angle X-ray scattering has been the subject of renewed interest in recent years. Neutron scattering, which is obviously more difficultly accessible, has proven to be extremely useful for studying various systems for which light and X-ray scattering remain relatively powerless. Whereas there is an abundant literature concerning various applications of the three methods, it should be noted that only a few articles have attempted to describe all three techniques at the same time. In this article we have tried to make up for this lack, and as such it was
Thermal neutron albedo measurements for multilithic reflectors
International Nuclear Information System (INIS)
Mehboob, Khurram; Ahmed, Raheel; Ali, Majid; Tabassam, Uzma
2013-01-01
Highlights: • Measurement of thermal neuron albedo for multilithic reflectors. • Modeling of experiments in MATLAB. • Comparison of numerical calculated and experimental values. • Study of thermal neutron albedo in different multilayered shielding. - Abstract: An experimental measurement of the thermal neutron (0.025 eV) albedo (αth) has been carried out for multilithic shielding by using Am–Be neutron source and BF 3 detector. The measured saturation value for the thermal albedo of paraffin wax has been found to be 0.734 ± 0.020, which is in close agreement to the corresponding value 0.83 quoted in the literature. The thermal neutron albedo has been measured for the multilayered shielding in copper–wood, copper–aluminum, wood–paraffin and paraffin–iron combinations in horizontal geometric configurations. Modeling and numerical simulation have been carried out by developing a MATLAB code which solves the diffusion equation in order to calculate the experimental results. Good agreement has been found between the numerical calculated and experimental results. The uncertainties in the measurements have also been calculated based on error propagation of the underlying Poisson distribution
Long range diffusion of hydrogen in yttrium
International Nuclear Information System (INIS)
Anderson, I.S.; Scherrer, P.; Ross, D.K.
1989-01-01
The diffusion of H in single crystals of YH 0.2 is investigated by means of Quasielastic neutron scattering between 593 K and 695 K. Individual jump rates giving rise to long range and local diffusion are determined. (orig.)
The numerical analysis of eigenvalue problem solutions in the multigroup diffusion theory
International Nuclear Information System (INIS)
Woznick, Z.I.
1994-01-01
In this paper a general iteration strategy for solving the discrete form of multidimensional neutron diffusion equations is described. Usually the solution method is based on the system of inner and outer iterations. The presented matrix formalism allows us to visualize clearly, how the used matrix splitting influences the structure of the matrix in an eigenvalue problem to be solved as well as the independence between inner and outer iterations within global iterations. To keep the page limit, the present version of the paper consists only with first three of five sections given in the original paper under the same title (which will be published soon). (author). 13 refs
Neutron transportation simulator
International Nuclear Information System (INIS)
Uenohara, Yuzo.
1995-01-01
In the present invention, problems in an existent parallelized monte carlo method is solved, and behaviors of neutrons in a large scaled system are accurately simulated at a high speed. Namely, a neutron transportation simulator according to the monte carlo method simulates movement of each of neutrons by using a parallel computer. In this case, the system to be processed is divided based on a space region and an energy region to which neutrons belong. Simulation of neutrons in the divided regions is allotted to each of performing devices of the parallel computer. Tarry data and nuclear data of the neutrons in each of the regions are memorized dispersedly to memories of each of the performing devices. A transmission means for simulating the behaviors of the neutrons in the region by each of the performing devices, as well as transmitting the information of the neutrons, when the neutrons are moved to other region, to the performing device in a transported portion are disposed to each of the performing devices. With such procedures, simulation for the neutrons in the allotted region can be conducted with small capacity of memories. (I.S.)
Luo, Chengtao; Bansal, Dipanshu; Li, Jiefang; Viehland, Dwight; Winn, Barry; Ren, Yang; Li, Xiaobing; Luo, Haosu; Delaire, Olivier
2017-11-01
Neutron and x-ray scattering measurements were performed on (N a1 /2B i1 /2 ) Ti O3-x at %BaTi O3 (NBT-x BT ) single crystals (x =4 , 5, 6.5, and 7.5) across the morphotropic phase boundary (MPB), as a function of both composition and temperature, and probing both structural and dynamical aspects. In addition to the known diffuse scattering pattern near the Γ points, our measurements revealed new, faint superlattice peaks, as well as an extensive diffuse scattering network, revealing a short-range ordering of polar nanoregions (PNR) with a static stacking morphology. In samples with compositions closest to the MPB, our inelastic neutron scattering investigations of the phonon dynamics showed two unusual features in the acoustic phonon branches, between the superlattice points, and between the superlattice points and Γ points, respectively. These critical elements are not present in the other compositions away from the MPB, which suggests that these features may be related to the tilt modes coupling behavior near the MPB.
Energy Technology Data Exchange (ETDEWEB)
Hugouvieux, V
2004-11-15
In this thesis, both theoretical and experimental studies of liquids are done. Neutron scattering enables structural and dynamical properties of liquids to be investigated. On the theoretical side, molecular dynamics simulations are of great interest since they give positions and velocities of the atoms and the forces acting on each of them. They also enable spatial and temporal correlations to be computed and these quantities are also available from neutron scattering experiments. Consequently, the comparison can be made between results from molecular dynamics simulations and from neutron scattering experiments, in order to improve our understanding of the structure and dynamics of liquids. However, since extracting reliable data from a neutron scattering experiment is difficult, we propose to simulate the experiment as a whole, including both instrument and sample, in order to gain understanding and to evaluate the impact of the different parasitic contributions (absorption, multiple scattering associated with elastic and inelastic scattering, instrument resolution). This approach, in which the sample is described by its structure and dynamics as computed from molecular dynamics simulations, is presented and tested on isotropic model systems. Then liquid germanium is investigated by inelastic neutron scattering and both classical and ab initio molecular dynamics simulations. This enables us to simulate the experiment we performed and to evaluate the influence of the contributions from the instrument and from the sample on the detected signal. (author)
A Hennart nodal method for the diffusion equation
International Nuclear Information System (INIS)
Lesaint, P.; Noceir, S.; Verwaerde, D.
1995-01-01
A modification of the Hennart nodal method for neutron diffusion problems is presented. The final system of equations obtained by this method is not positive definite. However, a flux elimination technique leads to a simple positive definite system, which can be solved by the traditional iterative methods. Calculations of a two-dimensional International Atomic Energy Agency benchmark problem are performed and compared with results of the original Hennart nodal method and some finite element methods. The high computational efficiency of this modified nodal method is clearly demonstrated
International Nuclear Information System (INIS)
Aufiero, Manuele; Brovchenko, Mariya; Cammi, Antonio; Clifford, Ivor; Geoffroy, Olivier; Heuer, Daniel; Laureau, Axel; Losa, Mario; Luzzi, Lelio; Merle-Lucotte, Elsa; Ricotti, Marco E.; Rouch, Hervé
2014-01-01
Highlights: • Calculation of effective delayed neutron fraction in circulating-fuel reactors. • Extension of the Monte Carlo SERPENT-2 code for delayed neutron precursor tracking. • Forward and adjoint multi-group diffusion eigenvalue problems in OpenFOAM. • Analytical approach for β eff calculation in simple geometries and flow conditions. • Good agreement among the three proposed approaches in the MSFR test-case. - Abstract: This paper deals with the calculation of the effective delayed neutron fraction (β eff ) in circulating-fuel nuclear reactors. The Molten Salt Fast Reactor is adopted as test case for the comparison of the analytical, deterministic and Monte Carlo methods presented. The Monte Carlo code SERPENT-2 has been extended to allow for delayed neutron precursors drift, according to the fuel velocity field. The forward and adjoint eigenvalue multi-group diffusion problems are implemented and solved adopting the multi-physics tool-kit OpenFOAM, by taking into account the convective and turbulent diffusive terms in the precursors balance. These two approaches show good agreement in the whole range of the MSFR operating conditions. An analytical formula for the circulating-to-static conditions β eff correction factor is also derived under simple hypotheses, which explicitly takes into account the spatial dependence of the neutron importance. Its accuracy is assessed against Monte Carlo and deterministic results. The effects of in-core recirculation vortex and turbulent diffusion are finally analysed and discussed
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)
Studies of the dynamic properties of materials using neutron scattering
International Nuclear Information System (INIS)
Lovesey, S.W.; Windsor, C.G.
1985-09-01
The dynamic properties of materials using the neutron scattering technique is reviewed. The basic properties of both nuclear scattering and magnetic scattering are summarized. The experimental methods used in neutron scattering are described, along with access to neutron sources, and neutron inelastic instruments. Applied materials science using inelastic neutron scattering; rotational tunnelling of a methyl group; molecular diffusion from quasi-elastic scattering; and the diffusion of colloidal particles and poly-nuclear complexes; are also briefly discussed. (U.K.)
International Nuclear Information System (INIS)
Cherny, V.; Danilytchev, A.; Korobeinikov, V.; Korobeinikova, L.; Stogov, V.
2000-01-01
The present paper includes the results of neutronic safety calculations of the BN-600 hybrid core benchmark problem. Results presented include: multiplication factors, Doppler coefficients, fuel and structure density coefficients, expansion coefficients, power distribution, beta-effective values, reaction rate distributions
International Nuclear Information System (INIS)
Williams, W.G.
1988-01-01
The book on 'polarized neutrons' is intended to inform researchers in condensed matter physics and chemistry of the diversity of scientific problems that can be investigated using polarized neutron beams. The contents include chapters on:- neutron polarizers and instrumentation, polarized neutron scattering, neutron polarization analysis experiments and precessing neutron polarization. (U.K.)
International Nuclear Information System (INIS)
Allen, L.S.
1977-01-01
A borehole logging tool includes a steady-state source of fast neutrons, two epithermal neutron detectors, and two thermal neutron detectors. A count rate meter is connected to each neutron detector. A first ratio detector provides an indication of the porosity of the formation surrounding the borehole by determining the ratio of the outputs of the two count rate meters connected to the two epithermal neutron detectors. A second ratio detector provides an indication of both porosity and macroscopic absorption cross section of the formation surrounding the borehole by determining the ratio of the outputs of the two count rate meters connected to the two thermal neutron detectors. By comparing the signals of the two ratio detectors, oil bearing zones and salt water bearing zones within the formation being logged can be distinguished and the amount of oil saturation can be determined. 6 claims, 2 figures
International Nuclear Information System (INIS)
Agazzi, A.; Forti, G.; Vincenti, E.
1984-01-01
1 - Nature of physical problem solved: Purpose of the programmes is to study reactor dynamics, considering the variation of the spatial flux distribution. The two programmes COSTANZA-CYL and COSTANZA-AX, solve the kinetics diffusion equations in two groups and one dimension (plane geometry for COSTANZA-AX, radial geometry for COSTANZA-CYL). The neutronic calculation is coupled with the calculation of the heat transmission from the fuel to the cladding and to the coolant, and with the thermo-hydraulics of channels with forced circulation of liquid coolant. The geometry of fuel element and channel may be cylindrical or slab. Up to ten groups of delayed neutrons are allowed. Temperature feedback of fuel (Doppler) and coolant are considered independently and affect the nuclear constants. Control rod movement or diffused poison concentrations are simulated by externally imposed variations of the thermal absorption cross section in the different regions of the reactors. Inlet temperatures and mass flow in the coolant channels may be varied according to any externally given time table. 2 - Method of solution: The kinetic diffusion equations in two groups are solved by finite-difference method. 3 - Restrictions on the complexity of the problem: 10 concentric regions; 10 coolant channels; 10 groups of delayed neutrons
Energy Technology Data Exchange (ETDEWEB)
Receveur, V
1997-04-28
During a long time, the neutron scattering and X-rays techniques have not been used for the studies bearing on the folding of proteins. The compactness and the globularness of a protein are two structural characteristics describing the denatured states and the intermediate states of folding, and the neutrons and x-rays scattering are probably the two techniques the most appropriate to give this kind of information; they are sensible to the spatial extent and to the molecules compactness, and to their general shape. For these three or four last years, the works using these techniques are increasing, giving precious knowledge on the different steps of folding and on the interactions stabilizing the denatured or intermediate states. This thesis falls into this category. (N.C.).
Energy Technology Data Exchange (ETDEWEB)
Malikova, N
2005-09-15
Montmorillonite clays in low hydration states, with Na{sup +} and Cs{sup +} compensating counter ions, are investigated by a combination of microscopic simulation and quasi-elastic neutron scattering to obtain information on the local structure and dynamics of water and ions in the interlayer. At first predictions of simulation into the dynamics of water and ions at elevate temperatures are shown (0 deg C 80 deg C, pertinent for the radioactive waste disposal scenario) Marked difference is observed between the modes of diffusion of the Na{sup +} and C{sup +} counter ions. In water dynamics, a significant step towards bulk water behaviour is seen on transition from the mono- to bilayer states. Secondly, a detailed comparison between simulation and quasi-elastic neutron scattering (Neutron Spin Echo and Time-of-Flight) regarding ambient temperature water dynamics is presented. Overall, the approaches are found to be in good agreement with each other and limitations of each of the methods are clearly shown. (author)
The secondary neutron sources for generation of particular neutron fluxes
International Nuclear Information System (INIS)
Tracz, G.
2007-07-01
The foregoing paper presents the doctor's thesis entitled '' The secondary neutron sources for generation of particular neutron fluxes ''. Two secondary neutron sources have been designed, which exploit already existing primary sources emitting neutrons of energies different from the desired ones. The first source is devoted to boron-neutron capture therapy (BNCT). The research reactor MARIA at the Institute of Atomic Energy in Swierk (Poland) is the primary source of the reactor thermal neutrons, while the secondary source should supply epithermal neutrons. The other secondary source is the pulsed source of thermal neutrons that uses fast 14 MeV neutrons from a pulsed generator at the Institute of Nuclear Physics PAN in Krakow (Poland). The physical problems to be solved in the two mentioned cases are different. Namely, in order to devise the BNCT source the initial energy of particles ought to be increased, whilst in the other case the fast neutrons have to be moderated. Slowing down of neutrons is relatively easy since these particles lose energy when they scatter in media; the most effective moderators are the materials which contain light elements (mostly hydrogen). In order to increase the energy of neutrons from thermal to epithermal (the BNCT case) the so-called neutron converter should be exploited. It contains a fissile material, 235 U. The thermal neutrons from the reactor cause fission of uranium and fast neutrons are emitted from the converter. Then fissile neutrons of energy of a few MeV are slowed down to the required epithermal energy range. The design of both secondary sources have been conducted by means of Monte Carlo simulations, which have been carried out using the MCNP code. In the case of the secondary pulsed thermal neutron source, some of the calculated results have been verified experimentally. (author)
International Nuclear Information System (INIS)
Sabundjian, G.; Nakata, H.
1983-02-01
The neutronic calculational procedure in a 4,75% w/O enriched UO 2 fueled light water moderated critical assembly was tested, using the transport codes and diffusin code available at the Instituto de Pesquisas Energeticas e Nucleares. The results of the tested codes, LEOPARD, CITHAMMER, LASER, GELS and CITATION, were found to be satisfatory and only a slight advantage is presented by CITHAMMER code. (Author) [pt
Hedoux , A.; Sauvajol , J.L.; More , M.
1988-01-01
La triéthylènediamine N(CH2CH2)3N cristallise jusqu'à Tc = 351 K dans une phase solide ordonnée de symétrie hexagonale compacte. Les expériences de diffusion cohérente inélastique des neutrons réalisées dans la phase basse température s'inscrivent dans le cadre de l'étude du processus de la transition martensitique à Tc à partir de l'évolution avec la température des paramètres dynamiques. Ainsi les courbes de dispersion ont été déterminées à 190 K, 245 K et 295 K. Les mesures effectuées à te...
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
Energy Technology Data Exchange (ETDEWEB)
Bruge, G [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1967-01-01
This report gives the results from a systematic study by 44 MeV {alpha} particle scattering on the collective states of closed shell nuclei with 28 neutrons, 28 and 50 protons especially in the energy region corresponding to the two phonon vibrational triplet. The nuclei studied are: {sup 46}Ti, {sup 48}Ti, {sup 50}Ti, {sup 52}Cr, {sup 54}Fe, {sup 56}Fe, {sup 58}Fe, {sup 58}Ni, {sup 60}Ni, {sup 62}Ni, {sup 64}Ni, {sup 112}Sn, {sup 114}Sn, {sup 116}Sn, {sup 118}Sn, {sup 120}Sn, {sup 122}Sn and {sup 124}Sn. The theoretical analysis has been made with the Austern and Blair model using a phase shift analysis of the elastic scattering. Deformation lengths {delta}{sub I} = {beta}{sub I}R and transition probabilities obtained are compared with several experimental and theoretical data. (author) [French] Ce rapport donne les resultats d'une etude systematique par diffusion de particules {alpha} de 44 MeV des etats collectifs des noyaux au voisinage des couches fermees a 28 neutrons et 28 et 50 protons, specialement dans la region correspondant au triplet vibrationnel a deux phonons. Les noyaux etudies sont: {sup 46}Ti, {sup 48}Ti, {sup 50}Ti, {sup 52}Cr, {sup 54}Fe, {sup 56}Fe, {sup 58}Fe, {sup 58}Ni, {sup 60}Ni, {sup 62}Ni, {sup 64}Ni, {sup 112}Sn, {sup 114}Sn, {sup 116}Sn, {sup 118}Sn, {sup 120}Sn, {sup 122}Sn et {sup 124}Sn. L'analyse theorique a ete faite a l'aide du modele de Austern et Blair utilisant une analyse en dephasages de la diffusion elastique. Les longueurs de deformation {delta}I = {beta}{sub I}R obtenues pour chaque niveau sont comparees a plusieurs donnees experimentales et theoriques. (auteur)
International Nuclear Information System (INIS)
Fujimura, Toichiro; Okumura, Keisuke
2002-11-01
A prototype version of a diffusion code has been developed to analyze the hexagonal core as reduced moderation reactor and the applicability of some acceleration methods have been investigated to accelerate the convergence of the iterative solution method. The hexagonal core is divided into regular triangular prisms in the three-dimensional code MOSRA-Prism and a polynomial expansion nodal method is applied to approximate the neutron flux distribution by a cubic polynomial. The multi-group diffusion equation is solved iteratively with ordinal inner and outer iterations and the effectiveness of acceleration methods is ascertained by applying an adaptive acceleration method and a neutron source extrapolation method, respectively. The formulation of the polynomial expansion nodal method is outlined in the report and the local and global effectiveness of the acceleration methods is discussed with various sample calculations. A new general expression of vacuum boundary condition, derived in the formulation is also described. (author)
International Nuclear Information System (INIS)
Steenstrup, S.
Briefly surveys recent developments in research work with ultracold neutrons (neutrons of very low velocity, up to 10 m/s at up to 10 -7 eV and 10 -3 K). Slow neutrons can be detected in an ionisation chamber filled with B 10 F 3 . Very slow neutrons can be used for investigations into the dipole moment of neutrons. Neutrons of large wave length have properties similar to those of light. The limit angle for total reflection is governed by the wave length and by the material. Total reflection can be used to filter ultracold neutrons out of the moderator material of a reactor. Total reflection can also be used to store ultracold neutrons but certain problems with storage have not yet been clarified. Slow neutrons can be made to lose speed in a neutron turbine, and come out as ultracold neutrons. A beam of ultracold neutrons could be used in a neutron microscope. (J.S.)
DEFF Research Database (Denmark)
Poulsen, H.F.; Andersen, N.H.; Lebech, B.
1991-01-01
which are identified to result from temperature independent twin-domain formation in to different orthorhombic phases with domain sizes 250 and 350 angstrom, respectively. The oxygen in-diffusion flow shows simple relaxation type behaviour J = J0 exp(-t/tau) despite a rather broad particle size...
Neutronics code VALE for two-dimensional triagonal (hexagonal) and three-dimensional geometries
International Nuclear Information System (INIS)
Vondy, D.R.; Fowler, T.B.
1981-08-01
This report documents the computer code VALE designed to solve multigroup neutronics problems with the diffusion theory approximation to neutron transport for a triagonal arrangement of mesh points on planes in two- and three-dimensional geometry. This code parallels the VENTURE neutronics code in the local computation system, making exposure and fuel management capabilities available. It uses and generates interface data files adopted in the cooperative effort sponsored by Reactor Physics RRT Division of the US DOE. The programming in FORTRAN is straightforward, although data is transferred in blocks between auxiliary storage devices and main core, and direct access schemes are used. The size of problems which can be handled is essentially limited only by cost of calculation since the arrays are variably dimensioned. The memory requirement is held down while data transfer during iteration is increased only as necessary with problem size. There is provision for the more common boundary conditions including the repeating boundary, 180 0 rotational symmetry, and the rotational symmetry conditions for the 30 0 , 60 0 , and 120 0 triangular grids on planes. A variety of types of problems may be solved: the usual neutron flux eignevalue problem, or a direct criticality search on the buckling, on a reciprocal velocity absorber (prompt mode), or on nuclide concentrations. The adjoint problem and fixed source problem may be solved, as well as the dominating higher harmonic, or the importance problem for an arbitrary fixed source
Michaud, Georges; Richer, Jacques
2015-01-01
This book gives an overview of atomic diffusion, a fundamental physical process, as applied to all types of stars, from the main sequence to neutron stars. The superficial abundances of stars as well as their evolution can be significantly affected. The authors show where atomic diffusion plays an essential role and how it can be implemented in modelling. In Part I, the authors describe the tools that are required to include atomic diffusion in models of stellar interiors and atmospheres. An important role is played by the gradient of partial radiative pressure, or radiative acceleration, which is usually neglected in stellar evolution. In Part II, the authors systematically review the contribution of atomic diffusion to each evolutionary step. The dominant effects of atomic diffusion are accompanied by more subtle effects on a large number of structural properties throughout evolution. One of the goals of this book is to provide the means for the astrophysicist or graduate student to evaluate the importanc...