WorldWideScience

Sample records for multi-dimensional neutron diffusion

  1. 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)

  2. 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)

  3. HEXAGA-III-120, -30. Three dimensional multi-group neutron diffusion programmes for a uniform triangular mesh with arbitrary group scattering

    International Nuclear Information System (INIS)

    Woznicki, Z.I.

    1983-07-01

    This report presents the HEXAGA-III-programme solving multi-group time-independent real and/or adjoint neutron diffusion equations for three-dimensional-triangular-z-geometry. The method of solution is based on the AGA two-sweep iterative method belonging to the family of factorization techniques. An arbitrary neutron scattering model is permitted. The report written for users provides the description of the programme input and output and the use of HEXAGA-III is illustrated by a sample reactor problem. (orig.) [de

  4. 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)

  5. Diffusion in membranes: Toward a two-dimensional diffusion map

    Directory of Open Access Journals (Sweden)

    Toppozini Laura

    2015-01-01

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

  6. HEXAGA-II-120, -60, -30 two-dimensional multi-group neutron diffusion programmes for a uniform triangular mesh with arbitrary group scattering

    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

  7. 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.

  8. 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

  9. SCOTCH: a program for solution of the one-dimensional, two-group, space-time neutron diffusion equations with temperature feedback of multi-channel fluid dynamics for HTGR cores

    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)

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

    International Nuclear Information System (INIS)

    Si, S.

    2012-01-01

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

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2002-12-01

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

  12. 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)

  13. HEXAGA-II. A two-dimensional multi-group neutron diffusion programme for a uniform triangular mesh with arbitrary group scattering for the IBM/370-168 computer

    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

  14. 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)

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

    International Nuclear Information System (INIS)

    Itagaki, Masafumi; Sahashi, Naoki.

    1997-01-01

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

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2011-07-01

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

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

    International Nuclear Information System (INIS)

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

    2011-01-01

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

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

    International Nuclear Information System (INIS)

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

    2017-01-01

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

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

    International Nuclear Information System (INIS)

    Kobayashi, Keisuke; Ishibashi, Hideo

    1978-01-01

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

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

    International Nuclear Information System (INIS)

    Chiba, Gou; Tsuji, Masashi; Shimazu, Yoichiro

    2001-01-01

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

  1. The use of diffusion theory to compute invasion effects for the pulsed neutron thermal decay time log

    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

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

    International Nuclear Information System (INIS)

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

    1977-01-01

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

  3. Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM.

    Science.gov (United States)

    Singh, Brajesh K; Srivastava, Vineet K

    2015-04-01

    The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations.

  4. 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)

  5. 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)

  6. Recursive solutions for multi-group neutron kinetics diffusion equations in homogeneous three-dimensional rectangular domains with time dependent perturbations

    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.

  7. 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)

  8. On an analytical evaluation of the flux and dominant eigenvalue problem for the steady state multi-group multi-layer neutron diffusion equation

    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.

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

    International Nuclear Information System (INIS)

    Kutner, R.; Sosnowska, I.

    1977-01-01

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

  10. Some reciprocity-like relations in multi-group neutron diffusion and transport theory over bare homogeneous regions

    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)

  11. The use of multi-energy-group neutron diffusion theory to numerically evaluate the relative utility of three dial-detector neutron porosity well logging tools

    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

  12. 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

  13. 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

  14. 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

  15. AUS98 - The 1998 version of the AUS modular neutronic code system

    Energy Technology Data Exchange (ETDEWEB)

    Robinson, G.S.; Harrington, B.V

    1998-07-01

    AUS is a neutronics code system which may be used for calculations of a wide range of fission reactors, fusion blankets and other neutron applications. The present version, AUS98, has a nuclear cross section library based on ENDF/B-VI and includes modules which provide for reactor lattice calculations, one-dimensional transport calculations, multi-dimensional diffusion calculations, cell and whole reactor burnup calculations, and flexible editing of results. Calculations of multi-region resonance shielding, coupled neutron and photon transport, energy deposition, fission product inventory and neutron diffusion are combined within the one code system. The major changes from the previous AUS publications are the inclusion of a cross-section library based on ENDF/B-VI, the addition of the MICBURN module for controlling whole reactor burnup calculations, and changes to the system as a consequence of moving from IBM main-frame computers to UNIX workstations This report gives details of all system aspects of AUS and all modules except the POW3D multi-dimensional diffusion module refs., tabs.

  16. AUS98 - The 1998 version of the AUS modular neutronic code system

    International Nuclear Information System (INIS)

    Robinson, G.S.; Harrington, B.V.

    1998-07-01

    AUS is a neutronics code system which may be used for calculations of a wide range of fission reactors, fusion blankets and other neutron applications. The present version, AUS98, has a nuclear cross section library based on ENDF/B-VI and includes modules which provide for reactor lattice calculations, one-dimensional transport calculations, multi-dimensional diffusion calculations, cell and whole reactor burnup calculations, and flexible editing of results. Calculations of multi-region resonance shielding, coupled neutron and photon transport, energy deposition, fission product inventory and neutron diffusion are combined within the one code system. The major changes from the previous AUS publications are the inclusion of a cross-section library based on ENDF/B-VI, the addition of the MICBURN module for controlling whole reactor burnup calculations, and changes to the system as a consequence of moving from IBM main-frame computers to UNIX workstations This report gives details of all system aspects of AUS and all modules except the POW3D multi-dimensional diffusion module

  17. 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

  18. 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)

  19. 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.

  20. 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)

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

    International Nuclear Information System (INIS)

    Honeck, H.C.

    1984-01-01

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

  2. Analytical modeling for fractional multi-dimensional diffusion equations by using Laplace transform

    Directory of Open Access Journals (Sweden)

    Devendra Kumar

    2015-01-01

    Full Text Available In this paper, we propose a simple numerical algorithm for solving multi-dimensional diffusion equations of fractional order which describes density dynamics in a material undergoing diffusion by using homotopy analysis transform method. The fractional derivative is described in the Caputo sense. This homotopy analysis transform method is an innovative adjustment in Laplace transform method and makes the calculation much simpler. The technique is not limited to the small parameter, such as in the classical perturbation method. The scheme gives an analytical solution in the form of a convergent series with easily computable components, requiring no linearization or small perturbation. The numerical solutions obtained by the proposed method indicate that the approach is easy to implement and computationally very attractive.

  3. 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)

  4. Verification of a three-dimensional neutronics model based on multi-point kinetics equations for transient problems

    Energy Technology Data Exchange (ETDEWEB)

    Park, Kyung Seok; Kim, Hyun Dae; Yeom, Choong Sub [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)

    1995-07-01

    A computer code for solving the three-dimensional reactor neutronic transient problems utilizing multi-point reactor kinetics equations recently developed has been developed. For evaluating its applicability, the code has been tested with typical 3-D LWR and CANDU reactor transient problems. The performance of the method and code has been compared with the results by fine and coarse meshes computer codes employing the direct methods.

  5. CTD: a computer program to solve the three dimensional multi-group diffusion equation in X, Y, Z, and triangular Z geometries

    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)

  6. 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.

  7. 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

  8. 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)

  9. Two-dimensional geometrical corner singularities in neutron diffusion. Part 2: Application to the SNR-300 benchmark

    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

  10. 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)

  11. Multi-level iteration optimization for diffusive critical calculation

    International Nuclear Information System (INIS)

    Li Yunzhao; Wu Hongchun; Cao Liangzhi; Zheng Youqi

    2013-01-01

    In nuclear reactor core neutron diffusion calculation, there are usually at least three levels of iterations, namely the fission source iteration, the multi-group scattering source iteration and the within-group iteration. Unnecessary calculations occur if the inner iterations are converged extremely tight. But the convergence of the outer iteration may be affected if the inner ones are converged insufficiently tight. Thus, a common scheme suit for most of the problems was proposed in this work to automatically find the optimized settings. The basic idea is to optimize the relative error tolerance of the inner iteration based on the corresponding convergence rate of the outer iteration. Numerical results of a typical thermal neutron reactor core problem and a fast neutron reactor core problem demonstrate the effectiveness of this algorithm in the variational nodal method code NODAL with the Gauss-Seidel left preconditioned multi-group GMRES algorithm. The multi-level iteration optimization scheme reduces the number of multi-group and within-group iterations respectively by a factor of about 1-2 and 5-21. (authors)

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

    International Nuclear Information System (INIS)

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

    2013-01-01

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

  13. AUS, Neutron Transport and Gamma Transport System for Fission Reactors and Fusion Reactors

    International Nuclear Information System (INIS)

    1990-01-01

    1 - Description of program or function: AUS is a neutronics code system which may be used for calculations of a wide range of fission reactors, fusion blankets and other neutron applications. The present version, AUS98, has a nuclear cross section library based on ENDF/B-VI and includes modules which provide for reactor lattice calculations, one-dimensional transport calculations, multi-dimensional diffusion calculations, cell and whole reactor burnup calculations, and flexible editing of results. Calculations of multi-region resonance shielding, coupled neutron and photon transport, energy deposition, fission product inventory and neutron diffusion are combined within the one code system. The major changes from the previous release, AUS87, are the inclusion of a cross-section library based on ENDF/B-VI, the addition of the POW3D multi-dimensional diffusion module, the addition of the MICBURN module for controlling whole reactor burnup calculations, and changes to the system as a consequence of moving from IBM mainframe computers to UNIX workstations. 2 - Method of solution: AUS98 is a modular system in which the modules are complete programs linked by a path given in the input stream. A simple path is simply a sequence of modules, but the path is actually pre-processed and compiled using the Fortran 77 compiler. This provides for complex module linking if required. Some of the modules included in AUS98 are: MIRANDA Cross-section generation in a multi-region resonance subgroup calculation and preliminary group condensation. ANAUSN One-dimensional discrete ordinates calculation. ICPP Isotropic collision probability calculation in one dimension and for rod clusters. POW3D Multi-dimensional neutron diffusion calculation including feedback-free kinetics. AUSIDD One-dimensional diffusion calculation. EDITAR Reaction-rate editing and group collapsing following a transport calculation. CHAR Lattice and global burnup calculation. MICBURN Control of global burnup

  14. 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.

  15. 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.

  16. 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.)

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

    International Nuclear Information System (INIS)

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

    2015-01-01

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

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2015-02-15

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

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

    International Nuclear Information System (INIS)

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

    2009-01-01

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

  20. Three-dimensional multiple reciprocity boundary element method for one-group neutron diffusion eigenvalue computations

    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)

  1. SRAC2006: A comprehensive neutronics calculation code system

    International Nuclear Information System (INIS)

    Okumura, Keisuke; Kugo, Teruhiko; Kaneko, Kunio; Tsuchihashi, Keichiro

    2007-02-01

    The SRAC is a code system applicable to neutronics analysis of a variety of reactor types. Since the publication of the second version of the users manual (JAERI-1302) in 1986 for the SRAC system, a number of additions and modifications to the functions and the library data have been made to establish a comprehensive neutronics code system. The current system includes major neutron data libraries (JENDL-3.3, JENDL-3.2, ENDF/B-VII, ENDF/B-VI.8, JEFF-3.1, JEF-2.2, etc.), and integrates five elementary codes for neutron transport and diffusion calculation; PIJ based on the collision probability method applicable to 16 kind of lattice models, S N transport codes ANISN(1D) and TWOTRN(2D), diffusion codes TUD(1D) and CITATION(multi-D). The system also includes an auxiliary code COREBN for multi-dimensional core burn-up calculation. (author)

  2. On Some New Properties of the Fundamental Solution to the Multi-Dimensional Space- and Time-Fractional Diffusion-Wave Equation

    Directory of Open Access Journals (Sweden)

    Yuri Luchko

    2017-12-01

    Full Text Available In this paper, some new properties of the fundamental solution to the multi-dimensional space- and time-fractional diffusion-wave equation are deduced. We start with the Mellin-Barnes representation of the fundamental solution that was derived in the previous publications of the author. The Mellin-Barnes integral is used to obtain two new representations of the fundamental solution in the form of the Mellin convolution of the special functions of the Wright type. Moreover, some new closed-form formulas for particular cases of the fundamental solution are derived. In particular, we solve the open problem of the representation of the fundamental solution to the two-dimensional neutral-fractional diffusion-wave equation in terms of the known special functions.

  3. Solution of two-dimensional equations of neutron transport in 4P0-approximation of spherical harmonics method

    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

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

    International Nuclear Information System (INIS)

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

    1992-01-01

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

  5. A prototype detector using the neutron image intensifier and multi-anode type photomultiplier tube for pulsed neutron imaging

    International Nuclear Information System (INIS)

    Ishikawa, Hirotaku; Sato, Hirotaka; Hara, Kaoru Y.; Kamiyama, Takashi

    2016-01-01

    We developed a neutron two-dimensional (2-D) detector for pulsed neutron imaging as a prototype detector, which was composed of a neutron image intensifier and a multi-anode type photomultiplier tube. A neutron transmission spectrum of α-Fe plate was measured by the prototype detector, and compared with the one measured by a typical neutron 2-D detector. The spectrum was in reasonable agreement with the one measured by the typical detector in the neutron wavelength region above 0.15 nm. In addition, a neutron transmission image of a cadmium indicator was obtained by the prototype detector. The usefulness of the prototype detector for pulsed neutron imaging was demonstrated. (author)

  6. 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

  7. EXPANDA-75: one-dimensional diffusion code for multi-region plate lattice heterogeneous system

    International Nuclear Information System (INIS)

    Kikuchi, Yasuyuki; Katsuragi, Satoru; Suzuki, Tomoo; Ogitsu, Makoto.

    1975-08-01

    An advanced treatment has been developed for analyzing a multi-region plate lattice heterogeneous system using the coarse group constants set provided for a homogeneous system. The essential points of this treatment are modification of effective admixture cross sections and improvement of effective elastic removal cross sections. By this treatment the heterogeneity effects for flux distributions and effective cross sections in the unit cell can be reproduced accurately in comparison with the ultra fine group treatment which consumes huge amounts of computing time. Based on the present treatment and using the JAERI-Fast set, a one-dimensional diffusion code, EXPANDA-75, was developed for extensive use for analyses of fast critical experiments. The user's guide is also presented in this report. (auth.)

  8. 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.)

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

    International Nuclear Information System (INIS)

    Lawrence, R.D.

    1983-03-01

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

  10. Decay rate in a multi-dimensional fission problem

    Energy Technology Data Exchange (ETDEWEB)

    Brink, D M; Canto, L F

    1986-06-01

    The multi-dimensional diffusion approach of Zhang Jing Shang and Weidenmueller (1983 Phys. Rev. C28, 2190) is used to study a simplified model for induced fission. In this model it is shown that the coupling of the fission coordinate to the intrinsic degrees of freedom is equivalent to an extra friction and a mass correction in the corresponding one-dimensional problem.

  11. Transport synthetic acceleration scheme for multi-dimensional neutron transport problems

    Energy Technology Data Exchange (ETDEWEB)

    Modak, R S; Kumar, Vinod; Menon, S V.G. [Theoretical Physics Div., Bhabha Atomic Research Centre, Mumbai (India); Gupta, Anurag [Reactor Physics Design Div., Bhabha Atomic Research Centre, Mumbai (India)

    2005-09-15

    The numerical solution of linear multi-energy-group neutron transport equation is required in several analyses in nuclear reactor physics and allied areas. Computer codes based on the discrete ordinates (Sn) method are commonly used for this purpose. These codes solve external source problem and K-eigenvalue problem. The overall solution technique involves solution of source problem in each energy group as intermediate procedures. Such a single-group source problem is solved by the so-called Source Iteration (SI) method. As is well-known, the SI-method converges very slowly for optically thick and highly scattering regions, leading to large CPU times. Over last three decades, many schemes have been tried to accelerate the SI; the most prominent being the Diffusion Synthetic Acceleration (DSA) scheme. The DSA scheme, however, often fails and is also rather difficult to implement. In view of this, in 1997, Ramone and others have developed a new acceleration scheme called Transport Synthetic Acceleration (TSA) which is much more robust and easy to implement. This scheme has been recently incorporated in 2-D and 3-D in-house codes at BARC. This report presents studies on the utility of TSA scheme for fairly general test problems involving many energy groups and anisotropic scattering. The scheme is found to be useful for problems in Cartesian as well as Cylindrical geometry. (author)

  12. Transport synthetic acceleration scheme for multi-dimensional neutron transport problems

    International Nuclear Information System (INIS)

    Modak, R.S.; Vinod Kumar; Menon, S.V.G.; Gupta, Anurag

    2005-09-01

    The numerical solution of linear multi-energy-group neutron transport equation is required in several analyses in nuclear reactor physics and allied areas. Computer codes based on the discrete ordinates (Sn) method are commonly used for this purpose. These codes solve external source problem and K-eigenvalue problem. The overall solution technique involves solution of source problem in each energy group as intermediate procedures. Such a single-group source problem is solved by the so-called Source Iteration (SI) method. As is well-known, the SI-method converges very slowly for optically thick and highly scattering regions, leading to large CPU times. Over last three decades, many schemes have been tried to accelerate the SI; the most prominent being the Diffusion Synthetic Acceleration (DSA) scheme. The DSA scheme, however, often fails and is also rather difficult to implement. In view of this, in 1997, Ramone and others have developed a new acceleration scheme called Transport Synthetic Acceleration (TSA) which is much more robust and easy to implement. This scheme has been recently incorporated in 2-D and 3-D in-house codes at BARC. This report presents studies on the utility of TSA scheme for fairly general test problems involving many energy groups and anisotropic scattering. The scheme is found to be useful for problems in Cartesian as well as Cylindrical geometry. (author)

  13. 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

  14. Spherical harmonics solutions of multi-dimensional neutron transport equation by finite Fourier transformation

    International Nuclear Information System (INIS)

    Kobayashi, Keisuke

    1977-01-01

    A method of solution of a monoenergetic neutron transport equation in P sub(L) approximation is presented for x-y and x-y-z geometries using the finite Fourier transformation. A reactor system is assumed to consist of multiregions in each of which the nuclear cross sections are spatially constant. Since the unknown functions of this method are the spherical harmonics components of the neutron angular flux at the material boundaries alone, the three- and two-dimensional equations are reduced to two- and one-dimensional equations, respectively. The present approach therefore gives fewer unknowns than in the usual series expansion method or in the finite difference method. Some numerical examples are shown for the criticality problem. (auth.)

  15. NESTLE: Few-group neutron diffusion equation solver utilizing the nodal expansion method for eigenvalue, adjoint, fixed-source steady-state and transient problems

    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

  16. VENTURE: a code block for solving multigroup neutronics problems applying the finite-difference diffusion-theory approximation to neutron transport

    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

  17. TUTANK a two-dimensional neutron kinetics code

    International Nuclear Information System (INIS)

    Watts, M.G.; Halsall, M.J.; Fayers, F.J.

    1975-04-01

    TUTANK is a two-dimensional neutron kinetics code which treats two neutron energy groups and up to six groups of delayed neutron precursors. A 'theta differencing' method is used to integrate the time dependence of the equations. A position dependent exponential transformation on the time variable is available as an option, which in many circumstances can remove much of the time dependence, and thereby allow longer time steps to be taken. A further manipulation is made to separate the solutions of the neutron fluxes and the precursor concentrations. The spatial equations are based on standard diffusion theory, and their solution is obtained from alternating direction sweeps with a transverse buckling - the so-called ADI-B 2 method. Other features of the code include an elementary temperature feedback and heat removal treatment, automatic time step adjustment, a flexible method of specifying cross-section and heat transfer coefficient variations during a transient, and a restart facility which requires a minimal data specification. Full details of the code input are given. An example of the solution of a NEACRP benchmark for an LWR control rod withdrawal is given. (author)

  18. Transport stochastic multi-dimensional media

    International Nuclear Information System (INIS)

    Haran, O.; Shvarts, D.

    1996-01-01

    Many physical phenomena evolve according to known deterministic rules, but in a stochastic media in which the composition changes in space and time. Examples to such phenomena are heat transfer in turbulent atmosphere with non uniform diffraction coefficients, neutron transfer in boiling coolant of a nuclear reactor and radiation transfer through concrete shields. The results of measurements conducted upon such a media are stochastic by nature, and depend on the specific realization of the media. In the last decade there has been a considerable efforts to describe linear particle transport in one dimensional stochastic media composed of several immiscible materials. However, transport in two or three dimensional stochastic media has been rarely addressed. The important effect in multi-dimensional transport that does not appear in one dimension is the ability to bypass obstacles. The current work is an attempt to quantify this effect. (authors)

  19. Transport stochastic multi-dimensional media

    Energy Technology Data Exchange (ETDEWEB)

    Haran, O; Shvarts, D [Israel Atomic Energy Commission, Beersheba (Israel). Nuclear Research Center-Negev; Thiberger, R [Ben-Gurion Univ. of the Negev, Beersheba (Israel)

    1996-12-01

    Many physical phenomena evolve according to known deterministic rules, but in a stochastic media in which the composition changes in space and time. Examples to such phenomena are heat transfer in turbulent atmosphere with non uniform diffraction coefficients, neutron transfer in boiling coolant of a nuclear reactor and radiation transfer through concrete shields. The results of measurements conducted upon such a media are stochastic by nature, and depend on the specific realization of the media. In the last decade there has been a considerable efforts to describe linear particle transport in one dimensional stochastic media composed of several immiscible materials. However, transport in two or three dimensional stochastic media has been rarely addressed. The important effect in multi-dimensional transport that does not appear in one dimension is the ability to bypass obstacles. The current work is an attempt to quantify this effect. (authors).

  20. Neutron beam test of multi-grid-type microstrip gas chamber

    International Nuclear Information System (INIS)

    Fujita, K.; Takahashi, H.; Siritiprussamee, P.; Niko, H.; Kai, M.; Nakazawa, M.; Ino, T.; Sato, S.; Yokoo, T.; Furusaka, M.; Kanazawa, M.

    2006-01-01

    Multi-grid-type microstrip gas chambers (M-MSGCs) are being developed for the next-generation pulsed neutron source. Two new concepts, a global-local-grouping (GLG) method and a graded cathode pattern readout method, were applied to the M-MSGC design for realizing higher counting rate than traditional 3 He proportional counters. One-dimensional detectors with 700 mm-long test plates were fabricated and tested with X-ray and neutron beams, which demonstrated position detection capability based on these concepts

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

    Energy Technology Data Exchange (ETDEWEB)

    Lawrence, R.D.

    1983-03-01

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

  2. Complex of two-dimensional multigroup programs for neutron-physical computations of nuclear reactor

    International Nuclear Information System (INIS)

    Karpov, V.A.; Protsenko, A.N.

    1975-01-01

    Briefly stated mathematical aspects of the two-dimensional multigroup method of neutron-physical computation of nuclear reactor. Problems of algorithmization and BESM-6 computer realisation of multigroup diffuse approximations in hexagonal and rectangular calculated lattices are analysed. The results of computation of fast critical assembly having complicated composition of the core are given. The estimation of computation accuracy of criticality, neutron fields distribution and efficiency of absorbing rods by means of computer programs developed is done. (author)

  3. Low-diffusion rotated upwind schemes, multigrid and defect correction for steady, multi-dimensional Euler flows

    NARCIS (Netherlands)

    Koren, B.; Hackbusch, W.; Trottenberg, U.

    1991-01-01

    Two simple, multi-dimensional upwind discretizations for the steady Euler equations are derived, with the emphasis Iying on bath a good accuracy and a good solvability. The multi-dimensional upwinding consists of applying a one-dimensional Riemann solver with a locally rotated left and right state,

  4. 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)

  5. 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)

  6. 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)

  7. 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

  8. Low dimensional neutron moderators for enhanced source brightness

    DEFF Research Database (Denmark)

    Mezei, Ferenc; Zanini, Luca; Takibayev, Alan

    2014-01-01

    In a recent numerical optimization study we have found that liquid para-hydrogen coupled cold neutron moderators deliver 3–5 times higher cold neutron brightness at a spallation neutron source if they take the form of a flat, quasi 2-dimensional disc, in contrast to the conventional more voluminous...... for cold neutrons. This model leads to the conclusions that the optimal shape for high brightness para-hydrogen neutron moderators is the quasi 1-dimensional tube and these low dimensional moderators can also deliver much enhanced cold neutron brightness in fission reactor neutron sources, compared...... to the much more voluminous liquid D2 or H2 moderators currently used. Neutronic simulation calculations confirm both of these theoretical conclusions....

  9. 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

  10. Analytical solution of the multigroup neutron diffusion kinetic equation in one-dimensional cartesian geometry by the integral transform technique

    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)

  11. 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.

  12. 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

  13. PIV measurements in a compact return diffuser under multi-conditions

    Science.gov (United States)

    Zhou, L.; Lu, W. G.; Shi, W. D.

    2013-12-01

    Due to the complex three-dimensional geometries of impellers and diffusers, their design is a delicate and difficult task. Slight change could lead to significant changes in hydraulic performance and internal flow structure. Conversely, the grasp of the pump's internal flow pattern could benefit from pump design improvement. The internal flow fields in a compact return diffuser have been investigated experimentally under multi-conditions. A special Particle Image Velocimetry (PIV) test rig is designed, and the two-dimensional PIV measurements are successfully conducted in the diffuser mid-plane to capture the complex flow patterns. The analysis of the obtained results has been focused on the flow structure in diffuser, especially under part-load conditions. The vortex and recirculation flow patterns in diffuser are captured and analysed accordingly. Strong flow separation and back flow appeared at the part-load flow rates. Under the design and over-load conditions, the flow fields in diffuser are uniform, and the flow separation and back flow appear at the part-load flow rates, strong back flow is captured at one diffuser passage under 0.2Qdes.

  14. The application of a multi-physics tool kit to spatial reactor dynamics

    International Nuclear Information System (INIS)

    Clifford, I.; Jasak, H.

    2009-01-01

    Traditionally coupled field nuclear reactor analysis has been carried out using several loosely coupled solvers, each having been developed independently from the others. In the field of multi-physics, the current generation of object-oriented tool kits provides robust close coupling of multiple fields on a single framework. This paper describes the initial results obtained as part of continuing research in the use of the OpenFOAM multi-physics tool kit for reactor dynamics application development. An unstructured, three-dimensional, time-dependent multi-group diffusion code Diffusion FOAM has been developed using the OpenFOAM multi-physics tool kit as a basis. The code is based on the finite-volume methodology and uses a newly developed block-coupled sparse matrix solver for the coupled solution of the multi-group diffusion equations. A description of this code is given with particular emphasis on the newly developed block-coupled solver, along with a selection of results obtained thus far. The code has performed well, indicating that the OpenFOAM tool kit is suited to reactor dynamics applications. This work has shown that the neutronics and simplified thermal-hydraulics of a reactor May be represented and solved for using a common calculation platform, and opens up the possibility for research into robust close-coupling of neutron diffusion and thermal-fluid calculations. This work has further opened up the possibility for research in a number of other areas, including research into three-dimensional unstructured meshes for reactor dynamics applications. (authors)

  15. 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

  16. Code Coupling for Multi-Dimensional Core Transient Analysis

    International Nuclear Information System (INIS)

    Park, Jin-Woo; Park, Guen-Tae; Park, Min-Ho; Ryu, Seok-Hee; Um, Kil-Sup; Lee Jae-Il

    2015-01-01

    After the CEA ejection, the nuclear power of the reactor dramatically increases in an exponential behavior until the Doppler effect becomes important and turns the reactivity balance and power down to lower levels. Although this happens in a very short period of time, only few seconds, the energy generated can be very significant and cause fuel failures. The current safety analysis methodology which is based on overly conservative assumptions with the point kinetics model results in quite adverse consequences. Thus, KEPCO Nuclear Fuel(KNF) is developing the multi-dimensional safety analysis methodology to mitigate the consequences of the single CEA ejection accident. For this purpose, three-dimensional core neutron kinetics code ASTRA, sub-channel analysis code THALES, and fuel performance analysis code FROST, which have transient calculation performance, were coupled using message passing interface (MPI). This paper presents the methodology used for code coupling and the preliminary simulation results with the coupled code system (CHASER). Multi-dimensional core transient analysis code system, CHASER, has been developed and it was applied to simulate a single CEA ejection accident. CHASER gave a good prediction of multi-dimensional core transient behaviors during transient. In the near future, the multi-dimension CEA ejection analysis methodology using CHASER is planning to be developed. CHASER is expected to be a useful tool to gain safety margin for reactivity initiated accidents (RIAs), such as a single CEA ejection accident

  17. Code Coupling for Multi-Dimensional Core Transient Analysis

    Energy Technology Data Exchange (ETDEWEB)

    Park, Jin-Woo; Park, Guen-Tae; Park, Min-Ho; Ryu, Seok-Hee; Um, Kil-Sup; Lee Jae-Il [KEPCO NF, Daejeon (Korea, Republic of)

    2015-05-15

    After the CEA ejection, the nuclear power of the reactor dramatically increases in an exponential behavior until the Doppler effect becomes important and turns the reactivity balance and power down to lower levels. Although this happens in a very short period of time, only few seconds, the energy generated can be very significant and cause fuel failures. The current safety analysis methodology which is based on overly conservative assumptions with the point kinetics model results in quite adverse consequences. Thus, KEPCO Nuclear Fuel(KNF) is developing the multi-dimensional safety analysis methodology to mitigate the consequences of the single CEA ejection accident. For this purpose, three-dimensional core neutron kinetics code ASTRA, sub-channel analysis code THALES, and fuel performance analysis code FROST, which have transient calculation performance, were coupled using message passing interface (MPI). This paper presents the methodology used for code coupling and the preliminary simulation results with the coupled code system (CHASER). Multi-dimensional core transient analysis code system, CHASER, has been developed and it was applied to simulate a single CEA ejection accident. CHASER gave a good prediction of multi-dimensional core transient behaviors during transient. In the near future, the multi-dimension CEA ejection analysis methodology using CHASER is planning to be developed. CHASER is expected to be a useful tool to gain safety margin for reactivity initiated accidents (RIAs), such as a single CEA ejection accident.

  18. 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

  19. 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)

  20. A fast semi-discrete Kansa method to solve the two-dimensional spatiotemporal fractional diffusion equation

    Science.gov (United States)

    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.

  1. Multi-dimensional Fuzzy Euler Approximation

    Directory of Open Access Journals (Sweden)

    Yangyang Hao

    2017-05-01

    Full Text Available Multi-dimensional Fuzzy differential equations driven by multi-dimen-sional Liu process, have been intensively applied in many fields. However, we can not obtain the analytic solution of every multi-dimensional fuzzy differential equation. Then, it is necessary for us to discuss the numerical results in most situations. This paper focuses on the numerical method of multi-dimensional fuzzy differential equations. The multi-dimensional fuzzy Taylor expansion is given, based on this expansion, a numerical method which is designed for giving the solution of multi-dimensional fuzzy differential equation via multi-dimensional Euler method will be presented, and its local convergence also will be discussed.

  2. Improvement of neutron kinetics module in TRAC-BF1code: one-dimensional nodal collocation method

    Energy Technology Data Exchange (ETDEWEB)

    Jambrina, Ana; Barrachina, Teresa; Miro, Rafael; Verdu, Gumersindo, E-mail: ajambrina@iqn.upv.es, E-mail: tbarrachina@iqn.upv.es, E-mail: rmiro@iqn.upv.es, E-mail: gverdu@iqn.upv.es [Universidade Politecnica de Valencia (UPV), Valencia (Spain); Soler, Amparo, E-mail: asoler@iberdrola.es [SEA Propulsion S.L., Madrid (Spain); Concejal, Alberto, E-mail: acbe@iberdrola.es [Iberdrola Ingenieria y Construcion S.A.U., Madrid (Spain)

    2013-07-01

    The TRAC-BF1 one-dimensional kinetic model is a formulation of the neutron diffusion equation in the two energy groups' approximation, based on the analytical nodal method (ANM). The advantage compared with a zero-dimensional kinetic model is that the axial power profile may vary with time due to thermal-hydraulic parameter changes and/or actions of the control systems but at has the disadvantages that in unusual situations it fails to converge. The nodal collocation method developed for the neutron diffusion equation and applied to the kinetics resolution of TRAC-BF1 thermal-hydraulics, is an adaptation of the traditional collocation methods for the discretization of partial differential equations, based on the development of the solution as a linear combination of analytical functions. It has chosen to use a nodal collocation method based on a development of Legendre polynomials of neutron fluxes in each cell. The qualification is carried out by the analysis of the turbine trip transient from the NEA benchmark in Peach Bottom NPP using both the original 1D kinetics implemented in TRAC-BF1 and the 1D nodal collocation method. (author)

  3. 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

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2017-05-15

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

  5. Development and assessment of multi-dimensional flow model in MARS compared with the RPI air-water experiment

    International Nuclear Information System (INIS)

    Lee, Seok Min; Lee, Un Chul; Bae, Sung Won; Chung, Bub Dong

    2004-01-01

    The Multi-Dimensional flow models in system code have been developed during the past many years. RELAP5-3D, CATHARE and TRACE has its specific multi-dimensional flow models and successfully applied it to the system safety analysis. In KAERI, also, MARS(Multi-dimensional Analysis of Reactor Safety) code was developed by integrating RELAP5/MOD3 code and COBRA-TF code. Even though COBRA-TF module can analyze three-dimensional flow models, it has a limitation to apply 3D shear stress dominant phenomena or cylindrical geometry. Therefore, Multi-dimensional analysis models are newly developed by implementing three-dimensional momentum flux and diffusion terms. The multi-dimensional model has been assessed compared with multi-dimensional conceptual problems and CFD code results. Although the assessment results were reasonable, the multi-dimensional model has not been validated to two-phase flow using experimental data. In this paper, the multi-dimensional air-water two-phase flow experiment was simulated and analyzed

  6. 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

  7. 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

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

    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

  9. PIV measurements in a compact return diffuser under multi-conditions

    International Nuclear Information System (INIS)

    Zhou, L; Lu, W G; Shi, W D

    2013-01-01

    Due to the complex three-dimensional geometries of impellers and diffusers, their design is a delicate and difficult task. Slight change could lead to significant changes in hydraulic performance and internal flow structure. Conversely, the grasp of the pump's internal flow pattern could benefit from pump design improvement. The internal flow fields in a compact return diffuser have been investigated experimentally under multi-conditions. A special Particle Image Velocimetry (PIV) test rig is designed, and the two-dimensional PIV measurements are successfully conducted in the diffuser mid-plane to capture the complex flow patterns. The analysis of the obtained results has been focused on the flow structure in diffuser, especially under part-load conditions. The vortex and recirculation flow patterns in diffuser are captured and analysed accordingly. Strong flow separation and back flow appeared at the part-load flow rates. Under the design and over-load conditions, the flow fields in diffuser are uniform, and the flow separation and back flow appear at the part-load flow rates, strong back flow is captured at one diffuser passage under 0.2Q des

  10. 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)

  11. 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.)

  12. 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

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

    Energy Technology Data Exchange (ETDEWEB)

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

    1977-11-01

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

  14. Electroless Ni-B plating on SiO2 with 3-aminopropyl-triethoxysilane as a barrier layer against Cu diffusion for through-Si via interconnections in a 3-dimensional multi-chip package

    International Nuclear Information System (INIS)

    Ikeda, Akihiro; Sakamoto, Atsushi; Hattori, Reiji; Kuroki, Yukinori

    2009-01-01

    Electroless Ni-B was plated on SiO 2 as a barrier layer against Cu diffusion for through-Si via (TSV) interconnections in a 3-dimensional multi-chip package. The electroless Ni-B was deposited on the entire area of the SiO 2 side wall of a deep via with vapor phase pre-deposition of 3-aminopropyl-triethoxysilane on the SiO 2 . The carrier lifetimes in the Si substrates plated with Ni-B/Cu did not decrease with an increase in annealing temperature up to 400 deg. C . The absence of degradation of carrier lifetimes indicates that Cu atoms did not diffuse into the Si through the Ni-B. The advantages of electroless Ni-B (good conformal deposition and forming an effective diffusion barrier against Cu) make it useful as a barrier layer for TSV interconnections in a 3-dimensional multi-chip package

  15. 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).

  16. 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

  17. 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

  18. Cassandre : a two-dimensional multigroup diffusion code for reactor transient analysis

    International Nuclear Information System (INIS)

    Arien, B.; Daniels, J.

    1986-12-01

    CASSANDRE is a two-dimensional (x-y or r-z) finite element neutronics code with thermohydraulics feedback for reactor dynamics prior to the disassembly phase. It uses the multigroup neutron diffusion theory. Its main characteristics are the use of a generalized quasistatic model, the use of a flexible multigroup point-kinetics algorithm allowing for spectral matching and the use of a finite element description. The code was conceived in order to be coupled with any thermohydraulics module, although thermohydraulics feedback is only considered in r-z geometry. In steady state criticality search is possible either by control rod insertion or by homogeneous poisoning of the coolant. This report describes the main characterstics of the code structure and provides all the information needed to use the code. (Author)

  19. 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.)

  20. 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

  1. STEP- A three-dimensional nodal diffusion code for LMR's

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Yeong Il; Kim, Taek Kyum [Korea Atomic Energy Research Institute, Taejon (Korea)

    1999-12-01

    STEP is a three-dimensional multigroup nodal diffusion code for the neutronics analysis of the LMR core. STEP employs DIF3D and HEXNOD nodal methods. In DIF3D, one-dimensional fluxes are approximated by polynomials while HEXNOD analytically solves transverse-integrated one-dimensional diffusion equations. The nodal equations are solved using a conventional fission source iteration procedure accelerated by coarse-mesh rebalancing and asymptotic extrapolation. At each fission source iteration, the interface currents for each group are computed by solving the response matrix equations with a known group source term. These partial currents are used to updata flux moments. This solution is accomplished by inner iteration, a series of sweeps through the spatial mesh. Inner iterations are performed by sweeping the axial mesh plane in a standard red-black checkerboard ordering, i.e. the odd-numbered planes are processed during the first pass, followed by the even-numbered planes on the second pass. On each plane, the nodes are swept in the four-color checkerboard ordering. STEP accepts microscopic cross section data from the CCCC standard interface file ISOTXS currently used for the neutronics analysis of LMR's at KAERI as well as macroscopic cross section data. Material cross sections are obtained by summing the product of atom densities and microscopic cross sections over all isotopes comprising the material. Energy is released from both fission ad capture. The thermal-hydraulics model calculates average fuel and coolant temperatures. STEP takes account of feedback effects from both fuel temperature and coolant temperature changes. The thermal-hydraulics model is a conservative, single channel model where there is no heat transfer between assemblies. Thus, STEP gives conservative results which, however, are of useful information for core design and can be useful tool for neutronics analysis of LMR core design and will be used for the base program of a future

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2011-07-15

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

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

    International Nuclear Information System (INIS)

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

    2011-01-01

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

  4. 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

  5. Analytical three-dimensional neutron transport benchmarks for verification of nuclear engineering codes. Final report

    International Nuclear Information System (INIS)

    Ganapol, B.D.; Kornreich, D.E.

    1997-01-01

    Because of the requirement of accountability and quality control in the scientific world, a demand for high-quality analytical benchmark calculations has arisen in the neutron transport community. The intent of these benchmarks is to provide a numerical standard to which production neutron transport codes may be compared in order to verify proper operation. The overall investigation as modified in the second year renewal application includes the following three primary tasks. Task 1 on two dimensional neutron transport is divided into (a) single medium searchlight problem (SLP) and (b) two-adjacent half-space SLP. Task 2 on three-dimensional neutron transport covers (a) point source in arbitrary geometry, (b) single medium SLP, and (c) two-adjacent half-space SLP. Task 3 on code verification, includes deterministic and probabilistic codes. The primary aim of the proposed investigation was to provide a suite of comprehensive two- and three-dimensional analytical benchmarks for neutron transport theory applications. This objective has been achieved. The suite of benchmarks in infinite media and the three-dimensional SLP are a relatively comprehensive set of one-group benchmarks for isotropically scattering media. Because of time and resource limitations, the extensions of the benchmarks to include multi-group and anisotropic scattering are not included here. Presently, however, enormous advances in the solution for the planar Green's function in an anisotropically scattering medium have been made and will eventually be implemented in the two- and three-dimensional solutions considered under this grant. Of particular note in this work are the numerical results for the three-dimensional SLP, which have never before been presented. The results presented were made possible only because of the tremendous advances in computing power that have occurred during the past decade

  6. Multi-dimensional information diffusion and balancing market supply: an agent-based approach

    NARCIS (Netherlands)

    Osinga, S.A.; Kramer, M.R.; Hofstede, G.J.; Beulens, A.J.M.

    2013-01-01

    This agent-based information management model is designed to explore how multi-dimensional information, spreading through a population of agents (for example farmers) affects market supply. Farmers make quality decisions that must be aligned with available markets. Markets distinguish themselves by

  7. 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

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

    Energy Technology Data Exchange (ETDEWEB)

    Guerin, P

    2007-12-15

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

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

    International Nuclear Information System (INIS)

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

    1984-12-01

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

  10. Three Dimensional Polarimetric Neutron Tomography of Magnetic Fields

    DEFF Research Database (Denmark)

    Sales, Morten; Strobl, Markus; Shinohara, Takenao

    2018-01-01

    Through the use of Time-of-Flight Three Dimensional Polarimetric Neutron Tomography (ToF 3DPNT) we have for the first time successfully demonstrated a technique capable of measuring and reconstructing three dimensional magnetic field strengths and directions unobtrusively and non-destructively wi......Through the use of Time-of-Flight Three Dimensional Polarimetric Neutron Tomography (ToF 3DPNT) we have for the first time successfully demonstrated a technique capable of measuring and reconstructing three dimensional magnetic field strengths and directions unobtrusively and non...... and reconstructed, thereby providing the proof-of-principle of a technique able to reveal hitherto unobtainable information on the magnetic fields in the bulk of materials and devices, due to a high degree of penetration into many materials, including metals, and the sensitivity of neutron polarisation to magnetic...... fields. The technique puts the potential of the ToF time structure of pulsed neutron sources to full use in order to optimise the recorded information quality and reduce measurement time....

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

    International Nuclear Information System (INIS)

    Guerin, P.

    2007-12-01

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

  12. 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

  13. Clinical application of multi-shot diffusion EPI in neurological disease

    International Nuclear Information System (INIS)

    Ishihara, Tetsuya; Hirata, Koichi; Kubo, Jin; Yamazaki, Kaoru; Sato, Toshihiko

    1998-01-01

    Using the multi-shot EPI method we investigated the clinical application of diffusion weighted imaging (DWI) in the diagnosis of neurological disease. The multi-shot method provided better susceptibility artifact-free DWI than the single-shot method particularly in the region of the posterior cranial fossa. DWI using the multi-shot EPI method readily shows the pyramidal tract extending from the internal capsule to the brainstems which is inaccessible by the conventional single-shot EPI method, and providing three-dimensional and distinct images of pyramidal tract changes in amyotrophic lateral sclerosis or cerebral infarction with pyramidal tract disturbance. Our findings suggest that the use of DWI with the multi-shot EPI method would provide a technique for the easy diagnosis and evaluation of various neurological diseases. (author)

  14. Clinical application of multi-shot diffusion EPI in neurological disease

    Energy Technology Data Exchange (ETDEWEB)

    Ishihara, Tetsuya; Hirata, Koichi; Kubo, Jin; Yamazaki, Kaoru [Dokkyo Univ., Mibu, Tochigi (Japan). School of Medicine; Sato, Toshihiko

    1998-05-01

    Using the multi-shot EPI method we investigated the clinical application of diffusion weighted imaging (DWI) in the diagnosis of neurological disease. The multi-shot method provided better susceptibility artifact-free DWI than the single-shot method particularly in the region of the posterior cranial fossa. DWI using the multi-shot EPI method readily shows the pyramidal tract extending from the internal capsule to the brainstems which is inaccessible by the conventional single-shot EPI method, and providing three-dimensional and distinct images of pyramidal tract changes in amyotrophic lateral sclerosis or cerebral infarction with pyramidal tract disturbance. Our findings suggest that the use of DWI with the multi-shot EPI method would provide a technique for the easy diagnosis and evaluation of various neurological diseases. (author)

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

    Energy Technology Data Exchange (ETDEWEB)

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

    1955-07-01

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

  16. 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.

  17. 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)

  18. Multi-element neutron activation analysis and solution of classification problems using multidimensional statistics

    International Nuclear Information System (INIS)

    Vaganov, P.A.; Kol'tsov, A.A.; Kulikov, V.D.; Mejer, V.A.

    1983-01-01

    The multi-element instrumental neutron activation analysis of samples of mountain rocks (sandstones, aleurolites and shales of one of gold deposits) is performed. The spectra of irradiated samples are measured by Ge(Li) detector of the volume of 35 mm 3 . The content of 22 chemical elements is determined in each sample. The results of analysis serve as reliable basis for multi-dimensional statistic information processing, they constitute the basis for the generalized characteristics of rocks which brings about the solution of classification problem for rocks of different deposits

  19. 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

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

    International Nuclear Information System (INIS)

    Premuda, F.

    1983-01-01

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

  1. Three-dimensional h-adaptivity for the multigroup neutron diffusion equations

    KAUST Repository

    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.

  2. 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)

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

    International Nuclear Information System (INIS)

    Zee, S.K.

    1987-01-01

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

  4. 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

  5. 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

  6. TWO-DIMENSIONAL CORE-COLLAPSE SUPERNOVA MODELS WITH MULTI-DIMENSIONAL TRANSPORT

    International Nuclear Information System (INIS)

    Dolence, Joshua C.; Burrows, Adam; Zhang, Weiqun

    2015-01-01

    We present new two-dimensional (2D) axisymmetric neutrino radiation/hydrodynamic models of core-collapse supernova (CCSN) cores. We use the CASTRO code, which incorporates truly multi-dimensional, multi-group, flux-limited diffusion (MGFLD) neutrino transport, including all relevant O(v/c) terms. Our main motivation for carrying out this study is to compare with recent 2D models produced by other groups who have obtained explosions for some progenitor stars and with recent 2D VULCAN results that did not incorporate O(v/c) terms. We follow the evolution of 12, 15, 20, and 25 solar-mass progenitors to approximately 600 ms after bounce and do not obtain an explosion in any of these models. Though the reason for the qualitative disagreement among the groups engaged in CCSN modeling remains unclear, we speculate that the simplifying ''ray-by-ray'' approach employed by all other groups may be compromising their results. We show that ''ray-by-ray'' calculations greatly exaggerate the angular and temporal variations of the neutrino fluxes, which we argue are better captured by our multi-dimensional MGFLD approach. On the other hand, our 2D models also make approximations, making it difficult to draw definitive conclusions concerning the root of the differences between groups. We discuss some of the diagnostics often employed in the analyses of CCSN simulations and highlight the intimate relationship between the various explosion conditions that have been proposed. Finally, we explore the ingredients that may be missing in current calculations that may be important in reproducing the properties of the average CCSNe, should the delayed neutrino-heating mechanism be the correct mechanism of explosion

  7. 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

  8. One-dimensional neutron imager for the Sandia Z facility.

    Science.gov (United States)

    Fittinghoff, David N; Bower, Dan E; Hollaway, James R; Jacoby, Barry A; Weiss, Paul B; Buckles, Robert A; Sammons, Timothy J; McPherson, Leroy A; Ruiz, Carlos L; Chandler, Gordon A; Torres, José A; Leeper, Ramon J; Cooper, Gary W; Nelson, Alan J

    2008-10-01

    A multiinstitution collaboration is developing a neutron imaging system for the Sandia Z facility. The initial system design is for slit aperture imaging system capable of obtaining a one-dimensional image of a 2.45 MeV source producing 5x10(12) neutrons with a resolution of 320 microm along the axial dimension of the plasma, but the design being developed can be modified for two-dimensional imaging and imaging of DT neutrons with other resolutions. This system will allow us to understand the spatial production of neutrons in the plasmas produced at the Z facility.

  9. An Experiment of Robust Parallel Algorithm for the Eigenvalue problem of a Multigroup Neutron Diffusion based on modified FETI-DP : Part 2

    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

  10. An Experiment of Robust Parallel Algorithm for the Eigenvalue problem of a Multigroup Neutron Diffusion based on modified FETI-DP : Part 2

    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.

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

    Energy Technology Data Exchange (ETDEWEB)

    Capdebosq, Y

    1999-09-01

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

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

    International Nuclear Information System (INIS)

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

    2014-10-01

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

  13. 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.

  14. Development and assessment of Multi-dimensional flow models in the thermal-hydraulic system analysis code MARS

    Energy Technology Data Exchange (ETDEWEB)

    Chung, B. D.; Bae, S. W.; Jeong, J. J.; Lee, S. M

    2005-04-15

    A new multi-dimensional component has been developed to allow for more flexible 3D capabilities in the system code, MARS. This component can be applied in the Cartesian and cylindrical coordinates. For the development of this model, the 3D convection and diffusion terms are implemented in the momentum and energy equation. And a simple Prandtl's mixing length model is applied for the turbulent viscosity. The developed multi-dimensional component was assessed against five conceptual problems with analytic solution. And some SETs are calculated and compared with experimental data. With this newly developed multi-dimensional flow module, the MARS code can realistic calculate the flow fields in pools such as those occurring in the core, steam generators and IRWST.

  15. Development and assessment of Multi-dimensional flow models in the thermal-hydraulic system analysis code MARS

    International Nuclear Information System (INIS)

    Chung, B. D.; Bae, S. W.; Jeong, J. J.; Lee, S. M.

    2005-04-01

    A new multi-dimensional component has been developed to allow for more flexible 3D capabilities in the system code, MARS. This component can be applied in the Cartesian and cylindrical coordinates. For the development of this model, the 3D convection and diffusion terms are implemented in the momentum and energy equation. And a simple Prandtl's mixing length model is applied for the turbulent viscosity. The developed multi-dimensional component was assessed against five conceptual problems with analytic solution. And some SETs are calculated and compared with experimental data. With this newly developed multi-dimensional flow module, the MARS code can realistic calculate the flow fields in pools such as those occurring in the core, steam generators and IRWST

  16. VAMPIR - A two-group two-dimensional diffusion computer code for burnup calculation

    International Nuclear Information System (INIS)

    Zmijarevic, I.; Petrovic, I.

    1985-01-01

    VAMPIR is a computer code which simulates the burnup within a reactor coe. It computes the neutron flux, power distribution and burnup taking into account spatial variations of temperature and xenon poisoning. Its overall reactor calculation uses diffusion theory with finite differences approximation in X-Y or R-Z geometry. Two-group macroscopic cross section data are prepared by the lattice cell code WIMS-D4 and stored in the library form of multi entry tabulation against the various parameters that significantly affect the physical conditions in the reactor core. herein, the main features of the program are presented. (author)

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

    International Nuclear Information System (INIS)

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

    2015-01-01

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

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2015-07-01

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

  19. Two-Dimensional Space-Time Dependent Multi-group Diffusion Equation with SLOR Method

    International Nuclear Information System (INIS)

    Yulianti, Y.; Su'ud, Z.; Waris, A.; Khotimah, S. N.

    2010-01-01

    The research of two-dimensional space-time diffusion equations with SLOR (Successive-Line Over Relaxation) has been done. SLOR method is chosen because this method is one of iterative methods that does not required to defined whole element matrix. The research is divided in two cases, homogeneous case and heterogeneous case. Homogeneous case has been inserted by step reactivity. Heterogeneous case has been inserted by step reactivity and ramp reactivity. In general, the results of simulations are agreement, even in some points there are differences.

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

    Energy Technology Data Exchange (ETDEWEB)

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

    1948-11-01

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

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2017-02-15

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

  2. Numerical solution of multigroup diffuse equations of one-dimensional geometry

    International Nuclear Information System (INIS)

    Pavelesku, M.; Adam, S.

    1975-01-01

    The one-dimensional diffuse theory is used for reactor physics calculations of fast reactors. Computer program based on the one-dimensional diffuse theory is speedy and not memory consuming. The algorithm is described for the three-zone fast reactor criticality computation in one-dimensional diffusion approximation. This algorithm is realised on IBM 370/135 computer. (I.T.)

  3. Solution of the multigroup diffusion equation for two-dimensional triangular regions by finite Fourier transformation

    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

  4. 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

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

    International Nuclear Information System (INIS)

    Gast, R.C.

    1981-08-01

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

  6. 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)

  7. 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

  8. 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

  9. 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

  10. 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

  11. A highly efficient parallel algorithm for solving the neutron diffusion nodal equations on shared-memory computers

    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

  12. Application of hexagonal element scheme in finite element method to three-dimensional diffusion problem of fast reactors

    International Nuclear Information System (INIS)

    Ishiguro, Misako; Higuchi, Kenji

    1983-01-01

    The finite element method is applied in Galerkin-type approximation to three-dimensional neutron diffusion equations of fast reactors. A hexagonal element scheme is adopted for treating the hexagonal lattice which is typical for fast reactors. The validity of the scheme is verified by applying the scheme as well as alternative schemes to the neutron diffusion calculation of a gas-cooled fast reactor of actual scale. The computed results are compared with corresponding values obtained using the currently applied triangular-element and also with conventional finite difference schemes. The hexagonal finite element scheme is found to yield a reasonable solution to the problem taken up here, with some merit in terms of saving in computing time, but the resulting multiplication factor differs by 1% and the flux by 9% compared with the triangular mesh finite difference scheme. The finite element method, even in triangular element scheme, would appear to incur error in inadmissible amount and which could not be easily eliminated by refining the nodes. (author)

  13. A nodal collocation approximation for the multi-dimensional PL equations - 2D applications

    International Nuclear Information System (INIS)

    Capilla, M.; Talavera, C.F.; Ginestar, D.; Verdu, G.

    2008-01-01

    A classical approach to solve the neutron transport equation is to apply the spherical harmonics method obtaining a finite approximation known as the P L equations. In this work, the derivation of the P L equations for multi-dimensional geometries is reviewed and a nodal collocation method is developed to discretize these equations on a rectangular mesh based on the expansion of the neutronic fluxes in terms of orthogonal Legendre polynomials. The performance of the method and the dominant transport Lambda Modes are obtained for a homogeneous 2D problem, a heterogeneous 2D anisotropic scattering problem, a heterogeneous 2D problem and a benchmark problem corresponding to a MOX fuel reactor core

  14. 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)

  15. 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

  16. NEULAND at R{sup 3}B: Multi-neutron response and resolution of the novel neutron detector

    Energy Technology Data Exchange (ETDEWEB)

    Kresan, Dmytro; Aumann, Thomas [Technische Universitaet Darmstadt, Darmstadt (Germany); Boretzky, Konstanze; Bertini, Denis; Heil, Michael; Rossi, Dominic; Simon, Haik [GSI Helmholtzzentrum fuer Schwerionenforschung, Darmstadt (Germany)

    2012-07-01

    NEULAND (New Large Area Neutron Detector) will serve for the detection of fast neutrons (200 - 1000 MeV) in the R3B experiment at the future FAIR. A high detection efficiency (> 90%), a high resolution (down to 20 keV) and a large multi-neutron-hit resolving power ({>=}5 neutrons) are demanded. The detector concept foresees a fully active and highly granular design of plastic scintillators. We present the detector capabilities, based on simulations performed within the FairRoot framework. The relevance of calorimetric properties for the multi-hit recognition is discussed, and exemplarily the performance for specific physics cases is presented.

  17. 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

  18. Multi-Dimensional Path Queries

    DEFF Research Database (Denmark)

    Bækgaard, Lars

    1998-01-01

    to create nested path structures. We present an SQL-like query language that is based on path expressions and we show how to use it to express multi-dimensional path queries that are suited for advanced data analysis in decision support environments like data warehousing environments......We present the path-relationship model that supports multi-dimensional data modeling and querying. A path-relationship database is composed of sets of paths and sets of relationships. A path is a sequence of related elements (atoms, paths, and sets of paths). A relationship is a binary path...

  19. A three-dimensional neutron transport benchmark solution

    International Nuclear Information System (INIS)

    Ganapol, B.D.; Kornreich, D.E.

    1993-01-01

    For one-group neutron transport theory in one dimension, several powerful analytical techniques have been developed to solve the neutron transport equation, including Caseology, Wiener-Hopf factorization, and Fourier and Laplace transform methods. In addition, after a Fourier transform in the transverse plane and formulation of a pseudo problem, two-dimensional (2-D) and three-dimensional (3-D) problems can be solved using the techniques specifically developed for the one-dimensional (1-D) case. Numerical evaluation of the resulting expressions requiring an inversion in the transverse plane have been successful for 2-D problems but becomes exceedingly difficult in the 3-D case. In this paper, we show that by using the symmetry along the beam direction, a 2-D problem can be transformed into a 3-D problem in an infinite medium. The numerical solution to the 3-D problem is then demonstrated. Thus, a true 3-D transport benchmark solution can be obtained from a well-established numerical solution to a 2-D problem

  20. Calculation of accurate albedo boundary conditions for three-dimensional nodal diffusion codes by the method of characteristics

    International Nuclear Information System (INIS)

    Petkov, Petko T.

    2000-01-01

    Most of the few-group three-dimensional nodal diffusion codes used for neutronics calculations of the WWER reactors use albedo type boundary conditions on the core-reflector boundary. The conventional albedo are group-to-group reflection probabilities, defined on each outer node face. The method of characteristics is used to calculate accurate albedo by the following procedure. A many-group two-dimensional heterogeneous core-reflector problem, including a sufficient part of the core and detailed description of the adjacent reflector, is solved first. From this solution the angular flux on the core-reflector boundary is calculated in all groups for all traced neutron directions. Accurate boundary conditions can be calculated for the radial, top and bottom reflectors as well as for the absorber part of the WWER-440 reactor control assemblies. The algorithm can be used to estimate also albedo, coupling outer node faces on the radial reflector in the axial direction. Numerical results for the WWER-440 reactor are presented. (Authors)

  1. Three-dimensional multi-physics model of the European sodium fast reactor design applied to DBA analysis - 15293

    International Nuclear Information System (INIS)

    Lazaro, A.; Ordonez, J.; Martorell, S.; Przemyslaw, S.; Ammirabile, L.; Tsige-Tamirat, H.

    2015-01-01

    The sodium cooled fast reactor (SFR) is one of the reactor types selected by the Generation IV International Forum. SFR stand out due to its remarkable past operational experience in related projects and its potential to achieve the ambitious goals laid for the new generation of nuclear reactors. Regardless its operational experience, there is a need to apply computational tools able to simulate the system behaviour under conditions that may overtake the reactor safety limits from the early stages of the design process, including the three-dimensional phenomena that may arise in these transients. This paper presents the different steps followed towards the development of a multi-physics platform with capabilities to simulate complex phenomena using a coupled neutronic-thermal-hydraulic scheme. The development started with a one-dimensional thermal-hydraulic model of the European Sodium Fast Reactor (ESFR) design with point kinetic neutronic feedback benchmarked with its peers in the framework of the FP7-CP-ESFR project using the state-of-the-art thermal-hydraulic system code TRACE. The model was successively extended into a three-dimensional model coupled with the spatial kinetic neutronic code PARCS able to simulate three-dimensional multi-physic phenomena along with the comparison of the results for symmetric cases. The last part of the paper shows the application of the developed tool to the analysis of transients involving asymmetrical effects, such as the coast-down of a primary and secondary pump or the withdrawal of a peripheral control rod bank, demonstrating the unique capability of the code to simulate such transients and the capability of the design to withstand them under design basis

  2. 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

  3. A multi-slice sliding cell technique for diffusion measurements in liquid metals

    Science.gov (United States)

    Zhong, Langxiang; Hu, Jinliang; Geng, Yongliang; Zhu, Chunao; Zhang, Bo

    2017-09-01

    The long capillary and shear-cell techniques are traditionally used for diffusion measurements in liquid metals. Inspired by the idea of the shear-cell method, we have built a multi-slice sliding cell device for inter-diffusion measurements in liquid metals. The device is designed based on a linear sliding movement rather than a rotational shearing as used in the traditional shear-cell method. Compared with the normal shear-cell method, the present device is a more compact setup thus easier to handle. Also, it is expected to be easier to monitor with X-rays or neutrons if used in in situ experiments. A series of benchmark time-dependent diffusion experiments in Al-Cu melts carried out with the present technique reveal that accurate diffusion constants can be achieved only after a sufficient time. For short annealing times, the initial shearing process causing convective flow dominates the measurement and leads to an increase of the measured diffusion coefficient by a factor three. The diffusion data obtained for Al-Cu liquids are consistent with the most accurate data measured by the in situ X-ray radiography method under well controlled conditions of no temperature gradient or other perturbation. High accuracy and easy handling as well as superior adaptability make the present technique suitable for diffusion studies in liquid metals.

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

    International Nuclear Information System (INIS)

    Czubek, J.A.; Woznicka, U.

    1997-01-01

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

  5. Neutron scattering investigation on low-dimensional, quantum and frustrated magnetism and utilization of neutron polarization analysis. My first encounter with neutron research

    International Nuclear Information System (INIS)

    Kakurai, Kazuhisa

    2013-01-01

    My first encounter with neutron scattering research on low-dimensional magnetism at the Hahn-Meitner Institut under the supervision of Prof. H. Dachs and Prof. M. Steiner, were it all began, is accounted for. The polarized neutron analysis research on low-dimensional magnetism at the Institut Laue Langevin under the supervision of Dr. R. Pynn is also reported. I would like to dedicate this article to late Prof. H. Dachs expressing may deepest gratitude for his warm guidance during the early period of my neutron science carrier. (author)

  6. Fuel assembly inspection by three-dimensional neutron radiography

    International Nuclear Information System (INIS)

    Lapinski, N.P.; Reimann, K.J.; Berger, H.

    1979-01-01

    Radiographic inspection of complex objects such as fuel subassemblies often presents problems because superimposition of images at different depths in the object complicates interpretation. One method for obtaining and displaying three-dimensional neutron radiographic images in multiple-film laminagraphy; a series of radiographs generated at different angular orientations are superimposed to provide focussed images of any object plane. In the present work multiple-film neutron laminagraphs were generated using direct and indirect exposure techniques, with neutrons in thermal, epithermal, and fast energy ranges

  7. LABAN-PEL: a two-dimensional, multigroup diffusion, high-order response matrix code

    International Nuclear Information System (INIS)

    Mueller, E.Z.

    1991-06-01

    The capabilities of LABAN-PEL is described. LABAN-PEL is a modified version of the two-dimensional, high-order response matrix code, LABAN, written by Lindahl. The new version extends the capabilities of the original code with regard to the treatment of neutron migration by including an option to utilize full group-to-group diffusion coefficient matrices. In addition, the code has been converted from single to double precision and the necessary routines added to activate its multigroup capability. The coding has also been converted to standard FORTRAN-77 to enhance the portability of the code. Details regarding the input data requirements and calculational options of LABAN-PEL are provided. 13 refs

  8. Performance, Accuracy and Efficiency Evaluation of a Three-Dimensional Whole-Core Neutron Transport Code AGENT

    International Nuclear Information System (INIS)

    Jevremovic, Tatjana; Hursin, Mathieu; Satvat, Nader; Hopkins, John; Xiao, Shanjie; Gert, Godfree

    2006-01-01

    The AGENT (Arbitrary Geometry Neutron Transport) an open-architecture reactor modeling tool is deterministic neutron transport code for two or three-dimensional heterogeneous neutronic design and analysis of the whole reactor cores regardless of geometry types and material configurations. The AGENT neutron transport methodology is applicable to all generations of nuclear power and research reactors. It combines three theories: (1) the theory of R-functions used to generate real three-dimensional whole-cores of square, hexagonal or triangular cross sections, (2) the planar method of characteristics used to solve isotropic neutron transport in non-homogenized 2D) reactor slices, and (3) the one-dimensional diffusion theory used to couple the planar and axial neutron tracks through the transverse leakage and angular mesh-wise flux values. The R-function-geometrical module allows a sequential building of the layers of geometry and automatic sub-meshing based on the network of domain functions. The simplicity of geometry description and selection of parameters for accurate treatment of neutron propagation is achieved through the Boolean algebraic hierarchically organized simple primitives into complex domains (both being represented with corresponding domain functions). The accuracy is comparable to Monte Carlo codes and is obtained by following neutron propagation through real geometrical domains that does not require homogenization or simplifications. The efficiency is maintained through a set of acceleration techniques introduced at all important calculation levels. The flux solution incorporates power iteration with two different acceleration techniques: Coarse Mesh Re-balancing (CMR) and Coarse Mesh Finite Difference (CMFD). The stand-alone originally developed graphical user interface of the AGENT code design environment allows the user to view and verify input data by displaying the geometry and material distribution. The user can also view the output data such

  9. 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.

  10. Investigation of the neutron detection statistics in fast critical assembly BFS-24-1

    International Nuclear Information System (INIS)

    Avramov, A.M.; Tyutyunnikov, P.L.; Mikulski, A.T.; Rafalska, E.; Chwaszczewski, S.; Jablonski, K.

    1974-01-01

    The results of the neutron detection statistics investigation at the fast critical assembly BFS-24-1 are given. The Ross-α measurements were carried out using: digital flash-start unit and 256 channel time analyzer, 10 channel time analyzer, alphameter device. Parallely the measurements using the variable dead time method and zero probability method were performed. The prompt neutron decay constants, the effectiveness of neutron detector and the intensity of external neutron source are determined using the experimental data. The experimental values of prompt neutron decay constant are compared with the calculated ones. The codes used in the calculation are following: one dimensional, diffusion, 26-group code 26-M and EWA-1, one dimensional, multiregion, nonstationary diffusion 3-group code SPECTR, 26-group, diffusion code in buckling approximation, MIXSPECTR. In all codes the 26 group nuclear constants BNAB-26 and BNAB-70 are used. (author)

  11. 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

  12. Sample positioning in neutron diffraction experiments using a multi-material fiducial marker

    Energy Technology Data Exchange (ETDEWEB)

    Marais, D., E-mail: Deon.Marais@necsa.co.za [Research and Development Division, South African Nuclear Energy Corporation (Necsa) SOC Limited, PO Box 582, Pretoria 0001 (South Africa); School of Mechanical and Nuclear Engineering, North-West University, Potchefstroom 2520 (South Africa); Venter, A.M., E-mail: Andrew.Venter@necsa.co.za [Research and Development Division, South African Nuclear Energy Corporation (Necsa) SOC Limited, PO Box 582, Pretoria 0001 (South Africa); Faculty of Agriculture Science and Technology, North-West University, Mahikeng 2790 (South Africa); Markgraaff, J., E-mail: Johan.Markgraaff@nwu.ac.za [School of Mechanical and Nuclear Engineering, North-West University, Potchefstroom 2520 (South Africa); James, J., E-mail: Jon.James@open.ac.uk [Faculty of Mathematics, Computing and Technology, The Open University, Milton Keynes, MK76AA England (United Kingdom)

    2017-01-01

    An alternative sample positioning method is reported for use in conjunction with sample positioning and experiment planning software systems deployed on some neutron diffraction strain scanners. In this approach, the spherical fiducial markers and location trackers used with optical metrology hardware are replaced with a specifically designed multi-material fiducial marker that requires one diffraction measurement. In a blind setting, the marker position can be determined within an accuracy of ±164 µm with respect to the instrument gauge volume. The scheme is based on a pre-determined relationship that links the diffracted peak intensity to the absolute positioning of the fiducial marker with respect to the instrument gauge volume. Two methods for establishing the linking relationship are presented, respectively based on fitting multi-dimensional quadratic functions and a cross-correlation artificial neural network.

  13. 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.)

  14. Multi-group transport methods for high-resolution neutron activation analysis

    International Nuclear Information System (INIS)

    Burns, K. A.; Smith, L. E.; Gesh, C. J.; Shaver, M. W.

    2009-01-01

    The accurate and efficient simulation of coupled neutron-photon problems is necessary for several important radiation detection applications. Examples include the detection of nuclear threats concealed in cargo containers and prompt gamma neutron activation analysis for nondestructive determination of elemental composition of unknown samples. In these applications, high-resolution gamma-ray spectrometers are used to preserve as much information as possible about the emitted photon flux, which consists of both continuum and characteristic gamma rays with discrete energies. Monte Carlo transport is the most commonly used modeling tool for this type of problem, but computational times for many problems can be prohibitive. This work explores the use of multi-group deterministic methods for the simulation of neutron activation problems. Central to this work is the development of a method for generating multi-group neutron-photon cross-sections in a way that separates the discrete and continuum photon emissions so that the key signatures in neutron activation analysis (i.e., the characteristic line energies) are preserved. The mechanics of the cross-section preparation method are described and contrasted with standard neutron-gamma cross-section sets. These custom cross-sections are then applied to several benchmark problems. Multi-group results for neutron and photon flux are compared to MCNP results. Finally, calculated responses of high-resolution spectrometers are compared. Preliminary findings show promising results when compared to MCNP. A detailed discussion of the potential benefits and shortcomings of the multi-group-based approach, in terms of accuracy, and computational efficiency, is provided. (authors)

  15. Solutions of diffusion equations in two-dimensional cylindrical geometry by series expansions

    International Nuclear Information System (INIS)

    Ohtani, Nobuo

    1976-01-01

    A solution of the multi-group multi-regional diffusion equation in two-dimensional cylindrical (rho-z) geometry is obtained in the form of a regionwise double series composed of Bessel and trigonometrical functions. The diffusion equation is multiplied by weighting functions, which satisfy the homogeneous part of the diffusion equation, and the products are integrated over the region for obtaining the equations to determine the fluxes and their normal derivatives at the region boundaries. Multiplying the diffusion equation by each function of the set used for the flux expansion, then integrating the products, the coefficients of the double series of the flux inside each region are calculated using the boundary values obtained above. Since the convergence of the series thus obtained is slow especially near the region boundaries, a method for improving the convergence has been developed. The double series of the flux is separated into two parts. The normal derivative at the region boundary of the first part is zero, and that of the second part takes the value which is obtained in the first stage of this method. The second part is replaced by a continuous function, and the flux is represented by the sum of the continuous function and the double series. A sample critical problem of a two-group two-region system is numerically studied. The results show that the present method yields very accurately the flux integrals in each region with only a small number of expansion terms. (auth.)

  16. Global Search of a Three-dimensional Low Solidity Circular Cascade Diffuser for Centrifugal Blowers by Meta-model Assisted Optimization

    Science.gov (United States)

    Sakaguchi, Daisaku; Sakue, Daiki; Tun, Min Thaw

    2018-04-01

    A three-dimensional blade of a low solidity circular cascade diffuser in centrifugal blowers is designed by means of a multi-point optimization technique. The optimization aims at improving static pressure coefficient at a design point and at a small flow rate condition. Moreover, a clear definition of secondary flow expressed by positive radial velocity at hub side is taken into consideration in constraints. The number of design parameters for three-dimensional blade reaches to 10 in this study, such as a radial gap, a radial chord length and mean camber angle distribution of the LSD blade with five control points, control point between hub and shroud with two design freedom. Optimization results show clear Pareto front and selected optimum design shows good improvement of pressure rise in diffuser at small flow rate conditions. It is found that three-dimensional blade has advantage to stabilize the secondary flow effect with improving pressure recovery of the low solidity circular cascade diffuser.

  17. Neutron radiography imaging with 2-dimensional photon counting method and its problems

    International Nuclear Information System (INIS)

    Ikeda, Y.; Kobayashi, H.; Niwa, T.; Kataoka, T.

    1988-01-01

    A ultra sensitive neutron imaging system has been deviced with a 2-dimensional photon counting camara (ARGUS 100). The imaging system is composed by a 2-dimensional single photon counting tube and a low background vidicon followed with an image processing unit and frame memories. By using the imaging system, electronic neutron radiography (NTV) has been possible under the neutron flux less than 3 x 10 4 n/cm 2 ·s. (author)

  18. 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.)

  19. 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...

  20. 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.)

  1. 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...

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

    Energy Technology Data Exchange (ETDEWEB)

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

    1997-12-31

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

  3. 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)

  4. Transport equivalent diffusion constants for reflector region in PWRs

    International Nuclear Information System (INIS)

    Tahara, Yoshihisa; Sekimoto, Hiroshi

    2002-01-01

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

  5. Two-dimensional DORT discrete ordinates X-Y geometry neutron flux calculations for the Halden Heavy Boiling Water Reactor core configurations

    Energy Technology Data Exchange (ETDEWEB)

    Slater, C.O.

    1990-07-01

    Results are reported for two-dimensional discrete ordinates, X-Y geometry calculations performed for seven Halden Heavy Boiling Water Reactor core configurations. The calculations were performed in support of an effort to reassess the neutron fluence received by the reactor vessel. Nickel foil measurement data indicated considerable underprediction of fluences by the previously used multigroup removal- diffusion method. Therefore, calculations by a more accurate method were deemed appropriate. For each core configuration, data are presented for (1) integral fluxes in the core and near the vessel wall, (2) neutron spectra at selected locations, (3) isoflux contours superimposed on the geometry models, (4) plots of the geometry models, and (5) input for the calculations. The initial calculations were performed with several mesh sizes. Comparisons of the results from these calculations indicated that the uncertainty in the calculated fluxes should be less than 10%. However, three-dimensional effects (such as axial asymmetry in the fuel loading) could contribute to much greater uncertainty in the calculated neutron fluxes. 7 refs., 22 figs., 11 tabs.

  6. Multi-Wavelength Polarimetry of Isolated Neutron Stars

    Directory of Open Access Journals (Sweden)

    Roberto P. Mignani

    2018-03-01

    Full Text Available Isolated neutron stars are known to be endowed with extreme magnetic fields, whose maximum intensity ranges from 10 12 – 10 15 G, which permeates their magnetospheres. Their surrounding environment is also strongly magnetized, especially in the compact nebulae powered by the relativistic wind from young neutron stars. The radiation from isolated neutron stars and their surrounding nebulae is, thus, supposed to bring a strong polarization signature. Measuring the neutron star polarization brings important information about the properties of their magnetosphere and of their highly magnetized environment. Being the most numerous class of isolated neutron stars, polarization measurements have been traditionally carried out for radio pulsars, hence in the radio band. In this review, I summarize multi-wavelength linear polarization measurements obtained at wavelengths other than radio both for pulsars and other types of isolated neutron stars and outline future perspectives with the upcoming observing facilities.

  7. Development of three dimensional transient analysis code STTA for SCWR core

    International Nuclear Information System (INIS)

    Wang, Lianjie; Zhao, Wenbo; Chen, Bingde; Yao, Dong; Yang, Ping

    2015-01-01

    Highlights: • A coupled three dimensional neutronics/thermal-hydraulics code STTA is developed for SCWR core transient analysis. • The Dynamic Link Libraries method is adopted for coupling computation for SCWR multi-flow core transient analysis. • The NEACRP-L-335 PWR benchmark problems are studied to verify STTA. • The SCWR rod ejection problems are studied to verify STTA. • STTA meets what is expected from a code for SCWR core 3-D transient preliminary analysis. - Abstract: A coupled three dimensional neutronics/thermal-hydraulics code STTA (SCWR Three dimensional Transient Analysis code) is developed for SCWR core transient analysis. Nodal Green’s Function Method based on the second boundary condition (NGFMN-K) is used for solving transient neutron diffusion equation. The SCWR sub-channel code ATHAS is integrated into NGFMN-K through the serial integration coupling approach. The NEACRP-L-335 PWR benchmark problem and SCWR rod ejection problems are studied to verify STTA. Numerical results show that the PWR solution of STTA agrees well with reference solutions and the SCWR solution is reasonable. The coupled code can be well applied to the core transients and accidents analysis with 3-D core model during both subcritical pressure and supercritical pressure operation

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

    International Nuclear Information System (INIS)

    Drozdowicz, K.

    1999-01-01

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

  9. Two-dimensional microstrip detector for neutrons

    Energy Technology Data Exchange (ETDEWEB)

    Oed, A [Institut Max von Laue - Paul Langevin (ILL), 38 - Grenoble (France)

    1997-04-01

    Because of their robust design, gas microstrip detectors, which were developed at ILL, can be assembled relatively quickly, provided the prefabricated components are available. At the beginning of 1996, orders were received for the construction of three two-dimensional neutron detectors. These detectors have been completed. The detectors are outlined below. (author). 2 refs.

  10. 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)

  11. 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.)

  12. PHISICS multi-group transport neutronic capabilities for RELAP5

    Energy Technology Data Exchange (ETDEWEB)

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

    2012-07-01

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

  13. 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)

  14. Analysis of the applicability of acceleration methods for a triangular prism geometry nodal diffusion code

    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)

  15. Lattice Boltzmann method for multi-component, non-continuum mass diffusion

    International Nuclear Information System (INIS)

    Joshi, Abhijit S; Peracchio, Aldo A; Grew, Kyle N; Chiu, Wilson K S

    2007-01-01

    Recently, there has been a great deal of interest in extending the lattice Boltzmann method (LBM) to model transport phenomena in the non-continuum regime. Most of these studies have focused on single-component flows through simple geometries. This work examines an ad hoc extension of a recently developed LBM model for multi-component mass diffusion (Joshi et al 2007 J. Phys. D: Appl. Phys. 40 2961) to model mass diffusion in the non-continuum regime. In order to validate the method, LBM results for ternary diffusion in a two-dimensional channel are compared with predictions of the dusty gas model (DGM) over a range of Knudsen numbers. A calibration factor based on the DGM is used in the LBM to correlate Knudsen diffusivity to pore size. Results indicate that the LBM can be a useful tool for predicting non-continuum mass diffusion (Kn > 0.001), but additional research is needed to extend the range of applicability of the algorithm for a larger parameter space. Guidelines are given on using the methodology described in this work to model non-continuum mass transport in more complex geometries where the DGM is not easily applicable. In addition, the non-continuum LBM methodology can be extended to three-dimensions. An envisioned application of this technique is to model non-continuum mass transport in porous solid oxide fuel cell electrodes

  16. Multi-group neutron transport theory

    International Nuclear Information System (INIS)

    Zelazny, R.; Kuszell, A.

    1962-01-01

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

  17. Investigation of multi-dimensional computational models for calculating pollutant transport

    International Nuclear Information System (INIS)

    Pepper, D.W.; Cooper, R.E.; Baker, A.J.

    1980-01-01

    A performance study of five numerical solution algorithms for multi-dimensional advection-diffusion prediction on mesoscale grids was made. Test problems include transport of point and distributed sources, and a simulation of a continuous source. In all cases, analytical solutions are available to assess relative accuracy. The particle-in-cell and second-moment algorithms, both of which employ sub-grid resolution coupled with Lagrangian advection, exhibit superior accuracy in modeling a point source release. For modeling of a distributed source, algorithms based upon the pseudospectral and finite element interpolation concepts, exhibit improved accuracy on practical discretizations

  18. Multi-dimensional imaging

    CERN Document Server

    Javidi, Bahram; Andres, Pedro

    2014-01-01

    Provides a broad overview of advanced multidimensional imaging systems with contributions from leading researchers in the field Multi-dimensional Imaging takes the reader from the introductory concepts through to the latest applications of these techniques. Split into 3 parts covering 3D image capture, processing, visualization and display, using 1) a Multi-View Approach and 2.) a Holographic Approach, followed by a 3rd part addressing other 3D systems approaches, applications and signal processing for advanced 3D imaging. This book describes recent developments, as well as the prospects and

  19. Two-dimensional boundary-value problem for ion-ion diffusion

    International Nuclear Information System (INIS)

    Tuszewski, M.; Lichtenberg, A.J.

    1977-01-01

    Like-particle diffusion is usually negligible compared with unlike-particle diffusion because it is two orders higher in spatial derivatives. When the ratio of the ion gyroradius to the plasma transverse dimension is of the order of the fourth root of the mass ratio, previous one-dimensional analysis indicated that like-particle diffusion is significant. A two-dimensional boundary-value problem for ion-ion diffusion is investigated. Numerical solutions are found with models for which the nonlinear partial differential equation reduces to an ordinary fourth-order differential equation. These solutions indicate that the ion-ion losses are higher by a factor of six for a slab geometry, and by a factor of four for circular geometry, than estimated from dimensional analysis. The solutions are applied to a multiple mirror experiment stabilized with a quadrupole magnetic field which generates highly elliptical flux surfaces. It is found that the ion-ion losses dominate the electron-ion losses and that these classical radial losses contribute to a significant decrease of plasma lifetime, in qualitiative agreement with the experimental results

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

    Energy Technology Data Exchange (ETDEWEB)

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

    1962-02-15

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

  1. A Shell Multi-dimensional Hierarchical Cubing Approach for High-Dimensional Cube

    Science.gov (United States)

    Zou, Shuzhi; Zhao, Li; Hu, Kongfa

    The pre-computation of data cubes is critical for improving the response time of OLAP systems and accelerating data mining tasks in large data warehouses. However, as the sizes of data warehouses grow, the time it takes to perform this pre-computation becomes a significant performance bottleneck. In a high dimensional data warehouse, it might not be practical to build all these cuboids and their indices. In this paper, we propose a shell multi-dimensional hierarchical cubing algorithm, based on an extension of the previous minimal cubing approach. This method partitions the high dimensional data cube into low multi-dimensional hierarchical cube. Experimental results show that the proposed method is significantly more efficient than other existing cubing methods.

  2. 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).

  3. 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)

  4. Two-dimensional void reconstruction by neutron transmission

    International Nuclear Information System (INIS)

    Zakaib, G.D.; Harms, A.A.; Vlachopoulos, J.

    1978-01-01

    Contemporary algebraic reconstruction methods are utilized in investigating the two-dimensional void distribution in a water analog from neutron transmission measurements. It is sought to ultimately apply these techniques to the determination of time-averaged void distribution in two-phase flow systems as well as for potential usage in neutron radiography. Initially, projection data were obtained from a digitized model of a hypothetical two-phase representation and later from neutron beam traverses across a voided methacrylate plastic model. From 10 to 15 views were incorporated, and decoupling of overlapped measurements was utilized to afford greater resolution. In general, the additive Algebraic Reconstruction Technique yielded the best reconstructions, with others showing promise for noisy data. Results indicate the need for some further development of the method in interpreting real data

  5. Studies on the numerical solution of three-dimensional stationary diffusion equations using the finite element method

    International Nuclear Information System (INIS)

    Franke, H.P.

    1976-05-01

    The finite element method is applied to the solution of the stationary 3D group diffusion equations. For this, a programme system with the name of FEM3D is established which also includes a module for semi-automatic mesh generation. Tetrahedral finite elements are used. The neutron fluxes are described by complete first- or second-order Lagrangian polynomials. General homogeneous boundary conditions are allowed. The studies show that realistic three-dimensional problems can be solved at less expense by iterative methods, in particular so when especially adapted matrix handling and storage schemes are used efficiently. (orig./RW) [de

  6. 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)

  7. 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)

  8. Algorithms for solving atomic structures of nanodimensional clusters in single crystals based on X-ray and neutron diffuse scattering data

    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

  9. 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

  10. Dimensional reduction of a general advection–diffusion equation in 2D channels

    Science.gov (United States)

    Kalinay, Pavol; Slanina, František

    2018-06-01

    Diffusion of point-like particles in a two-dimensional channel of varying width is studied. The particles are driven by an arbitrary space dependent force. We construct a general recurrence procedure mapping the corresponding two-dimensional advection-diffusion equation onto the longitudinal coordinate x. Unlike the previous specific cases, the presented procedure enables us to find the one-dimensional description of the confined diffusion even for non-conservative (vortex) forces, e.g. caused by flowing solvent dragging the particles. We show that the result is again the generalized Fick–Jacobs equation. Despite of non existing scalar potential in the case of vortex forces, the effective one-dimensional scalar potential, as well as the corresponding quasi-equilibrium and the effective diffusion coefficient can be always found.

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

    CERN Document Server

    Rubbia, Carlo

    1998-01-01

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

  12. 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

  13. 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.

  14. Image matrix processor for fast multi-dimensional computations

    Science.gov (United States)

    Roberson, George P.; Skeate, Michael F.

    1996-01-01

    An apparatus for multi-dimensional computation which comprises a computation engine, including a plurality of processing modules. The processing modules are configured in parallel and compute respective contributions to a computed multi-dimensional image of respective two dimensional data sets. A high-speed, parallel access storage system is provided which stores the multi-dimensional data sets, and a switching circuit routes the data among the processing modules in the computation engine and the storage system. A data acquisition port receives the two dimensional data sets representing projections through an image, for reconstruction algorithms such as encountered in computerized tomography. The processing modules include a programmable local host, by which they may be configured to execute a plurality of different types of multi-dimensional algorithms. The processing modules thus include an image manipulation processor, which includes a source cache, a target cache, a coefficient table, and control software for executing image transformation routines using data in the source cache and the coefficient table and loading resulting data in the target cache. The local host processor operates to load the source cache with a two dimensional data set, loads the coefficient table, and transfers resulting data out of the target cache to the storage system, or to another destination.

  15. NodHex3D: An application for solving the neutron diffusion equations in hexagonal-Z geometry and steady state; NodHex3D: Una aplicacion para solucionar las ecuaciones de difusion de neutrones en geometria hexagonal-Z y estado estacionario

    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)

  16. 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 ...

  17. Metal impurities profile in a 450kg multi-crystalline silicon ingot by Cold Neutron Prompt Gamma-ray Activation Analysis

    International Nuclear Information System (INIS)

    Baek, Hani; Sun, Gwang Min; Kim, Ji seok; Oh, Mok; Chung, Yong Sam; Moon, Jong Hwa; Kim, Sun Ha; Baek, Sung Yeol; Tuan, Hoang Sy Minh

    2014-01-01

    Metal impurities are harmful to multi-crystalline silicon solar cells. They reduce solar cell conversion efficiencies through increased carrier recombination. They are present as isolated point-like impurities or precipitates. This work is to study the concentration profiles of some metal impurities of the directionally solidified 450kg multi-crystalline silicon ingot grown for solar cell production. The concentration of such impurities are generally below 10 15 cm -3 , and as such cannot be detected by physical techniques such as secondary-ion-mass spectroscopy(SIMS). So, we have tried to apply Cold Neutron - Prompt Gamma ray Activation Analysis(CN-PGAA) at the HANARO reactor research. The impurity concentrations of Au, Mn, Pt, Mo of a photovoltaic grade multi-crystalline silicon ingot appear by segregation from the liquid to the solid phase in the central region of the ingot during the crystallization. In the impurities concentration of the bottom region is higher than middle region due to the solid state diffusion. Towards the top region the segregation impurities diffused, during cooling process

  18. 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)

  19. STEADY-SHIP: a computer code for three-dimensional nuclear and thermal-hydraulic analyses of marine reactors

    International Nuclear Information System (INIS)

    Itagaki, Masafumi; Naito, Yoshitaka; Tokuno, Yukio; Matsui, Yasushi.

    1988-01-01

    A code STEADY-SHIP has been developed to calculate three-dimensional distributions of neutron flux, power and coolant temperature in the reactor core of the nuclear ship MUTSU. The code consists of two parts, that is, a few-group three-dimensional neutron diffusion module DIFFUSION-SHIP and a thermal-hydraulic module HYDRO-SHIP: In the DIFFUSION-SHIP the leakage iteration method is used for solving the three-dimensional neutron diffusion equation with small computer core memory and short computing time; The HYDRO-SHIP performs the general thermal-hydraulic calculation for evaluating feedbacks required in the neutronic calculation by the DIFFUSION-SHIP. The macroscopic nuclear constants are generated by a module CROSS-SHIP as functions of xenon poison, fuel temperature, moderator temperature and moderator density. A module LOCAL-FINE has the capability of computing a detailed rod power distribution for each local node in the core, using the boundary conditions on the surface of the node which were supplied by the STEADY-SHIP whole-core calculation. The applicability of this code to marine reactors has been demonstrated by comparing the computed results with the data measured during the MUTSU land-loaded core critical experiments and with the data obtained during the hot-zero-power tests performed for the actual MUTSU plant. (author)

  20. An iterative algorithm for solving the multidimensional neutron diffusion nodal method equations on parallel computers

    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

  1. Solution of multi-group diffusion equation in x-y-z geometry by finite Fourier transformation

    International Nuclear Information System (INIS)

    Kobayashi, Keisuke

    1975-01-01

    The multi-group diffusion equation in three-dimensional x-y-z geometry is solved by finite Fourier transformation. Applying the Fourier transformation to a finite region with constant nuclear cross sections, the fluxes and currents at the material boundaries are obtained in terms of the Fourier series. Truncating the series after the first term, and assuming that the source term is piecewise linear within each mesh box, a set of coupled equations is obtained in the form of three-point equations for each coordinate. These equations can be easily solved by the alternative direction implicit method. Thus a practical procedure is established that could be applied to replace the currently used difference equation. This equation is used to solve the multi-group diffusion equation by means of the source iteration method; and sample calculations for thermal and fast reactors show that the present method yields accurate results with a smaller number of mesh points than the usual finite difference equations. (auth.)

  2. 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

  3. Data acquisition systems for uses of multi-counter time analyzer and one-dimensional PSD pulse height analyzer to neutron scattering measurements

    International Nuclear Information System (INIS)

    Ono, Masayoshi; Tasaki, Seiji; Okamoto, Sunao

    1989-01-01

    A data acquisition system having the various modern electronic devices was designed and tested for practical use of neutron time-of-flight (TOF) measurements with multiple counters. The system is principally composed of TOF logic units (load-able up to 128 units) with a control unit and a conventional micro-computer. The TOF logic unit (main memory, 2048 ch, 24 bits/ch) demonstrates about 1.7 times higher efficiency for neutron counting rate per channel than the one by a conventional TOF logic unit. Meanwhile, some data-access functions of the TOF logic unit were applied to position sensitive analyzer of one-dimensional neutron PSD for small angle scattering. The analyzer was tested with use of pulse generator. The result shows good linearity. (author)

  4. 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

  5. Development of an Analytic Nodal Diffusion Solver in Multi-groups for 3D Reactor Cores with Rectangular or Hexagonal Assemblies

    Energy Technology Data Exchange (ETDEWEB)

    Lozano, Juan Andres; Aragones, Jose Maria; Garcia-Herranz, Nuria [Universidad Politecnica de Madrid, 28006 Jose Gutierrez Abascal 2, Madrid (Spain)

    2008-07-01

    More accurate modelling of physical phenomena involved in present and future nuclear reactors requires a multi-scale and multi-physics approach. This challenge can be accomplished by the coupling of best-estimate core-physics, thermal-hydraulics and multi-physics solvers. In order to make viable that coupling, the current trends in reactor simulations are along the development of a new generation of tools based on user-friendly, modular, easily linkable, faster and more accurate codes to be integrated in common platforms. These premises are in the origin of the NURESIM Integrated Project within the 6. European Framework Program, which is envisaged to provide the initial step towards a Common European Standard Software Platform for nuclear reactors simulations. In the frame of this project and to reach the above-mentioned goals, a 3-D multigroup nodal solver for neutron diffusion calculations called ANDES (Analytic Nodal Diffusion Equation Solver) has been developed and tested in-depth in this Thesis. ANDES solves the steady-state and time-dependent neutron diffusion equation in three-dimensions and any number of energy groups, utilizing the Analytic Coarse-Mesh Finite-Difference (ACMFD) scheme to yield the nodal coupling equations. It can be applied to both Cartesian and triangular-Z geometries, so that simulations of LWR as well as VVER, HTR and fast reactors can be performed. The solver has been implemented in a fully encapsulated way, enabling it as a module to be readily integrated in other codes and platforms. In fact, it can be used either as a stand-alone nodal code or as a solver to accelerate the convergence of whole core pin-by-pin code systems. Verification of performance has shown that ANDES is a code with high order definition for whole core realistic nodal simulations. In this paper, the methodology developed and involved in ANDES is presented. (authors)

  6. Theoretical investigation of the neutron noise diagnostics of two-dimensional control rod vibrations in a PWR

    International Nuclear Information System (INIS)

    Pazsit, I.; Analytis, G.T.

    1980-01-01

    In order to develop a method for monitoring control rod vibrations by neutron noise measurements, the noise induced by two-dimensional vibrations of control elements is investigated. The two-dimensional Green's function relating the small stochastic cross-section fluctuations to the neutron noise is determined for a rectangular slab reactor in the modified one-group theory, and subsequently, the neutron response to two-dimensional vibrating noise sources is investigated. Two possible diagnostical applications are considered: (a) the reconstruction of the mechanical trajectory of the vibrating element by neutron noise measurements, and (b) the possibility of locating the vibrating element in the core. (author)

  7. 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

  8. 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)

  9. Multi dimensional analysis of Design Basis Events using MARS-LMR

    International Nuclear Information System (INIS)

    Woo, Seung Min; Chang, Soon Heung

    2012-01-01

    Highlights: ► The one dimensional analyzed sodium hot pool is modified to a three dimensional node system, because the one dimensional analysis cannot represent the phenomena of the inside pool of a big size pool with many compositions. ► The results of the multi-dimensional analysis compared with the one dimensional analysis results in normal operation, TOP (Transient of Over Power), LOF (Loss of Flow), and LOHS (Loss of Heat Sink) conditions. ► The difference of the sodium flow pattern due to structure effect in the hot pool and mass flow rates in the core lead the different sodium temperature and temperature history under transient condition. - Abstract: KALIMER-600 (Korea Advanced Liquid Metal Reactor), which is a pool type SFR (Sodium-cooled Fast Reactor), was developed by KAERI (Korea Atomic Energy Research Institute). DBE (Design Basis Events) for KALIMER-600 has been analyzed in the one dimension. In this study, the one dimensional analyzed sodium hot pool is modified to a three dimensional node system, because the one dimensional analysis cannot represent the phenomena of the inside pool of a big size pool with many compositions, such as UIS (Upper Internal Structure), IHX (Intermediate Heat eXchanger), DHX (Decay Heat eXchanger), and pump. The results of the multi-dimensional analysis compared with the one dimensional analysis results in normal operation, TOP (Transient of Over Power), LOF (Loss of Flow), and LOHS (Loss of Heat Sink) conditions. First, the results in normal operation condition show the good agreement between the one and multi-dimensional analysis. However, according to the sodium temperatures of the core inlet, outlet, the fuel central line, cladding and PDRC (Passive Decay heat Removal Circuit), the temperatures of the one dimensional analysis are generally higher than the multi-dimensional analysis in conditions except the normal operation state, and the PDRC operation time in the one dimensional analysis is generally longer than

  10. Effects of core models and neutron energy group structures on xenon oscillation in large graphite-moderated reactors

    International Nuclear Information System (INIS)

    Yamasita, Kiyonobu; Harada, Hiroo; Murata, Isao; Shindo, Ryuichi; Tsuruoka, Takuya.

    1993-01-01

    Xenon oscillations of large graphite-moderated reactors have been analyzed by a multi-group diffusion code with two- and three-dimensional core models to study the effects of the geometric core models and the neutron energy group structures on the evaluation of the Xe oscillation behavior. The study clarified the following. It is important for accurate Xe oscillation simulations to use the neutron energy group structure that describes well the large change in the absorption cross section of Xe in the thermal energy range of 0.1∼0.65 eV, because the energy structure in this energy range has significant influences on the amplitude and the period of oscillations in power distributions. Two-dimensional R-Z models can be used instead of three-dimensional R-θ-Z models for evaluation of the threshold power of Xe oscillation, but two-dimensional R-θ models cannot be used for evaluation of the threshold power. Although the threshold power evaluated with the R-θ-Z models coincides with that of the R-Z models, it does not coincide with that of the R-θ models. (author)

  11. 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

  12. Relativistic collective diffusion in one-dimensional systems

    Science.gov (United States)

    Lin, Gui-Wu; Lam, Yu-Yiu; Zheng, Dong-Qin; Zhong, Wei-Rong

    2018-05-01

    The relativistic collective diffusion in one-dimensional molecular system is investigated through nonequilibrium molecular dynamics with Monte Carlo methods. We have proposed the relationship among the speed, the temperature, the density distribution and the collective diffusion coefficient of particles in a relativistic moving system. It is found that the relativistic speed of the system has no effect on the temperature, but the collective diffusion coefficient decreases to zero as the velocity of the system approaches to the speed of light. The collective diffusion coefficient is modified as D‧ = D(1 ‑w2 c2 )3 2 for satisfying the relativistic circumstances. The present results may contribute to the understanding of the behavior of the particles transport diffusion in a high speed system, as well as enlighten the study of biological metabolism at relativistic high speed situation.

  13. 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.)

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

    International Nuclear Information System (INIS)

    Chakraverty, S.; Nayak, S.

    2013-01-01

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

  15. 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

  16. 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)

  17. Two-dimensional neutron scintillation detector with optimal gamma discrimination

    International Nuclear Information System (INIS)

    Kanyo, M.; Reinartz, R.; Schelten, J.; Mueller, K.D.

    1993-01-01

    The gamma sensitivity of a two-dimensional scintillation neutron detector based on position sensitive photomultipliers (Hamamatsu R2387 PM) has been minimized by a digital differential discrimination unit. Since the photomultiplier gain is position-dependent by ±25% a discrimination unit was developed where digital upper and lower discrimination levels are set due to the position-dependent photomultiplier gain obtained from calibration measurements. By this method narrow discriminator windows can be used to reduce the gamma background drastically without effecting the neutron sensitivity of the detector. The new discrimination method and its performance tested by neutron measurements will be described. Experimental results concerning spatial resolution and γ-sensitivity are presented

  18. 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

  19. Stochastic and collisional diffusion in two-dimensional periodic flows

    International Nuclear Information System (INIS)

    Doxas, I.; Horton, W.; Berk, H.L.

    1990-05-01

    The global effective diffusion coefficient D* for a two-dimensional system of convective rolls with a time dependent perturbation added, is calculated. The perturbation produces a background diffusion coefficient D, which is calculated analytically using the Menlikov-Arnold integral. This intrinsic diffusion coefficient is then enhanced by the unperturbed flow, to produce the global effective diffusion coefficient D*, which we can calculate theoretically for a certain range of parameters. The theoretical value agrees well with numerical simulations. 23 refs., 4 figs

  20. One dimensional neutron kinetics in the TRAC-BF1 code

    International Nuclear Information System (INIS)

    Weaver, W.L. III; Wagner, K.C.

    1987-01-01

    The TRAC-BWR code development program at the Idaho National Engineering Laboratory is developing a version of the TRAC code for the U.S. Nuclear Regulatory Commission (USNRC) to provide a best-estimate analysis capability for the simulation of postulated accidents in boiling water reactor (BWR) power systems and related experimental facilities. Recent development efforts in the TRAC-BWR program have focused on improving the computational efficiency through the incorporation of a hybrid Courant- limit-violating numerical solution scheme in the one-dimensional component models and on improving code accuracy through the development of a one-dimensional neutron kinetics model. Many other improvements have been incorporated into TRAC-BWR to improve code portability, accuracy, efficiency, and maintainability. This paper will describe the one- dimensional neutron kinetics model, the generation of the required input data for this model, and present results of the first calculations using the model

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

    Energy Technology Data Exchange (ETDEWEB)

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

    1959-07-01

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

  2. 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

  3. Multi-Dimensional Aggregation for Temporal Data

    DEFF Research Database (Denmark)

    Böhlen, M. H.; Gamper, J.; Jensen, Christian Søndergaard

    2006-01-01

    Business Intelligence solutions, encompassing technologies such as multi-dimensional data modeling and aggregate query processing, are being applied increasingly to non-traditional data. This paper extends multi-dimensional aggregation to apply to data with associated interval values that capture...... that the data holds for each point in the interval, as well as the case where the data holds only for the entire interval, but must be adjusted to apply to sub-intervals. The paper reports on an implementation of the new operator and on an empirical study that indicates that the operator scales to large data...

  4. 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)

  5. 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.

  6. 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.

  7. Diffusion of elements and vacancies in multi-component systems

    Czech Academy of Sciences Publication Activity Database

    Fischer, F. D.; Svoboda, Jiří

    2014-01-01

    Roč. 60, MAR (2014), s. 338-367 ISSN 0079-6425 Institutional support: RVO:68081723 Keywords : multi-component diffusion * vacancy activity * manning theory * stress-driven diffusion Subject RIV: BJ - Thermodynamics Impact factor: 27.417, year: 2014

  8. DIFFUSION OF THE PULSED ELECTROMAGNETIC FIELD INTO THE MULTI-LAYER CORE OF INDUCTOR AT PULSED DEVICES

    Directory of Open Access Journals (Sweden)

    Volodymyr T. Chemerys

    2008-02-01

    Full Text Available  The problem of the pulsed magnetic field distribution in the cross section of the inductor core at the induction accelerator of electron beam is under consideration in this paper. Owing to multi-layer structure of the core package it has the magnetic and electric anisotropy with different speed of the field diffusion along the sheets of magnetic and across the sheets. At the pulse duration less than one microsecond the essential non-uniformity of the field along both axes of the core cross section can be found. This effect reduces the efficiency of the ferromagnetic material using with corresponding loss of the accelerator efficiency. The main conclusion of the paper consists of the necessity to check the field diffusion characteristics in the process of inductor design to be sure that the pulsed field is able to fill the cross section of the core during the pulse switching. The magnetic characteristics of the anisotropic core have been investigated in the paper by one-dimensional and two-dimensional simulation in the quasi-stationary approximation using the traditional equation of the field diffusion.

  9. Neutron scattering studies of low dimensional magnetic systems

    DEFF Research Database (Denmark)

    Hansen, Ursula Bengård

    investigated at low temperaturesand in a longitudinal magnetic eld using neutron spectroscopy. Here we observe thehybridisation of the magnon bound states, inherent to the low dimensional nature ofCoCl2 · 2D2O.At higher temperature, signatures which can be attributed to Magnetic Bloch Oscillationsis observed...

  10. A semi-experimental nodal synthesis method for the on-line reconstruction of three-dimensional neutron flux-shapes and reactivity

    International Nuclear Information System (INIS)

    Jacqmin, R.P.

    1991-01-01

    The safety and optimal performance of large, commercial, light-water reactors require the knowledge at all time of the neutron-flux distribution in the core. In principle, this information can be obtained by solving the time-dependent neutron diffusion equations. However, this approach is complicated and very expensive. Sufficiently accurate, real-time calculations (time scale of approximately one second) are not yet possible on desktop computers, even with fast-running, nodal kinetics codes. A semi-experimental, nodal synthesis method which avoids the solution of the time-dependent, neutron diffusion equations is described. The essential idea of this method is to approximate instantaneous nodal group-fluxes by a linear combination of K, precomputed, three-dimensional, static expansion-functions. The time-dependent coefficients of the combination are found from the requirement that the reconstructed flux-distribution agree in a least-squares sense with the readings of J (≥K) fixed, prompt-responding neutron-detectors. Possible numerical difficulties with the least-squares solution of the ill-conditioned, J-by-K system of equations are brought under complete control by the use of a singular-value-decomposition technique. This procedure amounts to the rearrangement of the original, linear combination of K expansion functions into an equivalent more convenient, linear combination of R (≤K) orthogonalized ''modes'' of decreasing magnitude. Exceedingly small modes are zeroed to eliminate any risk of roundoff-error amplification, and to assure consistency with the limited accuracy of the data. Additional modes are zeroed when it is desirable to limit the sensitivity of the results to measurement noise

  11. A semi-experimental nodal synthesis method for the on-line reconstruction of three-dimensional neutron flux-shapes and reactivity

    Energy Technology Data Exchange (ETDEWEB)

    Jacqmin, R.P.

    1991-12-10

    The safety and optimal performance of large, commercial, light-water reactors require the knowledge at all time of the neutron-flux distribution in the core. In principle, this information can be obtained by solving the time-dependent neutron diffusion equations. However, this approach is complicated and very expensive. Sufficiently accurate, real-time calculations (time scale of approximately one second) are not yet possible on desktop computers, even with fast-running, nodal kinetics codes. A semi-experimental, nodal synthesis method which avoids the solution of the time-dependent, neutron diffusion equations is described. The essential idea of this method is to approximate instantaneous nodal group-fluxes by a linear combination of K, precomputed, three-dimensional, static expansion-functions. The time-dependent coefficients of the combination are found from the requirement that the reconstructed flux-distribution agree in a least-squares sense with the readings of J ({ge}K) fixed, prompt-responding neutron-detectors. Possible numerical difficulties with the least-squares solution of the ill-conditioned, J-by-K system of equations are brought under complete control by the use of a singular-value-decomposition technique. This procedure amounts to the rearrangement of the original, linear combination of K expansion functions into an equivalent more convenient, linear combination of R ({le}K) orthogonalized modes'' of decreasing magnitude. Exceedingly small modes are zeroed to eliminate any risk of roundoff-error amplification, and to assure consistency with the limited accuracy of the data. Additional modes are zeroed when it is desirable to limit the sensitivity of the results to measurement noise.

  12. On efficiently computing multigroup multi-layer neutron reflection and transmission conditions

    International Nuclear Information System (INIS)

    Abreu, Marcos P. de

    2007-01-01

    In this article, we present an algorithm for efficient computation of multigroup discrete ordinates neutron reflection and transmission conditions, which replace a multi-layered boundary region in neutron multiplication eigenvalue computations with no spatial truncation error. In contrast to the independent layer-by-layer algorithm considered thus far in our computations, the algorithm here is based on an inductive approach developed by the present author for deriving neutron reflection and transmission conditions for a nonactive boundary region with an arbitrary number of arbitrarily thick layers. With this new algorithm, we were able to increase significantly the computational efficiency of our spectral diamond-spectral Green's function method for solving multigroup neutron multiplication eigenvalue problems with multi-layered boundary regions. We provide comparative results for a two-group reactor core model to illustrate the increased efficiency of our spectral method, and we conclude this article with a number of general remarks. (author)

  13. An accurate solution of point reactor neutron kinetics equations of multi-group of delayed neutrons

    International Nuclear Information System (INIS)

    Yamoah, S.; Akaho, E.H.K.; Nyarko, B.J.B.

    2013-01-01

    Highlights: ► Analytical solution is proposed to solve the point reactor kinetics equations (PRKE). ► The method is based on formulating a coefficient matrix of the PRKE. ► The method was applied to solve the PRKE for six groups of delayed neutrons. ► Results shows good agreement with other traditional methods in literature. ► The method is accurate and efficient for solving the point reactor kinetics equations. - Abstract: The understanding of the time-dependent behaviour of the neutron population in a nuclear reactor in response to either a planned or unplanned change in the reactor conditions is of great importance to the safe and reliable operation of the reactor. In this study, an accurate analytical solution of point reactor kinetics equations with multi-group of delayed neutrons for specified reactivity changes is proposed to calculate the change in neutron density. The method is based on formulating a coefficient matrix of the homogenous differential equations of the point reactor kinetics equations and calculating the eigenvalues and the corresponding eigenvectors of the coefficient matrix. A small time interval is chosen within which reactivity relatively stays constant. The analytical method was applied to solve the point reactor kinetics equations with six-groups delayed neutrons for a representative thermal reactor. The problems of step, ramp and temperature feedback reactivities are computed and the results compared with other traditional methods. The comparison shows that the method presented in this study is accurate and efficient for solving the point reactor kinetics equations of multi-group of delayed neutrons

  14. Space synthesis: an application of synthesis method to two and three dimensional multigroup neutron diffusion equations; Synthese spatiale: une application de la methode de synthese aux equations de diffusion neutronique multigroupe a deux et trois dimensions

    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)

  15. Importance estimation in Monte Carlo modelling of neutron and photon transport

    International Nuclear Information System (INIS)

    Mickael, M.W.

    1992-01-01

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

  16. 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

  17. Lithium Depletion in Solar-like Stars: Effect of Overshooting Based on Realistic Multi-dimensional Simulations

    Science.gov (United States)

    Baraffe, I.; Pratt, J.; Goffrey, T.; Constantino, T.; Folini, D.; Popov, M. V.; Walder, R.; Viallet, M.

    2017-08-01

    We study lithium depletion in low-mass and solar-like stars as a function of time, using a new diffusion coefficient describing extra-mixing taking place at the bottom of a convective envelope. This new form is motivated by multi-dimensional fully compressible, time-implicit hydrodynamic simulations performed with the MUSIC code. Intermittent convective mixing at the convective boundary in a star can be modeled using extreme value theory, a statistical analysis frequently used for finance, meteorology, and environmental science. In this Letter, we implement this statistical diffusion coefficient in a one-dimensional stellar evolution code, using parameters calibrated from multi-dimensional hydrodynamic simulations of a young low-mass star. We propose a new scenario that can explain observations of the surface abundance of lithium in the Sun and in clusters covering a wide range of ages, from ˜50 Myr to ˜4 Gyr. Because it relies on our physical model of convective penetration, this scenario has a limited number of assumptions. It can explain the observed trend between rotation and depletion, based on a single additional assumption, namely, that rotation affects the mixing efficiency at the convective boundary. We suggest the existence of a threshold in stellar rotation rate above which rotation strongly prevents the vertical penetration of plumes and below which rotation has small effects. In addition to providing a possible explanation for the long-standing problem of lithium depletion in pre-main-sequence and main-sequence stars, the strength of our scenario is that its basic assumptions can be tested by future hydrodynamic simulations.

  18. Lithium Depletion in Solar-like Stars: Effect of Overshooting Based on Realistic Multi-dimensional Simulations

    International Nuclear Information System (INIS)

    Baraffe, I.; Pratt, J.; Goffrey, T.; Constantino, T.; Viallet, M.; Folini, D.; Popov, M. V.; Walder, R.

    2017-01-01

    We study lithium depletion in low-mass and solar-like stars as a function of time, using a new diffusion coefficient describing extra-mixing taking place at the bottom of a convective envelope. This new form is motivated by multi-dimensional fully compressible, time-implicit hydrodynamic simulations performed with the MUSIC code. Intermittent convective mixing at the convective boundary in a star can be modeled using extreme value theory, a statistical analysis frequently used for finance, meteorology, and environmental science. In this Letter, we implement this statistical diffusion coefficient in a one-dimensional stellar evolution code, using parameters calibrated from multi-dimensional hydrodynamic simulations of a young low-mass star. We propose a new scenario that can explain observations of the surface abundance of lithium in the Sun and in clusters covering a wide range of ages, from ∼50 Myr to ∼4 Gyr. Because it relies on our physical model of convective penetration, this scenario has a limited number of assumptions. It can explain the observed trend between rotation and depletion, based on a single additional assumption, namely, that rotation affects the mixing efficiency at the convective boundary. We suggest the existence of a threshold in stellar rotation rate above which rotation strongly prevents the vertical penetration of plumes and below which rotation has small effects. In addition to providing a possible explanation for the long-standing problem of lithium depletion in pre-main-sequence and main-sequence stars, the strength of our scenario is that its basic assumptions can be tested by future hydrodynamic simulations.

  19. Lithium Depletion in Solar-like Stars: Effect of Overshooting Based on Realistic Multi-dimensional Simulations

    Energy Technology Data Exchange (ETDEWEB)

    Baraffe, I.; Pratt, J.; Goffrey, T.; Constantino, T.; Viallet, M. [Astrophysics Group, University of Exeter, Exeter EX4 4QL (United Kingdom); Folini, D.; Popov, M. V.; Walder, R., E-mail: i.baraffe@ex.ac.uk [Ecole Normale Supérieure de Lyon, CRAL, UMR CNRS 5574, F-69364 Lyon Cedex 07 (France)

    2017-08-10

    We study lithium depletion in low-mass and solar-like stars as a function of time, using a new diffusion coefficient describing extra-mixing taking place at the bottom of a convective envelope. This new form is motivated by multi-dimensional fully compressible, time-implicit hydrodynamic simulations performed with the MUSIC code. Intermittent convective mixing at the convective boundary in a star can be modeled using extreme value theory, a statistical analysis frequently used for finance, meteorology, and environmental science. In this Letter, we implement this statistical diffusion coefficient in a one-dimensional stellar evolution code, using parameters calibrated from multi-dimensional hydrodynamic simulations of a young low-mass star. We propose a new scenario that can explain observations of the surface abundance of lithium in the Sun and in clusters covering a wide range of ages, from ∼50 Myr to ∼4 Gyr. Because it relies on our physical model of convective penetration, this scenario has a limited number of assumptions. It can explain the observed trend between rotation and depletion, based on a single additional assumption, namely, that rotation affects the mixing efficiency at the convective boundary. We suggest the existence of a threshold in stellar rotation rate above which rotation strongly prevents the vertical penetration of plumes and below which rotation has small effects. In addition to providing a possible explanation for the long-standing problem of lithium depletion in pre-main-sequence and main-sequence stars, the strength of our scenario is that its basic assumptions can be tested by future hydrodynamic simulations.

  20. Generalized Runge-Kutta method for two- and three-dimensional space-time diffusion equations with a variable time step

    International Nuclear Information System (INIS)

    Aboanber, A.E.; Hamada, Y.M.

    2008-01-01

    An extensive knowledge of the spatial power distribution is required for the design and analysis of different types of current-generation reactors, and that requires the development of more sophisticated theoretical methods. Therefore, the need to develop new methods for multidimensional transient reactor analysis still exists. The objective of this paper is to develop a computationally efficient numerical method for solving the multigroup, multidimensional, static and transient neutron diffusion kinetics equations. A generalized Runge-Kutta method has been developed for the numerical integration of the stiff space-time diffusion equations. The method is fourth-order accurate, using an embedded third-order solution to arrive at an estimate of the truncation error for automatic time step control. In addition, the A(α)-stability properties of the method are investigated. The analyses of two- and three-dimensional benchmark problems as well as static and transient problems, demonstrate that very accurate solutions can be obtained with assembly-sized spatial meshes. Preliminary numerical evaluations using two- and three-dimensional finite difference codes showed that the presented generalized Runge-Kutta method is highly accurate and efficient when compared with other optimized iterative numerical and conventional finite difference methods

  1. Two-dimensional numerical simulation of boron diffusion for pyramidally textured silicon

    International Nuclear Information System (INIS)

    Ma, Fa-Jun; Duttagupta, Shubham; Shetty, Kishan Devappa; Meng, Lei; Hoex, Bram; Peters, Ian Marius; Samudra, Ganesh S.

    2014-01-01

    Multidimensional numerical simulation of boron diffusion is of great relevance for the improvement of industrial n-type crystalline silicon wafer solar cells. However, surface passivation of boron diffused area is typically studied in one dimension on planar lifetime samples. This approach neglects the effects of the solar cell pyramidal texture on the boron doping process and resulting doping profile. In this work, we present a theoretical study using a two-dimensional surface morphology for pyramidally textured samples. The boron diffusivity and segregation coefficient between oxide and silicon in simulation are determined by reproducing measured one-dimensional boron depth profiles prepared using different boron diffusion recipes on planar samples. The established parameters are subsequently used to simulate the boron diffusion process on textured samples. The simulated junction depth is found to agree quantitatively well with electron beam induced current measurements. Finally, chemical passivation on planar and textured samples is compared in device simulation. Particularly, a two-dimensional approach is adopted for textured samples to evaluate chemical passivation. The intrinsic emitter saturation current density, which is only related to Auger and radiative recombination, is also simulated for both planar and textured samples. The differences between planar and textured samples are discussed

  2. 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

  3. Measurement of two-dimensional thermal neutron flux in a water phantom and evaluation of dose distribution characteristics

    International Nuclear Information System (INIS)

    Yamamoto, Kazuyoshi; Kumada, Hiroaki; Kishi, Toshiaki; Torii, Yoshiya; Horiguchi, Yoji

    2001-03-01

    To evaluate nitrogen dose, boron dose and gamma-ray dose occurred by neutron capture reaction of the hydrogen at the medical irradiation, two-dimensional distribution of the thermal neutron flux is very important because these doses are proportional to the thermal neutron distribution. This report describes the measurement of the two-dimensional thermal neutron distribution in a head water phantom by neutron beams of the JRR-4 and evaluation of the dose distribution characteristic. Thermal neutron flux in the phantom was measured by gold wire placed in the spokewise of every 30 degrees in order to avoid the interaction. Distribution of the thermal neutron flux was also calculated using two-dimensional Lagrange's interpolation program (radius, angle direction) developed this time. As a result of the analysis, it was confirmed to become distorted distribution which has annular peak at outside of the void, though improved dose profile of the deep direction was confirmed in the case which the radiation field in the phantom contains void. (author)

  4. AUS diffusion module POW checkout - 1- and 2-dimensional kinetics calculations

    International Nuclear Information System (INIS)

    Pollard, J.P.

    1977-01-01

    POW is the diffusion module 'workhorse' of the AUS reactor neutronics modular code system; its steady state calculations have been checked out against other diffusion codes (particularly CRAM and GOG). Checkout of kinetic aspects, however, is difficult as kinetic codes are not freely available. In this report POW has been checked against three benchmark calculations as well as a calculation on the 100 KW Argonaut reactor Moata. (author)

  5. The development of a collapsing method for the mixed group and point cross sections and its application on multi-dimensional deep penetration calculations

    International Nuclear Information System (INIS)

    Bor-Jing Chang; Yen-Wan H. Liu

    1992-01-01

    The HYBRID, or mixed group and point, method was developed to solve the neutron transport equation deterministically using detailed treatment at cross section minima for deep penetration calculations. Its application so far is limited to one-dimensional calculations due to the enormous computing time involved in multi-dimensional calculations. In this article, a collapsing method is developed for the mixed group and point cross section sets to provide a more direct and practical way of using the HYBRID method in the multi-dimensional calculations. A testing problem is run. The method is then applied to the calculation of a deep penetration benchmark experiment. It is observed that half of the window effect is smeared in the collapsing treatment, but it still provide a better cross section set than the VITAMIN-C cross sections for the deep penetrating calculations

  6. One dimensional reactor core model

    International Nuclear Information System (INIS)

    Kostadinov, V.; Stritar, A.; Radovo, M.; Mavko, B.

    1984-01-01

    The one dimensional model of neutron dynamic in reactor core was developed. The core was divided in several axial nodes. The one group neutron diffusion equation for each node is solved. Feedback affects of fuel and water temperatures is calculated. The influence of xenon, boron and control rods is included in cross section calculations for each node. The system of equations is solved implicitly. The model is used in basic principle Training Simulator of NPP Krsko. (author)

  7. Multi-dimensional design window search system using neural networks in reactor core design

    International Nuclear Information System (INIS)

    Kugo, Teruhiko; Nakagawa, Masayuki

    2000-02-01

    In the reactor core design, many parametric survey calculations should be carried out to decide an optimal set of basic design parameter values. They consume a large amount of computation time and labor in the conventional way. To support directly design work, we investigate a procedure to search efficiently a design window, which is defined as feasible design parameter ranges satisfying design criteria and requirements, in a multi-dimensional space composed of several basic design parameters. We apply the present method to the neutronics and thermal hydraulics fields and develop the multi-dimensional design window search system using it. The principle of the present method is to construct the multilayer neural network to simulate quickly a response of an analysis code through a training process, and to reduce computation time using the neural network without parametric study using analysis codes. The system works on an engineering workstation (EWS) with efficient man-machine interface for pre- and post-processing. This report describes the principle of the present method, the structure of the system, the guidance of the usages of the system, the guideline for the efficient training of neural networks, the instructions of the input data for analysis calculation and so on. (author)

  8. Two multi-dimensional uncertainty relations

    International Nuclear Information System (INIS)

    Skala, L; Kapsa, V

    2008-01-01

    Two multi-dimensional uncertainty relations, one related to the probability density and the other one related to the probability density current, are derived and discussed. Both relations are stronger than the usual uncertainty relations for the coordinates and momentum

  9. Two-dimensional analytical solution for nodal calculation of nuclear reactors

    International Nuclear Information System (INIS)

    Silva, Adilson C.; Pessoa, Paulo O.; Silva, Fernando C.; Martinez, Aquilino S.

    2017-01-01

    Highlights: • A proposal for a coarse mesh nodal method is presented. • The proposal uses the analytical solution of the two-dimensional neutrons diffusion equation. • The solution is performed homogeneous nodes with dimensions of the fuel assembly. • The solution uses four average fluxes on the node surfaces as boundary conditions. • The results show good accuracy and efficiency. - Abstract: In this paper, the two-dimensional (2D) neutron diffusion equation is analytically solved for two energy groups (2G). The spatial domain of reactor core is divided into a set of nodes with uniform nuclear parameters. To determine iteratively the multiplication factor and the neutron flux in the reactor we combine the analytical solution of the neutron diffusion equation with an iterative method known as power method. The analytical solution for different types of regions that compose the reactor is obtained, such as fuel and reflector regions. Four average fluxes in the node surfaces are used as boundary conditions for analytical solution. Discontinuity factors on the node surfaces derived from the homogenization process are applied to maintain averages reaction rates and the net current in the fuel assembly (FA). To validate the results obtained by the analytical solution a relative power density distribution in the FAs is determined from the neutron flux distribution and compared with the reference values. The results show good accuracy and efficiency.

  10. 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

  11. 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)

  12. Multi-dimensional Laplace transforms and applications

    International Nuclear Information System (INIS)

    Mughrabi, T.A.

    1988-01-01

    In this dissertation we establish new theorems for computing certain types of multidimensional Laplace transform pairs from known one-dimensional Laplace transforms. The theorems are applied to the most commonly used special functions and so we obtain many two and three dimensional Laplace transform pairs. As applications, some boundary value problems involving linear partial differential equations are solved by the use of multi-dimensional Laplace transformation. Also we establish some relations between the Laplace transformation and other integral transformation in two variables

  13. A Monte Carlo Green's function method for three-dimensional neutron transport

    International Nuclear Information System (INIS)

    Gamino, R.G.; Brown, F.B.; Mendelson, M.R.

    1992-01-01

    This paper describes a Monte Carlo transport kernel capability, which has recently been incorporated into the RACER continuous-energy Monte Carlo code. The kernels represent a Green's function method for neutron transport from a fixed-source volume out to a particular volume of interest. This method is very powerful transport technique. Also, since kernels are evaluated numerically by Monte Carlo, the problem geometry can be arbitrarily complex, yet exact. This method is intended for problems where an ex-core neutron response must be determined for a variety of reactor conditions. Two examples are ex-core neutron detector response and vessel critical weld fast flux. The response is expressed in terms of neutron transport kernels weighted by a core fission source distribution. In these types of calculations, the response must be computed for hundreds of source distributions, but the kernels only need to be calculated once. The advance described in this paper is that the kernels are generated with a highly accurate three-dimensional Monte Carlo transport calculation instead of an approximate method such as line-of-sight attenuation theory or a synthesized three-dimensional discrete ordinates solution

  14. Three-dimensional reconstruction of neutron, gamma-ray, and x-ray sources using spherical harmonic decomposition

    Science.gov (United States)

    Volegov, P. L.; Danly, C. R.; Fittinghoff, D.; Geppert-Kleinrath, V.; Grim, G.; Merrill, F. E.; Wilde, C. H.

    2017-11-01

    Neutron, gamma-ray, and x-ray imaging are important diagnostic tools at the National Ignition Facility (NIF) for measuring the two-dimensional (2D) size and shape of the neutron producing region, for probing the remaining ablator and measuring the extent of the DT plasmas during the stagnation phase of Inertial Confinement Fusion implosions. Due to the difficulty and expense of building these imagers, at most only a few two-dimensional projections images will be available to reconstruct the three-dimensional (3D) sources. In this paper, we present a technique that has been developed for the 3D reconstruction of neutron, gamma-ray, and x-ray sources from a minimal number of 2D projections using spherical harmonics decomposition. We present the detailed algorithms used for this characterization and the results of reconstructed sources from experimental neutron and x-ray data collected at OMEGA and NIF.

  15. Development of a coupled neutronic/thermal-hydraulic tool with multi-scale capabilities and applications to HPLWR core analysis

    International Nuclear Information System (INIS)

    Monti, Lanfranco; Starflinger, Joerg; Schulenberg, Thomas

    2011-01-01

    Highlights: → Advanced analysis and design techniques for innovative reactors are addressed. → Detailed investigation of a 3 pass core design with a multi-physics-scales tool. → Coupled 40-group neutron transport/equivalent channels TH core analyses methods. → Multi-scale capabilities: from equivalent channels to sub-channel pin-by-pin study. → High fidelity approach: reduction of conservatism involved in core simulations. - Abstract: The High Performance Light Water Reactor (HPLWR) is a thermal spectrum nuclear reactor cooled and moderated with light water operated at supercritical pressure. It is an innovative reactor concept, which requires developing and applying advanced analysis tools as described in the paper. The relevant water density reduction associated with the heat-up, together with the multi-pass core design, results in a pronounced coupling between neutronic and thermal-hydraulic analyses, which takes into account the strong natural influence of the in-core distribution of power generation and water properties. The neutron flux gradients within the multi-pass core, together with the pronounced dependence of water properties on the temperature, require to consider a fine spatial resolution in which the individual fuel pins are resolved to provide precise evaluation of the clad temperature, currently considered as one of the crucial design criteria. These goals have been achieved considering an advanced analysis method based on the usage of existing codes which have been coupled with developed interfaces. Initially neutronic and thermal-hydraulic full core calculations have been iterated until a consistent solution is found to determine the steady state full power condition of the HPLWR core. Results of few group neutronic analyses might be less reliable in case of HPLWR 3-pass core than for conventional LWRs because of considerable changes of the neutron spectrum within the core, hence 40 groups transport theory has been preferred to the

  16. Whole core pin-by-pin coupled neutronic-thermal-hydraulic steady state and transient calculations using COBAYA3 code

    International Nuclear Information System (INIS)

    Jimenez, J.; Herrero, J. J.; Cuervo, D.; Aragones, J. M.

    2010-10-01

    Nowadays coupled 3-dimensional neutron kinetics and thermal-hydraulic core calculations are performed by applying a radial average channel approach using a meshing of one quarter of assembly in the best case. This approach does not take into account the subchannels effects due to the averaging of the physical fields and the loose of heterogeneity in the thermal-hydraulic model. Therefore the models do not have enough resolution to predict those subchannels effects which are important for the fuel design safety margins, because it is in the local scale, where we can search the hottest pellet or the maximum heat flux. The Polytechnic University of Madrid advanced multi-scale neutron-kinetics and thermal-hydraulics methodologies being implemented in COBAYA3 include domain decomposition by alternate core dissections for the local 3-dimensional fine-mesh scale problems (pin cells/subchannels) and an analytical nodal diffusion solver for the coarse mesh scale coupled with the thermal-hydraulic using a model of one channel per assembly or per quarter of assembly. In this work, we address the domain decomposition by the alternate core dissections methodology applied to solve coupled 3-dimensional neutronic-thermal-hydraulic problems at the fine-mesh scale. The neutronic-thermal-hydraulic coupling at the cell-subchannel scale allows the treatment of the effects of the detailed thermal-hydraulic feedbacks on cross-sections, thus resulting in better estimates of the local safety margins at the pin level. (Author)

  17. Balanced sensitivity functions for tuning multi-dimensional Bayesian network classifiers

    NARCIS (Netherlands)

    Bolt, J.H.; van der Gaag, L.C.

    Multi-dimensional Bayesian network classifiers are Bayesian networks of restricted topological structure, which are tailored to classifying data instances into multiple dimensions. Like more traditional classifiers, multi-dimensional classifiers are typically learned from data and may include

  18. Calculating the effective delayed neutron fraction in the Molten Salt Fast Reactor: Analytical, deterministic and Monte Carlo approaches

    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

  19. Analytical solutions of one-dimensional advection–diffusion

    Indian Academy of Sciences (India)

    Analytical solutions are obtained for one-dimensional advection –diffusion equation with variable coefficients in a longitudinal finite initially solute free domain,for two dispersion problems.In the first one,temporally dependent solute dispersion along uniform flow in homogeneous domain is studied.In the second problem the ...

  20. Development of MARS for multi-dimensional and multi-purpose thermal-hydraulic system analysis

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Won Jae; Chung, Bub Dong; Kim, Kyung Doo; Hwang, Moon Kyu; Jeong, Jae Jun; Ha, Kwi Seok; Joo, Han Gyu [Korea Atomic Energy Research Institute, T/H Safety Research Team, Yusung, Daejeon (Korea)

    2000-10-01

    MARS (Multi-dimensional Analysis of Reactor Safety) code is being developed by KAERI for the realistic thermal-hydraulic simulation of light water reactor system transients. MARS 1.4 has been developed as a final version of basic code frame for the multi-dimensional analysis of system thermal-hydraulics. Since MARS 1.3, MARS 1.4 has been improved to have the enhanced code capability and user friendliness through the unification of input/output features, code models and code functions, and through the code modernization. Further improvements of thermal-hydraulic models, numerical method and user friendliness are being carried out for the enhanced code accuracy. As a multi-purpose safety analysis code system, a coupled analysis system, MARS/MASTER/CONTEMPT, has been developed using multiple DLL (Dynamic Link Library) techniques of Windows system. This code system enables the coupled, that is, more realistic analysis of multi-dimensional thermal-hydraulics (MARS 2.0), three-dimensional core kinetics (MASTER) and containment thermal-hydraulics (CONTEMPT). This paper discusses the MARS development program, and the developmental progress of the MARS 1.4 and the MARS/MASTER/CONTEMPT focusing on major features of the codes and their verification. It also discusses thermal hydraulic models and new code features under development. (author)

  1. Development of MARS for multi-dimensional and multi-purpose thermal-hydraulic system analysis

    International Nuclear Information System (INIS)

    Lee, Won Jae; Chung, Bub Dong; Kim, Kyung Doo; Hwang, Moon Kyu; Jeong, Jae Jun; Ha, Kwi Seok; Joo, Han Gyu

    2000-01-01

    MARS (Multi-dimensional Analysis of Reactor Safety) code is being developed by KAERI for the realistic thermal-hydraulic simulation of light water reactor system transients. MARS 1.4 has been developed as a final version of basic code frame for the multi-dimensional analysis of system thermal-hydraulics. Since MARS 1.3, MARS 1.4 has been improved to have the enhanced code capability and user friendliness through the unification of input/output features, code models and code functions, and through the code modernization. Further improvements of thermal-hydraulic models, numerical method and user friendliness are being carried out for the enhanced code accuracy. As a multi-purpose safety analysis code system, a coupled analysis system, MARS/MASTER/CONTEMPT, has been developed using multiple DLL (Dynamic Link Library) techniques of Windows system. This code system enables the coupled, that is, more realistic analysis of multi-dimensional thermal-hydraulics (MARS 2.0), three-dimensional core kinetics (MASTER) and containment thermal-hydraulics (CONTEMPT). This paper discusses the MARS development program, and the developmental progress of the MARS 1.4 and the MARS/MASTER/CONTEMPT focusing on major features of the codes and their verification. It also discusses thermal hydraulic models and new code features under development. (author)

  2. Application of neural network to multi-dimensional design window search

    International Nuclear Information System (INIS)

    Kugo, T.; Nakagawa, M.

    1996-01-01

    In the reactor core design, many parametric survey calculations should be carried out to decide an optimal set of basic design parameter values. They consume a large amount of computation time and labor in the conventional way. To support directly such a work, we investigate a procedure to search efficiently a design window, which is defined as feasible design parameter ranges satisfying design criteria and requirements, in a multi-dimensional space composed of several basic design parameters. A principle of the present method is to construct the multilayer neural network to simulate quickly a response of an analysis code through a training process, and to reduce computation time using the neural network as a substitute of an analysis code. We apply the present method to a fuel pin design of high conversion light water reactors for the neutronics and thermal hydraulics fields to demonstrate performances of the method. (author)

  3. Albedo analytical method for multi-scattered neutron flux calculation in cavity

    International Nuclear Information System (INIS)

    Shin, Kazuo; Selvi, S.; Hyodo, Tomonori

    1986-01-01

    A simple formula which describes multi-scattered neutron flux in a spherical cavity was derived based on the albedo concept. The formura treats a neutron source which has an arbitrary energy-angle distribution and is placed at any point in the cavity. The derived formula was applied to the estimation of neutron fluxes in two cavities, i.e. a spherical concrete cell with a 14-MeV neutron source at the center and the ''YAYOI'' reactor cavity with a pencil beam of reactor neutrons. The results of the analytical formula agreed very well with the reference data in the both problems. It was concluded that the formula is applicable to estimate the neutron fluxes in a spherical cell except for special cases that tangential source neutrons are incident to the cavity wall. (author)

  4. High-Dimensional Intrinsic Interpolation Using Gaussian Process Regression and Diffusion Maps

    International Nuclear Information System (INIS)

    Thimmisetty, Charanraj A.; Ghanem, Roger G.; White, Joshua A.; Chen, Xiao

    2017-01-01

    This article considers the challenging task of estimating geologic properties of interest using a suite of proxy measurements. The current work recast this task as a manifold learning problem. In this process, this article introduces a novel regression procedure for intrinsic variables constrained onto a manifold embedded in an ambient space. The procedure is meant to sharpen high-dimensional interpolation by inferring non-linear correlations from the data being interpolated. The proposed approach augments manifold learning procedures with a Gaussian process regression. It first identifies, using diffusion maps, a low-dimensional manifold embedded in an ambient high-dimensional space associated with the data. It relies on the diffusion distance associated with this construction to define a distance function with which the data model is equipped. This distance metric function is then used to compute the correlation structure of a Gaussian process that describes the statistical dependence of quantities of interest in the high-dimensional ambient space. The proposed method is applicable to arbitrarily high-dimensional data sets. Here, it is applied to subsurface characterization using a suite of well log measurements. The predictions obtained in original, principal component, and diffusion space are compared using both qualitative and quantitative metrics. Considerable improvement in the prediction of the geological structural properties is observed with the proposed method.

  5. A guide to the AUS modular neutronics code system

    International Nuclear Information System (INIS)

    Robinson, G.S.

    1987-04-01

    A general description is given of the AUS modular neutronics code system, which may be used for calculations of a very wide range of fission reactors, fusion blankets and other neutron applications. The present system has cross-section libraries derived from ENDF/B-IV and includes modules which provide for lattice calculations, one-dimensional transport calculations, and one, two, and three-dimensional diffusion calculations, burnup calculations and the flexible editing of results. Details of all system aspects of AUS are provided but the major individual modules are only outlined. Sufficient information is given to enable other modules to be added to the system

  6. A Multi-layer Hybrid Framework for Dimensional Emotion Classification

    NARCIS (Netherlands)

    Nicolaou, Mihalis A.; Gunes, Hatice; Pantic, Maja

    2011-01-01

    This paper investigates dimensional emotion prediction and classification from naturalistic facial expressions. Similarly to many pattern recognition problems, dimensional emotion classification requires generating multi-dimensional outputs. To date, classification for valence and arousal dimensions

  7. Three-dimensional h-adaptivity for the multigroup neutron diffusion equations

    KAUST Repository

    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

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

    Energy Technology Data Exchange (ETDEWEB)

    Garcia Fite, J

    1959-07-01

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

  9. Two-dimensional time dependent Riemann solvers for neutron transport

    International Nuclear Information System (INIS)

    Brunner, Thomas A.; Holloway, James Paul

    2005-01-01

    A two-dimensional Riemann solver is developed for the spherical harmonics approximation to the time dependent neutron transport equation. The eigenstructure of the resulting equations is explored, giving insight into both the spherical harmonics approximation and the Riemann solver. The classic Roe-type Riemann solver used here was developed for one-dimensional problems, but can be used in multidimensional problems by treating each face of a two-dimensional computation cell in a locally one-dimensional way. Several test problems are used to explore the capabilities of both the Riemann solver and the spherical harmonics approximation. The numerical solution for a simple line source problem is compared to the analytic solution to both the P 1 equation and the full transport solution. A lattice problem is used to test the method on a more challenging problem

  10. Neutron shielding point kernel integral calculation code for personal computer: PKN-pc

    International Nuclear Information System (INIS)

    Kotegawa, Hiroshi; Sakamoto, Yukio; Nakane, Yoshihiro; Tomita, Ken-ichi; Kurosawa, Naohiro.

    1994-07-01

    A personal computer version of PKN code, PKN-pc, has been developed to calculate neutron and secondary gamma-ray 1cm depth dose equivalents in water, ordinary concrete and iron for neutron source. Characteristics of PKN code are, to able to calculate dose equivalents in multi-layer three-dimensional system, which are described with two-dimensional surface, for monoenergetic neutron source from 0.01 to 14.9 MeV, 252 Cf fission and 241 Am-Be neutron source quick and easily. In addition to these features, the PKN-pc is possible to process interactive input and to get graphical system configuration and graphical results easily. (author)

  11. 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).

  12. Multi-compartment microscopic diffusion imaging

    OpenAIRE

    Kaden, Enrico; Kelm, Nathaniel D.; Carson, Robert P.; Does, Mark D.; Alexander, Daniel C.

    2016-01-01

    This paper introduces a multi-compartment model for microscopic diffusion anisotropy imaging. The aim is to estimate microscopic features specific to the intra- and extra-neurite compartments in nervous tissue unconfounded by the effects of fibre crossings and orientation dispersion, which are ubiquitous in the brain. The proposed MRI method is based on the Spherical Mean Technique (SMT), which factors out the neurite orientation distribution and thus provides direct estimates of the microsco...

  13. NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION.

    Science.gov (United States)

    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.

  14. NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION

    OpenAIRE

    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...

  15. A semi-experimental nodal synthesis method for the on-line reconstruction of three-dimensional neutron flux-shapes and reactivity. Final report

    Energy Technology Data Exchange (ETDEWEB)

    Jacqmin, Robert P. [Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

    1991-12-10

    The safety and optimal performance of large, commercial, light-water reactors require the knowledge at all time of the neutron-flux distribution in the core. In principle, this information can be obtained by solving the time-dependent neutron diffusion equations. However, this approach is complicated and very expensive. Sufficiently accurate, real-time calculations (time scale of approximately one second) are not yet possible on desktop computers, even with fast-running, nodal kinetics codes. A semi-experimental, nodal synthesis method which avoids the solution of the time-dependent, neutron diffusion equations is described. The essential idea of this method is to approximate instantaneous nodal group-fluxes by a linear combination of K, precomputed, three-dimensional, static expansion-functions. The time-dependent coefficients of the combination are found from the requirement that the reconstructed flux-distribution agree in a least-squares sense with the readings of J (≥K) fixed, prompt-responding neutron-detectors. Possible numerical difficulties with the least-squares solution of the ill-conditioned, J-by-K system of equations are brought under complete control by the use of a singular-value-decomposition technique. This procedure amounts to the rearrangement of the original, linear combination of K expansion functions into an equivalent more convenient, linear combination of R (≤K) orthogonalized ``modes`` of decreasing magnitude. Exceedingly small modes are zeroed to eliminate any risk of roundoff-error amplification, and to assure consistency with the limited accuracy of the data. Additional modes are zeroed when it is desirable to limit the sensitivity of the results to measurement noise.

  16. Diffusion in higher dimensional SYK model with complex fermions

    Science.gov (United States)

    Cai, Wenhe; Ge, Xian-Hui; Yang, Guo-Hong

    2018-01-01

    We construct a new higher dimensional SYK model with complex fermions on bipartite lattices. As an extension of the original zero-dimensional SYK model, we focus on the one-dimension case, and similar Hamiltonian can be obtained in higher dimensions. This model has a conserved U(1) fermion number Q and a conjugate chemical potential μ. We evaluate the thermal and charge diffusion constants via large q expansion at low temperature limit. The results show that the diffusivity depends on the ratio of free Majorana fermions to Majorana fermions with SYK interactions. The transport properties and the butterfly velocity are accordingly calculated at low temperature. The specific heat and the thermal conductivity are proportional to the temperature. The electrical resistivity also has a linear temperature dependence term.

  17. 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.

  18. 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

  19. Analytical performance bounds for multi-tensor diffusion-MRI.

    Science.gov (United States)

    Ahmed Sid, Farid; Abed-Meraim, Karim; Harba, Rachid; Oulebsir-Boumghar, Fatima

    2017-02-01

    To examine the effects of MR acquisition parameters on brain white matter fiber orientation estimation and parameter of clinical interest in crossing fiber areas based on the Multi-Tensor Model (MTM). We compute the Cramér-Rao Bound (CRB) for the MTM and the parameter of clinical interest such as the Fractional Anisotropy (FA) and the dominant fiber orientations, assuming that the diffusion MRI data are recorded by a multi-coil, multi-shell acquisition system. Considering the sum-of-squares method for the reconstructed magnitude image, we introduce an approximate closed-form formula for Fisher Information Matrix that has the simplicity and easy interpretation advantages. In addition, we propose to generalize the FA and the mean diffusivity to the multi-tensor model. We show the application of the CRB to reduce the scan time while preserving a good estimation precision. We provide results showing how the increase of the number of acquisition coils compensates the decrease of the number of diffusion gradient directions. We analyze the impact of the b-value and the Signal-to-Noise Ratio (SNR). The analysis shows that the estimation error variance decreases with a quadratic rate with the SNR, and that the optimum b-values are not unique but depend on the target parameter, the context, and eventually the target cost function. In this study we highlight the importance of choosing the appropriate acquisition parameters especially when dealing with crossing fiber areas. We also provide a methodology for the optimal tuning of these parameters using the CRB. Copyright © 2016 Elsevier Inc. All rights reserved.

  20. Simulation and prototyping of 2 m long resistive plate chambers for detection of fast neutrons and multi-neutron event identification

    Energy Technology Data Exchange (ETDEWEB)

    Elekes, Z., E-mail: z.elekes@hzdr.de [Helmholtz-Zentrum Dresden-Rossendorf, Dresden (Germany); Aumann, T. [GSI Helmholtzzentrumfür Schwerionenforschung, Darmstadt (Germany); Technische Universität Darmstadt, Darmstadt (Germany); Bemmerer, D. [Helmholtz-Zentrum Dresden-Rossendorf, Dresden (Germany); Boretzky, K. [GSI Helmholtzzentrumfür Schwerionenforschung, Darmstadt (Germany); Caesar, C. [GSI Helmholtzzentrumfür Schwerionenforschung, Darmstadt (Germany); Technische Universität Darmstadt, Darmstadt (Germany); Cowan, T.C. [Helmholtz-Zentrum Dresden-Rossendorf, Dresden (Germany); Technische Universität Dresden, Dresden (Germany); Hehner, J.; Heil, M. [GSI Helmholtzzentrumfür Schwerionenforschung, Darmstadt (Germany); Kempe, M. [Helmholtz-Zentrum Dresden-Rossendorf, Dresden (Germany); Rossi, D. [GSI Helmholtzzentrumfür Schwerionenforschung, Darmstadt (Germany); Röder, M. [Helmholtz-Zentrum Dresden-Rossendorf, Dresden (Germany); Technische Universität Dresden, Dresden (Germany); Simon, H. [GSI Helmholtzzentrumfür Schwerionenforschung, Darmstadt (Germany); Sobiella, M.; Stach, D. [Helmholtz-Zentrum Dresden-Rossendorf, Dresden (Germany); Reinhardt, T. [Helmholtz-Zentrum Dresden-Rossendorf, Dresden (Germany); Technische Universität Dresden, Dresden (Germany); Wagner, A.; Yakorev, D. [Helmholtz-Zentrum Dresden-Rossendorf, Dresden (Germany); Zilges, A. [Universität zu Köln, Köln (Germany); Zuber, K. [Technische Universität Dresden, Dresden (Germany)

    2013-02-11

    Resistive plate chamber (RPC) prototypes of 2 m length were simulated and built. The experimental tests using a 31 MeV electron beam, discussed in details, showed an efficiency higher than 90% and an excellent time resolution of around σ=100ps. Furthermore, comprehensive simulations were performed by GEANT4 toolkit in order to study the possible use of these RPCs for fast neutron (200 MeV–1 GeV) detection and multi-neutron event identification. The validation of simulation parameters was carried out via a comparison to experimental data. A possible setup for invariant mass spectroscopy of multi-neutron emission is presented and the characteristics are discussed. The results show that the setup has a high detection efficiency. Its capability of determining the momentum of the outgoing neutrons and reconstructing the relative energy between the fragments from nuclear reactions is demonstrated for different scenarios.

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

    International Nuclear Information System (INIS)

    Hursin, Mathieu; Xiao Shanjie; Jevremovic, Tatjana

    2006-01-01

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

  2. 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

  3. 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

  4. Towards Optimal Multi-Dimensional Query Processing with BitmapIndices

    Energy Technology Data Exchange (ETDEWEB)

    Rotem, Doron; Stockinger, Kurt; Wu, Kesheng

    2005-09-30

    Bitmap indices have been widely used in scientific applications and commercial systems for processing complex, multi-dimensional queries where traditional tree-based indices would not work efficiently. This paper studies strategies for minimizing the access costs for processing multi-dimensional queries using bitmap indices with binning. Innovative features of our algorithm include (a) optimally placing the bin boundaries and (b) dynamically reordering the evaluation of the query terms. In addition, we derive several analytical results concerning optimal bin allocation for a probabilistic query model. Our experimental evaluation with real life data shows an average I/O cost improvement of at least a factor of 10 for multi-dimensional queries on datasets from two different applications. Our experiments also indicate that the speedup increases with the number of query dimensions.

  5. 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)

  6. MOSRA-Light; high speed three-dimensional nodal diffusion code for vector computers

    Energy Technology Data Exchange (ETDEWEB)

    Okumura, Keisuke [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment

    1998-10-01

    MOSRA-Light is a three-dimensional neutron diffusion calculation code for X-Y-Z geometry. It is based on the 4th order polynomial nodal expansion method (NEM). As the 4th order NEM is not sensitive to mesh sizes, accurate calculation is possible by the use of coarse meshes of about 20 cm. The drastic decrease of number of unknowns in a 3-dimensional problem results in very fast computation. Furthermore, it employs newly developed computation algorithm `boundary separated checkerboard sweep method` appropriate to vector computers. This method is very efficient because the speedup factor by vectorization increases, as a scale of problem becomes larger. Speed-up factor compared to the scalar calculation is from 20 to 40 in the case of PWR core calculation. Considering the both effects by the vectorization and the coarse mesh method, total speedup factor is more than 1000 as compared with conventional scalar code with the finite difference method. MOSRA-Light can be available on most of vector or scalar computers with the UNIX or it`s similar operating systems (e.g. freeware like Linux). Users can easily install it by the help of the conversation style installer. This report contains the general theory of NEM, the fast computation algorithm, benchmark calculation results and detailed information for usage of this code including input data instructions and sample input data. (author)

  7. MOSRA-Light; high speed three-dimensional nodal diffusion code for vector computers

    International Nuclear Information System (INIS)

    Okumura, Keisuke

    1998-10-01

    MOSRA-Light is a three-dimensional neutron diffusion calculation code for X-Y-Z geometry. It is based on the 4th order polynomial nodal expansion method (NEM). As the 4th order NEM is not sensitive to mesh sizes, accurate calculation is possible by the use of coarse meshes of about 20 cm. The drastic decrease of number of unknowns in a 3-dimensional problem results in very fast computation. Furthermore, it employs newly developed computation algorithm 'boundary separated checkerboard sweep method' appropriate to vector computers. This method is very efficient because the speedup factor by vectorization increases, as a scale of problem becomes larger. Speed-up factor compared to the scalar calculation is from 20 to 40 in the case of PWR core calculation. Considering the both effects by the vectorization and the coarse mesh method, total speedup factor is more than 1000 as compared with conventional scalar code with the finite difference method. MOSRA-Light can be available on most of vector or scalar computers with the UNIX or it's similar operating systems (e.g. freeware like Linux). Users can easily install it by the help of the conversation style installer. This report contains the general theory of NEM, the fast computation algorithm, benchmark calculation results and detailed information for usage of this code including input data instructions and sample input data. (author)

  8. Application of the multi-rate diffusion approach in tracer test studies at Aespoe HRL. Final report

    International Nuclear Information System (INIS)

    Haggerty, R.

    1999-11-01

    This report summarizes an investigation into heterogeneous diffusivity and associated parameters within granitic rocks at the Aespoe Hard Rock Laboratory (HRL). Our tasks for this investigation were: (1) to assess the potential for either anomalous or multi-rate diffusion within Aespoe rocks; (2) to evaluate existing data relating to anomalous and multi-rate diffusion within Aespoe rocks; (3) to perform scoping calculations in support of a Long Term Diffusion Experiment (LTDE) design; and (4) to begin developing a mathematical and computer model for solute advection in the presence of anomalous matrix diffusion. In addition to carrying out these tasks, we also report on (5) the late-time behavior of breakthrough curves. First, in regard to the potential for anomalous and multi-rate diffusion and analyses of existing data, we find that (1) in a literature review of 100 column experiments in various types of rock and sediment, rate coefficients decrease with experimental observation time. This is precisely what would be expected of both multi-rate and anomalous diffusion. (2) Three sets of through-diffusion experiments in Fenno-Scandian granitic rock found decreasing effective diffusivity, D e , with sample length, while one set did not. (3) Based on diffusivity and sorption data, and speculation on matrix block size variability, the total variability of D a /a 2 may reasonably be expected to exceed 4 orders of magnitude. (4) Analyses of two-well tracer data completed to date are ambiguous with respect to multi-rate diffusion. Analyses of TRUE data are currently underway and may support multi-rate diffusion. Second, in regard to the potential consequences of multi-rate and anomalous diffusion on nuclear waste disposal, we found the following key points: (1) No single value of diffusivity can represent the diffusion process at all time- or length-scales if diffusion is truly anomalous, while a single value of diffusivity will represent diffusion adequately for some

  9. Application of the multi-rate diffusion approach in tracer test studies at Aespoe HRL. Final report

    Energy Technology Data Exchange (ETDEWEB)

    Haggerty, R. [Oregon State Univ., Corvallis, OR (United States). Dept. of Geosciences

    1999-11-01

    This report summarizes an investigation into heterogeneous diffusivity and associated parameters within granitic rocks at the Aespoe Hard Rock Laboratory (HRL). Our tasks for this investigation were: (1) to assess the potential for either anomalous or multi-rate diffusion within Aespoe rocks; (2) to evaluate existing data relating to anomalous and multi-rate diffusion within Aespoe rocks; (3) to perform scoping calculations in support of a Long Term Diffusion Experiment (LTDE) design; and (4) to begin developing a mathematical and computer model for solute advection in the presence of anomalous matrix diffusion. In addition to carrying out these tasks, we also report on (5) the late-time behavior of breakthrough curves. First, in regard to the potential for anomalous and multi-rate diffusion and analyses of existing data, we find that (1) in a literature review of 100 column experiments in various types of rock and sediment, rate coefficients decrease with experimental observation time. This is precisely what would be expected of both multi-rate and anomalous diffusion. (2) Three sets of through-diffusion experiments in Fenno-Scandian granitic rock found decreasing effective diffusivity, D{sub e}, with sample length, while one set did not. (3) Based on diffusivity and sorption data, and speculation on matrix block size variability, the total variability of D{sub a}/a{sup 2} may reasonably be expected to exceed 4 orders of magnitude. (4) Analyses of two-well tracer data completed to date are ambiguous with respect to multi-rate diffusion. Analyses of TRUE data are currently underway and may support multi-rate diffusion. Second, in regard to the potential consequences of multi-rate and anomalous diffusion on nuclear waste disposal, we found the following key points: (1) No single value of diffusivity can represent the diffusion process at all time- or length-scales if diffusion is truly anomalous, while a single value of diffusivity will represent diffusion

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

    Energy Technology Data Exchange (ETDEWEB)

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

    1959-07-01

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

  11. 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.

  12. A multi-dimensional sampling method for locating small scatterers

    International Nuclear Information System (INIS)

    Song, Rencheng; Zhong, Yu; Chen, Xudong

    2012-01-01

    A multiple signal classification (MUSIC)-like multi-dimensional sampling method (MDSM) is introduced to locate small three-dimensional scatterers using electromagnetic waves. The indicator is built with the most stable part of signal subspace of the multi-static response matrix on a set of combinatorial sampling nodes inside the domain of interest. It has two main advantages compared to the conventional MUSIC methods. First, the MDSM is more robust against noise. Second, it can work with a single incidence even for multi-scatterers. Numerical simulations are presented to show the good performance of the proposed method. (paper)

  13. An analytical approach for a nodal scheme of two-dimensional neutron transport problems

    International Nuclear Information System (INIS)

    Barichello, L.B.; Cabrera, L.C.; Prolo Filho, J.F.

    2011-01-01

    Research highlights: → Nodal equations for a two-dimensional neutron transport problem. → Analytical Discrete Ordinates Method. → Numerical results compared with the literature. - Abstract: In this work, a solution for a two-dimensional neutron transport problem, in cartesian geometry, is proposed, on the basis of nodal schemes. In this context, one-dimensional equations are generated by an integration process of the multidimensional problem. Here, the integration is performed for the whole domain such that no iterative procedure between nodes is needed. The ADO method is used to develop analytical discrete ordinates solution for the one-dimensional integrated equations, such that final solutions are analytical in terms of the spatial variables. The ADO approach along with a level symmetric quadrature scheme, lead to a significant order reduction of the associated eigenvalues problems. Relations between the averaged fluxes and the unknown fluxes at the boundary are introduced as the usually needed, in nodal schemes, auxiliary equations. Numerical results are presented and compared with test problems.

  14. Elaboration of a nodal method to solve the steady state multigroup diffusion equation. Study and use of the multigroup diffusion code DAHRA

    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

  15. 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

  16. Modeling of three-dimensional diffusible resistors with the one-dimensional tube multiplexing method

    International Nuclear Information System (INIS)

    Gillet, Jean-Numa; Degorce, Jean-Yves; Meunier, Michel

    2009-01-01

    Electronic-behavior modeling of three-dimensional (3D) p + -π-p + and n + -ν-n + semiconducting diffusible devices with highly accurate resistances for the design of analog resistors, which are compatible with the CMOS (complementary-metal-oxide-semiconductor) technologies, is performed in three dimensions with the fast tube multiplexing method (TMM). The current–voltage (I–V) curve of a silicon device is usually computed with traditional device simulators of technology computer-aided design (TCAD) based on the finite-element method (FEM). However, for the design of 3D p + -π-p + and n + -ν-n + diffusible resistors, they show a high computational cost and convergence that may fail with fully non-separable 3D dopant concentration profiles as observed in many diffusible resistors resulting from laser trimming. These problems are avoided with the proposed TMM, which divides the 3D resistor into one-dimensional (1D) thin tubes with longitudinal axes following the main orientation of the average electrical field in the tubes. The I–V curve is rapidly obtained for a device with a realistic 3D dopant profile, since a system of three first-order ordinary differential equations has to be solved for each 1D multiplexed tube with the TMM instead of three second-order partial differential equations in the traditional TCADs. Simulations with the TMM are successfully compared to experimental results from silicon-based 3D resistors fabricated by laser-induced dopant diffusion in the gaps of MOSFETs (metal-oxide-semiconductor field-effect transistors) without initial gate. Using thin tubes with other shapes than parallelepipeds as ring segments with toroidal lateral surfaces, the TMM can be generalized to electronic devices with other types of 3D diffusible microstructures

  17. Multi-dimensional database design and implementation of dam safety monitoring system

    Directory of Open Access Journals (Sweden)

    Zhao Erfeng

    2008-09-01

    Full Text Available To improve the effectiveness of dam safety monitoring database systems, the development process of a multi-dimensional conceptual data model was analyzed and a logic design was achieved in multi-dimensional database mode. The optimal data model was confirmed by identifying data objects, defining relations and reviewing entities. The conversion of relations among entities to external keys and entities and physical attributes to tables and fields was interpreted completely. On this basis, a multi-dimensional database that reflects the management and analysis of a dam safety monitoring system on monitoring data information has been established, for which factual tables and dimensional tables have been designed. Finally, based on service design and user interface design, the dam safety monitoring system has been developed with Delphi as the development tool. This development project shows that the multi-dimensional database can simplify the development process and minimize hidden dangers in the database structure design. It is superior to other dam safety monitoring system development models and can provide a new research direction for system developers.

  18. {sup 10}B multi-grid proportional gas counters for large area thermal neutron detectors

    Energy Technology Data Exchange (ETDEWEB)

    Andersen, K. [ESS, P.O. Box 176, SE-221 00 Lund (Sweden); Bigault, T. [ILL, BP 156, 6, rue Jules Horowitz, 38042 Grenoble Cedex 9 (France); Birch, J. [Linköping University, SE-581, 83 Linköping (Sweden); Buffet, J. C.; Correa, J. [ILL, BP 156, 6, rue Jules Horowitz, 38042 Grenoble Cedex 9 (France); Hall-Wilton, R. [ESS, P.O. Box 176, SE-221 00 Lund (Sweden); Hultman, L. [Linköping University, SE-581, 83 Linköping (Sweden); Höglund, C. [ESS, P.O. Box 176, SE-221 00 Lund (Sweden); Linköping University, SE-581, 83 Linköping (Sweden); Guérard, B., E-mail: guerard@ill.fr [ILL, BP 156, 6, rue Jules Horowitz, 38042 Grenoble Cedex 9 (France); Jensen, J. [Linköping University, SE-581, 83 Linköping (Sweden); Khaplanov, A. [ILL, BP 156, 6, rue Jules Horowitz, 38042 Grenoble Cedex 9 (France); ESS, P.O. Box 176, SE-221 00 Lund (Sweden); Kirstein, O. [Linköping University, SE-581, 83 Linköping (Sweden); Piscitelli, F.; Van Esch, P. [ILL, BP 156, 6, rue Jules Horowitz, 38042 Grenoble Cedex 9 (France); Vettier, C. [ESS, P.O. Box 176, SE-221 00 Lund (Sweden)

    2013-08-21

    {sup 3}He was a popular material in neutrons detectors until its availability dropped drastically in 2008. The development of techniques based on alternative convertors is now of high priority for neutron research institutes. Thin films of {sup 10}B or {sup 10}B{sub 4}C have been used in gas proportional counters to detect neutrons, but until now, only for small or medium sensitive area. We present here the multi-grid design, introduced at the ILL and developed in collaboration with ESS for LAN (large area neutron) detectors. Typically thirty {sup 10}B{sub 4}C films of 1 μm thickness are used to convert neutrons into ionizing particles which are subsequently detected in a proportional gas counter. The principle and the fabrication of the multi-grid are described and some preliminary results obtained with a prototype of 200 cm×8 cm are reported; a detection efficiency of 48% has been measured at 2.5 Å with a monochromatic neutron beam line, showing the good potential of this new technique.

  19. The spectral element approach for the solution of neutron transport problems

    International Nuclear Information System (INIS)

    Barbarino, A.; Dulla, S.; Ravetto, P.; Mund, E.H.

    2011-01-01

    In this paper a possible application of the Spectral Element Method to neutron transport problems is presented. The basic features of the numerical scheme on the one-dimensional diffusion equation are illustrated. Then, the AN model for neutron transport is introduced, and the basic steps for the construction of a bi-dimensional solver are described. The AN equations are chosen for their structure, involving a system of coupled elliptic-type equations. Some calculations are carried out on typical benchmark problems and results are compared with the Finite Element Method, in order to evaluate their performances. (author)

  20. Multi-dimensional quasitoeplitz Markov chains

    Directory of Open Access Journals (Sweden)

    Alexander N. Dudin

    1999-01-01

    Full Text Available This paper deals with multi-dimensional quasitoeplitz Markov chains. We establish a sufficient equilibrium condition and derive a functional matrix equation for the corresponding vector-generating function, whose solution is given algorithmically. The results are demonstrated in the form of examples and applications in queues with BMAP-input, which operate in synchronous random environment.

  1. Arbitrary quadrature: its application in the solution of one-dimensional, planar neutron transport problems

    International Nuclear Information System (INIS)

    Sanchez, J.

    2010-10-01

    A standard numerical procedure for the solution of singular integral equations is applied to the one-dimensional transport equation for monoenergetic neutrons. As is usual in quadrature methods, the procedure yields an Eigen system whose solution provide, for the critical slab, both the eigenvalue which is proportional to the number of secondary neutrons per collision, and the density as a function of position. The results obtained with two versions of the procedure, differing only in the extent of the basic region to which they are applied, are compared with analytically derived results available for benchmarking. The procedures considered yield consistent results for the calculated neutron densities and eigenvalues. Since the one-dimensional transport kernel and its spatial moments are integrable and their integrals can be put in terms of exponential integral functions, the resulting approximations to the neutron density yield somewhat lengthy but closed, forms. These approximate expressions of the neutron density can be used to render, after they are operated on, closed-form formulas for build-up factors, extrapolation distances or angular densities or employed for other purposes that require an analytical expression of the neutron density. As an example of this latter capability, the results of the calculation of the angular density at the surface of the slab are provided. (Author)

  2. 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

  3. 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.

  4. Three dimensional simulated modelling of diffusion capacitance of ...

    African Journals Online (AJOL)

    A three dimensional (3-D) simulated modelling was developed to analyse the excess minority carrier density in the base of a polycrystalline bifacial silicon solar cell. The concept of junction recombination velocity was ado-pted to quantify carrier flow through the junction, and to examine the solar cell diffusion capacitance for ...

  5. A procedure for solving the neutron diffusion equation on a parallel micro-processor; modifications to the nodal expansion codes RECNEC and HEXNEC to implement the procedure

    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.)

  6. Analytical approach for collective diffusion: one-dimensional heterogeneous lattice

    Czech Academy of Sciences Publication Activity Database

    Tarasenko, Alexander

    2016-01-01

    Roč. 144, č. 14 (2016), 1-11, č. článku 144105. ISSN 0021-9606 Institutional support: RVO:68378271 Keywords : diffusion * Monte Carlo simulations * one-dimensional heterogeneous lattice Subject RIV: BE - Theoretical Physics Impact factor: 2.965, year: 2016

  7. Multi-dimensional virtual system introduced to enhance canonical sampling

    Science.gov (United States)

    Higo, Junichi; Kasahara, Kota; Nakamura, Haruki

    2017-10-01

    When an important process of a molecular system occurs via a combination of two or more rare events, which occur almost independently to one another, computational sampling for the important process is difficult. Here, to sample such a process effectively, we developed a new method, named the "multi-dimensional Virtual-system coupled Monte Carlo (multi-dimensional-VcMC)" method, where the system interacts with a virtual system expressed by two or more virtual coordinates. Each virtual coordinate controls sampling along a reaction coordinate. By setting multiple reaction coordinates to be related to the corresponding rare events, sampling of the important process can be enhanced. An advantage of multi-dimensional-VcMC is its simplicity: Namely, the conformation moves widely in the multi-dimensional reaction coordinate space without knowledge of canonical distribution functions of the system. To examine the effectiveness of the algorithm, we introduced a toy model where two molecules (receptor and its ligand) bind and unbind to each other. The receptor has a deep binding pocket, to which the ligand enters for binding. Furthermore, a gate is set at the entrance of the pocket, and the gate is usually closed. Thus, the molecular binding takes place via the two events: ligand approach to the pocket and gate opening. In two-dimensional (2D)-VcMC, the two molecules exhibited repeated binding and unbinding, and an equilibrated distribution was obtained as expected. A conventional canonical simulation, which was 200 times longer than 2D-VcMC, failed in sampling the binding/unbinding effectively. The current method is applicable to various biological systems.

  8. Anomalous dimensionality dependence of diffusion in a rugged energy landscape: How pathological is one dimension?

    Science.gov (United States)

    Seki, Kazuhiko; Bagchi, Kaushik; Bagchi, Biman

    2016-05-01

    Diffusion in one dimensional rugged energy landscape (REL) is predicted to be pathologically different (from any higher dimension) with a much larger chance of encountering broken ergodicity [D. L. Stein and C. M. Newman, AIP Conf. Proc. 1479, 620 (2012)]. However, no quantitative study of this difference has been reported, despite the prevalence of multidimensional physical models in the literature (like a high dimensional funnel guiding protein folding/unfolding). Paradoxically, some theoretical studies of these phenomena still employ a one dimensional diffusion description for analytical tractability. We explore the dimensionality dependent diffusion on REL by carrying out an effective medium approximation based analytical calculations and compare them with the available computer simulation results. We find that at an intermediate level of ruggedness (assumed to have a Gaussian distribution), where diffusion is well-defined, the value of the effective diffusion coefficient depends on dimensionality and changes (increases) by several factors (˜5-10) in going from 1d to 2d. In contrast, the changes in subsequent transitions (like 2d to 3d and 3d to 4d and so on) are far more modest, of the order of 10-20% only. When ruggedness is given by random traps with an exponential distribution of barrier heights, the mean square displacement (MSD) is sub-diffusive (a well-known result), but the growth of MSD is described by different exponents in one and higher dimensions. The reason for such strong ruggedness induced retardation in the case of one dimensional REL is discussed. We also discuss the special limiting case of infinite dimension (d = ∞) where the effective medium approximation becomes exact and where theoretical results become simple. We discuss, for the first time, the role of spatial correlation in the landscape on diffusion of a random walker.

  9. Possibilities of production of neutron-rich Md isotopes in multi-nucleon transfer reactions

    Energy Technology Data Exchange (ETDEWEB)

    Mun, Myeong-Hwan; Lee, Young-Ouk [Korea Atomic Energy Research Institue, Daejeon (Korea, Republic of); Adamian, G.G.; Antonenko, N.V. [Joint Institute for Nuclear Research, Dubna (Russian Federation)

    2016-12-15

    The possibilities of production of yet unknown neutron-rich isotopes of Md are explored in several multi-nucleon transfer reactions with actinide targets and stable and radioactive beams. The projectile-target combinations and bombarding energies are suggested to produce new neutron-rich isotopes of Md in future experiments. (orig.)

  10. Calculations of the spectra of fast neutrons in iron spheres using the vitamin-C file

    International Nuclear Information System (INIS)

    Ahmed, F.; Aizawa, O.; Kadotani, H.

    1984-01-01

    Steady-state space-dependent fast neutron angular and scalar spectra and total flux in various iron spheres have been calculated using the one-dimensional discrete ordinate transport code ANISN and Vitamin-C nuclear data file. The results have been used to study the question of establishment of equilibrium and of an associated fast neutron diffusion length in iron. The authors find that true equilibrium conditions are not established even inside a 3-m-radius iron sphere. However, from the study of spatial decay of total flux, one can obtain the value of the fast neutron diffusion length in iron, which in the present case is found to be 24.4 cm

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

    International Nuclear Information System (INIS)

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

    2014-01-01

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

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2014-05-15

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

  13. The measuring technique developed to evaluate the thermal diffusivity of the multi-layered thin film specimens

    Directory of Open Access Journals (Sweden)

    Li Tse-Chang

    2017-01-01

    Full Text Available In the present study, the thermal diffusivities of the Al, Si and ITO films deposited on the SUS304 steel substrate are evaluated via the present technique. Before applying this technique, the temperature for the thin film of the multi-layered specimen is developed theoretically for the one- dimensional steady heat conduction in response to amplitude and frequency of the periodically oscillating temperature imposed by a peltier placed beneath the specimen's substrate. By the thermal-electrical data processing system excluding the lock-in amplifier, the temperature frequency a3 has been proved first to be independent of the electrical voltage applied to the peltier and the contact position of the thermocouples. The experimental data of phase difference for three kinds of specimen are regressed well by a straight line with a slope. Then, the thermal diffusivity of the thin film is thus determined if the slope value and the film- thickness are available. In the present arrangements for the thermocouples, two thermal diffusivity values are quite close each other and valid for every kind of specimen. This technique can provide an efficient, low-cost method for the thermal diffusivity measurements of thin films.

  14. Development of multi-dimensional body image scale for malaysian female adolescents.

    Science.gov (United States)

    Chin, Yit Siew; Taib, Mohd Nasir Mohd; Shariff, Zalilah Mohd; Khor, Geok Lin

    2008-01-01

    The present study was conducted to develop a Multi-dimensional Body Image Scale for Malaysian female adolescents. Data were collected among 328 female adolescents from a secondary school in Kuantan district, state of Pahang, Malaysia by using a self-administered questionnaire and anthropometric measurements. The self-administered questionnaire comprised multiple measures of body image, Eating Attitude Test (EAT-26; Garner & Garfinkel, 1979) and Rosenberg Self-esteem Inventory (Rosenberg, 1965). The 152 items from selected multiple measures of body image were examined through factor analysis and for internal consistency. Correlations between Multi-dimensional Body Image Scale and body mass index (BMI), risk of eating disorders and self-esteem were assessed for construct validity. A seven factor model of a 62-item Multi-dimensional Body Image Scale for Malaysian female adolescents with construct validity and good internal consistency was developed. The scale encompasses 1) preoccupation with thinness and dieting behavior, 2) appearance and body satisfaction, 3) body importance, 4) muscle increasing behavior, 5) extreme dieting behavior, 6) appearance importance, and 7) perception of size and shape dimensions. Besides, a multidimensional body image composite score was proposed to screen negative body image risk in female adolescents. The result found body image was correlated with BMI, risk of eating disorders and self-esteem in female adolescents. In short, the present study supports a multi-dimensional concept for body image and provides a new insight into its multi-dimensionality in Malaysian female adolescents with preliminary validity and reliability of the scale. The Multi-dimensional Body Image Scale can be used to identify female adolescents who are potentially at risk of developing body image disturbance through future intervention programs.

  15. Performance characteristics of specified power reactors in multidimensional neutron diffusion problems

    International Nuclear Information System (INIS)

    Kim, M.G.

    1980-01-01

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

  16. The 'thousand words' problem: Summarizing multi-dimensional data

    International Nuclear Information System (INIS)

    Scott, David M.

    2011-01-01

    Research highlights: → Sophisticated process sensors produce large multi-dimensional data sets. → Plant control systems cannot handle images or large amounts of data. → Various techniques reduce the dimensionality, extracting information from raw data. → Simple 1D and 2D methods can often be extended to 3D and 4D applications. - Abstract: An inherent difficulty in the application of multi-dimensional sensing to process monitoring and control is the extraction and interpretation of useful information. Ultimately the measured data must be collapsed into a relatively small number of values that capture the salient characteristics of the process. Although multiple dimensions are frequently necessary to isolate a particular physical attribute (such as the distribution of a particular chemical species in a reactor), plant control systems are not equipped to use such data directly. The production of a multi-dimensional data set (often displayed as an image) is not the final step of the measurement process, because information must still be extracted from the raw data. In the metaphor of one picture being equal to a thousand words, the problem becomes one of paraphrasing a lengthy description of the image with one or two well-chosen words. Various approaches to solving this problem are discussed using examples from the fields of particle characterization, image processing, and process tomography.

  17. One-dimensional nodal neutronics routines for the TRAC-BD1 thermal-hydraulics program

    International Nuclear Information System (INIS)

    Nigg, D.W.

    1983-09-01

    Nuclear reactor core transient neutronic behavior is currently modeled in the TRAC-BD1 code using a point-reactor kinetics formulation. This report describes a set of subroutines based on the Analytic Nodal Method that were written to provide TRAC-BD1 with a one-dimensional space-dependent neutronics capability. Use of the routines is illustrated with several test problems. The results of these problems show that the Analytic Nodal neutronics routines have desirable accuracy and computing time characteristics and should be a useful addition to TRAC-BD1

  18. 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)

  19. On the application of finite element method in the solution of steady state diffusion equation

    International Nuclear Information System (INIS)

    Ono, S.

    1982-01-01

    The solution of the steady state neutron diffusion equation is obtained by using the finite element method. Specifically the variational approach is used for one dimensional problems and the weighted residual method (Galerkin) for one and two dimensional problems. The spatial domain is divided into retangular elements and the neutron flux is approximated by linear (one dimensional case), and bilinear (two-dimensional case) functions. Numerical results are obtained with a FORTRAN IV computer program and compared with those obtained by the finite difference CITATION code. The results show that linear or bilinear functions, do not satisfactorily describe the differential parameters in highly heterogeneous reactor cases, but provide good results for integral parameters such as multiplication factor. (Author) [pt

  20. Multi-dimensional simulations of core-collapse supernova explosions with CHIMERA

    Science.gov (United States)

    Messer, O. E. B.; Harris, J. A.; Hix, W. R.; Lentz, E. J.; Bruenn, S. W.; Mezzacappa, A.

    2018-04-01

    Unraveling the core-collapse supernova (CCSN) mechanism is a problem that remains essentially unsolved despite more than four decades of effort. Spherically symmetric models with otherwise high physical fidelity generally fail to produce explosions, and it is widely accepted that CCSNe are inherently multi-dimensional. Progress in realistic modeling has occurred recently through the availability of petascale platforms and the increasing sophistication of supernova codes. We will discuss our most recent work on understanding neutrino-driven CCSN explosions employing multi-dimensional neutrino-radiation hydrodynamics simulations with the Chimera code. We discuss the inputs and resulting outputs from these simulations, the role of neutrino radiation transport, and the importance of multi-dimensional fluid flows in shaping the explosions. We also highlight the production of 48Ca in long-running Chimera simulations.

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

    International Nuclear Information System (INIS)

    Drozdowicz, K.; Woznicka, U.

    1982-01-01

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

  2. Preliminary shielding analysis in support of the CSNS target station shutter neutron beam stop design

    Institute of Scientific and Technical Information of China (English)

    ZHANG Bin; CHEN Yi-Xue; WANG Wei-Jin; YANG Shou-Hai; WU Jun; YIN Wen; LIANG Tian-Jiao; JIA Xue-Jun

    2011-01-01

    The construction of China Spallation Neutron Source (CSNS) has been initiated in Dongguan,Guangdong, China.Thus a detailed radiation transport analysis of the shutter neutron beam stop is of vital importance. The analyses are performed using the coupled Monte Carlo and multi-dimensional discrete ordinates method. The target of calculations is to optimize the neutron beamline shielding design to guarantee personal safety and minimize cost. Successful elimination of the primary ray effects via the two-dimensional uncollided flux and the first collision source methodology is also illustrated. Two-dimensional dose distribution is calculated. The dose at the end of the neutron beam line is less than 2.5μSv/h. The models have ensured that the doses received by the hall staff members are below the standard limit required.

  3. Master-3.0: multi-purpose analyzer for static and transient effects of reactors

    International Nuclear Information System (INIS)

    Cho, Byung Oh; Joo, Han Gyu; Cho, Jin Young; Song, Jae Seung; Zee, Sung Quun

    2002-03-01

    MASTER-3.0 (Multi-purpose Analyzer for Static and Transient Effects of Reactors) is a nuclear design code based on the multi-group diffusion theory to calculate the steady-state and transient pressurized water reactor core in a 3-dimensional Cartesian or hexagonal geometry. Its neutronics model solves the space-time dependent neutron diffusion equations with NIM (Nodal Integration Method), NEM (Nodal Expansion Method), AFEN (Analytic Function Expansion Nodal Method)/NEM Hybrid Method, NNEM (Non-linear Nodal Expansion Method) or NANM (Non-linear Analytic Nodal Method) for a Cartesian geometry and with NTPEN (Non-linear Triangle-based Polynomial Expansion Nodal Method), AFEN (Analytic Function Expansion Nodal)/NEM Hybrid Method or NLFM (Non-linear Local Fine-Mesh Method) for a hexagonal one. Coarse mesh rebalancing, Krylov Subspace method, energy group restriction/prolongation method and asymptotic extrapolation method are implemented to accelerate the convergence of iteration process. MASTER-3.0 performs microscopic depletion calculations using microscopic cross sections provided by CASMO-3 or HELIOS and also has the reconstruction capability of pin information by use of MSS-IAS (Method of Successive Smoothing with Improved Analytic Solution). For the thermal-hydraulic calculation, fuel temperature table or COBRA3-C/P or MATRA model can be used selectively. In addition, MASTER-3.0 is designed to cover various PWRs including SMART as well as WH- and CE-type reactors, providing all data required in their design procedures

  4. Multi-Dimensional Customer Data Analysis in Online Auctions

    Institute of Scientific and Technical Information of China (English)

    LAO Guoling; XIONG Kuan; QIN Zheng

    2007-01-01

    In this paper, we designed a customer-centered data warehouse system with five subjects: listing, bidding, transaction,accounts, and customer contact based on the business process of online auction companies. For each subject, we analyzed its fact indexes and dimensions. Then take transaction subject as example,analyzed the data warehouse model in detail, and got the multi-dimensional analysis structure of transaction subject. At last, using data mining to do customer segmentation, we divided customers into four types: impulse customer, prudent customer, potential customer, and ordinary customer. By the result of multi-dimensional customer data analysis, online auction companies can do more target marketing and increase customer loyalty.

  5. Three dimensional multi-pass repair weld simulations

    International Nuclear Information System (INIS)

    Elcoate, C.D.; Dennis, R.J.; Bouchard, P.J.; Smith, M.C.

    2005-01-01

    Full 3-dimensional (3-D) simulation of multi-pass weld repairs is now feasible and practical given the development of improved analysis tools and significantly greater computer power. This paper presents residual stress results from 3-D finite element (FE) analyses simulating a long (arc length of 62 deg. ) and a short (arc length of 20 deg. ) repair to a girth weld in a 19.6 mm thick, 432 mm outer diameter cylindrical test component. Sensitivity studies are used to illustrate the importance of weld bead inter-pass temperature assumptions and to show where model symmetry can be used to reduce the analysis size. The predicted residual stress results are compared with measured axial, hoop and radial through-wall profiles in the heat affected zone of the test component repairs. A good overall agreement is achieved between neutron diffraction and deep hole drilling measurements and the prediction at the mid-length position of the short repair. These results demonstrate that a coarse 3-D FE model, using a 'block-dumped' weld bead deposition approach (rather than progressively depositing weld metal), can accurately capture the important components of a short repair weld residual stress field. However, comparisons of measured with predicted residual stress at mid-length and stop-end positions in the long repair are less satisfactory implying some shortcomings in the FE modelling approach that warrant further investigation

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2017-07-01

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

  7. A Kronecker product splitting preconditioner for two-dimensional space-fractional diffusion equations

    Science.gov (United States)

    Chen, Hao; Lv, Wen; Zhang, Tongtong

    2018-05-01

    We study preconditioned iterative methods for the linear system arising in the numerical discretization of a two-dimensional space-fractional diffusion equation. Our approach is based on a formulation of the discrete problem that is shown to be the sum of two Kronecker products. By making use of an alternating Kronecker product splitting iteration technique we establish a class of fixed-point iteration methods. Theoretical analysis shows that the new method converges to the unique solution of the linear system. Moreover, the optimal choice of the involved iteration parameters and the corresponding asymptotic convergence rate are computed exactly when the eigenvalues of the system matrix are all real. The basic iteration is accelerated by a Krylov subspace method like GMRES. The corresponding preconditioner is in a form of a Kronecker product structure and requires at each iteration the solution of a set of discrete one-dimensional fractional diffusion equations. We use structure preserving approximations to the discrete one-dimensional fractional diffusion operators in the action of the preconditioning matrix. Numerical examples are presented to illustrate the effectiveness of this approach.

  8. Advances in the solution of three-dimensional nodal neutron transport equation

    International Nuclear Information System (INIS)

    Pazos, Ruben Panta; Hauser, Eliete Biasotto; Vilhena, Marco Tullio de

    2003-01-01

    In this paper we study the three-dimensional nodal discrete-ordinates approximations of neutron transport equation in a convex domain with piecewise smooth boundaries. We use the combined collocation method of the angular variables and nodal approach for the spatial variables. By nodal approach we mean the iterated transverse integration of the S N equations. This procedure leads to the set of one-dimensional averages angular fluxes in each spatial variable. The resulting system of equations is solved with the LTS N method, first applying the Laplace transform to the set of the nodal S N equations and then obtaining the solution by symbolic computation. We include the LTS N method by diagonalization to solve the nodal neutron transport equation and then we outline the convergence of these nodal-LTS N approximations with the help of a norm associated to the quadrature formula used to approximate the integral term of the neutron transport equation. We give numerical results obtained with an algebraic computer system (for N up to 8) and with a code for higher values of N. We compare our results for the geometry of a box with a source in a vertex and a leakage zone in the opposite with others techniques used in this problem. (author)

  9. Moving toward multi-dimensional radiotherapy and the role of radiobiology

    International Nuclear Information System (INIS)

    Oita, Masataka; Uto, Yoshihiro; Aoyama, Hideki

    2014-01-01

    Recent radiotherapy for cancer treatment enable the high-precision irradiation to the target under the computed image guidance. Developments of such radiotherapy has played large role in the improved strategy of cancer treatments. In addition, the molecular mechanistic studies related to proliferations of cancer cell contribute the multidisciplinary fields of clinical radiotherapies. Therefore, the combination of the image guidance and molecular targeting of cancer cells make it possible for individualized cancer treatment. Especially, the use of particle beam or boron neutron capture therapy (BNCT) has been spotlighted, and installations of such devices are planned widely. As the progress and collaborations of radiation biology and engineering physics, establishment of a new style of radiotherapy becomes available in post-genome era. In 2010s, the hi-tech machines controlling the spaciotemporal radiotherapy become in practice. Although, there still remains to be improved, e.g., more precise prediction of radiosensitivity or growth of individual tumors, and adverse outcomes after treatments, multi-dimensional optimizations of the individualized irradiations based on the molecular radiation biologies and medical physics are important for further development of radiotherapy. (author)

  10. Application of the three-dimensional transport code to analysis of the neutron streaming experiment

    International Nuclear Information System (INIS)

    Chatani, K.; Slater, C.O.

    1990-01-01

    The neutron streaming through an experimental mock-up of a Clinch River Breeder Reactor (CRBR) prototypic coolant pipe chaseway was recalculated with a three-dimensional discrete ordinates code. The experiment was conducted at the Tower Shielding Facility at Oak Ridge National Laboratory in 1976 and 1977. The measurement of the neutron flux, using Bonner ball detectors, indicated nine orders of attenuation in the empty pipeway, which contained two 90-deg bends and was surrounded by concrete walls. The measurement data were originally analyzed using the DOT3.5 two-dimensional discrete ordinates radiation transport code. However, the results did not agree with measurement data at the bend because of the difficulties in modeling the three-dimensional configurations using two-dimensional methods. The two-dimensional calculations used a three-step procedure in which each of the three legs making the two 90-deg bends was a separate calculation. The experiment was recently analyzed with the TORT three-dimensional discrete ordinates radiation transport code, not only to compare the calculational results with the experimental results, but also to compare with results obtained from analyses in Japan using DOT3.5, MORSE, and ENSEMBLE, which is a three-dimensional discrete ordinates radiation transport code developed in Japan

  11. Computation of diffusion coefficients for waters of Gauthami Godavari estuary using one-dimensional advection-diffusion model

    Digital Repository Service at National Institute of Oceanography (India)

    Jyothi, D.; Murty, T.V.R.; Sarma, V.V.; Rao, D.P.

    conditions. As the pollutant load on the estuary increases, the. water quality may deteriorate rapidly and therefore the scientific interests are centered on the analysis of water quality. The pollutants will be subjected to a number of physical, chemical... study we have applied one-dimensional advection-diffusion model for the waters of Gauthami Godavari estuary to determine the axial diffusion coefficients and thereby to predict the impact assessment. The study area (Fig. 1) is the lower most 32 km...

  12. Physical Properties of (NH4)2Pt(CN)4[Clo.42].3H2O: A new Quasi-One-Dimensional Conductor

    DEFF Research Database (Denmark)

    Carneiro, Kim; Petersen, A. S.; Underhill, A. E.

    1979-01-01

    The quasi-one-dimensional conductor (NH4)2[Pt(CN)4]Cl0.42·3H2O, ACP(Cl), has been studied experimentally by means of electrical conduction measurements, x-ray diffuse scattering, and neutron inelastic scattering. This allows the determination of all the physical parameters of interest for the the......The quasi-one-dimensional conductor (NH4)2[Pt(CN)4]Cl0.42·3H2O, ACP(Cl), has been studied experimentally by means of electrical conduction measurements, x-ray diffuse scattering, and neutron inelastic scattering. This allows the determination of all the physical parameters of interest...

  13. 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

  14. NSPEC - A neutron spectrum code for beam-heated fusion plasmas

    International Nuclear Information System (INIS)

    Scheffel, J.

    1983-06-01

    A 3-dimensional computer code is described, which computes neutron spectra due to beam heating of fusion plasmas. Three types of interactions are considered; thermonuclear of plasma-plasma, beam-plasma and beam-beam interactions. Beam deposition is modelled by the NFREYA code. The applied steady state beam distribution as a function of pitch angle and velocity contains the effects of energy diffusion, friction, angular scattering, charge exchange, electric field and source pitch angle distribution. The neutron spectra, generated by Monte-Carlo methods, are computed with respect to given lines of sight. This enables the code to be used for neutron diagnostics. (author)

  15. Solar systems diffusion in local markets

    International Nuclear Information System (INIS)

    Sidiras, D.K.; Koukios, E.G.

    2004-01-01

    This paper reports on a study of the driving forces and barriers of the spectacular diffusion of solar energy use for domestic hot-water production in Greece. Through the various kinds of questionnaires used in this work, the main diffusion actors have been requested to grade the various diffusion factors identified by desk and preliminary field research. Households identify a number of economic (available family income), technical (new technologies), political (new incentives), and socio-cultural (sensitivity in energy matters) factors as dominant. According to the solar industry, advertising, distribution and quality control standards have to be added to the list of critical factors. Technical experts contribute with identifying, besides R and D, public awareness on energy matters. Solar collector diffusion, despite the fact that it has followed a market-driven mechanism, was revealed to be a multi-actor, multi-dimensional and multi-parametric phenomenon. Presently, the phenomenon is constrained by the available family income, with technology-related factors, i.e., research, and standardization quality control, playing increasing roles

  16. Numerical modelling of random walk one-dimensional diffusion

    International Nuclear Information System (INIS)

    Vamos, C.; Suciu, N.; Peculea, M.

    1996-01-01

    The evolution of a particle which moves on a discrete one-dimensional lattice, according to a random walk low, approximates better the diffusion process smaller the steps of the spatial lattice and time are. For a sufficiently large assembly of particles one can assume that their relative frequency at lattice knots approximates the distribution function of the diffusion process. This assumption has been tested by simulating on computer two analytical solutions of the diffusion equation: the Brownian motion and the steady state linear distribution. To evaluate quantitatively the similarity between the numerical and analytical solutions we have used a norm given by the absolute value of the difference of the two solutions. Also, a diffusion coefficient at any lattice knots and moment of time has been calculated, by using the numerical solution both from the diffusion equation and the particle flux given by Fick's low. The difference between diffusion coefficient of analytical solution and the spatial lattice mean coefficient of numerical solution constitutes another quantitative indication of the similarity of the two solutions. The results obtained show that the approximation depends first on the number of particles at each knot of the spatial lattice. In conclusion, the random walk is a microscopic process of the molecular dynamics type which permits simulations precision of the diffusion processes with given precision. The numerical method presented in this work may be useful both in the analysis of real experiments and for theoretical studies

  17. Estimate of the damage in organs induced by neutrons in three-dimensional conformal radiotherapy

    International Nuclear Information System (INIS)

    Benites R, J. L.; Vega C, H. R.; Uribe, M. del R.

    2014-08-01

    By means of Monte Carlo methods was considered the damage in the organs, induced by neutrons, of patients with cancer that receive treatment in modality of three-dimensional conformal radiotherapy (3D-CRT) with lineal accelerator Varian Ix. The objective of this work was to estimate the damage probability in radiotherapy patients, starting from the effective dose by neutrons in the organs and tissues out of the treatment region. For that a three-dimensional mannequin of equivalent tissue of 30 x 100 x 30 cm 3 was modeled and spherical cells were distributed to estimate the Kerma in equivalent tissue and the absorbed dose by neutrons. With the absorbed dose the effective dose was calculated using the weighting factors for the organ type and radiation type. With the effective dose and the damage factors, considered in the ICRP 103, was considered the probability of damage induction in organs. (Author)

  18. Experiment and analysis of neutron spectra in a concrete assembly bombarded by 14 MeV neutrons

    International Nuclear Information System (INIS)

    Oishi, Koji; Tomioka, Kazuyuki; Ikeda, Yujiro; Nakamura, Tomoo.

    1988-01-01

    Neutron spectrum in concrete bombarded by 14 MeV neutrons was measured using a miniature NE213 spectrometer and multi-foil activation method. A good agreement between those two experimental methods was obtained within experimental errors. The measured spectrum was compared with calculated ones using two-dimensional transport code DOT3.5 with 125 group structure cross section libraries based on ENDF/B-IV, JENDL-2, and JENDL-3T (the testing version of JENDL-3.) In the D-T neutron peak region, measured and calculated neutron spectra agreed well with each other for those libraries. However, disagreements of about -10 % to +50 % and -30 % to +40 % were obtained in the MeV region and still lower neutron energy range, respectively. As a result, it was concluded that those discrepancies were caused by the overestimation of secondary neutrons emitted by inelastic scattering from O, Si, and/or Ca which were the main components of concrete. (author)

  19. Multi-scale diffuse interface modeling of multi-component two-phase flow with partial miscibility

    KAUST Repository

    Kou, Jisheng; Sun, Shuyu

    2016-01-01

    In this paper, we introduce a diffuse interface model to simulate multi-component two-phase flow with partial miscibility based on a realistic equation of state (e.g. Peng-Robinson equation of state). Because of partial miscibility, thermodynamic

  20. Application of fast neutron radiography to three-dimensional visualization of steady two-phase flow in a rod bundle

    CERN Document Server

    Takenaka, N; Fujii, T; Mizubata, M; Yoshii, K

    1999-01-01

    Three-dimensional void fraction distribution of air-water two-phase flow in a 4x4 rod-bundle near a spacer was visualized by fast neutron radiography using a CT method. One-dimensional cross sectional averaged void fraction distribution was also calculated. The behaviors of low void fraction (thick water) two-phase flow in the rod bundle around the spacer were clearly visualized. It was shown that the void fraction distributions were visualized with a quality similar to those by thermal neutron radiography for low void fraction two-phase flow which is difficult to visualize by thermal neutron radiography. It is concluded that the fast neutron radiography is efficiently applicable to two-phase flow studies.

  1. Multi-dimensional Bin Packing Problems with Guillotine Constraints

    DEFF Research Database (Denmark)

    Amossen, Rasmus Resen; Pisinger, David

    2010-01-01

    The problem addressed in this paper is the decision problem of determining if a set of multi-dimensional rectangular boxes can be orthogonally packed into a rectangular bin while satisfying the requirement that the packing should be guillotine cuttable. That is, there should exist a series of face...... parallel straight cuts that can recursively cut the bin into pieces so that each piece contains a box and no box has been intersected by a cut. The unrestricted problem is known to be NP-hard. In this paper we present a generalization of a constructive algorithm for the multi-dimensional bin packing...... problem, with and without the guillotine constraint, based on constraint programming....

  2. Statistical Projections for Multi-resolution, Multi-dimensional Visual Data Exploration and Analysis

    Energy Technology Data Exchange (ETDEWEB)

    Nguyen, Hoa T. [Univ. of Utah, Salt Lake City, UT (United States); Stone, Daithi [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Bethel, E. Wes [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

    2016-01-01

    An ongoing challenge in visual exploration and analysis of large, multi-dimensional datasets is how to present useful, concise information to a user for some specific visualization tasks. Typical approaches to this problem have proposed either reduced-resolution versions of data, or projections of data, or both. These approaches still have some limitations such as consuming high computation or suffering from errors. In this work, we explore the use of a statistical metric as the basis for both projections and reduced-resolution versions of data, with a particular focus on preserving one key trait in data, namely variation. We use two different case studies to explore this idea, one that uses a synthetic dataset, and another that uses a large ensemble collection produced by an atmospheric modeling code to study long-term changes in global precipitation. The primary findings of our work are that in terms of preserving the variation signal inherent in data, that using a statistical measure more faithfully preserves this key characteristic across both multi-dimensional projections and multi-resolution representations than a methodology based upon averaging.

  3. 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)

  4. On the Sodium Concentration Diffusion with Three-Dimensional Extracellular Stimulation

    Directory of Open Access Journals (Sweden)

    Luisa Consiglieri

    2011-01-01

    Full Text Available We deal with the transmembrane sodium diffusion in a nerve. We study a mathematical model of a nerve fibre in response to an imposed extracellular stimulus. The presented model is constituted by a diffusion-drift vectorial equation in a bidomain, that is, two parabolic equations defined in each of the intra- and extra-regions. This system of partial differential equations can be understood as a reduced three-dimensional Poisson-Nernst-Planck model of the sodium concentration. The representation of the membrane includes a jump boundary condition describing the mechanisms involved in the excitation-contraction couple. Our first novelty comes from this general dynamical boundary condition. The second one is the three-dimensional behaviour of the extracellular stimulus. An analytical solution to the mathematical model is proposed depending on the morphology of the excitation.

  5. 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

  6. Diffusion coefficients for multi-step persistent random walks on lattices

    International Nuclear Information System (INIS)

    Gilbert, Thomas; Sanders, David P

    2010-01-01

    We calculate the diffusion coefficients of persistent random walks on lattices, where the direction of a walker at a given step depends on the memory of a certain number of previous steps. In particular, we describe a simple method which enables us to obtain explicit expressions for the diffusion coefficients of walks with a two-step memory on different classes of one-, two- and higher dimensional lattices.

  7. Corrected simulations for one-dimensional diffusion processes with naturally occurring boundaries.

    Science.gov (United States)

    Shafiey, Hassan; Gan, Xinjun; Waxman, David

    2017-11-01

    To simulate a diffusion process, a usual approach is to discretize the time in the associated stochastic differential equation. This is the approach used in the Euler method. In the present work we consider a one-dimensional diffusion process where the terms occurring, within the stochastic differential equation, prevent the process entering a region. The outcome is a naturally occurring boundary (which may be absorbing or reflecting). A complication occurs in a simulation of this situation. The term involving a random variable, within the discretized stochastic differential equation, may take a trajectory across the boundary into a "forbidden region." The naive way of dealing with this problem, which we refer to as the "standard" approach, is simply to reset the trajectory to the boundary, based on the argument that crossing the boundary actually signifies achieving the boundary. In this work we show, within the framework of the Euler method, that such resetting introduces a spurious force into the original diffusion process. This force may have a significant influence on trajectories that come close to a boundary. We propose a corrected numerical scheme, for simulating one-dimensional diffusion processes with naturally occurring boundaries. This involves correcting the standard approach, so that an exact property of the diffusion process is precisely respected. As a consequence, the proposed scheme does not introduce a spurious force into the dynamics. We present numerical test cases, based on exactly soluble one-dimensional problems with one or two boundaries, which suggest that, for a given value of the discrete time step, the proposed scheme leads to substantially more accurate results than the standard approach. Alternatively, the standard approach needs considerably more computation time to obtain a comparable level of accuracy to the proposed scheme, because the standard approach requires a significantly smaller time step.

  8. Development of three-dimensional nuclear design program for large fast breeder reactor

    International Nuclear Information System (INIS)

    Inoue, Kohtaro

    1987-01-01

    The report describes a calculation program for core design, called HICOM, and its calculation accuracy. HICOM is designed for three-dimensional neutron diffusion calculation and combustion calculation for large fast breeder reactors to be conducted according to a control rod plan and fuel replacement plan. The improved coarse mesh technique is applied to neutron diffusion calculation. It is demostrated that HICOM permits rapid and accurate operation. For the evaluation of the applicability of HICOM, three-dimensional six-group neutron diffusion calculation is conducted for a 1,000 MWe axial heterogeneous FBR core. Results demonstrate that the program can perform numerical calculation in a time period shorter than 1-40 that for calculation by CITATION (triangle mesh method). This is achieved by using the improved coarse mesh method and carrying out the operation by a vectorial procedure. For the evaluation of the nuclear calculation accuracy of HICOM, analysis is made of reactivity, output distribution and B 4 C control rod worth emasured in an FCA criticality experiment carried out by the Japan Atomic Energy Research Institute. Calculations are found to agree with measurements within a permissible error. The same level of calculation accuracy is obtained for homogneous core, axial heterogeneous core and cores with internal blankets with different forms. (Nogami, K.)

  9. The multi leaf collimator for fast neutron therapy at louvain-la-Neuve

    International Nuclear Information System (INIS)

    Denis, J.M.; Richard, F.; Vynckier, S.; Wambersie, A.; Meulders, J.P.; Lannoye, E.; Longree, Y.; Ryckewaert, G.

    1996-01-01

    The multi-leaf collimator of the fast neutron therapy facility at Louvain-la-Neuve is described, as well as some of the physics experiments performed in order to evaluate the attenuation of neutron beams in different materials and thus optimize the composition of collimator leaves. The multi-leaf collimator consists of two sets of 22 leaves each, which can be moved independently. They are made of iron and their thickness is 95 cm. Seven borated polyethylene disks are located in the distal part of the leaves in order to absorb more efficiently the low-energy component of the neutron spectrum. The width of the leaves is 1 cm at their distal part. The leaves can more 11 cm outwards and 6 cm inwards from their reference position, and field size up to 25.7 x 24.8 cm as well as irregular field shapes, can be obtained. The inner part of the leaves and their two sides are always focused on the target. The complete multi-leaf collimator can rotate around the beam axis, from -90 deg to + 90 deg from the reference position. The width of the penumbra (80 - 20 % isodoses) is 0.64 cm and 1.17 cm at the depth of the maximum buildup and at 10 cm in depth respectively, for a 10 x 10 cm field size. The collimator is adequate for the energy of the p(65)+Be neutron beam of Louvain-la-Neuve and has been adapted to the fixed vertical beam. It has been designed following the original plans of Scanditronix, adjusted and fully assembled at the workshop of the Centre de Recherches du Cyclotron (CRC). Systematic measurements were performed in order to optimize the design and the composition of the leaves. In particular the attenuations of the actual beam and of monoenergetic neutron beams were measured in different materials such as iron and polyethylene. Above (upstream) the multi-leaf collimator, a fixed pre-collimator (iron thickness 50 cm; section 1 x 1 m) defines a conical aperture aligned on the largest opening of the leaves. It contains the two transmission chambers and a 2 cm thick

  10. Cold-neutron multi-chopper spectrometer for MLF, J-PARC

    International Nuclear Information System (INIS)

    Nakajima, Kenji; Kajimoto, Ryoich; Nakamura, Mistutaka; Arai, Masatoshi; Sato, Taku J.; Osakabe, Toyotaka; Matsuda, Masaaki; Metoki, Naoto; Kakurai, Kazuhisa; Itoh, Shinichi

    2005-01-01

    We are planning to construct a cold-neutron multi-chopper spectrometer for a new spallation neutron source at Materials and Life Science Facility (MLF) at J-PARC, which is dedicated to investigation of low energy excitations and quasi-elastic excitations in the field of solid state physics, chemistry, materials science, soft matter science and biomaterial science. The planned spectrometer will be installed at a H 2 -coupled moderator and will be equipped with a pulse-shaping disk-chopper in addition to a monochromating disk-chopper, and realizes both high-energy resolution (ΔE/E i ≥1%) and high-intensity (one order of magnitude higher than the present state-of-the-art chopper spectrometers)

  11. PAD: a one-dimensional, coupled neutronic-thermodynamic-hydrodynamic computer code

    International Nuclear Information System (INIS)

    Peterson, D.M.; Stratton, W.R.; McLaughlin, T.P.

    1976-12-01

    Theoretical and numerical foundations, utilization guide, sample problems, and program listing and glossary are given for the PAD computer code which describes dynamic systems with interactive neutronics, thermodynamics, and hydrodynamics in one-dimensional spherical, cylindrical, and planar geometries. The code has been applied to prompt critical excursions in various fissioning systems (solution, metal, LMFBR, etc.) as well as to nonfissioning systems

  12. Multi-element analysis of crude-oil samples by 14.6 MeV neutron activation

    International Nuclear Information System (INIS)

    Cam, N.F.; Cigeroglu, F.; Erduran, M.N.

    1997-01-01

    The instrumental neutron activation technique, using the SAMEST T-400 neutron generator with 14.6 MeV neutrons produced from 3 H(d,n) 4 He reaction, is demonstrated for multi-element analysis of Saudi-Arabian crude-oil samples. The system parameters for the absolute method (e.g., the counting solid-angle, intrinsic efficiency of the γ-ray detector, effective neutron flux, activation cross sections, etc.)were determined and the results of elemental concentrations were presented with the corrections for all possible interferences having been carefully considered. (author)

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

    Energy Technology Data Exchange (ETDEWEB)

    Descotes, L

    1994-05-01

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

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

    Energy Technology Data Exchange (ETDEWEB)

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

    1962-07-01

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

  15. Measurement of multi-dimensional flow structure for flow boiling in a tube

    International Nuclear Information System (INIS)

    Adachi, Yu; Ito, Daisuke; Saito, Yasushi

    2014-01-01

    With an aim of the measurement of multi-dimensional flow structure of in-tube boiling two-phase flow, the authors built their own wire mesh measurement system based on electrical conductivity measurement, and examined the relationship between the electrical conductivity obtained by the wire mesh sensor and the void fraction. In addition, the authors measured the void fraction using neutron radiography, and compared the result with the measured value using the wire mesh sensor. From the comparison with neutron radiography, it was found that the new method underestimated the void fraction in the flow in the vicinity of the void fraction of 0.2-0.5, similarly to the conventional result. In addition, since the wire mesh sensor cannot measure dispersed droplets, it tends to overestimate the void fraction in the high void fraction region, such as churn flow accompanied by droplet generation. In the electrical conductivity wire-mesh sensor method, it is necessary to correctly take into account the effect of liquid film or droplets. The authors also built a measurement system based on the capacitance wire mesh sensor method using the difference in dielectric constant, performed the confirmation of transmission and reception signals using deionized water as a medium, and showed the validity of the system. As for the dispersed droplets, the capacitance method has a potential to be able to measure them. (A.O.)

  16. Research and development of the software for visualizing nuclear reactor and neutronics analysis

    International Nuclear Information System (INIS)

    Okui, Shota; Sekimoto, Hiroshi

    2009-01-01

    It is not easy to image three-dimensional construct of a nuclear reactor with only its two-dimensional figure because it contains a number of structures and its construction is very complicated. Several visualization softwares for the nuclear reactor or some other plant exist, but require high skills and their operation is not simple. In this study, we developed nuclear reactor visualization software, called 'Visual Reactor (VR)', which does not require specific skills. We added the neutronics analysis code to that software. This code executes cell calculation, neutron diffusion calculation and nuclide burnup calculation by itself without any other codes. We tried to treat simple physics model in order to perform these calculation in a short time. Neutronics characteristics, such as neutron flux and power density distribution, are visualized on structure of nuclear reactor. Target operating system is Microsoft Windows XP or Vista. VR is utilized to figure out the structure of nuclear reactor and whole picture of neutronics characteristics. (author)

  17. The analysis of RPV fast neutron flux calculation for PWR with three-dimensional SN method

    International Nuclear Information System (INIS)

    Yang Shouhai; Chen Yixue; Wang Weijin; Shi Shengchun; Lu Daogang

    2011-01-01

    Discrete ordinates (S N ) method is one of the most widely used method for reactor pressure vessel (RPV) design. As the fast development of computer CPU speed and memory capacity and consummation of three-dimensional discrete-ordinates method, it is mature for 3-D S N method to be used to engineering design for nuclear facilities. This work was done specifically for PWR model, with the results of 3-D core neutron transport calculation by 3-D core calculation, 3-D RPV fast neutron flux distribution obtain by 3-D S N method were compared with gained by 1-D and 2-D S N method and the 3-D Monte Carlo (MC) method. In this paper, the application of three-dimensional S N method in calculating RPV fast neutron flux distribution for pressurized water reactor (PWR) is presented and discussed. (authors)

  18. An approximate stationary solution for multi-allele neutral diffusion with low mutation rates.

    Science.gov (United States)

    Burden, Conrad J; Tang, Yurong

    2016-12-01

    We address the problem of determining the stationary distribution of the multi-allelic, neutral-evolution Wright-Fisher model in the diffusion limit. A full solution to this problem for an arbitrary K×K mutation rate matrix involves solving for the stationary solution of a forward Kolmogorov equation over a (K-1)-dimensional simplex, and remains intractable. In most practical situations mutations rates are slow on the scale of the diffusion limit and the solution is heavily concentrated on the corners and edges of the simplex. In this paper we present a practical approximate solution for slow mutation rates in the form of a set of line densities along the edges of the simplex. The method of solution relies on parameterising the general non-reversible rate matrix as the sum of a reversible part and a set of (K-1)(K-2)/2 independent terms corresponding to fluxes of probability along closed paths around faces of the simplex. The solution is potentially a first step in estimating non-reversible evolutionary rate matrices from observed allele frequency spectra. Copyright © 2016 Elsevier Inc. All rights reserved.

  19. Mathematical processing of experimental data on neutron yield from separate fission fragments

    International Nuclear Information System (INIS)

    Basova, B.G.; Rabinovich, A.D.; Ryazanov, D.K.

    1975-01-01

    The algorithm is described for processing the multi-dimensional experiments on measurements of prompt emission of neutrons from separate fission fragments. While processing the data the effect of a number of experimental corrections is correctly taken into account; random coincidence background, neutron spectrum, neutron detector efficiency, instrument angular resolution. On the basis of the described algorithm a program for BESM-4 computer is realized and the treatment of experimental data is performed according to the spontaneous fission of 252 Cf

  20. Multi-Grid detector for neutron spectroscopy: results obtained on time-of-flight spectrometer CNCS

    Science.gov (United States)

    Anastasopoulos, M.; Bebb, R.; Berry, K.; Birch, J.; Bryś, T.; Buffet, J.-C.; Clergeau, J.-F.; Deen, P. P.; Ehlers, G.; van Esch, P.; Everett, S. M.; Guerard, B.; Hall-Wilton, R.; Herwig, K.; Hultman, L.; Höglund, C.; Iruretagoiena, I.; Issa, F.; Jensen, J.; Khaplanov, A.; Kirstein, O.; Lopez Higuera, I.; Piscitelli, F.; Robinson, L.; Schmidt, S.; Stefanescu, I.

    2017-04-01

    The Multi-Grid detector technology has evolved from the proof-of-principle and characterisation stages. Here we report on the performance of the Multi-Grid detector, the MG.CNCS prototype, which has been installed and tested at the Cold Neutron Chopper Spectrometer, CNCS at SNS. This has allowed a side-by-side comparison to the performance of 3He detectors on an operational instrument. The demonstrator has an active area of 0.2 m2. It is specifically tailored to the specifications of CNCS. The detector was installed in June 2016 and has operated since then, collecting neutron scattering data in parallel to the He-3 detectors of CNCS. In this paper, we present a comprehensive analysis of this data, in particular on instrument energy resolution, rate capability, background and relative efficiency. Stability, gamma-ray and fast neutron sensitivity have also been investigated. The effect of scattering in the detector components has been measured and provides input to comparison for Monte Carlo simulations. All data is presented in comparison to that measured by the 3He detectors simultaneously, showing that all features recorded by one detector are also recorded by the other. The energy resolution matches closely. We find that the Multi-Grid is able to match the data collected by 3He, and see an indication of a considerable advantage in the count rate capability. Based on these results, we are confident that the Multi-Grid detector will be capable of producing high quality scientific data on chopper spectrometers utilising the unprecedented neutron flux of the ESS.

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

    International Nuclear Information System (INIS)

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

    2016-01-01

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

  2. Geometrical bucklings for two-dimensional regular polygonal regions using the finite Fourier transformation

    International Nuclear Information System (INIS)

    Mori, N.; Kobayashi, K.

    1996-01-01

    A two-dimensional neutron diffusion equation is solved for regular polygonal regions by the finite Fourier transformation, and geometrical bucklings are calculated for regular 3-10 polygonal regions. In the case of the regular triangular region, it is found that a simple and rigorous analytic solution is obtained for the geometrical buckling and the distribution of the neutron current along the outer boundary. (author)

  3. 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

  4. Development and Validation of Multi-Dimensional Personality ...

    African Journals Online (AJOL)

    This study was carried out to establish the scientific processes for the development and validation of Multi-dimensional Personality Inventory (MPI). The process of development and validation occurred in three phases with five components of Agreeableness, Conscientiousness, Emotional stability, Extroversion, and ...

  5. Implementation of three-dimension AFEN module to STAR code

    International Nuclear Information System (INIS)

    Kim, Young Il; Jeong, Hyung Kuk; Noh, Jae Man; Kim, Taek Kyum; Ju, Hyung Kuk; Kim, Young Jin.

    1997-05-01

    Recently, the AFEN method has been developed to overcome limitations caused by the transverse integration. The method solves the multi-dimensional diffusion equation directly by expanding its solution into non-separable analytic basis functions. The non-separable analytic function expansion satisfying the multi-dimensional diffusion equation at any points in node makes it possible to model accurately the strong flux gradient near the interface of two fuel assemblies with quite different neutronic properties. In this study, we developed the three-dimensional AFEN formulations, and implemented them into the Static/Transient Core Analysis computer code STAR. The accuracy of the implemented AFEN scheme was tested against two benchmark problems: IAEA benchmark problem and a small session problem composed of MOX and UO 2 fuel assemblies. In these tests the superiority of the AFEN method in predicting the neutron flux distribution and the effective core multiplication factor was verified. (author). 4 figs., 5 refs

  6. 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

  7. Computational modelling for diffusion of neutrons problems inside nuclear multiplying medium on bidimensional cartesian rectangular geometry; Modelagem computacional de problemas de difusao de neutrons em meios multiplicativos em geometria retangular cartesiana bi-dimensional

    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)

  8. Alignment dynamics of diffusive scalar gradient in a two-dimensional model flow

    Science.gov (United States)

    Gonzalez, M.

    2018-04-01

    The Lagrangian two-dimensional approach of scalar gradient kinematics is revisited accounting for molecular diffusion. Numerical simulations are performed in an analytic, parameterized model flow, which enables considering different regimes of scalar gradient dynamics. Attention is especially focused on the influence of molecular diffusion on Lagrangian statistical orientations and on the dynamics of scalar gradient alignment.

  9. Neutron and photon (light) scattering on solitons in the quasi-one-dimensional magnetics

    CERN Document Server

    Abdulloev, K O

    1999-01-01

    The general expression we have found earlier for the dynamics form-factor is used to analyse experiments on the neutron and photon (light) scattering by the gas of solitons in quasi-one-dimensional magnetics (Authors)

  10. A three-dimensional nodal neutron kinetics capability for relaps

    International Nuclear Information System (INIS)

    Judd, J.L.; Weaver, W.L.

    1996-01-01

    The incorporation of a three-dimensional neutron kinetics capability into the DOE version of the RELAP5/MOD3.2 reactor safety code is discussed. A brief discussion of the kinetics method is given along with a discussion of the cross section parameterization models available in RELAP5/MOD3.2. The RELAP5/MOD3.2 code is then used to perform calculations of the NEACRP rod ejection and rod withdrawal benchmarks, and results are presented

  11. Green's function method and its application to verification of diffusion models of GASFLOW code

    International Nuclear Information System (INIS)

    Xu, Z.; Travis, J.R.; Breitung, W.

    2007-07-01

    To validate the diffusion model and the aerosol particle model of the GASFLOW computer code, theoretical solutions of advection diffusion problems are developed by using the Green's function method. The work consists of a theory part and an application part. In the first part, the Green's functions of one-dimensional advection diffusion problems are solved in infinite, semi-infinite and finite domains with the Dirichlet, the Neumann and/or the Robin boundary conditions. Novel and effective image systems especially for the advection diffusion problems are made to find the Green's functions in a semi-infinite domain. Eigenfunction method is utilized to find the Green's functions in a bounded domain. In the case, key steps of a coordinate transform based on a concept of reversed time scale, a Laplace transform and an exponential transform are proposed to solve the Green's functions. Then the product rule of the multi-dimensional Green's functions is discussed in a Cartesian coordinate system. Based on the building blocks of one-dimensional Green's functions, the multi-dimensional Green's function solution can be constructed by applying the product rule. Green's function tables are summarized to facilitate the application of the Green's function. In the second part, the obtained Green's function solutions benchmark a series of validations to the diffusion model of gas species in continuous phase and the diffusion model of discrete aerosol particles in the GASFLOW code. Perfect agreements are obtained between the GASFLOW simulations and the Green's function solutions in case of the gas diffusion. Very good consistencies are found between the theoretical solutions of the advection diffusion equations and the numerical particle distributions in advective flows, when the drag force between the micron-sized particles and the conveying gas flow meets the Stokes' law about resistance. This situation is corresponding to a very small Reynolds number based on the particle

  12. 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)

  13. Best-estimated multi-dimensional calculation during LB LOCA for APR1400

    International Nuclear Information System (INIS)

    Oh, D. Y.; Bang, Y. S.; Cheong, A. J.; Woong, S.; Korea, W.

    2010-01-01

    Best-estimated (BE) calculation with uncertainty quantification for the emergency core cooling system (ECCS) performance analysis during Loss of Coolant Accident (LOCA) is more broadly used in nuclear industries and regulations. In Korea, demand on regulatory audit calculation is continuously increasing to support the safety review for life extension, power up-rating and advanced nuclear reactor design. The thermal-hydraulic system code, MARS (Multi-dimensional Analysis of Reactor Safety), with multi-dimensional capability is used for audit calculation. It achieves to describe the complicated phenomena in reactor coolant system by very effectively consolidating the one dimensional RELAP5/MOD3 with the multidimensional COBRA-TF codes. The advanced power reactors (APR1400) to be evaluated has four separated hydraulic trains of the high pressure injection system (HPSI) with direct vessel injection (DVI) which is different from the existing commercial PWRs. Also, the therma-hydraulic behavior of DVI plant would be considerably different from that of a cold-leg safety injection since the low pressure safety injection system are eliminated and the high pressure safety flow are injected into the specific elevation of reactor vessel downcomer. The ECCS bypass induced by the downcomer boiling due to hot wall heating of reactor vessel during reflooding phase is one of the important phenomena which should be considered in DVI plants. Therefore, in this study, BE calculation with one-dimensional (1-D) and multi-dimensional (multi-D) MARS models during LBLOCA are performed for APR1400 plant. In the multi-D evaluation, the reactor vessel is modeled by multi-D components and the specific treatment of flow path inside reactor vessel, e.g., upper guide structure, is essential. The concept of hot zone is adopted to simulate the limiting thermal-hydraulic conditions surrounding hot rod, which is similar to hot channel in 1-D. Also, alternative treatment of the hot rods in multi-D is

  14. A suspended boron foil multi-wire proportional counter neutron detector

    Energy Technology Data Exchange (ETDEWEB)

    Nelson, Kyle A.; Edwards, Nathaniel S.; Hinson, Niklas J.; Wayant, Clayton D.; McGregor, Douglas S.

    2014-12-11

    Three natural boron foils, approximately 1.0 cm in diameter and 1.0 µm thick, were obtained from The Lebow Company and suspended in a multi-wire proportional counter. Suspending the B foils allowed the alpha particle and Li ion reaction products to escape simultaneously, one on each side of the foil, and be measured concurrently in the gas volume. The thermal neutron response pulse-height spectrum was obtained and two obvious peaks appear from the 94% and 6% branches of the {sup 10}B(n,α){sup 7}Li neutron reaction. Scanning electron microscope images were collected to obtain the exact B foil thicknesses and MCNP6 simulations were completed for those same B thicknesses. Pulse-height spectra obtained from the simulations were compared to experimental data and matched well. The theoretical intrinsic thermal–neutron detection efficiency for enriched {sup 10}B foils was calculated and is presented. Additionally, the intrinsic thermal neutron detection efficiency of the three natural B foils was calculated to be 3.2±0.2%.

  15. A suspended boron foil multi-wire proportional counter neutron detector

    Science.gov (United States)

    Nelson, Kyle A.; Edwards, Nathaniel S.; Hinson, Niklas J.; Wayant, Clayton D.; McGregor, Douglas S.

    2014-12-01

    Three natural boron foils, approximately 1.0 cm in diameter and 1.0 μm thick, were obtained from The Lebow Company and suspended in a multi-wire proportional counter. Suspending the B foils allowed the alpha particle and Li ion reaction products to escape simultaneously, one on each side of the foil, and be measured concurrently in the gas volume. The thermal neutron response pulse-height spectrum was obtained and two obvious peaks appear from the 94% and 6% branches of the 10B(n,α)7Li neutron reaction. Scanning electron microscope images were collected to obtain the exact B foil thicknesses and MCNP6 simulations were completed for those same B thicknesses. Pulse-height spectra obtained from the simulations were compared to experimental data and matched well. The theoretical intrinsic thermal-neutron detection efficiency for enriched 10B foils was calculated and is presented. Additionally, the intrinsic thermal neutron detection efficiency of the three natural B foils was calculated to be 3.2±0.2%.

  16. Darboux transformations for (1+2)-dimensional Fokker-Planck equations with constant diffusion matrix

    International Nuclear Information System (INIS)

    Schulze-Halberg, Axel

    2012-01-01

    We construct a Darboux transformation for (1+2)-dimensional Fokker-Planck equations with constant diffusion matrix. Our transformation is based on the two-dimensional supersymmetry formalism for the Schrödinger equation. The transformed Fokker-Planck equation and its solutions are obtained in explicit form.

  17. 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

  18. Diffusion related isotopic fractionation effects with one-dimensional advective–dispersive transport

    Energy Technology Data Exchange (ETDEWEB)

    Xu, Bruce S. [Civil Engineering Department, University of Toronto, 35 St George Street, Toronto, ON M5S 1A4 (Canada); Lollar, Barbara Sherwood [Earth Sciences Department, University of Toronto, 22 Russell Street, Toronto, ON M5S 3B1 (Canada); Passeport, Elodie [Civil Engineering Department, University of Toronto, 35 St George Street, Toronto, ON M5S 1A4 (Canada); Chemical Engineering and Applied Chemistry Department, University of Toronto, 200 College Street, Toronto, ON M5S 3E5 (Canada); Sleep, Brent E., E-mail: sleep@ecf.utoronto.ca [Civil Engineering Department, University of Toronto, 35 St George Street, Toronto, ON M5S 1A4 (Canada)

    2016-04-15

    Aqueous phase diffusion-related isotope fractionation (DRIF) for carbon isotopes was investigated for common groundwater contaminants in systems in which transport could be considered to be one-dimensional. This paper focuses not only on theoretically observable DRIF effects in these systems but introduces the important concept of constraining “observable” DRIF based on constraints imposed by the scale of measurements in the field, and on standard limits of detection and analytical uncertainty. Specifically, constraints for the detection of DRIF were determined in terms of the diffusive fractionation factor, the initial concentration of contaminants (C{sub 0}), the method detection limit (MDL) for isotopic analysis, the transport time, and the ratio of the longitudinal mechanical dispersion coefficient to effective molecular diffusion coefficient (D{sub mech}/D{sub eff}). The results allow a determination of field conditions under which DRIF may be an important factor in the use of stable carbon isotope measurements for evaluation of contaminant transport and transformation for one-dimensional advective–dispersive transport. This study demonstrates that for diffusion-dominated transport of BTEX, MTBE, and chlorinated ethenes, DRIF effects are only detectable for the smaller molar mass compounds such as vinyl chloride for C{sub 0}/MDL ratios of 50 or higher. Much larger C{sub 0}/MDL ratios, corresponding to higher source concentrations or lower detection limits, are necessary for DRIF to be detectable for the higher molar mass compounds. The distance over which DRIF is observable for VC is small (less than 1 m) for a relatively young diffusive plume (< 100 years), and DRIF will not easily be detected by using the conventional sampling approach with “typical” well spacing (at least several meters). With contaminant transport by advection, mechanical dispersion, and molecular diffusion this study suggests that in field sites where D{sub mech}/D{sub eff} is

  19. Diffusion related isotopic fractionation effects with one-dimensional advective–dispersive transport

    International Nuclear Information System (INIS)

    Xu, Bruce S.; Lollar, Barbara Sherwood; Passeport, Elodie; Sleep, Brent E.

    2016-01-01

    Aqueous phase diffusion-related isotope fractionation (DRIF) for carbon isotopes was investigated for common groundwater contaminants in systems in which transport could be considered to be one-dimensional. This paper focuses not only on theoretically observable DRIF effects in these systems but introduces the important concept of constraining “observable” DRIF based on constraints imposed by the scale of measurements in the field, and on standard limits of detection and analytical uncertainty. Specifically, constraints for the detection of DRIF were determined in terms of the diffusive fractionation factor, the initial concentration of contaminants (C_0), the method detection limit (MDL) for isotopic analysis, the transport time, and the ratio of the longitudinal mechanical dispersion coefficient to effective molecular diffusion coefficient (D_m_e_c_h/D_e_f_f). The results allow a determination of field conditions under which DRIF may be an important factor in the use of stable carbon isotope measurements for evaluation of contaminant transport and transformation for one-dimensional advective–dispersive transport. This study demonstrates that for diffusion-dominated transport of BTEX, MTBE, and chlorinated ethenes, DRIF effects are only detectable for the smaller molar mass compounds such as vinyl chloride for C_0/MDL ratios of 50 or higher. Much larger C_0/MDL ratios, corresponding to higher source concentrations or lower detection limits, are necessary for DRIF to be detectable for the higher molar mass compounds. The distance over which DRIF is observable for VC is small (less than 1 m) for a relatively young diffusive plume (< 100 years), and DRIF will not easily be detected by using the conventional sampling approach with “typical” well spacing (at least several meters). With contaminant transport by advection, mechanical dispersion, and molecular diffusion this study suggests that in field sites where D_m_e_c_h/D_e_f_f is larger than 10, DRIF

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

    Energy Technology Data Exchange (ETDEWEB)

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

    1965-08-15

    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

  1. Fast multi-dimensional NMR by minimal sampling

    Science.gov (United States)

    Kupče, Ēriks; Freeman, Ray

    2008-03-01

    A new scheme is proposed for very fast acquisition of three-dimensional NMR spectra based on minimal sampling, instead of the customary step-wise exploration of all of evolution space. The method relies on prior experiments to determine accurate values for the evolving frequencies and intensities from the two-dimensional 'first planes' recorded by setting t1 = 0 or t2 = 0. With this prior knowledge, the entire three-dimensional spectrum can be reconstructed by an additional measurement of the response at a single location (t1∗,t2∗) where t1∗ and t2∗ are fixed values of the evolution times. A key feature is the ability to resolve problems of overlap in the acquisition dimension. Applied to a small protein, agitoxin, the three-dimensional HNCO spectrum is obtained 35 times faster than systematic Cartesian sampling of the evolution domain. The extension to multi-dimensional spectroscopy is outlined.

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

    International Nuclear Information System (INIS)

    Ozgener, B.

    1998-01-01

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

  3. Development of a two-dimensional imaging detector based on a neutron scintillator with wavelength-shifting fibers

    CERN Document Server

    Sakai, K; Oku, T; Morimoto, K; Shimizu, H M; Tokanai, F; Gorin, A; Manuilov, I V; Ryazantsev, A; Ino, T; Kuroda, K; Suzuki, J

    2002-01-01

    For evaluating neutron optical devices, a two-dimensional (2D) detector based on a neutron scintillator with wavelength-shifting fibers has been developed at RIKEN. We have investigated a ZnS(Ag)+LiF and a Li glass plate as neutron scintillators with the coding technique for realizing the large sensitive area of 50 x 50 mm sup 2. After fabricating the 2D detector, its performance was tested using cold neutrons at JAERI. As a result, a spatial resolution of propor to 1.0 mm was obtained. (orig.)

  4. Analytical representation of the solution of the space kinetic diffusion equation in a one-dimensional and homogeneous domain

    Energy Technology Data Exchange (ETDEWEB)

    Tumelero, Fernanda; Bodmann, Bardo E. J.; Vilhena, Marco T. [Universidade Federal do Rio Grande do Sul (PROMEC/UFRGS), Porto Alegre, RS (Brazil). Programa de Pos Graduacao em Engenharia Mecanica; Lapa, Celso M.F., E-mail: fernanda.tumelero@yahoo.com.br, E-mail: bardo.bodmann@ufrgs.br, E-mail: mtmbvilhena@gmail.com, E-mail: lapa@ien.gov.br [Instituto de Engenharia Nuclear (IEN/CNEN-RJ), Rio de Janeiro, RJ (Brazil)

    2017-07-01

    In this work we solve the space kinetic diffusion equation in a one-dimensional geometry considering a homogeneous domain, for two energy groups and six groups of delayed neutron precursors. The proposed methodology makes use of a Taylor expansion in the space variable of the scalar neutron flux (fast and thermal) and the concentration of delayed neutron precursors, allocating the time dependence to the coefficients. Upon truncating the Taylor series at quadratic order, one obtains a set of recursive systems of ordinary differential equations, where a modified decomposition method is applied. The coefficient matrix is split into two, one constant diagonal matrix and the second one with the remaining time dependent and off-diagonal terms. Moreover, the equation system is reorganized such that the terms containing the latter matrix are treated as source terms. Note, that the homogeneous equation system has a well known solution, since the matrix is diagonal and constant. This solution plays the role of the recursion initialization of the decomposition method. The recursion scheme is set up in a fashion where the solutions of the previous recursion steps determine the source terms of the subsequent steps. A second feature of the method is the choice of the initial and boundary conditions, which are satisfied by the recursion initialization, while from the rst recursion step onward the initial and boundary conditions are homogeneous. The recursion depth is then governed by a prescribed accuracy for the solution. (author)

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

    International Nuclear Information System (INIS)

    Mansur, Ralph S.; Barros, Ricardo C.

    2011-01-01

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

  6. Self-diffusion in monodisperse three-dimensional magnetic fluids by molecular dynamics simulations

    Energy Technology Data Exchange (ETDEWEB)

    Dobroserdova, A.B. [Ural Federal University, Lenin Av. 51, Ekaterinburg (Russian Federation); Kantorovich, S.S., E-mail: alla.dobroserdova@urfu.ru [Ural Federal University, Lenin Av. 51, Ekaterinburg (Russian Federation); University of Vienna, Sensengasse 8, Vienna (Austria)

    2017-06-01

    In the present work we study the self-diffusion behaviour in the three-dimensional monodisperse magnetic fluids using the Molecular Dynamics Simulation and Density Functional Theory. The peculiarity of computer simulation is to study two different systems: dipolar and soft sphere ones. In the theoretical method, it is important to choose the approximation for the main structures, which are chains. We compare the theoretical results and the computer simulation data for the self-diffusion coefficient as a function of the particle volume fraction and magnetic dipole-dipole interaction parameter and find the qualitative and quantitative agreement to be good. - Highlights: • The paper deals with the study of the self-diffusion in monodisperse three-dimensional magnetic fluids. • The theoretical approach contains the free energy density functional minimization. • Computer simulations are performed by the molecular dynamics method. • We have a good qualitative and quantitative agreement between the theoretical results and computer simulation data.

  7. EURATOM work on standard defects and dimensional measurements in neutron radiography of nuclear fuel elements

    International Nuclear Information System (INIS)

    Domanus, J.C.

    1981-10-01

    In 1979 a working group on neutron radiography was formed at Euratom. The purpose of this group is the standardization of neutron radiographic methods in the field of nuclear fuel. First priority was given to the development of image quality indicators and standard objects for the determination of accuracy of dimensional measurements from neutron radiographs. For that purpose beam purity and sensitivity indicators as well as a calibration fuel pin were designed and fabricated at Risoe. All the Euratom neutron radiography centers have recieved the above items for comparative neutron radiography. The measuring results obtained, using various measuring apparatus, will form the basis to formulate conclusions about the best measuring methods and instruments to be used in that field. (author)

  8. Code HEX-Z-DMG for support of accounting for and control of nuclear material software system as part of international safeguards system at BN-350 site

    International Nuclear Information System (INIS)

    Bushmakin, A.G.; Schaefer, B.

    1999-01-01

    A code for the computation of the global neutron distribution in the three-dimensional hexagonal-z geometry and multi-group diffusion approximation was developed at BN-350 as the main part of the BN-350 accounting for and control of nuclear material software system. This software system includes: the model for stationary distributions of neutrons; the model to calculate isotope compositions changing; the model of refueling operations; To develop this system next two principal problems were solved: to make a micro cross sections library for all nuclides for the BN-350 reactor core; to develop the code for the computation of the global neutron distribution. To solve first task the twenty-six-energy-groups micro cross sections library for more than seventy nuclides was produced. To solve second task the three-dimensional hexagonal-z geometry and multi-group diffusion approximation code was developed. This code (HEX-Z-DMG) was based on the solution of the multi groups diffusion equation using the standard net approach. The series of calculations was performed in the twenty-six-energy-groups representation using this code. We compared eigenvalues (k eff ), a worth added during refueling operations, spatial and energy-group-dependent neutron flux distributions with results of calculation using other code (DIF3D). After the series of these calculations we can say that the HEX-Z-DMG code is well established to use as the part of the BN-350 accounting for and control of nuclear material software system. (author)

  9. 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).

  10. TMCC: a transient three-dimensional neutron transport code by the direct simulation method - 222

    International Nuclear Information System (INIS)

    Shen, H.; Li, Z.; Wang, K.; Yu, G.

    2010-01-01

    A direct simulation method (DSM) is applied to solve the transient three-dimensional neutron transport problems. DSM is based on the Monte Carlo method, and can be considered as an application of the Monte Carlo method in the specific type of problems. In this work, the transient neutronics problem is solved by simulating the dynamic behaviors of neutrons and precursors of delayed neutrons during the transient process. DSM gets rid of various approximations which are always necessary to other methods, so it is precise and flexible in the requirement of geometric configurations, material compositions and energy spectrum. In this paper, the theory of DSM is introduced first, and the numerical results obtained with the new transient analysis code, named TMCC (Transient Monte Carlo Code), are presented. (authors)

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

    International Nuclear Information System (INIS)

    Correia Filho, A.

    1981-04-01

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

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

    Energy Technology Data Exchange (ETDEWEB)

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

    1964-07-01

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

  13. Computational modelling for diffusion of neutrons problems inside nuclear multiplying medium on bidimensional cartesian rectangular geometry; Modelagem computacional de problemas de difusao de neutrons em meios multiplicativos em geometria retangular cartesiana bi-dimensional

    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)

  14. Computational complexity in multidimensional neutron transport theory calculations. Progress report, September 1, 1974--August 31, 1975

    International Nuclear Information System (INIS)

    Bareiss, E.H.

    1975-01-01

    The objectives of the research remain the same as outlined in the original proposal. They are in short as follows: Develop mathematically and computationally founded criteria for the design of highly efficient and reliable multi-dimensional neutron transport codes to solve a variety of neutron migration and radiation problems and analyze existing and new methods for performance. (U.S.)

  15. Two-dimensional over-all neutronics analysis of the ITER device

    Science.gov (United States)

    Zimin, S.; Takatsu, Hideyuki; Mori, Seiji; Seki, Yasushi; Satoh, Satoshi; Tada, Eisuke; Maki, Koichi

    1993-07-01

    The present work attempts to carry out a comprehensive neutronics analysis of the International Thermonuclear Experimental Reactor (ITER) developed during the Conceptual Design Activities (CDA). The two-dimensional cylindrical over-all calculational models of ITER CDA device including the first wall, blanket, shield, vacuum vessel, magnets, cryostat and support structures were developed for this purpose with a help of the DOGII code. Two dimensional DOT 3.5 code with the FUSION-40 nuclear data library was employed for transport calculations of neutron and gamma ray fluxes, tritium breeding ratio (TBR), and nuclear heating in reactor components. The induced activity calculational code CINAC was employed for the calculations of exposure dose rate after reactor shutdown around the ITER CDA device. The two-dimensional over-all calculational model includes the design specifics such as the pebble bed Li2O/Be layered blanket, the thin double wall vacuum vessel, the concrete cryostat integrated with the over-all ITER design, the top maintenance shield plug, the additional ring biological shield placed under the top cryostat lid around the above-mentioned top maintenance shield plug etc. All the above-mentioned design specifics were included in the employed calculational models. Some alternative design options, such as the water-rich shielding blanket instead of lithium-bearing one, the additional biological shield plug at the top zone between the poloidal field (PF) coil No. 5, and the maintenance shield plug, were calculated as well. Much efforts have been focused on analyses of obtained results. These analyses aimed to obtain necessary recommendations on improving the ITER CDA design.

  16. Two-dimensional over-all neutronics analysis of the ITER device

    International Nuclear Information System (INIS)

    Zimin, S.; Takatsu, Hideyuki; Mori, Seiji; Seki, Yasushi; Satoh, Satoshi; Tada, Eisuke; Maki, Koichi.

    1993-07-01

    The present work attempts to carry out a comprehensive neutronics analysis of the International Thermonuclear Experimental Reactor (ITER) developed during the Conceptual Design Activities (CDA). The two-dimensional cylindrical over-all calculational models of ITER CDA device including the first wall, blanket, shield, vacuum vessel, magnets, cryostat and support structures were developed for this purpose with a help of the DOGII code. Two dimensional DOT 3.5 code with the FUSION-40 nuclear data library was employed for transport calculations of neutron and gamma ray fluxes, tritium breeding ratio (TBR) and nuclear heating in reactor components. The induced activity calculational code CINAC was employed for the calculations of exposure dose rate after reactor shutdown around the ITER CDA device. The two-dimensional over-all calculational model includes the design specifics such as the pebble bed Li 2 O/Be layered blanket, the thin double wall vacuum vessel, the concrete cryostat integrated with the over-all ITER design, the top maintenance shield plug, the additional ring biological shield placed under the top cryostat lid around the above-mentioned top maintenance shield plug etc. All the above-mentioned design specifics were included in the employed calculational models. Some alternative design options, such as the water-rich shielding blanket instead of lithium-bearing one, the additional biological shield plug at the top zone between the poloidal field (PF) coil No.5 and the maintenance shield plug, were calculated as well. Much efforts have been focused on analyses of obtained results. These analyses aimed to obtain necessary recommendations on improving the ITER CDA design. (author)

  17. Five-dimensional Lattice Gauge Theory as Multi-Layer World

    OpenAIRE

    Murata, Michika; So, Hiroto

    2003-01-01

    A five-dimensional lattice space can be decomposed into a number of four-dimens ional lattices called as layers. The five-dimensional gauge theory on the lattice can be interpreted as four-dimensional gauge theories on the multi-layer with interactions between neighboring layers. In the theory, there exist two independent coupling constants; $\\beta_4$ controls the dynamics inside a layer and $\\beta_5$ does the strength of the inter-layer interaction.We propose the new possibility to realize t...

  18. Multi-resolution and multi-scale simulation of the thermal hydraulics in fast neutron reactor assemblies

    International Nuclear Information System (INIS)

    Angeli, P.-E.

    2011-01-01

    The present work is devoted to a multi-scale numerical simulation of an assembly of fast neutron reactor. In spite of the rapid growth of the computer power, the fine complete CFD of a such system remains out of reach in a context of research and development. After the determination of the thermalhydraulic behaviour of the assembly at the macroscopic scale, we propose to carry out a local reconstruction of the fine scale information. The complete approach will require a much lower CPU time than the CFD of the entire structure. The macro-scale description is obtained using either the volume averaging formalism in porous media, or an alternative modeling historically developed for the study of fast neutron reactor assemblies. It provides some information used as constraint of a down-scaling problem, through a penalization technique of the local conservation equations. This problem lean on the periodic nature of the structure by integrating periodic boundary conditions for the required microscale fields or their spatial deviation. After validating the methodologies on some model applications, we undertake to perform them on 'industrial' configurations which demonstrate the viability of this multi-scale approach. (author) [fr

  19. Comparison of preconditioned generalized conjugate gradient methods to two-dimensional neutron and photon transport equation

    International Nuclear Information System (INIS)

    Chen, G.S.

    1997-01-01

    We apply and compare the preconditioned generalized conjugate gradient methods to solve the linear system equation that arises in the two-dimensional neutron and photon transport equation in this paper. Several subroutines are developed on the basis of preconditioned generalized conjugate gradient methods for time-independent, two-dimensional neutron and photon transport equation in the transport theory. These generalized conjugate gradient methods are used. TFQMR (transpose free quasi-minimal residual algorithm), CGS (conjuage gradient square algorithm), Bi-CGSTAB (bi-conjugate gradient stabilized algorithm) and QMRCGSTAB (quasi-minimal residual variant of bi-conjugate gradient stabilized algorithm). These sub-routines are connected to computer program DORT. Several problems are tested on a personal computer with Intel Pentium CPU. (author)

  20. Uncertainty Evaluation with Multi-Dimensional Model of LBLOCA in OPR1000 Plant

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Jieun; Oh, Deog Yeon; Seul, Kwang-Won; Lee, Jin Ho [Korea Institute of Nuclear Safety, Daejeon (Korea, Republic of)

    2016-10-15

    KINS has used KINS-REM (KINS-Realistic Evaluation Methodology) which developed for Best- Estimate (BE) calculation and uncertainty quantification for regulatory audit. This methodology has been improved continuously by numerous studies, such as uncertainty parameters and uncertainty ranges. In this study, to evaluate the applicability of improved KINS-REM for OPR1000 plant, uncertainty evaluation with multi-dimensional model for confirming multi-dimensional phenomena was conducted with MARS-KS code. In this study, the uncertainty evaluation with multi- dimensional model of OPR1000 plant was conducted for confirming the applicability of improved KINS- REM The reactor vessel modeled using MULTID component of MARS-KS code, and total 29 uncertainty parameters were considered by 124 sampled calculations. Through 124 calculations using Mosaique program with MARS-KS code, peak cladding temperature was calculated and final PCT was determined by the 3rd order Wilks' formula. The uncertainty parameters which has strong influence were investigated by Pearson coefficient analysis. They were mostly related with plant operation and fuel material properties. Evaluation results through the 124 calculations and sensitivity analysis show that improved KINS-REM could be reasonably applicable for uncertainty evaluation with multi-dimensional model calculations of OPR1000 plants.

  1. 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

  2. Multi-dimensional analysis of high resolution γ-ray data

    International Nuclear Information System (INIS)

    Flibotte, S.; Huttmeier, U.J.; France, G. de; Haas, B.; Romain, P.; Theisen, Ch.; Vivien, J.P.; Zen, J.; Bednarczyk, P.

    1992-01-01

    High resolution γ-ray multi-detectors capable of measuring high-fold coincidences with a large efficiency are presently under construction (EUROGAM, GASP, GAMMASPHERE). The future experimental progress in our understanding of nuclear structure at high spin critically depends on our ability to analyze the data in a multi-dimensional space and to resolve small photopeaks of interest from the generally large background. Development of programs to process such high-fold events is still in its infancy and only the 3-fold case has been treated so far. As a contribution to the software development associated with the EUROGAM spectrometer, we have written and tested the performances of computer codes designed to select multi-dimensional gates from 3-, 4- and 5-fold coincidence databases. The tests were performed on events generated with a Monte Carlo simulation and also on experimental data (triples) recorded with the 8π spectrometer and with a preliminary version of the EUROGAM array. (author). 7 refs., 3 tabs., 1 fig

  3. Multi-dimensional analysis of high resolution {gamma}-ray data

    Energy Technology Data Exchange (ETDEWEB)

    Flibotte, S; Huttmeier, U J; France, G de; Haas, B; Romain, P; Theisen, Ch; Vivien, J P; Zen, J [Centre National de la Recherche Scientifique (CNRS), 67 - Strasbourg (France); Bednarczyk, P [Institute of Nuclear Physics, Cracow (Poland)

    1992-08-01

    High resolution {gamma}-ray multi-detectors capable of measuring high-fold coincidences with a large efficiency are presently under construction (EUROGAM, GASP, GAMMASPHERE). The future experimental progress in our understanding of nuclear structure at high spin critically depends on our ability to analyze the data in a multi-dimensional space and to resolve small photopeaks of interest from the generally large background. Development of programs to process such high-fold events is still in its infancy and only the 3-fold case has been treated so far. As a contribution to the software development associated with the EUROGAM spectrometer, we have written and tested the performances of computer codes designed to select multi-dimensional gates from 3-, 4- and 5-fold coincidence databases. The tests were performed on events generated with a Monte Carlo simulation and also on experimental data (triples) recorded with the 8{pi} spectrometer and with a preliminary version of the EUROGAM array. (author). 7 refs., 3 tabs., 1 fig.

  4. Analyticity of event horizons of five-dimensional multi-black holes with nontrivial asymptotic structure

    International Nuclear Information System (INIS)

    Kimura, Masashi

    2008-01-01

    We show that there exist five-dimensional multi-black hole solutions which have analytic event horizons when the space-time has nontrivial asymptotic structure, unlike the case of five-dimensional multi-black hole solutions in asymptotically flat space-time.

  5. One-dimensional Turbulence Models of Type I X-ray Bursts

    Energy Technology Data Exchange (ETDEWEB)

    Hou, Chen [Univ. of Minnesota, Minneapolis, MN (United States)

    2016-01-06

    Type I X-ray bursts are caused by thermonuclear explosions occurring on the surface of an accreting neutron star in a binary star system. Observations and simulations of these phenomena are of great importance for understanding the fundamental properties of neutron stars and dense matter because the equation of state for cold dense matter can be constrained by the mass-radius relationship of neutron stars. During the bursts, turbulence plays a key role in mixing the fuels and driving the unstable nuclear burning process. This dissertation presents one-dimensional models of photospheric radius expansion bursts with a new approach to simulate turbulent advection. Compared with the traditional mixing length theory, the one-dimensional turbulence (ODT) model represents turbulent motions by a sequence of maps that are generated according to a stochastic process. The light curves I obtained with the ODT models are in good agreement with those of the KEPLER model in which the mixing length theory and various diffusive processes are applied. The abundance comparison, however, indicates that the differences in turbulent regions and turbulent diffusivities result in more 12C survival during the bursts in the ODT models, which can make a difference in the superbursts phenomena triggered by unstable carbon burning.

  6. One-dimensional Turbulence Models of Type I X-ray Bursts

    International Nuclear Information System (INIS)

    Hou, Chen

    2016-01-01

    Type I X-ray bursts are caused by thermonuclear explosions occurring on the surface of an accreting neutron star in a binary star system. Observations and simulations of these phenomena are of great importance for understanding the fundamental properties of neutron stars and dense matter because the equation of state for cold dense matter can be constrained by the mass-radius relationship of neutron stars. During the bursts, turbulence plays a key role in mixing the fuels and driving the unstable nuclear burning process. This dissertation presents one-dimensional models of photospheric radius expansion bursts with a new approach to simulate turbulent advection. Compared with the traditional mixing length theory, the one-dimensional turbulence (ODT) model represents turbulent motions by a sequence of maps that are generated according to a stochastic process. The light curves I obtained with the ODT models are in good agreement with those of the KEPLER model in which the mixing length theory and various diffusive processes are applied. The abundance comparison, however, indicates that the differences in turbulent regions and turbulent diffusivities result in more 12 C survival during the bursts in the ODT models, which can make a difference in the superbursts phenomena triggered by unstable carbon burning.

  7. An inverse problem for a one-dimensional time-fractional diffusion problem

    KAUST Repository

    Jin, Bangti; Rundell, William

    2012-01-01

    We study an inverse problem of recovering a spatially varying potential term in a one-dimensional time-fractional diffusion equation from the flux measurements taken at a single fixed time corresponding to a given set of input sources. The unique

  8. 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

  9. An Overview of Multi-Dimensional Models of the Sacramento–San Joaquin Delta

    Directory of Open Access Journals (Sweden)

    Michael L. MacWilliams

    2016-12-01

    Full Text Available doi: https://doi.org/10.15447/sfews.2016v14iss4art2Over the past 15 years, the development and application of multi-dimensional hydrodynamic models in San Francisco Bay and the Sacramento–San Joaquin Delta has transformed our ability to analyze and understand the underlying physics of the system. Initial applications of three-dimensional models focused primarily on salt intrusion, and provided a valuable resource for investigating how sea level rise and levee failures in the Delta could influence water quality in the Delta under future conditions. However, multi-dimensional models have also provided significant insights into some of the fundamental biological relationships that have shaped our thinking about the system by exploring the relationship among X2, flow, fish abundance, and the low salinity zone. Through the coupling of multi-dimensional models with wind wave and sediment transport models, it has been possible to move beyond salinity to understand how large-scale changes to the system are likely to affect sediment dynamics, and to assess the potential effects on species that rely on turbidity for habitat. Lastly, the coupling of multi-dimensional hydrodynamic models with particle tracking models has led to advances in our thinking about residence time, the retention of food organisms in the estuary, the effect of south Delta exports on larval entrainment, and the pathways and behaviors of salmonids that travel through the Delta. This paper provides an overview of these recent advances and how they have increased our understanding of the distribution and movement of fish and food organisms. The applications presented serve as a guide to the current state of the science of Delta modeling and provide examples of how we can use multi-dimensional models to predict how future Delta conditions will affect both fish and water supply.

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

    International Nuclear Information System (INIS)

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

    1995-01-01

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

  11. Skip-webs: Efficient distributed data structures for multi-dimensional data sets

    DEFF Research Database (Denmark)

    Arge, Lars; Eppstein, David; Goodrich, Michael T.

    2005-01-01

    querying scenarios, which include linear (one-dimensional) data, such as sorted sets, as well as multi-dimensional data, such as d-dimensional octrees and digital tries of character strings defined over a fixed alphabet. We show how to perform a query over such a set of n items spread among n hosts using O...

  12. Experiment on neutron transmission through depleted uranium layers and analysis with DOT 3.5 and MCNP

    International Nuclear Information System (INIS)

    Oka, Y.; Kodama, T.; Akiyama, M.; Hashikura, H.; Kondo, S.

    1987-01-01

    The reaction rates in the multi-layers containing depleted uranium were measured by activation foils and micro-fission chambers. The analysis of the experiment was carried out by using the multi-group transport calculation code, DOT 3.5 and the continuous energy Monte Carlo code, MCNP. The multi-group calculation overpredicted the low energy reaction rates in the DU layers, while the continuous energy calculation agreed well. The multi-group and continuous energy calculation was compared for the one-dimensional transmission of iron spheres. The results revealed overprediction of the multi-group calculation near the fast neutron source. The averaging of the resonance shapes in generating the multi-group cross sections made minima of the resonance valleys higher than that of the pointwise cross section. This increased the scattering of the neutrons inside and caused the overprediction of the multi-group calculation

  13. 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

  14. Solution and Study of the Two-Dimensional Nodal Neutron Transport Equation

    International Nuclear Information System (INIS)

    Panta Pazos, Ruben; Biasotto Hauser, Eliete; Tullio de Vilhena, Marco

    2002-01-01

    In the last decade Vilhena and coworkers reported an analytical solution to the two-dimensional nodal discrete-ordinates approximations of the neutron transport equation in a convex domain. The key feature of these works was the application of the combined collocation method of the angular variable and nodal approach in the spatial variables. By nodal approach we mean the transverse integration of the SN equations. This procedure leads to a set of one-dimensional S N equations for the average angular fluxes in the variables x and y. These equations were solved by the old version of the LTS N method, which consists in the application of the Laplace transform to the set of nodal S N equations and solution of the resulting linear system by symbolic computation. It is important to recall that this procedure allow us to increase N the order of S N up to 16. To overcome this drawback we step forward performing a spectral painstaking analysis of the nodal S N equations for N up to 16 and we begin the convergence of the S N nodal equations defining an error for the angular flux and estimating the error in terms of the truncation error of the quadrature approximations of the integral term. Furthermore, we compare numerical results of this approach with those of other techniques used to solve the two-dimensional discrete approximations of the neutron transport equation. (authors)

  15. Assessment of wall friction model in multi-dimensional component of MARS with air–water cross flow experiment

    Energy Technology Data Exchange (ETDEWEB)

    Yang, Jin-Hwa [Nuclear Thermal-Hydraulic Engineering Laboratory, Seoul National University, Gwanak 599, Gwanak-ro, Gwanak-gu, Seoul 151-742 (Korea, Republic of); Korea Atomic Energy Research Institute, 989-111, Daedeok-daero, Yuseong-gu, Daejeon 305-600 (Korea, Republic of); Choi, Chi-Jin [Nuclear Thermal-Hydraulic Engineering Laboratory, Seoul National University, Gwanak 599, Gwanak-ro, Gwanak-gu, Seoul 151-742 (Korea, Republic of); Cho, Hyoung-Kyu, E-mail: chohk@snu.ac.kr [Nuclear Thermal-Hydraulic Engineering Laboratory, Seoul National University, Gwanak 599, Gwanak-ro, Gwanak-gu, Seoul 151-742 (Korea, Republic of); Euh, Dong-Jin [Korea Atomic Energy Research Institute, 989-111, Daedeok-daero, Yuseong-gu, Daejeon 305-600 (Korea, Republic of); Park, Goon-Cherl [Nuclear Thermal-Hydraulic Engineering Laboratory, Seoul National University, Gwanak 599, Gwanak-ro, Gwanak-gu, Seoul 151-742 (Korea, Republic of)

    2017-02-15

    Recently, high precision and high accuracy analysis on multi-dimensional thermal hydraulic phenomena in a nuclear power plant has been considered as state-of-the-art issues. System analysis code, MARS, also adopted a multi-dimensional module to simulate them more accurately. Even though it was applied to represent the multi-dimensional phenomena, but implemented models and correlations in that are one-dimensional empirical ones based on one-dimensional pipe experimental results. Prior to the application of the multi-dimensional simulation tools, however, the constitutive models for a two-phase flow need to be carefully validated, such as the wall friction model. Especially, in a Direct Vessel Injection (DVI) system, the injected emergency core coolant (ECC) on the upper part of the downcomer interacts with the lateral steam flow during the reflood phase in the Large-Break Loss-Of-Coolant-Accident (LBLOCA). The interaction between the falling film and lateral steam flow induces a multi-dimensional two-phase flow. The prediction of ECC flow behavior plays a key role in determining the amount of coolant that can be used as core cooling. Therefore, the wall friction model which is implemented to simulate the multi-dimensional phenomena should be assessed by multidimensional experimental results. In this paper, the air–water cross film flow experiments simulating the multi-dimensional phenomenon in upper part of downcomer as a conceptual problem will be introduced. The two-dimensional local liquid film velocity and thickness data were used as benchmark data for code assessment. And then the previous wall friction model of the MARS-MultiD in the annular flow regime was modified. As a result, the modified MARS-MultiD produced improved calculation result than previous one.

  16. Three-dimensional neutron dose distribution in the environment around a 1-GeV electron synchrotron facility at INS

    International Nuclear Information System (INIS)

    Uwamino, Y.; Nakamura, T.

    1987-01-01

    The three-dimensional (surface and altitude) skyshine neutron-dose-equivalent distribution around the 1-GeV electron synchrotron (ES) of the Institute for Nuclear Study, University of Tokyo, was measured with a high-sensitivity dose-equivalent counter. The neutron spectrum in the environment was also measured with a multimoderator spectrometer incorporating a 3 He counter. The dose-equivalent distribution and the leakage neutron spectrum at the surface of the ES building were measured with a Studsvik 2202D counter and the multimoderator spectrometer, including an indium activation detector. Skyshine neutron transport calculations, beginning with the photoneutron spectrum and yielding the dose-equivalent distribution in the environment, were performed with the DOT3.5 code and two Monte Carlo codes, MMCR-2 and MMCR-3, using the DLC-87/HILO group cross sections. The calculated neutron spectra at the top surface of the concrete ceiling and at a point 111 m from the ES agreed well with the measured results, and the calculated three-dimensional dose-equivalent distribution also agreed. The dose value increased linearly with altitude, and the slope was estimated for neutron-producing facilities. (author)

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

    DEFF Research Database (Denmark)

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

    2012-01-01

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

  18. EURISOL-DS Multi-MW Target Neutronic Calculations for the Baseline Configuration of the Multi-MW Target

    CERN Document Server

    Herrera-Martínez, A

    2006-01-01

    This document summarises the study performed within the Task #2 of the European Isotope Separation On-Line Radioactive Ion Beam Facility Design Study (EURISOL DS) [1] to design the Multi-MW proton-to-neutron converter. A preliminary study [2] was carried out in order to understand the nature of the interactions taking place in the proton-to-neutron converter and their impact on the design of the facility. Namely, the target dimensions and material composition, type of incident particle, its energy and the beam profile were analysed in the aforementioned technical note, and their optimum values were suggested in the conclusions. The present work is based on the results of the previous study and uses the same methodology, namely Monte Carlo simulations with FLUKA [3]. This note describes the performance of a Hg target design and addresses more detailed issues, such as the composition of the fission target and use of a neutron reflector. It also attempts to integrate those components together and estimate the wh...

  19. Three-dimensional simulation of the electromagnetic ion/ion beam instability: cross field diffusion

    Directory of Open Access Journals (Sweden)

    H. Kucharek

    2000-01-01

    Full Text Available In a system with at least one ignorable spatial dimension charged particles moving in fluctuating fields are tied to the magnetic field lines. Thus, in one-and two-dimensional simulations cross-field diffusion is inhibited and important physics may be lost. We have investigated cross-field diffusion in self-consistent 3-D magnetic turbulence by fully 3-dimensional hybrid simulation (macro-particle ions, massless electron fluid. The turbulence is generated by the electromagnetic ion/ion beam instability. A cold, low density, ion beam with a high velocity stream relative to the background plasma excites the right-hand resonant instability. Such ion beams may be important in the region of the Earth's foreshock. The field turbulence scatters the beam ions parallel as well as perpendicular to the magnetic field. We have determined the parallel and perpendicular diffusion coefficient for the beam ions in the turbulent wave field. The result compares favourably well (within a factor 2 with hard-sphere scattering theory for the cross-field diffusion coefficient. The cross-field diffusion coefficient is larger than that obtained in a static field with a Kolmogorov type spectrum and similar total fluctuation power. This is attributed to the resonant behaviour of the particles in the fluctuating field.

  20. Optimisation of a collimator array for a multi-detector time-of-flight spectrometer for fast neutrons

    International Nuclear Information System (INIS)

    Schlegel-Bickmann, D.

    1979-01-01

    A Monte Carlo program has been developed which calculates the neutron background due to the interaction between incident neutrons and the collimator fan near the detector in dependence of geometry and material parameters. The position of the neutron source with regard to the collimators may be chosen at random. The program is also suitable for other three-dimensional transport problems of fast neutrons in the energy range between 0.5 and 20 MeV. The modular structure makes it easy to adapt it to highly specific problems. (orig.) 891 HP 892 MB [de

  1. 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

  2. Thermal hydraulic and neutronic interaction in the rotating bed reactor

    International Nuclear Information System (INIS)

    Lee, C.C.

    1986-01-01

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

  3. Neutronics methods for transient and safety analysis of fast reactors

    Energy Technology Data Exchange (ETDEWEB)

    Marchetti, Marco

    2017-07-01

    Modeling the evolution of possible or postulated accidents in nuclear reactors is fundamental in designing safe systems. For the next generation of reactors, in particular fast reactors, fuel movement during an accident can, in principle, drive an energetic event. Such is the issue of recriticality. The thermal energy produced during these events will, possibly, be converted into mechanical energy by some mechanisms. For example, the nuclear heat deposited in the fuel could cause fuel vaporization and its subsequent expansion. This movement would accelerate the surrounding sodium: part of the initial energy in the fuel is thus converted into sodium kinetic energy. This mechanical energy will finally be absorbed, in some way or another, by the reactor vessel. Providing an accurate estimate for the maximum mechanical work that any accidental sequence can do onto the reactor vessel is an essential step in designing a reactor containment that would withstand any load generated by any accident. That would assure accident containment, without consequences for the general public. Fast reactor accident modeling is a complicated task. The outcome of an accident is determined by different physical phenomena, all acting at almost the same time. Safety analysts must track all these different phenomena. Multi-physics codes have been developed for this task. They must contain accurate models for fluid-dynamics, neutronics, and structures. This work has to do with neutronics modeling of such accidents. Past and recent analyses have been limited to the approximate description of the neutronic field, for example by using a rough description of the energy and/or of the angular dependence of the neutron flux. In this work, different neutronic solvers are selected and coupled into a general multi-physics code for fast reactor accident analysis. Performances of each of them is then assessed. Some emphasis has been put also in assessing the speed of these solvers for determining the

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

    International Nuclear Information System (INIS)

    Herzig, C.

    1995-01-01

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

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

    Energy Technology Data Exchange (ETDEWEB)

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

    1963-01-15

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

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

    Energy Technology Data Exchange (ETDEWEB)

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

    1963-01-15

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

  7. Assessment of the TASS 1-D neutronics model for the westinghouse and ABB-CE type PWR reactivity induced transients

    International Nuclear Information System (INIS)

    Choi, J.D.; Yoon, H.Y.; Um, K.S.; Kim, H.C.; Sim, S.K.

    1997-01-01

    Best estimate transient analysis code, TASS, has been developed for the normal and transient simulation of the Westinghouse and ABB-CE type PWRs. TASS thermal hydraulic model is based on the non-homogeneous, non-equilibrium two-phase continuity, energy and mixture momentum equations with constitutive relations for closure. Core neutronics model employs both the point kinetics and one-dimensional neutron diffusion model. Semi-implicit numerical scheme is used to solve the discretized finite difference equations. TASS one dimensional neutronics core model has been assessed through the reactivity induced transient analyses for the KORI-3, three loop Westinghouse PWR, and Younggwang-3 (YGN-3), two-loop ABB-CE PWR, nuclear power plants currently operating in Korea. The assessment showed that the TASS one dimensional neutronics core model can be applied for the Westinghouse and ABB-CE type PWRs to gain thermal margin which is necessary for a potential use of the high fuel burnup, extended fuel cycle, power upgrading and for the plant life extension

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

    Energy Technology Data Exchange (ETDEWEB)

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

    1958-12-15

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

  9. Chemical ageing and transformation of diffusivity in semi-solid multi-component organic aerosol particles

    Science.gov (United States)

    Pfrang, C.; Shiraiwa, M.; Pöschl, U.

    2011-07-01

    Recent experimental evidence underlines the importance of reduced diffusivity in amorphous semi-solid or glassy atmospheric aerosols. This paper investigates the impact of diffusivity on the ageing of multi-component reactive organic particles approximating atmospheric cooking aerosols. We apply and extend the recently developed KM-SUB model in a study of a 12-component mixture containing oleic and palmitoleic acids. We demonstrate that changes in the diffusivity may explain the evolution of chemical loss rates in ageing semi-solid particles, and we resolve surface and bulk processes under transient reaction conditions considering diffusivities altered by oligomerisation. This new model treatment allows prediction of the ageing of mixed organic multi-component aerosols over atmospherically relevant timescales and conditions. We illustrate the impact of changing diffusivity on the chemical half-life of reactive components in semi-solid particles, and we demonstrate how solidification and crust formation at the particle surface can affect the chemical transformation of organic aerosols.

  10. Chemical ageing and transformation of diffusivity in semi-solid multi-component organic aerosol particles

    Directory of Open Access Journals (Sweden)

    C. Pfrang

    2011-07-01

    Full Text Available Recent experimental evidence underlines the importance of reduced diffusivity in amorphous semi-solid or glassy atmospheric aerosols. This paper investigates the impact of diffusivity on the ageing of multi-component reactive organic particles approximating atmospheric cooking aerosols. We apply and extend the recently developed KM-SUB model in a study of a 12-component mixture containing oleic and palmitoleic acids. We demonstrate that changes in the diffusivity may explain the evolution of chemical loss rates in ageing semi-solid particles, and we resolve surface and bulk processes under transient reaction conditions considering diffusivities altered by oligomerisation. This new model treatment allows prediction of the ageing of mixed organic multi-component aerosols over atmospherically relevant timescales and conditions. We illustrate the impact of changing diffusivity on the chemical half-life of reactive components in semi-solid particles, and we demonstrate how solidification and crust formation at the particle surface can affect the chemical transformation of organic aerosols.

  11. 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

  12. Fundamentals and applications of neutron diffraction. Applications 7. Crystal structure analysis of fuel cell materials by means of neutron diffractometry

    International Nuclear Information System (INIS)

    Itoh, Takanori

    2010-01-01

    Perovskite oxides, which have 'A' atoms of an alkaline earth metal and/or a rare earth metal and 'B' atoms of a transition metal, have considerable potential for use in electrochemical devices such as cathodes of solid oxide fuel cells (SOFC), oxygen pumps, oxygen sensors, catalysts, and other devices such as oxygen separation membranes. The oxygen ion behavior is studied with relation performance of electrochemical devices. I have analyzed the crystal structure of SOFC materials by neutron diffraction. Using the Rietveld refinement technique, I showed that the O1(4c) and O2(8d) sites in a perovskite oxide of SOFC cathode material has different oxygen site occupancies. Furthermore, oxygen diffusion behavior is associated with temperature dependence of oxygen anisotropic atomic displacement parameters. The maximum entropy method (MEM) analysis of neutron diffraction measurements revealed nuclear scattering length distribution at high temperature by three-dimensional images in detail, therefore 1 found oxygen diffusion pass and new proton site in SOFC materials. From these results, neutron diffraction is confirmed to be very useful tool for the study of light element behavior in fuel cell materials. (author)

  13. Application of finite Fourier transformation for the solution of the diffusion equation

    International Nuclear Information System (INIS)

    Kobayashi, Keisuke

    1991-01-01

    The application of the finite Fourier transformation to the solution of the neutron diffusion equation in one dimension, two dimensional x-y and triangular geometries is discussed. It can be shown that the equation obtained by the Nodal Green's function method in Cartesian coordinates can be derived as a special case of the finite Fourier transformation method. (author)

  14. Diffusive transport in a one dimensional disordered potential involving correlations

    International Nuclear Information System (INIS)

    Monthus, C.; Paris-6 Univ., 75

    1995-03-01

    Transport properties of one dimensional Brownian diffusion under the influence of a quenched random force, distributed as a two-level Poisson process is discussed. Large time scaling laws of the position of the Brownian particle, and the probability distribution of the stationary flux going through a sample between two prescribed concentrations are studied. (author) 14 refs.; 3 figs

  15. Meredys, a multi-compartment reaction-diffusion simulator using multistate realistic molecular complexes

    Directory of Open Access Journals (Sweden)

    Le Novère Nicolas

    2010-03-01

    Full Text Available Abstract Background Most cellular signal transduction mechanisms depend on a few molecular partners whose roles depend on their position and movement in relation to the input signal. This movement can follow various rules and take place in different compartments. Additionally, the molecules can form transient complexes. Complexation and signal transduction depend on the specific states partners and complexes adopt. Several spatial simulator have been developed to date, but none are able to model reaction-diffusion of realistic multi-state transient complexes. Results Meredys allows for the simulation of multi-component, multi-feature state molecular species in two and three dimensions. Several compartments can be defined with different diffusion and boundary properties. The software employs a Brownian dynamics engine to simulate reaction-diffusion systems at the reactive particle level, based on compartment properties, complex structure, and hydro-dynamic radii. Zeroth-, first-, and second order reactions are supported. The molecular complexes have realistic geometries. Reactive species can contain user-defined feature states which can modify reaction rates and outcome. Models are defined in a versatile NeuroML input file. The simulation volume can be split in subvolumes to speed up run-time. Conclusions Meredys provides a powerful and versatile way to run accurate simulations of molecular and sub-cellular systems, that complement existing multi-agent simulation systems. Meredys is a Free Software and the source code is available at http://meredys.sourceforge.net/.

  16. 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

  17. BASHAN: A few-group three-dimensional diffusion code with burnup and fuel management features

    International Nuclear Information System (INIS)

    Pearce, D.F.

    1970-12-01

    The diffusion equation for a two or three-dimensional, two-group or multi-group downscatter problem is solved by conventional finite difference techniques. An x-y-z geometry is assumed with an 'in-channel' mesh point representation. Options are available which allow representation of a soluble poison dispersed throughout the reactor, and also absorber rods in specified channels. The power distribution and multiplication factor k eff are calculated and a point rating map is used to advance the irradiation at each mesh point by a specified time-step so that burnup is followed. Fuel changes may be made so that radial shuffling and axial shuffling fuel management schemes can be studies. The code has been written in FORTRAN S2 for an IBM 7030 (STRETCH) computer which, with a fast store of 80,000 locations, allows problems of up to 15,000 mesh points to be dealt with. Conversion to FORTRAN IV for IBM 360 has now been completed. (author)

  18. MASTER-2.0: Multi-purpose analyzer for static and transient effects of reactors

    Energy Technology Data Exchange (ETDEWEB)

    Cho, Byung Oh; Song, Jae Seung; Joo, Han Gyu [Korea Atomic Energy Research Institute, Taejon (Korea)

    1999-01-01

    MASTER-2.0 (Multi-purpose Analyzer for Static and Transient Effects of Reactors) is a nuclear design code based on the two group diffusion theory to calculate the steady-state and transient pressurized water reactor core in a 3-dimensional Cartesian or hexagonal geometry. Its neutronics model solves the space-time dependent neutron diffusion equations with NIM(Nodal Integration Method), NEM (Nodal Expansion Method), AFEN (Analytic Function Expansion Nodal Method)/NEM Hybrid Method, NNEM (Non-linear Nodal Expansion Method) or NANM (Non-linear Analytic Nodal Method) for a Cartesian geometry and with AFEN/NEM Hybrid Method or NLFM (Non-linear Local Fine-Mesh Method) for a hexagonal one. Coarse mesh rebalancing, Krylov Subspace method and asymptotic extrapolation method are implemented to accelerate the convergence of iteration process. Master-2.0 performs microscopic depletion calculations using microscopic cross sections provided by CASMO-3 or HELIOS and also has the reconstruction capability of pin information by use of MSS-IAS (Method of Successive Smoothing with Improved Analytic Solution). For the thermal-hydraulic calculation, fuel temperature table or COBRA3-C/P model can be used selectively. In addition, MASTER-2.0 is designed to cover various PWRs including SMART as well as WH-and CE-type reactors, providing all data required in their design procedures. (author). 39 refs., 12 figs., 4 tabs.

  19. Deep-tissue temperature mapping by multi-illumination photoacoustic tomography aided by a diffusion optical model: a numerical study

    Science.gov (United States)

    Zhou, Yuan; Tang, Eric; Luo, Jianwen; Yao, Junjie

    2018-01-01

    Temperature mapping during thermotherapy can help precisely control the heating process, both temporally and spatially, to efficiently kill the tumor cells and prevent the healthy tissues from heating damage. Photoacoustic tomography (PAT) has been used for noninvasive temperature mapping with high sensitivity, based on the linear correlation between the tissue's Grüneisen parameter and temperature. However, limited by the tissue's unknown optical properties and thus the optical fluence at depths beyond the optical diffusion limit, the reported PAT thermometry usually takes a ratiometric measurement at different temperatures and thus cannot provide absolute measurements. Moreover, ratiometric measurement over time at different temperatures has to assume that the tissue's optical properties do not change with temperatures, which is usually not valid due to the temperature-induced hemodynamic changes. We propose an optical-diffusion-model-enhanced PAT temperature mapping that can obtain the absolute temperature distribution in deep tissue, without the need of multiple measurements at different temperatures. Based on the initial acoustic pressure reconstructed from multi-illumination photoacoustic signals, both the local optical fluence and the optical parameters including absorption and scattering coefficients are first estimated by the optical-diffusion model, then the temperature distribution is obtained from the reconstructed Grüneisen parameters. We have developed a mathematic model for the multi-illumination PAT of absolute temperatures, and our two-dimensional numerical simulations have shown the feasibility of this new method. The proposed absolute temperature mapping method may set the technical foundation for better temperature control in deep tissue in thermotherapy.

  20. 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)

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

    Energy Technology Data Exchange (ETDEWEB)

    Duerigen, Susan

    2013-05-15

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

  2. Multi-dimensional Code Development for Safety Analysis of LMR

    International Nuclear Information System (INIS)

    Ha, K. S.; Jeong, H. Y.; Kwon, Y. M.; Lee, Y. B.

    2006-08-01

    A liquid metal reactor loaded a metallic fuel has the inherent safety mechanism due to the several negative reactivity feedback. Although this feature demonstrated through experiments in the EBR-II, any of the computer programs until now did not exactly analyze it because of the complexity of the reactivity feedback mechanism. A multi-dimensional detail program was developed through the International Nuclear Energy Research Initiative(INERI) from 2003 to 2005. This report includes the numerical coupling the multi-dimensional program and SSC-K code which is used to the safety analysis of liquid metal reactors in KAERI. The coupled code has been proved by comparing the analysis results using the code with the results using SAS-SASSYS code of ANL for the UTOP, ULOF, and ULOHS applied to the safety analysis for KALIMER-150

  3. 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

  4. Application of neural network to multi-dimensional design window search in reactor core design

    International Nuclear Information System (INIS)

    Kugo, Teruhiko; Nakagawa, Masayuki

    1999-01-01

    In the reactor core design, many parametric survey calculations should be carried out to decide an optimal set of basic design parameter values. They consume a large amount of computation time and labor in the conventional way. To support design work, we investigate a procedure to search efficiently a design window, which is defined as feasible design parameter ranges satisfying design criteria and requirements, in a multi-dimensional space composed of several basic design parameters. The present method is applied to the neutronics and thermal hydraulics fields. The principle of the present method is to construct the multilayer neural network to simulate quickly a response of an analysis code through a training process, and to reduce computation time using the neural network without parametric study using analysis codes. To verify the applicability of the present method to the neutronics and the thermal hydraulics design, we have applied it to high conversion water reactors and examined effects of the structure of the neural network and the number of teaching patterns on the accuracy of the design window estimated by the neural network. From the results of the applications, a guideline to apply the present method is proposed and the present method can predict an appropriate design window in a reasonable computation time by following the guideline. (author)

  5. Neutron kinetics of fluid-fuel systems by the quasi-static method

    International Nuclear Information System (INIS)

    Dulla, S.; Ravetto, P.; Rostagno, M.M.

    2004-01-01

    The quasi-static method for the neutron kinetics of nuclear reactors is generalized for application to neutron multiplying systems fueled by a fluid multiplying material, typically a mixture of fissile molten salts. The method is derived by the application of factorization formulae for both the neutron density and the delayed precursor concentrations and the projection of the balance equations upon a weighting function. A physically meaningful weight can be assumed as the solution of the adjoint model, which is constructed for the situation considered, including delayed neutrons. The quasi-static scheme is then applied to calculations of some transients for a typical configuration of a molten-salt reactor, in a multigroup diffusion model with a one-dimensional slug-flow velocity field. The physical features associated to the motion of the fissile material are highlighted

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

    Science.gov (United States)

    You, Yan; Yoshida, Katsumi; Yano, Toyohiko

    2018-05-01

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

  7. Operative and scientific set-up to treat diffused and multi-focal metastases in the explanted liver. Preliminary indications from the first case

    International Nuclear Information System (INIS)

    Pinelli, T.; Altieri, S.; Bruschi, P.; Fossati, F.; Zonta, A.; Ferrari, C.; Prati, U.; Roveda, L.; Barni, S.; Chiari, P.; Nano, R.

    2002-01-01

    A new method has been developed for the therapy of human liver affected with multi-focal and diffused metastases. The therapeutic concept is based on the neutron irradiation of the explanted organ which, soon after such a treatment, is re-implanted according to the self-transplant procedure. Metastases are generally numerous and not completely detectable by the current diagnostic methodologies: so it is necessary to irradiate the whole organ in a thermal neutron field to treat all metastases and to minimize the recurrence probability. The irradiation position into the thermal column of the Triga Mark II reactor of University of Pavia was designed by means of neutron transport code MCNP. The neutron flux components in air at the irradiation position are shown. During the irradiation, to have a neutron flux inside the liver as flat as possible (in the longitudinal axis of the irradiation channel), we rotate the liver of an angle of 180 deg around the vertical axis. The irradiation of the liver is performed putting the organ inside a two teflon bags and than in another rigid teflon container equipped with two thermocouples to monitor the liver temperature. The first clinical trial consist in the treatment of a male 48 years old made on December 19th 2001. The self-graft procedure and the neutron therapy were performed at S. Matteo Polyclinic and inside the thermal column of Triga Mark II reactor of the University of Pavia respectively. The patient's liver contained more than 20 metastases following the removal of a colon-adenocarcinoma few months before. Six months after treatment all radiological and clinical checks indicated a positive and hopeful trend of the patient's condition

  8. Neutron energy spectra calculations in the low power research reactor

    International Nuclear Information System (INIS)

    Omar, H.; Khattab, K.; Ghazi, N.

    2011-01-01

    The neutron energy spectra have been calculated in the fuel region, inner and outer irradiation sites of the zero power research reactor using the MCNP-4C code and the combination of the WIMS-D/4 transport code for generation of group constants and the three-dimensional CITATION diffusion code for core analysis calculations. The neutron energy spectrum has been divided into three regions and compared with the proposed empirical correlations. The calculated thermal and fast neutron fluxes in the low power research reactor MNSR inner and outer irradiation sites have been compared with the measured results. Better agreements have been noticed between the calculated and measured results using the MCNP code than those obtained by the CITATION code. (author)

  9. 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.

  10. Two dimensional finite element modelling for dynamic water diffusion through stratum corneum.

    Science.gov (United States)

    Xiao, Perry; Imhof, Robert E

    2012-10-01

    Solvents penetration through in vivo human stratum corneum (SC) has always been an interesting research area for trans-dermal drug delivery studies, and the importance of intercellular routes (diffuse in between corneocytes) and transcellular routes (diffuse through corneocytes) during diffusion is often debatable. In this paper, we have developed a two dimensional finite element model to simulate the dynamic water diffusion through the SC. It is based on the brick-and-mortar model, with brick represents corneocytes and mortar represents lipids, respectively. It simulates the dynamic water diffusion process through the SC from pre-defined initial conditions and boundary conditions. Although the simulation is based on water diffusions, the principles can also be applied to the diffusions of other topical applied substances. The simulation results show that both intercellular routes and transcellular routes are important for water diffusion. Although intercellular routes have higher flux rates, most of the water still diffuse through transcellular routes because of the high cross area ratio of corneocytes and lipids. The diffusion water flux, or trans-epidermal water loss (TEWL), is reversely proportional to corneocyte size, i.e. the larger the corneocyte size, the lower the TEWL, and vice versa. There is also an effect of the SC thickness, external air conditions and diffusion coefficients on the water diffusion through SC on the resulting TEWL. Copyright © 2012 Elsevier B.V. All rights reserved.

  11. Extension of the GeN-Foam neutronic solver to SP3 analysis and application to the CROCUS experimental reactor

    International Nuclear Information System (INIS)

    Fiorina, Carlo; Hursin, Mathieu; Pautz, Andreas

    2017-01-01

    Highlights: • Development and verification of an SP 3 solver based on OpenFOAM. • Integration into the GeN-Foam multi-physics platform. • Application of the new GeN-Foam SP 3 solver to the CROCUS reactor. - Abstract: The Laboratory for Reactor Physics and Systems Behaviour at the PSI and at the EPFL has been developing since 2013 a multi-physics platform for coupled reactor analysis named GeN-Foam. The developed tool includes a solver for the eigenvalue and transient solution of multi-group neutron diffusion equations. Although frequently used in reactor analysis, the diffusion theory shows some limitations for core configurations involving strong anisotropies, which is the case for the CROCUS research reactor at the EPFL. The use of an SP 3 approximation to neutron transport can often lead to visible improvements in a code predictive capabilities, especially for one-directional anisotropies, with acceptable added computational cost vs diffusion. Following some modelling issues for the CROCUS reactor, and in order to improve the GeN-Foam modelling capabilities, the GeN-Foam diffusion solver has been extended to allow for SP 3 analyses. The present paper describes such extension and a preliminary verification using a mini-core PWR benchmark. The newly developed solver is then applied to the analysis of the CROCUS experimental reactor and results are compared to Monte Carlo calculations, as well as to the results of the diffusion solver.

  12. 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

  13. Nuclear borehole logging for oil exploration

    International Nuclear Information System (INIS)

    Oelgaard, P.L.

    1989-01-01

    Reactor physics can be applied to the logging of boreholes for the exploration of oil and gas and the results obtained can be interpreted more correctly by use of reactor physics models, e.g. one-dimensional multi-group diffusion theory adapted for gamma quanta. The standard nuclear logging tools are: natural gamma, gamma density, neutron porosity and the pulsed-neutron tool. The models and interpretation procedures are discussed. 1 fig

  14. 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)

  15. Solution of multigroup diffusion equations in cylindrical configuration by local polynomial approximation

    International Nuclear Information System (INIS)

    Jakab, J.

    1979-05-01

    Local approximations of neutron flux density by 2nd degree polynomials are used in calculating light water reactors. The calculations include spatial kinetics tasks for the models of two- and three-dimensional reactors in the Cartesian geometry. The resulting linear algebraic equations are considered to be formally identical to the results of the differential method of diffusion equation solution. (H.S.)

  16. 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.).

  17. 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.)

  18. Neutronic evolution of SENA reactor during the first and second cycles. Comparison between the experimental power distributions obtained from the in-core instrumentation evaluation code CIRCE and the theoretical power values computed with the two-dimensional diffusion-evolution code EVOE

    International Nuclear Information System (INIS)

    Andrieux, Chantal

    1976-03-01

    The neutronic evolution of the reacteur Sena during the first and second cycles is presented. The experimental power distributions, obtained from the in-core instrumentation evaluation code CIRCE are compared with the theoretical powers calculated with the two-dimensional diffusion-evolution code EVOE. The CIRCE code allows: the study of the evolution of the principal parameters of the core, the comparison of the results of measured and theoretical estimates. Therefore this study has a great interest for the knowledge of the neutronic evolution of the core, as well as the validation of the refinement of theoretical estimation methods. The core calculation methods and requisite data for the evaluation of the measurements are presented after a brief description of the SENA core and its inner instrumentation. The principle of the in-core instrumentation evaluation code CIRCE, and calculation of the experimental power distributions and nuclear core parameters are then exposed. The results of the evaluation are discussed, with a comparison of the theoretical and experimental results. Taking account of the approximations used, these results, as far as the first and second cycles at SENA are concerned, are satisfactory, the deviations between theoretical and experimental power distributions being lower than 3% at the middle of the reactor and 9% at the periphery [fr

  19. On multi-spectral quantitative photoacoustic tomography in diffusive regime

    International Nuclear Information System (INIS)

    Bal, Guillaume; Ren, Kui

    2012-01-01

    The objective of quantitative photoacoustic tomography (qPAT) is to reconstruct the diffusion, absorption and Grüneisen thermodynamic coefficients of heterogeneous media from knowledge of the interior absorbed radiation. It has been shown in Bal and Ren (2011 Inverse Problems 27 075003), based on diffusion theory, that with data acquired at one given wavelength, all three coefficients cannot be reconstructed uniquely. In this work, we study the multi-spectral qPAT problem and show that when multiple wavelength data are available, all coefficients can be reconstructed simultaneously under minor prior assumptions. Moreover, the reconstructions are shown to be very stable. We present some numerical simulations that support the theoretical results. (paper)

  20. Multi-Scale Factor Analysis of High-Dimensional Brain Signals

    KAUST Repository

    Ting, Chee-Ming; Ombao, Hernando; Salleh, Sh-Hussain

    2017-01-01

    In this paper, we develop an approach to modeling high-dimensional networks with a large number of nodes arranged in a hierarchical and modular structure. We propose a novel multi-scale factor analysis (MSFA) model which partitions the massive