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Sample records for discrete ordinates method

  1. Acceleration techniques for the discrete ordinate method

    International Nuclear Information System (INIS)

    Efremenko, Dmitry; Doicu, Adrian; Loyola, Diego; Trautmann, Thomas

    2013-01-01

    In this paper we analyze several acceleration techniques for the discrete ordinate method with matrix exponential and the small-angle modification of the radiative transfer equation. These techniques include the left eigenvectors matrix approach for computing the inverse of the right eigenvectors matrix, the telescoping technique, and the method of false discrete ordinate. The numerical simulations have shown that on average, the relative speedup of the left eigenvector matrix approach and the telescoping technique are of about 15% and 30%, respectively. -- Highlights: ► We presented the left eigenvector matrix approach. ► We analyzed the method of false discrete ordinate. ► The telescoping technique is applied for matrix operator method. ► Considered techniques accelerate the computations by 20% in average.

  2. SPANDOM - source projection analytic nodal discrete ordinates method

    International Nuclear Information System (INIS)

    Kim, Tae Hyeong; Cho, Nam Zin

    1994-01-01

    We describe a new discrete ordinates nodal method for the two-dimensional transport equation. We solve the discrete ordinates equation analytically after the source term is projected and represented in polynomials. The method is applied to two fast reactor benchmark problems and compared with the TWOHEX code. The results indicate that the present method accurately predicts not only multiplication factor but also flux distribution

  3. Multiband discrete ordinates method: formalism and results

    International Nuclear Information System (INIS)

    Luneville, L.

    1998-06-01

    The multigroup discrete ordinates method is a classical way to solve transport equation (Boltzmann) for neutral particles. Self-shielding effects are not correctly treated due to large variations of cross sections in a group (in the resonance range). To treat the resonance domain, the multiband method is introduced. The main idea is to divide the cross section domain into bands. We obtain the multiband parameters using the moment method; the code CALENDF provides probability tables for these parameters. We present our implementation in an existing discrete ordinates code: SN1D. We study deep penetration benchmarks and show the improvement of the method in the treatment of self-shielding effects. (author)

  4. Sputtering calculations with the discrete ordinated method

    International Nuclear Information System (INIS)

    Hoffman, T.J.; Dodds, H.L. Jr.; Robinson, M.T.; Holmes, D.K.

    1977-01-01

    The purpose of this work is to investigate the applicability of the discrete ordinates (S/sub N/) method to light ion sputtering problems. In particular, the neutral particle discrete ordinates computer code, ANISN, was used to calculate sputtering yields. No modifications to this code were necessary to treat charged particle transport. However, a cross section processing code was written for the generation of multigroup cross sections; these cross sections include a modification to the total macroscopic cross section to account for electronic interactions and small-scattering-angle elastic interactions. The discrete ordinates approach enables calculation of the sputtering yield as functions of incident energy and angle and of many related quantities such as ion reflection coefficients, angular and energy distributions of sputtering particles, the behavior of beams penetrating thin foils, etc. The results of several sputtering problems as calculated with ANISN are presented

  5. Discrete-ordinates finite-element method for atmospheric radiative transfer and remote sensing

    International Nuclear Information System (INIS)

    Gerstl, S.A.W.; Zardecki, A.

    1985-01-01

    Advantages and disadvantages of modern discrete-ordinates finite-element methods for the solution of radiative transfer problems in meteorology, climatology, and remote sensing applications are evaluated. After the common basis of the formulation of radiative transfer problems in the fields of neutron transport and atmospheric optics is established, the essential features of the discrete-ordinates finite-element method are described including the limitations of the method and their remedies. Numerical results are presented for 1-D and 2-D atmospheric radiative transfer problems where integral as well as angular dependent quantities are compared with published results from other calculations and with measured data. These comparisons provide a verification of the discrete-ordinates results for a wide spectrum of cases with varying degrees of absorption, scattering, and anisotropic phase functions. Accuracy and computational speed are also discussed. Since practically all discrete-ordinates codes offer a builtin adjoint capability, the general concept of the adjoint method is described and illustrated by sample problems. Our general conclusion is that the strengths of the discrete-ordinates finite-element method outweight its weaknesses. We demonstrate that existing general-purpose discrete-ordinates codes can provide a powerful tool to analyze radiative transfer problems through the atmosphere, especially when 2-D geometries must be considered

  6. Multiband discrete ordinates method: formalism and results; Methode multibande aux ordonnees discretes: formalisme et resultats

    Energy Technology Data Exchange (ETDEWEB)

    Luneville, L

    1998-06-01

    The multigroup discrete ordinates method is a classical way to solve transport equation (Boltzmann) for neutral particles. Self-shielding effects are not correctly treated due to large variations of cross sections in a group (in the resonance range). To treat the resonance domain, the multiband method is introduced. The main idea is to divide the cross section domain into bands. We obtain the multiband parameters using the moment method; the code CALENDF provides probability tables for these parameters. We present our implementation in an existing discrete ordinates code: SN1D. We study deep penetration benchmarks and show the improvement of the method in the treatment of self-shielding effects. (author) 15 refs.

  7. Evaluation of the streaming-matrix method for discrete-ordinates duct-streaming calculations

    International Nuclear Information System (INIS)

    Clark, B.A.; Urban, W.T.; Dudziak, D.J.

    1983-01-01

    A new deterministic streaming technique called the Streaming Matrix Hybrid Method (SMHM) is applied to two realistic duct-shielding problems. The results are compared to standard discrete-ordinates and Monte Carlo calculations. The SMHM shows promise as an alternative deterministic streaming method to standard discrete-ordinates

  8. Time dependence linear transport III convergence of the discrete ordinate method

    International Nuclear Information System (INIS)

    Wilson, D.G.

    1983-01-01

    In this paper the uniform pointwise convergence of the discrete ordinate method for weak and strong solutions of the time dependent, linear transport equation posed in a multidimensional, rectangular parallelepiped with partially reflecting walls is established. The first result is that a sequence of discrete ordinate solutions converges uniformly on the quadrature points to a solution of the continuous problem provided that the corresponding sequence of truncation errors for the solution of the continuous problem converges to zero in the same manner. The second result is that continuity of the solution with respect to the velocity variables guarantees that the truncation erros in the quadrature formula go the zero and hence that the discrete ordinate approximations converge to the solution of the continuous problem as the discrete ordinate become dense. An existence theory for strong solutions of the the continuous problem follows as a result

  9. Development of three-dimensional program based on Monte Carlo and discrete ordinates bidirectional coupling method

    International Nuclear Information System (INIS)

    Han Jingru; Chen Yixue; Yuan Longjun

    2013-01-01

    The Monte Carlo (MC) and discrete ordinates (SN) are the commonly used methods in the design of radiation shielding. Monte Carlo method is able to treat the geometry exactly, but time-consuming in dealing with the deep penetration problem. The discrete ordinate method has great computational efficiency, but it is quite costly in computer memory and it suffers from ray effect. Single discrete ordinates method or single Monte Carlo method has limitation in shielding calculation for large complex nuclear facilities. In order to solve the problem, the Monte Carlo and discrete ordinates bidirectional coupling method is developed. The bidirectional coupling method is implemented in the interface program to transfer the particle probability distribution of MC and angular flux of discrete ordinates. The coupling method combines the advantages of MC and SN. The test problems of cartesian and cylindrical coordinate have been calculated by the coupling methods. The calculation results are performed with comparison to MCNP and TORT and satisfactory agreements are obtained. The correctness of the program is proved. (authors)

  10. A variational synthesis nodal discrete ordinates method

    International Nuclear Information System (INIS)

    Favorite, J.A.; Stacey, W.M.

    1999-01-01

    A self-consistent nodal approximation method for computing discrete ordinates neutron flux distributions has been developed from a variational functional for neutron transport theory. The advantage of the new nodal method formulation is that it is self-consistent in its definition of the homogenized nodal parameters, the construction of the global nodal equations, and the reconstruction of the detailed flux distribution. The efficacy of the method is demonstrated by two-dimensional test problems

  11. Recent developments in discrete ordinates electron transport

    International Nuclear Information System (INIS)

    Morel, J.E.; Lorence, L.J. Jr.

    1986-01-01

    The discrete ordinates method is a deterministic method for numerically solving the Boltzmann equation. It was originally developed for neutron transport calculations, but is routinely used for photon and coupled neutron-photon transport calculations as well. The computational state of the art for coupled electron-photon transport (CEPT) calculations is not as developed as that for neutron transport calculations. The only production codes currently available for CEPT calculations are condensed-history Monte Carlo codes such as the ETRAN and ITS codes. A deterministic capability for production calculations is clearly needed. In response to this need, we have begun the development of a production discrete ordinates code for CEPT calculations. The purpose of this paper is to describe the basic approach we are taking, discuss the current status of the project, and present some new computational results. Although further characterization of the coupled electron-photon discrete ordinates method remains to be done, the results to date indicate that the discrete ordinates method can be just as accurate and from 10 to 100 times faster than the Monte Carlo method for a wide variety of problems. We stress that these results are obtained with standard discrete ordinates codes such as ONETRAN. It is clear that even greater efficiency can be obtained by developing a new generation of production discrete ordinates codes specifically designed to solve the Boltzmann-Fokker-Planck equation. However, the prospects for such development in the near future appear to be remote

  12. The discrete ordinates method for solving the azimuthally dependent transport equation in plane geometry

    International Nuclear Information System (INIS)

    Chalhoub, Ezzat Selim

    1997-01-01

    The method of discrete ordinates is applied to the solution of the slab albedo problem with azimuthal dependence in transport theory. A new set of quadratures appropriate to the problem is introduced. In addition to the ANISN code, modified to include the proposed formalism, two new programs, PEESNC and PEESNA, which were created on the basis of the discrete ordinates formalism, using the direct integration method and the analytic solution method respectively, are used in the generation of results for a few sample problems. Program PEESNC was created to validate the results obtained with the discrete ordinates method and the finite difference approximation (ANISN), while program PEESNA was developed in order to implement an analytical discrete ordinates formalism, which provides more accurate results. The obtained results for selected sample problems are compared with highly accurate numerical results published in the literature. Compared to ANISN and PEESNC, program PEESNA presents a greater efficiency in execution time and much more precise numerical results. (author)

  13. Discrete Ordinates Method-Like Computation with Group Condensation and Angle Collapsing in Transport Theory

    International Nuclear Information System (INIS)

    Won, Jong Hyuck; Cho, Nam Zin

    2010-01-01

    In group condensation for transport method, it is well-known that angle-dependent total cross section is generated. To remove this difficulty on angledependent total cross section, we normally perform the group condensation on total cross section by using scalar flux weight as used in neutron diffusion method. In this study, angle-dependent total cross section is directly applied to the discrete ordinates method. In addition, angle collapsing concept is introduced based on equivalence to reduce calculational burden of transport computation. We also show numerical results for a heterogeneous 1-D slab problem with local/global iteration, in which fine-group discrete ordinates calculation is used in local problem while few-group angle collapsed discrete ordinates calculation is used in global problem iteratively

  14. Deterministic absorbed dose estimation in computed tomography using a discrete ordinates method

    International Nuclear Information System (INIS)

    Norris, Edward T.; Liu, Xin; Hsieh, Jiang

    2015-01-01

    Purpose: Organ dose estimation for a patient undergoing computed tomography (CT) scanning is very important. Although Monte Carlo methods are considered gold-standard in patient dose estimation, the computation time required is formidable for routine clinical calculations. Here, the authors instigate a deterministic method for estimating an absorbed dose more efficiently. Methods: Compared with current Monte Carlo methods, a more efficient approach to estimating the absorbed dose is to solve the linear Boltzmann equation numerically. In this study, an axial CT scan was modeled with a software package, Denovo, which solved the linear Boltzmann equation using the discrete ordinates method. The CT scanning configuration included 16 x-ray source positions, beam collimators, flat filters, and bowtie filters. The phantom was the standard 32 cm CT dose index (CTDI) phantom. Four different Denovo simulations were performed with different simulation parameters, including the number of quadrature sets and the order of Legendre polynomial expansions. A Monte Carlo simulation was also performed for benchmarking the Denovo simulations. A quantitative comparison was made of the simulation results obtained by the Denovo and the Monte Carlo methods. Results: The difference in the simulation results of the discrete ordinates method and those of the Monte Carlo methods was found to be small, with a root-mean-square difference of around 2.4%. It was found that the discrete ordinates method, with a higher order of Legendre polynomial expansions, underestimated the absorbed dose near the center of the phantom (i.e., low dose region). Simulations of the quadrature set 8 and the first order of the Legendre polynomial expansions proved to be the most efficient computation method in the authors’ study. The single-thread computation time of the deterministic simulation of the quadrature set 8 and the first order of the Legendre polynomial expansions was 21 min on a personal computer

  15. Diffusion-synthetic acceleration methods for discrete-ordinates problems

    International Nuclear Information System (INIS)

    Larsen, E.W.

    1984-01-01

    The diffusion-synthetic acceleration (DSA) method is an iterative procedure for obtaining numerical solutions of discrete-ordinates problems. The DSA method is operationally more complicated than the standard source-iteration (SI) method, but if encoded properly it converges much more rapidly, especially for problems with diffusion-like regions. In this article we describe the basic ideas behind the DSA method and give a (roughly chronological) review of its long development. We conclude with a discussion which covers additional topics, including some remaining open problems an the status of current efforts aimed at solving these problems

  16. Variable discrete ordinates method for radiation transfer in plane-parallel semi-transparent media with variable refractive index

    Science.gov (United States)

    Sarvari, S. M. Hosseini

    2017-09-01

    The traditional form of discrete ordinates method is applied to solve the radiative transfer equation in plane-parallel semi-transparent media with variable refractive index through using the variable discrete ordinate directions and the concept of refracted radiative intensity. The refractive index are taken as constant in each control volume, such that the direction cosines of radiative rays remain non-variant through each control volume, and then, the directions of discrete ordinates are changed locally by passing each control volume, according to the Snell's law of refraction. The results are compared by the previous studies in this field. Despite simplicity, the results show that the variable discrete ordinate method has a good accuracy in solving the radiative transfer equation in the semi-transparent media with arbitrary distribution of refractive index.

  17. Diffusion-synthetic acceleration methods for the discrete-ordinates equations

    International Nuclear Information System (INIS)

    Larsen, E.W.

    1983-01-01

    The diffusion-synthetic acceleration (DSA) method is an iterative procedure for obtaining numerical solutions of discrete-ordinates problems. The DSA method is operationally more complicated than the standard source-iteration (SI) method, but if encoded properly it converges much more rapidly, especially for problems with diffusion-like regions. In this article we describe the basic ideas beind the DSA method and give a (roughly chronological) review of its long development. We conclude with a discussion which covers additional topics, including some remaining open problems and the status of current efforts aimed at solving these problems

  18. Multidimensional electron-photon transport with standard discrete ordinates codes

    International Nuclear Information System (INIS)

    Drumm, C.R.

    1995-01-01

    A method is described for generating electron cross sections that are compatible with standard discrete ordinates codes without modification. There are many advantages of using an established discrete ordinates solver, e.g. immediately available adjoint capability. Coupled electron-photon transport capability is needed for many applications, including the modeling of the response of electronics components to space and man-made radiation environments. The cross sections have been successfully used in the DORT, TWODANT and TORT discrete ordinates codes. The cross sections are shown to provide accurate and efficient solutions to certain multidimensional electronphoton transport problems

  19. The discrete ordinate method in association with the finite-volume method in non-structured mesh; Methode des ordonnees discretes associee a la methode des volumes finis en maillage non structure

    Energy Technology Data Exchange (ETDEWEB)

    Le Dez, V; Lallemand, M [Ecole Nationale Superieure de Mecanique et d` Aerotechnique (ENSMA), 86 - Poitiers (France); Sakami, M; Charette, A [Quebec Univ., Chicoutimi, PQ (Canada). Dept. des Sciences Appliquees

    1997-12-31

    The description of an efficient method of radiant heat transfer field determination in a grey semi-transparent environment included in a 2-D polygonal cavity with surface boundaries that reflect the radiation in a purely diffusive manner is proposed, at the equilibrium and in radiation-conduction coupling situation. The technique uses simultaneously the finite-volume method in non-structured triangular mesh, the discrete ordinate method and the ray shooting method. The main mathematical developments and comparative results with the discrete ordinate method in orthogonal curvilinear coordinates are included. (J.S.) 10 refs.

  20. The discrete ordinate method in association with the finite-volume method in non-structured mesh; Methode des ordonnees discretes associee a la methode des volumes finis en maillage non structure

    Energy Technology Data Exchange (ETDEWEB)

    Le Dez, V.; Lallemand, M. [Ecole Nationale Superieure de Mecanique et d`Aerotechnique (ENSMA), 86 - Poitiers (France); Sakami, M.; Charette, A. [Quebec Univ., Chicoutimi, PQ (Canada). Dept. des Sciences Appliquees

    1996-12-31

    The description of an efficient method of radiant heat transfer field determination in a grey semi-transparent environment included in a 2-D polygonal cavity with surface boundaries that reflect the radiation in a purely diffusive manner is proposed, at the equilibrium and in radiation-conduction coupling situation. The technique uses simultaneously the finite-volume method in non-structured triangular mesh, the discrete ordinate method and the ray shooting method. The main mathematical developments and comparative results with the discrete ordinate method in orthogonal curvilinear coordinates are included. (J.S.) 10 refs.

  1. Particular solution of the discrete-ordinate method.

    Science.gov (United States)

    Qin, Yi; Box, Michael A; Jupp, David L

    2004-06-20

    We present two methods that can be used to derive the particular solution of the discrete-ordinate method (DOM) for an arbitrary source in a plane-parallel atmosphere, which allows us to solve the transfer equation 12-18% faster in the case of a single beam source and is even faster for the atmosphere thermal emission source. We also remove the divide by zero problem that occurs when a beam source coincides with a Gaussian quadrature point. In our implementation, solution for multiple sources can be obtained simultaneously. For each extra source, it costs only 1.3-3.6% CPU time required for a full solution. The GDOM code that we developed previously has been revised to integrate with the DOM. Therefore we are now able to compute the Green's function and DOM solutions simultaneously.

  2. On the convergence of multigroup discrete-ordinates approximations

    International Nuclear Information System (INIS)

    Victory, H.D. Jr.; Allen, E.J.; Ganguly, K.

    1987-01-01

    Our analysis is divided into two distinct parts which we label for convenience as Part A and Part B. In Part A, we demonstrate that the multigroup discrete-ordinates approximations are well-defined and converge to the exact transport solution in any subcritical setting. For the most part, we focus on transport in two-dimensional Cartesian geometry. A Nystroem technique is used to extend the discrete ordinates multigroup approximates to all values of the angular and energy variables. Such an extension enables us to employ collectively compact operator theory to deduce stability and convergence of the approximates. In Part B, we perform a thorough convergence analysis for the multigroup discrete-ordinates method for an anisotropically-scattering subcritical medium in slab geometry. The diamond-difference and step-characteristic spatial approximation methods are each studied. The multigroup neutron fluxes are shown to converge in a Banach space setting under realistic smoothness conditions on the solution. This is the first thorough convergence analysis for the fully-discretized multigroup neutron transport equations

  3. Development and application of the discrete ordinate method in orthogonal curvilinear coordinates; Developpement et application de la methode des ordonnees discretes en coordonnees curvilignes orthogonales

    Energy Technology Data Exchange (ETDEWEB)

    Vaillon, R; Lallemand, M; Lemonnier, D [Ecole Nationale Superieure de Mecanique et d` Aerotechnique (ENSMA), 86 - Poitiers (France)

    1997-12-31

    The method of discrete ordinates, which is more and more widely used in radiant heat transfer studies, is mainly developed in Cartesian, (r,z) and (r,{Theta}) cylindrical, and spherical coordinates. In this study, the approach of this method is performed in orthogonal curvilinear coordinates: determination of the radiant heat transfer equation, treatment of the angular redistribution terms, numerical procedure. Some examples of application are described in 2-D geometry defined in curvilinear coordinates along a curve and at the thermal equilibrium. A comparison is made with the discrete ordinates method in association with the finite-volumes method in non structured mesh. (J.S.) 27 refs.

  4. Development and application of the discrete ordinate method in orthogonal curvilinear coordinates; Developpement et application de la methode des ordonnees discretes en coordonnees curvilignes orthogonales

    Energy Technology Data Exchange (ETDEWEB)

    Vaillon, R.; Lallemand, M.; Lemonnier, D. [Ecole Nationale Superieure de Mecanique et d`Aerotechnique (ENSMA), 86 - Poitiers (France)

    1996-12-31

    The method of discrete ordinates, which is more and more widely used in radiant heat transfer studies, is mainly developed in Cartesian, (r,z) and (r,{Theta}) cylindrical, and spherical coordinates. In this study, the approach of this method is performed in orthogonal curvilinear coordinates: determination of the radiant heat transfer equation, treatment of the angular redistribution terms, numerical procedure. Some examples of application are described in 2-D geometry defined in curvilinear coordinates along a curve and at the thermal equilibrium. A comparison is made with the discrete ordinates method in association with the finite-volumes method in non structured mesh. (J.S.) 27 refs.

  5. Simplified discrete ordinates method in spherical geometry

    International Nuclear Information System (INIS)

    Elsawi, M.A.; Abdurrahman, N.M.; Yavuz, M.

    1999-01-01

    The authors extend the method of simplified discrete ordinates (SS N ) to spherical geometry. The motivation for such an extension is that the appearance of the angular derivative (redistribution) term in the spherical geometry transport equation makes it difficult to decide which differencing scheme best approximates this term. In the present method, the angular derivative term is treated implicitly and thus avoids the need for the approximation of such term. This method can be considered to be analytic in nature with the advantage of being free from spatial truncation errors from which most of the existing transport codes suffer. In addition, it treats the angular redistribution term implicitly with the advantage of avoiding approximations to that term. The method also can handle scattering in a very general manner with the advantage of spending almost the same computational effort for all scattering modes. Moreover, the methods can easily be applied to higher-order S N calculations

  6. A linear multiple balance method for discrete ordinates neutron transport equations

    International Nuclear Information System (INIS)

    Park, Chang Je; Cho, Nam Zin

    2000-01-01

    A linear multiple balance method (LMB) is developed to provide more accurate and positive solutions for the discrete ordinates neutron transport equations. In this multiple balance approach, one mesh cell is divided into two subcells with quadratic approximation of angular flux distribution. Four multiple balance equations are used to relate center angular flux with average angular flux by Simpson's rule. From the analysis of spatial truncation error, the accuracy of the linear multiple balance scheme is ο(Δ 4 ) whereas that of diamond differencing is ο(Δ 2 ). To accelerate the linear multiple balance method, we also describe a simplified additive angular dependent rebalance factor scheme which combines a modified boundary projection acceleration scheme and the angular dependent rebalance factor acceleration schme. It is demonstrated, via fourier analysis of a simple model problem as well as numerical calculations, that the additive angular dependent rebalance factor acceleration scheme is unconditionally stable with spectral radius < 0.2069c (c being the scattering ration). The numerical results tested so far on slab-geometry discrete ordinates transport problems show that the solution method of linear multiple balance is effective and sufficiently efficient

  7. The ADO-nodal method for solving two-dimensional discrete ordinates transport problems

    International Nuclear Information System (INIS)

    Barichello, L.B.; Picoloto, C.B.; Cunha, R.D. da

    2017-01-01

    Highlights: • Two-dimensional discrete ordinates neutron transport. • Analytical Discrete Ordinates (ADO) nodal method. • Heterogeneous media fixed source problems. • Local solutions. - Abstract: In this work, recent results on the solution of fixed-source two-dimensional transport problems, in Cartesian geometry, are reported. Homogeneous and heterogeneous media problems are considered in order to incorporate the idea of arbitrary number of domain division into regions (nodes) when applying the ADO method, which is a method of analytical features, to those problems. The ADO-nodal formulation is developed, for each node, following previous work devoted to heterogeneous media problem. Here, however, the numerical procedure is extended to higher number of domain divisions. Such extension leads, in some cases, to the use of an iterative method for solving the general linear system which defines the arbitrary constants of the general solution. In addition to solve alternative heterogeneous media configurations than reported in previous works, the present approach allows comparisons with results provided by other metodologies generated with refined meshes. Numerical results indicate the ADO solution may achieve a prescribed accuracy using coarser meshes than other schemes.

  8. Multidimensional electron-photon transport with standard discrete ordinates codes

    International Nuclear Information System (INIS)

    Drumm, C.R.

    1997-01-01

    A method is described for generating electron cross sections that are comparable with standard discrete ordinates codes without modification. There are many advantages of using an established discrete ordinates solver, e.g. immediately available adjoint capability. Coupled electron-photon transport capability is needed for many applications, including the modeling of the response of electronics components to space and man-made radiation environments. The cross sections have been successfully used in the DORT, TWODANT and TORT discrete ordinates codes. The cross sections are shown to provide accurate and efficient solutions to certain multidimensional electron-photon transport problems. The key to the method is a simultaneous solution of the continuous-slowing-down (CSD) portion and elastic-scattering portion of the scattering source by the Goudsmit-Saunderson theory. The resulting multigroup-Legendre cross sections are much smaller than the true scattering cross sections that they represent. Under certain conditions, the cross sections are guaranteed positive and converge with a low-order Legendre expansion

  9. Multidimensional electron-photon transport with standard discrete ordinates codes

    International Nuclear Information System (INIS)

    Drumm, C.R.

    1997-01-01

    A method is described for generating electron cross sections that are compatible with standard discrete ordinates codes without modification. There are many advantages to using an established discrete ordinates solver, e.g., immediately available adjoint capability. Coupled electron-photon transport capability is needed for many applications, including the modeling of the response of electronics components to space and synthetic radiation environments. The cross sections have been successfully used in the DORT, TWODANT, and TORT discrete ordinates codes. The cross sections are shown to provide accurate and efficient solutions to certain multidimensional electron-photon transport problems. The key to the method is a simultaneous solution of the continuous-slowing-down and elastic-scattering portions of the scattering source by the Goudsmit-Saunderson theory. The resulting multigroup-Legendre cross sections are much smaller than the true scattering cross sections that they represent. Under certain conditions, the cross sections are guaranteed positive and converge with a low-order Legendre expansion

  10. On the equivalence between the discrete ordinates and the spherical harmonics methods in radiative transfer

    International Nuclear Information System (INIS)

    Barichello, L.B.; Siewert, C.E.

    1998-01-01

    In this work concerning steady-state radiative-transfer calculations in plane-parallel media, the equivalence between the discrete ordinates method and the spherical harmonics method is proved. More specifically, it is shown that for standard radiative-transfer problems without the imposed restriction of azimuthal symmetry the two methods yield identical results for the radiation intensity when the quadrature scheme for the discrete ordinates method is defined by the zeros of the associated Legendre functions and when generalized Mark boundary conditions are used to define the spherical harmonics solution. It is also shown that, with these choices for a quadrature scheme and for the boundary conditions, the two methods can be formulated so as to require the same computational effort. Finally a justification for using the generalized Mark boundary conditions in the spherical harmonics solution is given

  11. Energy-pointwise discrete ordinates transport methods

    International Nuclear Information System (INIS)

    Williams, M.L.; Asgari, M.; Tashakorri, R.

    1997-01-01

    A very brief description is given of a one-dimensional code, CENTRM, which computes a detailed, space-dependent flux spectrum in a pointwise-energy representation within the resolved resonance range. The code will become a component in the SCALE system to improve computation of self-shielded cross sections, thereby enhancing the accuracy of codes such as KENO. CENTRM uses discrete-ordinates transport theory with an arbitrary angular quadrature order and a Legendre expansion of scattering anisotropy for moderator materials and heavy nuclides. The CENTRM program provides capability to deterministically compute full energy range, space-dependent angular flux spectra, rigorously accounting for resonance fine-structure and scattering anisotropy effects

  12. Use of the Streaming Matrix Hybrid Method for discrete-ordinates fusion reactor calculations

    International Nuclear Information System (INIS)

    Battat, M.E.; Davidson, J.W.; Dudziak, D.J.; Thayer, G.R.

    1984-01-01

    The use of the discrete-ordinates method for solving two-dimensional, neutral-particle transport in fusion reactor blankets and shields is often limited by inherent inaccuracies due to the ray-effect. This effect presents a particular problem in the case of neutron streaming in the large internal void regions of a fusion reactor. A deterministic streaming technique called the Streaming Matrix Hybrid Method (SMHM) has been incorporated in the two-dimensional discrete-ordinates code TRIDENT-CTR. Calculations have been performed for an actual inertial-confinement fusion (ICF) reactor design using TRIDENT-CTR both with and without the SMHM. Comparisons of the calculated fluxes indicate that substantial mitigation of the ray effect can be achieved with the SMHM. Calculations were performed for the Los Alamos FIRST STEP hybrid ICF reactor designed for tritium production. Conventional 238 U fuel rod assemblies surround the spherical steel target chamber to form an annular cylindrical blanket. An axial fuel region is included to complete the blanket

  13. Modifications Of Discrete Ordinate Method For Computations With High Scattering Anisotropy: Comparative Analysis

    Science.gov (United States)

    Korkin, Sergey V.; Lyapustin, Alexei I.; Rozanov, Vladimir V.

    2012-01-01

    A numerical accuracy analysis of the radiative transfer equation (RTE) solution based on separation of the diffuse light field into anisotropic and smooth parts is presented. The analysis uses three different algorithms based on the discrete ordinate method (DOM). Two methods, DOMAS and DOM2+, that do not use the truncation of the phase function, are compared against the TMS-method. DOMAS and DOM2+ use the Small-Angle Modification of RTE and the single scattering term, respectively, as an anisotropic part. The TMS method uses Delta-M method for truncation of the phase function along with the single scattering correction. For reference, a standard discrete ordinate method, DOM, is also included in analysis. The obtained results for cases with high scattering anisotropy show that at low number of streams (16, 32) only DOMAS provides an accurate solution in the aureole area. Outside of the aureole, the convergence and accuracy of DOMAS, and TMS is found to be approximately similar: DOMAS was found more accurate in cases with coarse aerosol and liquid water cloud models, except low optical depth, while the TMS showed better results in case of ice cloud.

  14. Spatial Treatment of the Slab-geometry Discrete Ordinates Equations Using Artificial Neural Networks

    International Nuclear Information System (INIS)

    Brantley, P S

    2001-01-01

    An artificial neural network (ANN) method is developed for treating the spatial variable of the one-group slab-geometry discrete ordinates (S N ) equations in a homogeneous medium with linearly anisotropic scattering. This ANN method takes advantage of the function approximation capability of multilayer ANNs. The discrete ordinates angular flux is approximated by a multilayer ANN with a single input representing the spatial variable x and N outputs representing the angular flux in each of the discrete ordinates angular directions. A global objective function is formulated which measures how accurately the output of the ANN approximates the solution of the discrete ordinates equations and boundary conditions at specified spatial points. Minimization of this objective function determines the appropriate values for the parameters of the ANN. Numerical results are presented demonstrating the accuracy of the method for both fixed source and incident angular flux problems

  15. Advances in the discrete ordinates and finite volume methods for the solution of radiative heat transfer problems in participating media

    International Nuclear Information System (INIS)

    Coelho, Pedro J.

    2014-01-01

    Many methods are available for the solution of radiative heat transfer problems in participating media. Among these, the discrete ordinates method (DOM) and the finite volume method (FVM) are among the most widely used ones. They provide a good compromise between accuracy and computational requirements, and they are relatively easy to integrate in CFD codes. This paper surveys recent advances on these numerical methods. Developments concerning the grid structure (e.g., new formulations for axisymmetrical geometries, body-fitted structured and unstructured meshes, embedded boundaries, multi-block grids, local grid refinement), the spatial discretization scheme, and the angular discretization scheme are described. Progress related to the solution accuracy, solution algorithm, alternative formulations, such as the modified DOM and FVM, even-parity formulation, discrete-ordinates interpolation method and method of lines, and parallelization strategies is addressed. The application to non-gray media, variable refractive index media, and transient problems is also reviewed. - Highlights: • We survey recent advances in the discrete ordinates and finite volume methods. • Developments in spatial and angular discretization schemes are described. • Progress in solution algorithms and parallelization methods is reviewed. • Advances in the transient solution of the radiative transfer equation are appraised. • Non-gray media and variable refractive index media are briefly addressed

  16. Method for coupling two-dimensional to three-dimensional discrete ordinates calculations

    International Nuclear Information System (INIS)

    Thompson, J.L.; Emmett, M.B.; Rhoades, W.A.; Dodds, H.L. Jr.

    1985-01-01

    A three-dimensional (3-D) discrete ordinates transport code, TORT, has been developed at the Oak Ridge National Laboratory for radiation penetration studies. It is not feasible to solve some 3-D penetration problems with TORT, such as a building located a large distance from a point source, because (a) the discretized 3-D problem is simply too big to fit on the computer or (b) the computing time (and corresponding cost) is prohibitive. Fortunately, such problems can be solved with a hybrid approach by coupling a two-dimensional (2-D) description of the point source, which is assumed to be azimuthally symmetric, to a 3-D description of the building, the region of interest. The purpose of this paper is to describe this hybrid methodology along with its implementation and evaluation in the DOTTOR (Discrete Ordinates to Three-dimensional Oak Ridge Transport) code

  17. Improved treatment of two-dimensional neutral particle transport through voids within the discrete ordinates method by use of generalized view factors

    International Nuclear Information System (INIS)

    Brockmann, H.

    1992-01-01

    Using the discrete ordinates method for the treatment of neutral particle transport through voids serious flux distortions may occur due to the restricted streaming of particles along discrete directions. For mitigating this type of ray effect the method of view factors is proposed which has been developed in the theory of thermal radiation for describing the radiant exchange among surfaces. In order to apply this method to transport theory generalized view factors are defined which regard the angular dependence of the radiation leaving the surfaces. The generalized view factors are calculated analytically for r-z cylinder geometries and by applying the view factor algebra. The method was realized in the discrete ordinates transport code DOT 4.2 and applied to an r-z analogue of the S I S (Square-In-Square) sample problem. The results of the proposed method are compared with those calculated by the common discrete ordinates method and the Monte Carlo method

  18. Parallel performance of the angular versus spatial domain decomposition for discrete ordinates transport methods

    International Nuclear Information System (INIS)

    Fischer, J.W.; Azmy, Y.Y.

    2003-01-01

    A previously reported parallel performance model for Angular Domain Decomposition (ADD) of the Discrete Ordinates method for solving multidimensional neutron transport problems is revisited for further validation. Three communication schemes: native MPI, the bucket algorithm, and the distributed bucket algorithm, are included in the validation exercise that is successfully conducted on a Beowulf cluster. The parallel performance model is comprised of three components: serial, parallel, and communication. The serial component is largely independent of the number of participating processors, P, while the parallel component decreases like 1/P. These two components are independent of the communication scheme, in contrast with the communication component that typically increases with P in a manner highly dependent on the global reduced algorithm. Correct trends for each component and each communication scheme were measured for the Arbitrarily High Order Transport (AHOT) code, thus validating the performance models. Furthermore, extensive experiments illustrate the superiority of the bucket algorithm. The primary question addressed in this research is: for a given problem size, which domain decomposition method, angular or spatial, is best suited to parallelize Discrete Ordinates methods on a specific computational platform? We address this question for three-dimensional applications via parallel performance models that include parameters specifying the problem size and system performance: the above-mentioned ADD, and a previously constructed and validated Spatial Domain Decomposition (SDD) model. We conclude that for large problems the parallel component dwarfs the communication component even on moderately large numbers of processors. The main advantages of SDD are: (a) scalability to higher numbers of processors of the order of the number of computational cells; (b) smaller memory requirement; (c) better performance than ADD on high-end platforms and large number of

  19. The adaptive collision source method for discrete ordinates radiation transport

    International Nuclear Information System (INIS)

    Walters, William J.; Haghighat, Alireza

    2017-01-01

    Highlights: • A new adaptive quadrature method to solve the discrete ordinates transport equation. • The adaptive collision source (ACS) method splits the flux into n’th collided components. • Uncollided flux requires high quadrature; this is lowered with number of collisions. • ACS automatically applies appropriate quadrature order each collided component. • The adaptive quadrature is 1.5–4 times more efficient than uniform quadrature. - Abstract: A novel collision source method has been developed to solve the Linear Boltzmann Equation (LBE) more efficiently by adaptation of the angular quadrature order. The angular adaptation method is unique in that the flux from each scattering source iteration is obtained, with potentially a different quadrature order used for each. Traditionally, the flux from every iteration is combined, with the same quadrature applied to the combined flux. Since the scattering process tends to distribute the radiation more evenly over angles (i.e., make it more isotropic), the quadrature requirements generally decrease with each iteration. This method allows for an optimal use of processing power, by using a high order quadrature for the first iterations that need it, before shifting to lower order quadratures for the remaining iterations. This is essentially an extension of the first collision source method, and is referred to as the adaptive collision source (ACS) method. The ACS methodology has been implemented in the 3-D, parallel, multigroup discrete ordinates code TITAN. This code was tested on a several simple and complex fixed-source problems. The ACS implementation in TITAN has shown a reduction in computation time by a factor of 1.5–4 on the fixed-source test problems, for the same desired level of accuracy, as compared to the standard TITAN code.

  20. Singular characteristic tracking algorithm for improved solution accuracy of the discrete ordinates method with isotropic scattering

    International Nuclear Information System (INIS)

    Duo, J. I.; Azmy, Y. Y.

    2007-01-01

    A new method, the Singular Characteristics Tracking algorithm, is developed to account for potential non-smoothness across the singular characteristics in the exact solution of the discrete ordinates approximation of the transport equation. Numerical results show improved rate of convergence of the solution to the discrete ordinates equations in two spatial dimensions with isotropic scattering using the proposed methodology. Unlike the standard Weighted Diamond Difference methods, the new algorithm achieves local convergence in the case of discontinuous angular flux along the singular characteristics. The method also significantly reduces the error for problems where the angular flux presents discontinuous spatial derivatives across these lines. For purposes of verifying the results, the Method of Manufactured Solutions is used to generate analytical reference solutions that permit estimating the local error in the numerical solution. (authors)

  1. New developments in the discrete ordinate method for the resolution of the radiative transfer equation

    International Nuclear Information System (INIS)

    Ben Jaffel, L.; Vidal-Madjar, A.

    1989-01-01

    The discrete ordinate method for the resolution of the radiative transfer equation is developed. We show that the construction of a quasi-analytical solution to the corresponding matrix diagonalization problem reduces the time calculation and allows the use of more dense discrete frequency and angle grids. Comparison with previous work is made, showing that the present method reduces by more than a factor of ten the computational time, and is more appropriate in all cases

  2. DOMINO, Coupling of Discrete Ordinate Program DOT with Monte-Carlo Program MORSE

    International Nuclear Information System (INIS)

    1974-01-01

    1 - Nature of physical problem solved: DOMINO is a general purpose code for coupling discrete ordinates and Monte Carlo radiation transport calculations. 2 - Method of solution: DOMINO transforms the angular flux as a function of energy group, mesh interval and discrete angle into current and subsequently into normalized probability distributions. 3 - Restrictions on the complexity of the problem: The discrete ordinates calculation is limited to an r-z geometry

  3. Ordinal Welfare Comparisons with Multiple Discrete Indicators

    DEFF Research Database (Denmark)

    Arndt, Channing; Distante, Roberta; Hussain, M. Azhar

    We develop an ordinal method for making welfare comparisons between populations with multidimensional discrete well-being indicators observed at the micro level. The approach assumes that, for each well-being indicator, the levels can be ranked from worse to better; however, no assumptions are made...

  4. Discrete-ordinate method with matrix exponential for a pseudo-spherical atmosphere: Scalar case

    International Nuclear Information System (INIS)

    Doicu, A.; Trautmann, T.

    2009-01-01

    We present a discrete-ordinate algorithm using the matrix-exponential solution for pseudo-spherical radiative transfer. Following the finite-element technique we introduce the concept of layer equation and formulate the discrete radiative transfer problem in terms of the level values of the radiance. The layer quantities are expressed by means of matrix exponentials, which are computed by using the matrix eigenvalue method and the Pade approximation. These solution methods lead to a compact and versatile formulation of the radiative transfer. Simulated nadir and limb radiances for an aerosol-loaded atmosphere and a cloudy atmosphere are presented along with a discussion of the model intercomparisons and timings

  5. A discrete ordinate response matrix method for massively parallel computers

    International Nuclear Information System (INIS)

    Hanebutte, U.R.; Lewis, E.E.

    1991-01-01

    A discrete ordinate response matrix method is formulated for the solution of neutron transport problems on massively parallel computers. The response matrix formulation eliminates iteration on the scattering source. The nodal matrices which result from the diamond-differenced equations are utilized in a factored form which minimizes memory requirements and significantly reduces the required number of algorithm utilizes massive parallelism by assigning each spatial node to a processor. The algorithm is accelerated effectively by a synthetic method in which the low-order diffusion equations are also solved by massively parallel red/black iterations. The method has been implemented on a 16k Connection Machine-2, and S 8 and S 16 solutions have been obtained for fixed-source benchmark problems in X--Y geometry

  6. Discrete ordinates transport methods for problems with highly forward-peaked scattering

    International Nuclear Information System (INIS)

    Pautz, S.D.

    1998-04-01

    The author examines the solutions of the discrete ordinates (S N ) method for problems with highly forward-peaked scattering kernels. He derives conditions necessary to obtain reasonable solutions in a certain forward-peaked limit, the Fokker-Planck (FP) limit. He also analyzes the acceleration of the iterative solution of such problems and offer improvements to it. He extends the analytic Fokker-Planck limit analysis to the S N equations. This analysis shows that in this asymptotic limit the S N solution satisfies a pseudospectral discretization of the FP equation, provided that the scattering term is handled in a certain way (which he describes) and that the analytic transport solution satisfies an analytic FP equation. Similar analyses of various spatially discretized S N equations reveal that they too produce solutions that satisfy discrete FP equations, given the same provisions. Numerical results agree with these theoretical predictions. He defines a multidimensional angular multigrid (ANMG) method to accelerate the iterative solution of highly forward-peaked problems. The analyses show that a straightforward application of this scheme is subject to high-frequency instabilities. However, by applying a diffusive filter to the ANMG corrections he is able to stabilize this method. Fourier analyses of model problems show that the resulting method is effective at accelerating the convergence rate when the scattering is forward-peaked. The numerical results demonstrate that these analyses are good predictors of the actual performance of the ANMG method

  7. Extended discrete-ordinate method considering full polarization state

    International Nuclear Information System (INIS)

    Box, Michael A.; Qin Yi

    2006-01-01

    This paper presents an extension to the standard discrete-ordinate method (DOM) to consider generalized sources including: beam sources which can be placed at any (vertical) position and illuminate in any direction, thermal emission from the atmosphere and angularly distributed sources which illuminate from a surface as continuous functions of zenith and azimuth angles. As special cases, the thermal emission from the surface and deep space can be implemented as angularly distributed sources. Analytical-particular solutions for all source types are derived using the infinite medium Green's function. Radiation field zenith angle interpolation using source function integration is developed for all source types. The development considers the full state of polarization, including the sources (as applicable) and the (BRDF) surface, but the development can be reduced easily to scalar problems and is ready to be implemented in a single set of code for both scalar and vector radiative transfer computation

  8. Matrix albedo for discrete ordinates infinite-medium boundary condition

    International Nuclear Information System (INIS)

    Mathews, K.; Dishaw, J.

    2007-01-01

    Discrete ordinates problems with an infinite exterior medium (reflector) can be more efficiently computed by eliminating grid cells in the exterior medium and applying a matrix albedo boundary condition. The albedo matrix is a discretized bidirectional reflection distribution function (BRDF) that accounts for the angular quadrature set, spatial quadrature method, and spatial grid that would have been used to model a portion of the exterior medium. The method is exact in slab geometry, and could be used as an approximation in multiple dimensions or curvilinear coordinates. We present an adequate method for computing albedo matrices and demonstrate their use in verifying a discrete ordinates code in slab geometry by comparison with Ganapol's infinite medium semi-analytic TIEL benchmark. With sufficient resolution in the spatial and angular grids and iteration tolerance to yield solutions converged to 6 digits, the conventional (scalar) albedo boundary condition yielded 2-digit accuracy at the boundary, but the matrix albedo solution reproduced the benchmark scalar flux at the boundary to all 6 digits. (authors)

  9. A Laplace transform method for energy multigroup hybrid discrete ordinates

    International Nuclear Information System (INIS)

    Segatto, C.F.; Vilhena, M.T.; Barros, R.C.

    2010-01-01

    In typical lattice cells where a highly absorbing, small fuel element is embedded in the moderator, a large weakly absorbing medium, high-order transport methods become unnecessary. In this work we describe a hybrid discrete ordinates (S N) method for energy multigroup slab lattice calculations. This hybrid S N method combines the convenience of a low-order S N method in the moderator with a high-order S N method in the fuel. The idea is based on the fact that in weakly absorbing media whose physical size is several neutron mean free paths in extent, even the S 2 method (P 1 approximation), leads to an accurate result. We use special fuel-moderator interface conditions and the Laplace transform (LTS N ) analytical numerical method to calculate the two-energy group neutron flux distributions and the thermal disadvantage factor. We present numerical results for a range of typical model problems.

  10. A numerical method for multigroup slab-geometry discrete ordinates problems with no spatial truncation error

    International Nuclear Information System (INIS)

    Barros, R.C. de; Larsen, E.W.

    1991-01-01

    A generalization of the one-group Spectral Green's Function (SGF) method is developed for multigroup, slab-geometry discrete ordinates (S N ) problems. The multigroup SGF method is free from spatial truncation errors; it generated numerical values for the cell-edge and cell-average angular fluxes that agree with the analytic solution of the multigroup S N equations. Numerical results are given to illustrate the method's accuracy

  11. Extended discrete-ordinate method considering full polarization state

    Energy Technology Data Exchange (ETDEWEB)

    Box, Michael A. [School of Physics, University of New South Wales (Australia)]. E-mail: m.box@unsw.edu.au; Qin Yi [School of Physics, University of New South Wales (Australia)]. E-mail: yi.qin@csiro.au

    2006-01-15

    This paper presents an extension to the standard discrete-ordinate method (DOM) to consider generalized sources including: beam sources which can be placed at any (vertical) position and illuminate in any direction, thermal emission from the atmosphere and angularly distributed sources which illuminate from a surface as continuous functions of zenith and azimuth angles. As special cases, the thermal emission from the surface and deep space can be implemented as angularly distributed sources. Analytical-particular solutions for all source types are derived using the infinite medium Green's function. Radiation field zenith angle interpolation using source function integration is developed for all source types. The development considers the full state of polarization, including the sources (as applicable) and the (BRDF) surface, but the development can be reduced easily to scalar problems and is ready to be implemented in a single set of code for both scalar and vector radiative transfer computation.

  12. Discrete elements method of neutron transport

    International Nuclear Information System (INIS)

    Mathews, K.A.

    1988-01-01

    In this paper a new neutron transport method, called discrete elements (L N ) is derived and compared to discrete ordinates methods, theoretically and by numerical experimentation. The discrete elements method is based on discretizing the Boltzmann equation over a set of elements of angle. The discrete elements method is shown to be more cost-effective than discrete ordinates, in terms of accuracy versus execution time and storage, for the cases tested. In a two-dimensional test case, a vacuum duct in a shield, the L N method is more consistently convergent toward a Monte Carlo benchmark solution

  13. GPU accelerated simulations of 3D deterministic particle transport using discrete ordinates method

    International Nuclear Information System (INIS)

    Gong Chunye; Liu Jie; Chi Lihua; Huang Haowei; Fang Jingyue; Gong Zhenghu

    2011-01-01

    Graphics Processing Unit (GPU), originally developed for real-time, high-definition 3D graphics in computer games, now provides great faculty in solving scientific applications. The basis of particle transport simulation is the time-dependent, multi-group, inhomogeneous Boltzmann transport equation. The numerical solution to the Boltzmann equation involves the discrete ordinates (S n ) method and the procedure of source iteration. In this paper, we present a GPU accelerated simulation of one energy group time-independent deterministic discrete ordinates particle transport in 3D Cartesian geometry (Sweep3D). The performance of the GPU simulations are reported with the simulations of vacuum boundary condition. The discussion of the relative advantages and disadvantages of the GPU implementation, the simulation on multi GPUs, the programming effort and code portability are also reported. The results show that the overall performance speedup of one NVIDIA Tesla M2050 GPU ranges from 2.56 compared with one Intel Xeon X5670 chip to 8.14 compared with one Intel Core Q6600 chip for no flux fixup. The simulation with flux fixup on one M2050 is 1.23 times faster than on one X5670.

  14. GPU accelerated simulations of 3D deterministic particle transport using discrete ordinates method

    Science.gov (United States)

    Gong, Chunye; Liu, Jie; Chi, Lihua; Huang, Haowei; Fang, Jingyue; Gong, Zhenghu

    2011-07-01

    Graphics Processing Unit (GPU), originally developed for real-time, high-definition 3D graphics in computer games, now provides great faculty in solving scientific applications. The basis of particle transport simulation is the time-dependent, multi-group, inhomogeneous Boltzmann transport equation. The numerical solution to the Boltzmann equation involves the discrete ordinates ( Sn) method and the procedure of source iteration. In this paper, we present a GPU accelerated simulation of one energy group time-independent deterministic discrete ordinates particle transport in 3D Cartesian geometry (Sweep3D). The performance of the GPU simulations are reported with the simulations of vacuum boundary condition. The discussion of the relative advantages and disadvantages of the GPU implementation, the simulation on multi GPUs, the programming effort and code portability are also reported. The results show that the overall performance speedup of one NVIDIA Tesla M2050 GPU ranges from 2.56 compared with one Intel Xeon X5670 chip to 8.14 compared with one Intel Core Q6600 chip for no flux fixup. The simulation with flux fixup on one M2050 is 1.23 times faster than on one X5670.

  15. Application of a discrete-energy, discrete-ordinates technique to the study of neutron transport in iron

    International Nuclear Information System (INIS)

    Ching, J.T.

    1975-01-01

    An algebraic equivalence between the point-energy and multigroup forms of the Boltzmann transport equation is demonstrated which allows the development of a discrete-energy, discrete-ordinates method for the solution of radiation transport problems. The method utilizes a modified version of a cross section processing scheme devised for the moments method code BMT and the transport equation solution algorithm from the one-dimensional discrete-ordinates transport code ANISN. The combined system, identified as MOMANS, computes fluxes directly from point cross sections in a single operation. In the cross-section processing, the group averaging required for multigroup calculations is replaced by a fast numerical scheme capable of generating a set of transfer cross sections containing all the physical features of interest, thereby increasing the detail in the calculated results. Test calculations in which the discrete-energy method was compared with the multigroup method have shown that for the same energy grid (number of points = number of groups), the discrete-energy method is faster but somewhat less accurate than the multigroup method. However, the accuracy of the discrete-energy method increases rapidly as the spacing between energy points is decreased, approaching that of multigroup calculations. For problems requiring great detail in the energy spectrum the discrete-energy method has therefore proven to be as accurate as, and more economical than, the multigroup technique. This was demonstrated by the application of the method to the study of the transport of neutrons in an iron sphere. Using the capability of the discrete-energy method for rapidly treating changes in cross-section sets, the propagation of neutrons from a 14 MeV source in a 22 cm radius sphere of iron was analyzed for sensitivity to changes in the microscopic scattering mechanisms

  16. Discrete energy formulation of neutron transport theory applied to solving the discrete ordinates equations

    International Nuclear Information System (INIS)

    Ching, J.; Oblow, E.M.; Goldstein, H.

    1976-01-01

    An algebraic equivalence between the point-energy and multigroup forms of the Boltzmann transport equation is demonstrated that allows the development of a discrete energy, discrete ordinates method for the solution of radiation transport problems. In the discrete energy method, the group averaging required in the cross-section processing for multigroup calculations is replaced by a faster numerical quadrature scheme capable of generating transfer cross sections describing all the physical processes of interest on a fine point-energy grid. Test calculations in which the discrete energy method is compared with the multigroup method show that, for the same energy grid, the discrete energy method is much faster, although somewhat less accurate, than the multigroup method. However, the accuracy of the discrete energy method increases rapidly as the spacing between energy grid points is decreased, approaching that of multigroup calculations. For problems requiring great detail in the energy spectrum, the discrete energy method is therefore expected to be far more economical than the multigroup technique for equivalent accuracy solutions. This advantage of the point method is demonstrated by application to the study of neutron transport in a thick iron slab

  17. The method of lines solution of discrete ordinates method for non-grey media

    International Nuclear Information System (INIS)

    Cayan, Fatma Nihan; Selcuk, Nevin

    2007-01-01

    A radiation code based on method of lines (MOL) solution of discrete ordinates method (DOM) for radiative heat transfer in non-grey absorbing-emitting media was developed by incorporation of a gas spectral radiative property model, namely wide band correlated-k (WBCK) model, which is compatible with MOL solution of DOM. Predictive accuracy of the code was evaluated by applying it to 1-D parallel plate and 2-D axisymmetric cylindrical enclosure problems containing absorbing-emitting medium and benchmarking its predictions against line-by-line solutions available in the literature. Comparisons reveal that MOL solution of DOM with WBCK model produces accurate results for radiative heat fluxes and source terms and can be used with confidence in conjunction with computational fluid dynamics codes based on the same approach

  18. High-order solution methods for grey discrete ordinates thermal radiative transfer

    Energy Technology Data Exchange (ETDEWEB)

    Maginot, Peter G., E-mail: maginot1@llnl.gov [Lawrence Livermore National Laboratory, Livermore, CA 94551 (United States); Ragusa, Jean C., E-mail: jean.ragusa@tamu.edu [Department of Nuclear Engineering, Texas A& M University, College Station, TX 77843 (United States); Morel, Jim E., E-mail: morel@tamu.edu [Department of Nuclear Engineering, Texas A& M University, College Station, TX 77843 (United States)

    2016-12-15

    This work presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation is accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.

  19. A massively parallel discrete ordinates response matrix method for neutron transport

    International Nuclear Information System (INIS)

    Hanebutte, U.R.; Lewis, E.E.

    1992-01-01

    In this paper a discrete ordinates response matrix method is formulated with anisotropic scattering for the solution of neutron transport problems on massively parallel computers. The response matrix formulation eliminates iteration on the scattering source. The nodal matrices that result from the diamond-differenced equations are utilized in a factored form that minimizes memory requirements and significantly reduces the number of arithmetic operations required per node. The red-black solution algorithm utilizes massive parallelism by assigning each spatial node to one or more processors. The algorithm is accelerated by a synthetic method in which the low-order diffusion equations are also solved by massively parallel red-black iterations. The method is implemented on a 16K Connection Machine-2, and S 8 and S 16 solutions are obtained for fixed-source benchmark problems in x-y geometry

  20. An analytical nodal method for time-dependent one-dimensional discrete ordinates problems

    International Nuclear Information System (INIS)

    Barros, R.C. de

    1992-01-01

    In recent years, relatively little work has been done in developing time-dependent discrete ordinates (S N ) computer codes. Therefore, the topic of time integration methods certainly deserves further attention. In this paper, we describe a new coarse-mesh method for time-dependent monoenergetic S N transport problesm in slab geometry. This numerical method preserves the analytic solution of the transverse-integrated S N nodal equations by constants, so we call our method the analytical constant nodal (ACN) method. For time-independent S N problems in finite slab geometry and for time-dependent infinite-medium S N problems, the ACN method generates numerical solutions that are completely free of truncation errors. Bsed on this positive feature, we expect the ACN method to be more accurate than conventional numerical methods for S N transport calculations on coarse space-time grids

  1. Computation of 2-D pinhole image-formation process of large-scale furnaces using the discrete ordinates method

    CERN Document Server

    Li Hong; Lu Ji Dong; Zheng Chu Guan

    2003-01-01

    In most of the discrete ordinate schemes (DOS) reported in the literature, the discrete directions are fixed, and unable to be arbitrarily adjusted; therefore, it is difficult to employ these schemes to calculate the radiative energy image-formation of pulverized-coal furnaces. On the basis of a new DOS, named the discrete ordinate scheme with (an) infinitely small weight(s), which was recently proposed by the authors, a novel algorithm for computing the pinhole image-formation process is developed in this work. The performance of this algorithm is tested, and is found to be also suitable for parallel computation.

  2. Computation of 2-D pinhole image-formation process of large-scale furnaces using the discrete ordinates method

    International Nuclear Information System (INIS)

    Li Hongshun; Zhou Huaichun; Lu Jidong; Zheng Chuguang

    2003-01-01

    In most of the discrete ordinate schemes (DOS) reported in the literature, the discrete directions are fixed, and unable to be arbitrarily adjusted; therefore, it is difficult to employ these schemes to calculate the radiative energy image-formation of pulverized-coal furnaces. On the basis of a new DOS, named the discrete ordinate scheme with (an) infinitely small weight(s), which was recently proposed by the authors, a novel algorithm for computing the pinhole image-formation process is developed in this work. The performance of this algorithm is tested, and is found to be also suitable for parallel computation

  3. Radiative heat transfer in strongly forward scattering media using the discrete ordinates method

    Science.gov (United States)

    Granate, Pedro; Coelho, Pedro J.; Roger, Maxime

    2016-03-01

    The discrete ordinates method (DOM) is widely used to solve the radiative transfer equation, often yielding satisfactory results. However, in the presence of strongly forward scattering media, this method does not generally conserve the scattering energy and the phase function asymmetry factor. Because of this, the normalization of the phase function has been proposed to guarantee that the scattering energy and the asymmetry factor are conserved. Various authors have used different normalization techniques. Three of these are compared in the present work, along with two other methods, one based on the finite volume method (FVM) and another one based on the spherical harmonics discrete ordinates method (SHDOM). In addition, the approximation of the Henyey-Greenstein phase function by a different one is investigated as an alternative to the phase function normalization. The approximate phase function is given by the sum of a Dirac delta function, which accounts for the forward scattering peak, and a smoother scaled phase function. In this study, these techniques are applied to three scalar radiative transfer test cases, namely a three-dimensional cubic domain with a purely scattering medium, an axisymmetric cylindrical enclosure containing an emitting-absorbing-scattering medium, and a three-dimensional transient problem with collimated irradiation. The present results show that accurate predictions are achieved for strongly forward scattering media when the phase function is normalized in such a way that both the scattered energy and the phase function asymmetry factor are conserved. The normalization of the phase function may be avoided using the FVM or the SHDOM to evaluate the in-scattering term of the radiative transfer equation. Both methods yield results whose accuracy is similar to that obtained using the DOM along with normalization of the phase function. Very satisfactory predictions were also achieved using the delta-M phase function, while the delta

  4. A discrete-ordinates solution for a radiation therapy problem

    International Nuclear Information System (INIS)

    Goldschmidt, Gustavo Brun; Reichert, Janice Teresinha; Barichello, Liliane Basso

    2008-01-01

    A concise and accurate procedure for evaluating dose distribution, in a radiation therapy planning, is presented. The analytical discrete-ordinates method (ADO method) is used to develop a complete solution for a spectral dependent radiative transfer equation, in a one-dimensional medium, according to a multigroup scheme. Numerical results are presented for test problems, where the Klein-Nishina scattering kernel was used to describe the interaction processes. (author)

  5. Performance of the discrete ordinates method-like neutron transport computation with equivalent group condensation and angle-collapsing

    International Nuclear Information System (INIS)

    Yoo, Han Jong; Won, Jong Hyuck; Cho, Nam Zin

    2011-01-01

    In computational studies of neutron transport equations, the fine-group to few-group condensation procedure leads to equivalent total cross section that becomes angle dependent. The difficulty of this angle dependency has been traditionally treated by consistent P or extended transport approximation in the literature. In a previous study, we retained the angle dependency of the total cross section and applied directly to the discrete ordinates equation, with additional concept of angle-collapsing, and tested in a one-dimensional slab problem. In this study, we provide further results of this discrete ordinates-like method in comparison with the typical traditional methods. In addition, IRAM acceleration (based on Krylov subspace method) is tested for the purpose of further reducing the computational burden of few-group calculation. From the test results, it is ascertained that the angle-dependent total cross section with angle-collapsing gives excellent estimation of k_e_f_f and flux distribution and that IRAM acceleration effectively reduces the number of outer iterations. However, since IRAM requires sufficient convergence in inner iterations, speedup in total computer time is not significant for problems with upscattering. (author)

  6. Use of exact albedo conditions in numerical methods for one-dimensional one-speed discrete ordinates eigenvalue problems

    International Nuclear Information System (INIS)

    Abreu, M.P. de

    1994-01-01

    The use of exact albedo boundary conditions in numerical methods applied to one-dimensional one-speed discrete ordinates (S n ) eigenvalue problems for nuclear reactor global calculations is described. An albedo operator that treats the reflector region around a nuclear reactor core implicitly is described and exactly was derived. To illustrate the method's efficiency and accuracy, it was used conventional linear diamond method with the albedo option to solve typical model problems. (author)

  7. Data visualization for ONEDANT and TWODANT discrete ordinates codes

    International Nuclear Information System (INIS)

    Lee, C.L.

    1993-01-01

    Effective graphical display of code calculations allow for efficient analysis of results. This is especially true in the case of discrete ordinates transport codes, which can generate thousands of flux or reaction rate data points per calculation. For this reason, a package of portable interface programs called OTTUI (ONEDANT-TWODANT-Tecplot trademark Unix-Based Interface) has been developed at Los Alamos National Laboratory to permit rapid visualization of ONEDANT and TWODANT discrete ordinates results using the graphics package Tecplot. This paper describes the various uses of OTTUI for display of ONEDANT and TWODANT problem geometries and calculational results

  8. Effect of flux discontinuity on spatial approximations for discrete ordinates methods

    International Nuclear Information System (INIS)

    Duo, J.I.; Azmy, Y.Y.

    2005-01-01

    This work presents advances on error analysis of the spatial approximation of the discrete ordinates method for solving the neutron transport equation. Error norms for different non-collided flux problems over a two dimensional pure absorber medium are evaluated using three numerical methods. The problems are characterized by the incoming flux boundary conditions to obtain solutions with different level of differentiability. The three methods considered are the Diamond Difference (DD) method, the Arbitrarily High Order Transport method of the Nodal type (AHOT-N), and of the Characteristic type (AHOT-C). The last two methods are employed in constant, linear and quadratic orders of spatial approximation. The cell-wise error is computed as the difference between the cell-averaged flux computed by each method and the exact value, then the L 1 , L 2 , and L ∞ error norms are calculated. The results of this study demonstrate that the level of differentiability of the exact solution profoundly affects the rate of convergence of the numerical methods' solutions. Furthermore, in the case of discontinuous exact flux the methods fail to converge in the maximum error norm, or in the pointwise sense, in accordance with previous local error analysis. (authors)

  9. Benchmarking of EPRI-cell epithermal methods with the point-energy discrete-ordinates code (OZMA)

    International Nuclear Information System (INIS)

    Williams, M.L.; Wright, R.Q.; Barhen, J.; Rothenstein, W.

    1982-01-01

    The purpose of the present study is to benchmark E-C resonance-shielding and cell-averaging methods against a rigorous deterministic solution on a fine-group level (approx. 30 groups between 1 eV and 5.5 keV). The benchmark code used is OZMA, which solves the space-dependent slowing-down equations using continuous-energy discrete ordinates or integral transport theory to produce fine-group cross sections. Results are given for three water-moderated lattices - a mixed oxide, a uranium method, and a tight-pitch high-conversion uranium oxide configuration. The latter two lattices were chosen because of the strong self shielding of the 238 U resonances

  10. Comparison of the auxiliary function method and the discrete-ordinate method for solving the radiative transfer equation for light scattering.

    Science.gov (United States)

    da Silva, Anabela; Elias, Mady; Andraud, Christine; Lafait, Jacques

    2003-12-01

    Two methods for solving the radiative transfer equation are compared with the aim of computing the angular distribution of the light scattered by a heterogeneous scattering medium composed of a single flat layer or a multilayer. The first method [auxiliary function method (AFM)], recently developed, uses an auxiliary function and leads to an exact solution; the second [discrete-ordinate method (DOM)] is based on the channel concept and needs an angular discretization. The comparison is applied to two different media presenting two typical and extreme scattering behaviors: Rayleigh and Mie scattering with smooth or very anisotropic phase functions, respectively. A very good agreement between the predictions of the two methods is observed in both cases. The larger the number of channels used in the DOM, the better the agreement. The principal advantages and limitations of each method are also listed.

  11. Specular reflection treatment for the 3D radiative transfer equation solved with the discrete ordinates method

    Energy Technology Data Exchange (ETDEWEB)

    Le Hardy, D. [Université de Nantes, LTN UMR CNRS 6607 (France); Favennec, Y., E-mail: yann.favennec@univ-nantes.fr [Université de Nantes, LTN UMR CNRS 6607 (France); Rousseau, B. [Université de Nantes, LTN UMR CNRS 6607 (France); Hecht, F. [Sorbonne Universités, UPMC Université Paris 06, UMR 7598, inria de Paris, Laboratoire Jacques-Louis Lions, F-75005, Paris (France)

    2017-04-01

    The contribution of this paper relies in the development of numerical algorithms for the mathematical treatment of specular reflection on borders when dealing with the numerical solution of radiative transfer problems. The radiative transfer equation being integro-differential, the discrete ordinates method allows to write down a set of semi-discrete equations in which weights are to be calculated. The calculation of these weights is well known to be based on either a quadrature or on angular discretization, making the use of such method straightforward for the state equation. Also, the diffuse contribution of reflection on borders is usually well taken into account. However, the calculation of accurate partition ratio coefficients is much more tricky for the specular condition applied on arbitrary geometrical borders. This paper presents algorithms that calculate analytically partition ratio coefficients needed in numerical treatments. The developed algorithms, combined with a decentered finite element scheme, are validated with the help of comparisons with analytical solutions before being applied on complex geometries.

  12. Solution of the one-dimensional time-dependent discrete ordinates problem in a slab by the spectral and LTSN methods

    International Nuclear Information System (INIS)

    Oliveira, J.V.P. de; Cardona, A.V.; Vilhena, M.T.M.B. de

    2002-01-01

    In this work, we present a new approach to solve the one-dimensional time-dependent discrete ordinates problem (S N problem) in a slab. The main idea is based upon the application of the spectral method to the set of S N time-dependent differential equations and solution of the resulting coupling equations by the LTS N method. We report numerical simulations

  13. Discrete elements method of neutral particle transport

    International Nuclear Information System (INIS)

    Mathews, K.A.

    1983-01-01

    A new discrete elements (L/sub N/) transport method is derived and compared to the discrete ordinates S/sub N/ method, theoretically and by numerical experimentation. The discrete elements method is more accurate than discrete ordinates and strongly ameliorates ray effects for the practical problems studied. The discrete elements method is shown to be more cost effective, in terms of execution time with comparable storage to attain the same accuracy, for a one-dimensional test case using linear characteristic spatial quadrature. In a two-dimensional test case, a vacuum duct in a shield, L/sub N/ is more consistently convergent toward a Monte Carlo benchmark solution than S/sub N/, using step characteristic spatial quadrature. An analysis of the interaction of angular and spatial quadrature in xy-geometry indicates the desirability of using linear characteristic spatial quadrature with the L/sub N/ method

  14. The linear characteristic method for spatially discretizing the discrete ordinates equations in (x,y)-geometry

    International Nuclear Information System (INIS)

    Larsen, E.W.; Alcouffe, R.E.

    1981-01-01

    In this article a new linear characteristic (LC) spatial differencing scheme for the discrete ordinates equations in (x,y)-geometry is described and numerical comparisons are given with the diamond difference (DD) method. The LC method is more stable with mesh size and is generally much more accurate than the DD method on both fine and coarse meshes, for eigenvalue and deep penetration problems. The LC method is based on computations involving the exact solution of a cell problem which has spatially linear boundary conditions and interior source. The LC method is coupled to the diffusion synthetic acceleration (DSA) algorithm in that the linear variations of the source are determined in part by the results of the DSA calculation from the previous inner iteration. An inexpensive negative-flux fixup is used which has very little effect on the accuracy of the solution. The storage requirements for LC are essentially the same as that for DD, while the computational times for LC are generally less than twice the DD computational times for the same mesh. This increase in computational cost is offset if one computes LC solutions on somewhat coarser meshes than DD; the resulting LC solutions are still generally much more accurate than the DD solutions. (orig.) [de

  15. Parallel ray tracing for one-dimensional discrete ordinate computations

    International Nuclear Information System (INIS)

    Jarvis, R.D.; Nelson, P.

    1996-01-01

    The ray-tracing sweep in discrete-ordinates, spatially discrete numerical approximation methods applied to the linear, steady-state, plane-parallel, mono-energetic, azimuthally symmetric, neutral-particle transport equation can be reduced to a parallel prefix computation. In so doing, the often severe penalty in convergence rate of the source iteration, suffered by most current parallel algorithms using spatial domain decomposition, can be avoided while attaining parallelism in the spatial domain to whatever extent desired. In addition, the reduction implies parallel algorithm complexity limits for the ray-tracing sweep. The reduction applies to all closed, linear, one-cell functional (CLOF) spatial approximation methods, which encompasses most in current popular use. Scalability test results of an implementation of the algorithm on a 64-node nCube-2S hypercube-connected, message-passing, multi-computer are described. (author)

  16. Mining the multigroup-discrete ordinates algorithm for high quality solutions

    International Nuclear Information System (INIS)

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

    2005-01-01

    A novel approach to the numerical solution of the neutron transport equation via the discrete ordinates (SN) method is presented. The new technique is referred to as 'mining' low order (SN) numerical solutions to obtain high order accuracy. The new numerical method, called the Multigroup Converged SN (MGCSN) algorithm, is a combination of several sequence accelerators: Romberg and Wynn-epsilon. The extreme accuracy obtained by the method is demonstrated through self consistency and comparison to the independent semi-analytical benchmark BLUE. (authors)

  17. Adaptive discrete-ordinates algorithms and strategies

    International Nuclear Information System (INIS)

    Stone, J.C.; Adams, M.L.

    2005-01-01

    We present our latest algorithms and strategies for adaptively refined discrete-ordinates quadrature sets. In our basic strategy, which we apply here in two-dimensional Cartesian geometry, the spatial domain is divided into regions. Each region has its own quadrature set, which is adapted to the region's angular flux. Our algorithms add a 'test' direction to the quadrature set if the angular flux calculated at that direction differs by more than a user-specified tolerance from the angular flux interpolated from other directions. Different algorithms have different prescriptions for the method of interpolation and/or choice of test directions and/or prescriptions for quadrature weights. We discuss three different algorithms of different interpolation orders. We demonstrate through numerical results that each algorithm is capable of generating solutions with negligible angular discretization error. This includes elimination of ray effects. We demonstrate that all of our algorithms achieve a given level of error with far fewer unknowns than does a standard quadrature set applied to an entire problem. To address a potential issue with other algorithms, we present one algorithm that retains exact integration of high-order spherical-harmonics functions, no matter how much local refinement takes place. To address another potential issue, we demonstrate that all of our methods conserve partial currents across interfaces where quadrature sets change. We conclude that our approach is extremely promising for solving the long-standing problem of angular discretization error in multidimensional transport problems. (authors)

  18. On the spectrum of the one-speed slab-geometry discrete ordinates operator in neutron transport theory

    International Nuclear Information System (INIS)

    Abreu, Marcos Pimenta de

    1998-01-01

    We describe a numerical method applied to the first-order form of one-speed slab-geometry discrete ordinates equations modelling time-independent neutron transport problems with anisotropic scattering, with no interior source and defined in a nonmultiplying homogeneous host medium. Our numerical method is concerned with the generation of the spectrum and of a vector basis for the null space of the one-speed slab-geometry discrete ordinates operator. Moreover, it allows us to overcome the difficulties introduced in previous methods by anisotropic scattering and by angular quadrature sets of high order. To illustrate the positive features of our numerical method, we present numerical results for one-speed slab-geometry neutron transport model problems with anisotropic scattering

  19. Hydrogen transport in a toroidal plasma using multigroup discrete-ordinates methodology

    International Nuclear Information System (INIS)

    Wienke, B.R.; Miller, W.F. Jr.; Seed, T.J.

    1979-01-01

    Neutral hydrogen transport in a fully ionized two-dimensional tokamak plasma was examined using discrete ordinates and contrasted with earlier analyses. In particular, curvature effects induced by toroidal geometries and ray effects caused by possible source localization were investigated. From an overview of the multigroup discrete-ordinates approximation, methodology in two-dimensional cylindrical geometry is detailed, mesh and plasma zoning procedures are sketched, and the piecewise polynomial solution algorithm on a triangular domain is obtained. Toroidal effects and comparisons as related to reaction rates and perticle spectra are examined for various model and source configurations

  20. A response matrix method for slab-geometry discrete ordinates adjoint calculations in energy-dependent source-detector problems

    Energy Technology Data Exchange (ETDEWEB)

    Mansur, Ralph S.; Moura, Carlos A., E-mail: ralph@ime.uerj.br, E-mail: demoura@ime.uerj.br [Universidade do Estado do Rio de Janeiro (UERJ), RJ (Brazil). Departamento de Engenharia Mecanica; Barros, Ricardo C., E-mail: rcbarros@pq.cnpq.br [Universidade do Estado do Rio de Janeiro (UERJ), Nova Friburgo, RJ (Brazil). Departamento de Modelagem Computacional

    2017-07-01

    Presented here is an application of the Response Matrix (RM) method for adjoint discrete ordinates (S{sub N}) problems in slab geometry applied to energy-dependent source-detector problems. The adjoint RM method is free from spatial truncation errors, as it generates numerical results for the adjoint angular fluxes in multilayer slabs that agree with the numerical values obtained from the analytical solution of the energy multigroup adjoint SN equations. Numerical results are given for two typical source-detector problems to illustrate the accuracy and the efficiency of the offered RM computer code. (author)

  1. Energy dependent mesh adaptivity of discontinuous isogeometric discrete ordinate methods with dual weighted residual error estimators

    Science.gov (United States)

    Owens, A. R.; Kópházi, J.; Welch, J. A.; Eaton, M. D.

    2017-04-01

    In this paper a hanging-node, discontinuous Galerkin, isogeometric discretisation of the multigroup, discrete ordinates (SN) equations is presented in which each energy group has its own mesh. The equations are discretised using Non-Uniform Rational B-Splines (NURBS), which allows the coarsest mesh to exactly represent the geometry for a wide range of engineering problems of interest; this would not be the case using straight-sided finite elements. Information is transferred between meshes via the construction of a supermesh. This is a non-trivial task for two arbitrary meshes, but is significantly simplified here by deriving every mesh from a common coarsest initial mesh. In order to take full advantage of this flexible discretisation, goal-based error estimators are derived for the multigroup, discrete ordinates equations with both fixed (extraneous) and fission sources, and these estimators are used to drive an adaptive mesh refinement (AMR) procedure. The method is applied to a variety of test cases for both fixed and fission source problems. The error estimators are found to be extremely accurate for linear NURBS discretisations, with degraded performance for quadratic discretisations owing to a reduction in relative accuracy of the "exact" adjoint solution required to calculate the estimators. Nevertheless, the method seems to produce optimal meshes in the AMR process for both linear and quadratic discretisations, and is ≈×100 more accurate than uniform refinement for the same amount of computational effort for a 67 group deep penetration shielding problem.

  2. Radiative transfer modelling in combusting systems using discrete ordinates method on three-dimensional unstructured grids; Modelisation des transferts radiatifs en combustion par methode aux ordonnees discretes sur des maillages non structures tridimensionnels

    Energy Technology Data Exchange (ETDEWEB)

    Joseph, D.

    2004-04-01

    The prediction of pollutant species such as soots and NO{sub x} emissions and lifetime of the walls in a combustion chamber is strongly dependant on heat transfer by radiation at high temperatures. This work deals with the development of a code based on the Discrete Ordinates Method (DOM) aiming at providing radiative source terms and wall fluxes with a good compromise between cpu time and accuracy. Radiative heat transfers are calculated using the unstructured grids defined by the Computational Fluid Dynamics (CFD) codes. The spectral properties of the combustion gases are taken into account by a statistical narrow bands correlated-k model (SNB-ck). Various types of angular quadrature are tested and three different spatial differencing schemes were integrated and compared. The validation tests show the limit at strong optical thicknesses of the finite volume approximation used the Discrete Ordinates Method. The first calculations performed on LES solutions are presented, it provides instantaneous radiative source terms and wall heat fluxes. Those results represent a first step towards radiation/combustion coupling. (author)

  3. On radiative transfer in water spray curtains using the discrete ordinates method

    Energy Technology Data Exchange (ETDEWEB)

    Collin, A. [Laboratoire d' Energetique et de Mecanique Theorique and Appliquee (LEMTA), CNRS UMR 7563, Faculte des Sciences et Techniques BP 239 - 54506 VANDOEUVRE Cedex (France); Boulet, P. [Laboratoire d' Energetique et de Mecanique Theorique and Appliquee (LEMTA), CNRS UMR 7563, Faculte des Sciences et Techniques BP 239 - 54506 VANDOEUVRE Cedex (France)]. E-mail: Pascal.Boulet@lemta.uhp-nancy.fr; Lacroix, D. [Laboratoire d' Energetique et de Mecanique Theorique and Appliquee (LEMTA), CNRS UMR 7563, Faculte des Sciences et Techniques BP 239 - 54506 VANDOEUVRE Cedex (France); Jeandel, G. [Laboratoire d' Energetique et de Mecanique Theorique and Appliquee (LEMTA), CNRS UMR 7563, Faculte des Sciences et Techniques BP 239 - 54506 VANDOEUVRE Cedex (France)

    2005-04-15

    Radiative transfer through water spray curtains has been presently addressed in conditions similar to devices used in fire protection systems. The radiation propagation from the heat source through the medium is simulated using a 2D Discrete Ordinates Method. The curtain is treated as an absorbing and anisotropically scattering medium, made of droplets injected in a mixing of air, water vapor and carbon dioxide. Such a participating medium requires a careful treatment of its spectral response in order to model the radiative transfer accurately. This particular problem is dealt with using a correlated-K method. Radiative properties for the droplets are calculated applying the Mie theory. Transmissivities under realistic conditions are then simulated after a validation thanks to comparisons with some experimental data available in the literature. Owing to promising results which are already observed in this case of uncoupled radiative problem, next step will be to combine the present study with a companion work dedicated to the careful treatment of the spray dynamics and of the induced heat transfer phenomena.

  4. High-order discrete ordinate transport in non-conforming 2D Cartesian meshes

    International Nuclear Information System (INIS)

    Gastaldo, L.; Le Tellier, R.; Suteau, C.; Fournier, D.; Ruggieri, J. M.

    2009-01-01

    We present in this paper a numerical scheme for solving the time-independent first-order form of the Boltzmann equation in non-conforming 2D Cartesian meshes. The flux solution technique used here is the discrete ordinate method and the spatial discretization is based on discontinuous finite elements. In order to have p-refinement capability, we have chosen a hierarchical polynomial basis based on Legendre polynomials. The h-refinement capability is also available and the element interface treatment has been simplified by the use of special functions decomposed over the mesh entities of an element. The comparison to a classical S N method using the Diamond Differencing scheme as spatial approximation confirms the good behaviour of the method. (authors)

  5. Nuclear data preparation and discrete ordinates calculation

    International Nuclear Information System (INIS)

    Carmignani, B.

    1980-01-01

    These lectures deal with the use of the GAM-GATHER and GAM-THERMOS chains for the calculation of lattice cross sections and within use of the discrete ordinates one dimensional ANISN code for the calculation of criticality and flux distribution of the cell and of the whole reactor. As an example the codes are applied to the calculation of a PWR. Results of different approximations are compared. (author)

  6. Discrete-ordinates electron transport calculations using standard neutron transport codes

    International Nuclear Information System (INIS)

    Morel, J.E.

    1979-01-01

    The primary purpose of this work was to develop a method for using standard neutron transport codes to perform electron transport calculations. The method is to develop approximate electron cross sections which are sufficiently well-behaved to be treated with standard S/sub n/ methods, but which nonetheless yield flux solutions which are very similar to the exact solutions. The main advantage of this approach is that, once the approximate cross sections are constructed, their multigroup Legendre expansion coefficients can be calculated and input to any standard S/sub n/ code. Discrete-ordinates calculations were performed to determine the accuracy of the flux solutions for problems corresponding to 1.0-MeV electrons incident upon slabs of aluminum and gold. All S/sub n/ calculations were compared with similar calculations performed with an electron Monte Carlo code, considered to be exact. In all cases, the discrete-ordinates solutions for integral flux quantities (i.e., scalar flux, energy deposition profiles, etc.) are generally in agreement with the Monte Carlo solutions to within approximately 5% or less. The central conclusion is that integral electron flux quantities can be efficiently and accurately calculated using standard S/sub n/ codes in conjunction with approximate cross sections. Furthermore, if group structures and approximate cross section construction are optimized, accurate differential flux energy spectra may also be obtainable without having to use an inordinately large number of energy groups. 1 figure

  7. Three-dimensional coupled Monte Carlo-discrete ordinates computational scheme for shielding calculations of large and complex nuclear facilities

    International Nuclear Information System (INIS)

    Chen, Y.; Fischer, U.

    2005-01-01

    Shielding calculations of advanced nuclear facilities such as accelerator based neutron sources or fusion devices of the tokamak type are complicated due to their complex geometries and their large dimensions, including bulk shields of several meters thickness. While the complexity of the geometry in the shielding calculation can be hardly handled by the discrete ordinates method, the deep penetration of radiation through bulk shields is a severe challenge for the Monte Carlo particle transport technique. This work proposes a dedicated computational scheme for coupled Monte Carlo-Discrete Ordinates transport calculations to handle this kind of shielding problems. The Monte Carlo technique is used to simulate the particle generation and transport in the target region with both complex geometry and reaction physics, and the discrete ordinates method is used to treat the deep penetration problem in the bulk shield. The coupling scheme has been implemented in a program system by loosely integrating the Monte Carlo transport code MCNP, the three-dimensional discrete ordinates code TORT and a newly developed coupling interface program for mapping process. Test calculations were performed with comparison to MCNP solutions. Satisfactory agreements were obtained between these two approaches. The program system has been chosen to treat the complicated shielding problem of the accelerator-based IFMIF neutron source. The successful application demonstrates that coupling scheme with the program system is a useful computational tool for the shielding analysis of complex and large nuclear facilities. (authors)

  8. Computational Modeling of a Time-Independent, Heterogeneous Reactor Core Using Simplified Discrete Ordinates Neutron Transport Techniques

    National Research Council Canada - National Science Library

    Labowski, Kristofer

    2001-01-01

    The Linear Characteristic (LC) method on rectangular boxoid meshes is a discrete ordinate neutron transport technique that uses both zeroth and first moments of the angular neutron flux to construct a relatively accurate...

  9. A response matrix method for one-speed discrete ordinates fixed source problems in slab geometry with no spatial truncation error

    International Nuclear Information System (INIS)

    Lydia, Emilio J.; Barros, Ricardo C.

    2011-01-01

    In this paper we describe a response matrix method for one-speed slab-geometry discrete ordinates (SN) neutral particle transport problems that is completely free from spatial truncation errors. The unknowns in the method are the cell-edge angular fluxes of particles. The numerical results generated for these quantities are exactly those obtained from the analytic solution of the SN problem apart from finite arithmetic considerations. Our method is based on a spectral analysis that we perform in the SN equations with scattering inside a discretization cell of the spatial grid set up on the slab. As a result of this spectral analysis, we are able to obtain an expression for the local general solution of the SN equations. With this local general solution, we determine the response matrix and use the prescribed boundary conditions and continuity conditions to sweep across the discretization cells from left to right and from right to left across the slab, until a prescribed convergence criterion is satisfied. (author)

  10. The three-dimensional, discrete ordinates neutral particle transport code TORT: An overview

    International Nuclear Information System (INIS)

    Azmy, Y.Y.

    1996-01-01

    The centerpiece of the Discrete Ordinates Oak Ridge System (DOORS), the three-dimensional neutral particle transport code TORT is reviewed. Its most prominent features pertaining to large applications, such as adjustable problem parameters, memory management, and coarse mesh methods, are described. Advanced, state-of-the-art capabilities including acceleration and multiprocessing are summarized here. Future enhancement of existing graphics and visualization tools is briefly presented

  11. High order discrete ordinates transport in two dimensions

    International Nuclear Information System (INIS)

    Arkuszewski, J.J.

    1980-01-01

    A two-dimensional neutron transport equation in (x,y) geometry is solved by the subdomain version of the weighted residual method. The weight functions are chosen to be characteristic functions of computational boxes (subdomains). In the case of bilinear interpolant the conventional diamond relations are obtained, while the quadratic one produces generalized diamond relations containing first derivatives of the solution. The balance equation remains the same. The derivation yields also additional relations for extrapolating boundary values of derivatives and leaves the room for supplementing the interpolant with specially curtailed higher order polynomials. The method requires only slight modifications in inner iteration process used by conventional discrete ordinates programs, and has been introduced as an option into the program DOT2. The paper contains comparisons of the proposed method with conventional one based on calculations of IAEA-CRP transport theory benchmarks. (author)

  12. Discrete Ordinates Approximations to the First- and Second-Order Radiation Transport Equations

    International Nuclear Information System (INIS)

    FAN, WESLEY C.; DRUMM, CLIFTON R.; POWELL, JENNIFER L. email wcfan@sandia.gov

    2002-01-01

    The conventional discrete ordinates approximation to the Boltzmann transport equation can be described in a matrix form. Specifically, the within-group scattering integral can be represented by three components: a moment-to-discrete matrix, a scattering cross-section matrix and a discrete-to-moment matrix. Using and extending these entities, we derive and summarize the matrix representations of the second-order transport equations

  13. Discrete Ordinates Approximations to the First- and Second-Order Radiation Transport Equations

    CERN Document Server

    Fan, W C; Powell, J L

    2002-01-01

    The conventional discrete ordinates approximation to the Boltzmann transport equation can be described in a matrix form. Specifically, the within-group scattering integral can be represented by three components: a moment-to-discrete matrix, a scattering cross-section matrix and a discrete-to-moment matrix. Using and extending these entities, we derive and summarize the matrix representations of the second-order transport equations.

  14. First and second collision source for mitigating ray effects in discrete ordinate calculations

    International Nuclear Information System (INIS)

    Gomes, L.T.; Stevens, P.N.

    1991-01-01

    This work revisits the problem of ray effects in discrete ordinates calculations that frequently occurs in two- and three-dimensional systems which contain isolated sources within a highly absorbing medium. The effectiveness of using a first collision source or a second collision source are analyzed as possible remedies to mitigate this problem. The first collision and second collision sources are generated by three-dimensional Monte Carlo calculations that enables its application to a variety of source configurations, and the results can be coupled to a two- or three-dimensional discrete ordinates transport code. (author)

  15. CEPXS/ONELD: A one-dimensional coupled electron-photon discrete ordinates code package

    International Nuclear Information System (INIS)

    Lorence, L.J. Jr.; Morel, J.E.

    1992-01-01

    CEPXS/ONELD is a discrete ordinates transport code package that can model the electron-photon cascade from 100 MeV to 1 keV. The CEPXS code generates fully-coupled multigroup-Legendre cross section data. This data is used by the general-purpose discrete ordinates code, ONELD, which is derived from the Los Alamos ONEDANT and ONBTRAN codes. Version 1.0 of CEPXS/ONELD was released in 1989 and has been primarily used to analyze the effect of radiation environments on electronics. Version 2.0 is under development and will include user-friendly features such as the automatic selection of group structure, spatial mesh structure, and S N order

  16. A multi-layer discrete-ordinate method for vector radiative transfer in a vertically-inhomogeneous, emitting and scattering atmosphere. I - Theory. II - Application

    Science.gov (United States)

    Weng, Fuzhong

    1992-01-01

    A theory is developed for discretizing the vector integro-differential radiative transfer equation including both solar and thermal radiation. A complete solution and boundary equations are obtained using the discrete-ordinate method. An efficient numerical procedure is presented for calculating the phase matrix and achieving computational stability. With natural light used as a beam source, the Stokes parameters from the model proposed here are compared with the analytical solutions of Chandrasekhar (1960) for a Rayleigh scattering atmosphere. The model is then applied to microwave frequencies with a thermal source, and the brightness temperatures are compared with those from Stamnes'(1988) radiative transfer model.

  17. An analytical discrete-ordinates solution for an improved one-dimensional model of three-dimensional transport in ducts

    International Nuclear Information System (INIS)

    Garcia, R.D.M.

    2015-01-01

    Highlights: • An improved 1-D model of 3-D particle transport in ducts is studied. • The cases of isotropic and directional incidence are treated with the ADO method. • Accurate numerical results are reported for ducts of circular cross section. • A comparison with results of other authors is included. • The ADO method is found to be very efficient. - Abstract: An analytical discrete-ordinates solution is developed for the problem of particle transport in ducts, as described by a one-dimensional model constructed with two basis functions. Two types of particle incidence are considered: isotropic incidence and incidence described by the Dirac delta distribution. Accurate numerical results are tabulated for the reflection probabilities of semi-infinite ducts and the reflection and transmission probabilities of finite ducts. It is concluded that the developed solution is more efficient than commonly used numerical implementations of the discrete-ordinates method.

  18. Experiences in the parallelization of the discrete ordinates method using OpenMP and MPI

    Energy Technology Data Exchange (ETDEWEB)

    Pautz, A. [TUV Hannover/Sachsen-Anhalt e.V. (Germany); Langenbuch, S. [Gesellschaft fur Anlagen- und Reaktorsicherheit (GRS) mbH (Germany)

    2003-07-01

    The method of Discrete Ordinates is in principle parallelizable to a high degree, since the transport 'mesh sweeps' are mutually independent for all angular directions. However, in the well-known production code Dort such a type of angular domain decomposition has to be done on a spatial line-byline basis, causing the parallelism in the code to be very fine-grained. The construction of scalar fluxes and moments requires a large effort for inter-thread or inter-process communication. We have implemented two different parallelization approaches in Dort: firstly, we have used a shared-memory model suitable for SMP (Symmetric Multiprocessor) machines based on the standard OpenMP. The second approach uses the well-known Message Passing Interface (MPI) to establish communication between parallel processes running in a distributed-memory environment. We investigate the benefits and drawbacks of both models and show first results on performance and scaling behaviour of the parallel Dort code. (authors)

  19. Experiences in the parallelization of the discrete ordinates method using OpenMP and MPI

    International Nuclear Information System (INIS)

    Pautz, A.; Langenbuch, S.

    2003-01-01

    The method of Discrete Ordinates is in principle parallelizable to a high degree, since the transport 'mesh sweeps' are mutually independent for all angular directions. However, in the well-known production code Dort such a type of angular domain decomposition has to be done on a spatial line-byline basis, causing the parallelism in the code to be very fine-grained. The construction of scalar fluxes and moments requires a large effort for inter-thread or inter-process communication. We have implemented two different parallelization approaches in Dort: firstly, we have used a shared-memory model suitable for SMP (Symmetric Multiprocessor) machines based on the standard OpenMP. The second approach uses the well-known Message Passing Interface (MPI) to establish communication between parallel processes running in a distributed-memory environment. We investigate the benefits and drawbacks of both models and show first results on performance and scaling behaviour of the parallel Dort code. (authors)

  20. On discontinuous Galerkin and discrete ordinates approximations for neutron transport equation and the critical eigenvalue

    International Nuclear Information System (INIS)

    Asadzadeh, M.; Thevenot, L.

    2010-01-01

    The objective of this paper is to give a mathematical framework for a fully discrete numerical approach for the study of the neutron transport equation in a cylindrical domain (container model,). More specifically, we consider the discontinuous Galerkin (D G) finite element method for spatial approximation of the mono-energetic, critical neutron transport equation in an infinite cylindrical domain ??in R3 with a polygonal convex cross-section ? The velocity discretization relies on a special quadrature rule developed to give optimal estimates in discrete ordinate parameters compatible with the quasi-uniform spatial mesh. We use interpolation spaces and derive optimal error estimates, up to maximal available regularity, for the fully discrete scalar flux. Finally we employ a duality argument and prove superconvergence estimates for the critical eigenvalue.

  1. Boltzmann-Fokker-Planck calculations using standard discrete-ordinates codes

    International Nuclear Information System (INIS)

    Morel, J.E.

    1987-01-01

    The Boltzmann-Fokker-Planck (BFP) equation can be used to describe both neutral and charged-particle transport. Over the past several years, the author and several collaborators have developed methods for representing Fokker-Planck operators with standard multigroup-Legendre cross-section data. When these data are input to a standard S/sub n/ code such as ONETRAN, the code actually solves the Boltzmann-Fokker-Planck equation rather than the Boltzmann equation. This is achieved wihout any modification to the S/sub n/ codes. Because BFP calculations can be more demanding from a numerical viewpoint than standard neutronics calculations, we have found it useful to implement new quadrature methods ad convergence acceleration methods in the standard discrete-ordinates code, ONETRAN. We discuss our BFP cross-section representation techniques, our improved quadrature and acceleration techniques, and present results from BFP coupled electron-photon transport calculations performed with ONETRAN. 19 refs., 7 figs

  2. Generalized perturbation theory using two-dimensional, discrete ordinates transport theory

    International Nuclear Information System (INIS)

    Childs, R.L.

    1979-01-01

    Perturbation theory for changes in linear and bilinear functionals of the forward and adjoint fluxes in a critical reactor has been implemented using two-dimensional discrete ordinates transport theory. The computer program DOT IV was modified to calculate the generalized functions Λ and Λ*. Demonstration calculations were performed for changes in a reaction-rate ratio and a reactivity worth caused by system perturbations. The perturbation theory predictions agreed with direct calculations to within about 2%. A method has been developed for calculating higher lambda eigenvalues and eigenfunctions using techniques similar to those developed for generalized functions. Demonstration calculations have been performed to obtain these eigenfunctions

  3. Parallel Jacobian-free Newton Krylov solution of the discrete ordinates method with flux limiters for 3D radiative transfer

    International Nuclear Information System (INIS)

    Godoy, William F.; Liu Xu

    2012-01-01

    The present study introduces a parallel Jacobian-free Newton Krylov (JFNK) general minimal residual (GMRES) solution for the discretized radiative transfer equation (RTE) in 3D, absorbing, emitting and scattering media. For the angular and spatial discretization of the RTE, the discrete ordinates method (DOM) and the finite volume method (FVM) including flux limiters are employed, respectively. Instead of forming and storing a large Jacobian matrix, JFNK methods allow for large memory savings as the required Jacobian-vector products are rather approximated by semiexact and numerical formulations, for which convergence and computational times are presented. Parallelization of the GMRES solution is introduced in a combined memory-shared/memory-distributed formulation that takes advantage of the fact that only large vector arrays remain in the JFNK process. Results are presented for 3D test cases including a simple homogeneous, isotropic medium and a more complex non-homogeneous, non-isothermal, absorbing–emitting and anisotropic scattering medium with collimated intensities. Additionally, convergence and stability of Gram–Schmidt and Householder orthogonalizations for the Arnoldi process in the parallel GMRES algorithms are discussed and analyzed. Overall, the introduction of JFNK methods results in a parallel, yet scalable to the tested 2048 processors, and memory affordable solution to 3D radiative transfer problems without compromising the accuracy and convergence of a Newton-like solution.

  4. TRIDENT: a two-dimensional, multigroup, triangular mesh discrete ordinates, explicit neutron transport code

    International Nuclear Information System (INIS)

    Seed, T.J.; Miller, W.F. Jr.; Brinkley, F.W. Jr.

    1977-03-01

    TRIDENT solves the two-dimensional-multigroup-transport equations in rectangular (x-y) and cylindrical (r-z) geometries using a regular triangular mesh. Regular and adjoint, inhomogeneous and homogeneous (k/sub eff/ and eigenvalue searches) problems subject to vacuum, reflective, white, or source boundary conditions are solved. General anisotropic scattering is allowed and anisotropic-distributed sources are permitted. The discrete-ordinates approximation is used for the neutron directional variables. An option is included to append a fictitious source to the discrete-ordinates equations that is defined such that spherical-harmonics solutions (in x-y geometry) or spherical-harmonics-like solutions (in r-z geometry) are obtained. A spatial-finite-element method is used in which the angular flux is expressed as a linear polynomial in each triangle that is discontinous at triangle boundaries. Unusual Features of the program: Provision is made for creation of standard interface output files for S/sub N/ constants, angle-integrated (scalar) fluxes, and angular fluxes. Standard interface input files for S/sub N/ constants, inhomogeneous sources, cross sections, and the scalar flux may be read. Flexible edit options as well as a dump and restart capability are provided

  5. Numerical solution of neutron transport equations in discrete ordinates and slab geometry

    International Nuclear Information System (INIS)

    Serrano Pedraza, F.

    1985-01-01

    An unified formalism to solve numerically, between other equation, the neutron transport in discrete ordinates, slab geometry, several energy groups and independents of time, has been developed recently. Such a formalism cover some of the conventional schemes as diamond difference, (WDD) characteristic step (SC) lineal characteristic (LC), quadratic characteristic (QC) and lineal discontinuous. Unified formation gives before hand the convergence order of the previously selected scheme. In fact it allows besides to generate a big amount of numerical schemes, with which is also possible to solve numerical equations as soon as neutron transport. The essential purpose of this work was to solve the neutron transport equations in slab geometry and discrete ordinates considering several energy groups without to take under advisement time dependence based in the above mentioned unified formalism. To reach this purpose it was necesary to design a computer code with the name TNOD1 (Neutron transport in discrete ordinates and 1 dimension) which includes each one of the schemes already pointed out. there exist two numerical schemes, also recently developed, quadratic continuous (QC) and cubic continuous (CN), although covered by unified formalism, it has been possible to include them inside this computer code without make substantial changes in its structure. In chapter I, derivative of neutron transport equation independent of time is taken, for angular flux, including boundary conditions and discontinuity. In chapter II the neutron transport equations are obtained in multigroups, independents of time, for approximation of discrete ordinates. Description of theory related with unified formalism and its relationship with mentioned discretization schemes is presented in chapter III. Chapter IV describes the computer code developed and finally, in chapter V different numerical results obtained with TNOD1 program are shown. In Appendix A theorems and mathematical arguments used

  6. Three-dimensional discrete ordinates reactor assembly calculations on GPUs

    Energy Technology Data Exchange (ETDEWEB)

    Evans, Thomas M [ORNL; Joubert, Wayne [ORNL; Hamilton, Steven P [ORNL; Johnson, Seth R [ORNL; Turner, John A [ORNL; Davidson, Gregory G [ORNL; Pandya, Tara M [ORNL

    2015-01-01

    In this paper we describe and demonstrate a discrete ordinates sweep algorithm on GPUs. This sweep algorithm is nested within a multilevel comunication-based decomposition based on energy. We demonstrated the effectiveness of this algorithm on detailed three-dimensional critical experiments and PWR lattice problems. For these problems we show improvement factors of 4 6 over conventional communication-based, CPU-only sweeps. These sweep kernel speedups resulted in a factor of 2 total time-to-solution improvement.

  7. Discrete ordinate solution of the radiative transfer equation in the 'polarization normal wave representation'

    Science.gov (United States)

    Kylling, A.

    1991-01-01

    The transfer equations for normal waves in finite, inhomogeneous and plane-parallel magnetoactive media are solved using the discrete ordinate method. The physical process of absorption, emission, and multiple scattering are accounted for, and the medium may be forced both at the top and bottom boundary by anisotropic radiation as well as by internal anisotropic sources. The computational procedure is numerically stable for arbitrarily large optical depths, and the computer time is independent of optical thickness.

  8. Gamma-Weighted Discrete Ordinate Two-Stream Approximation for Computation of Domain Averaged Solar Irradiance

    Science.gov (United States)

    Kato, S.; Smith, G. L.; Barker, H. W.

    2001-01-01

    An algorithm is developed for the gamma-weighted discrete ordinate two-stream approximation that computes profiles of domain-averaged shortwave irradiances for horizontally inhomogeneous cloudy atmospheres. The algorithm assumes that frequency distributions of cloud optical depth at unresolved scales can be represented by a gamma distribution though it neglects net horizontal transport of radiation. This algorithm is an alternative to the one used in earlier studies that adopted the adding method. At present, only overcast cloudy layers are permitted.

  9. Explicit formulation of a nodal transport method for discrete ordinates calculations in two-dimensional fixed-source problems

    Energy Technology Data Exchange (ETDEWEB)

    Tres, Anderson [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Matematica Aplicada; Becker Picoloto, Camila [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica; Prolo Filho, Joao Francisco [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Inst de Matematica, Estatistica e Fisica; Dias da Cunha, Rudnei; Basso Barichello, Liliane [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Inst de Matematica

    2014-04-15

    In this work a study of two-dimensional fixed-source neutron transport problems, in Cartesian geometry, is reported. The approach reduces the complexity of the multidimensional problem using a combination of nodal schemes and the Analytical Discrete Ordinates Method (ADO). The unknown leakage terms on the boundaries that appear from the use of the derivation of the nodal scheme are incorporated to the problem source term, such as to couple the one-dimensional integrated solutions, made explicit in terms of the x and y spatial variables. The formulation leads to a considerable reduction of the order of the associated eigenvalue problems when combined with the usual symmetric quadratures, thereby providing solutions that have a higher degree of computational efficiency. Reflective-type boundary conditions are introduced to represent the domain on a simpler form than that previously considered in connection with the ADO method. Numerical results obtained with the technique are provided and compared to those present in the literature. (orig.)

  10. Discrete ordinates cross-section generation in parallel plane geometry -- 2: Computational results

    International Nuclear Information System (INIS)

    Yavuz, M.

    1998-01-01

    In Ref. 1, the author presented inverse discrete ordinates (S N ) methods for cross-section generation with an arbitrary scattering anisotropy of order L (L ≤ N - 1) in parallel plane geometry. The solution techniques depend on the S N eigensolutions. The eigensolutions are determined by the inverse simplified S N method (ISS N ), which uses the surface Green's function matrices (T and R). Inverse problems are generally designed so that experimentally measured physical quantities can be used in the formulations. In the formulations, although T and R (TR matrices) are measurable quantities, the author does not have such data to check the adequacy and accuracy of the methods. However, it is possible to compute TR matrices by S N methods. The author presents computational results and computationally observed properties

  11. The response matrix discrete ordinates solution to the 1D radiative transfer equation

    International Nuclear Information System (INIS)

    Ganapol, Barry D.

    2015-01-01

    The discrete ordinates method (DOM) of solution to the 1D radiative transfer equation has been an effective method of solution for nearly 70 years. During that time, the method has experienced numerous improvements as numerical and computational techniques have become more powerful and efficient. Here, we again consider the analytical solution to the discrete radiative transfer equation in a homogeneous medium by proposing a new, and consistent, form of solution that improves upon previous forms. Aided by a Wynn-epsilon convergence acceleration, its numerical evaluation can achieve extreme precision as demonstrated by comparison with published benchmarks. Finally, we readily extend the solution to a heterogeneous medium through the star product formulation producing a novel benchmark for closed form Henyey–Greenstein scattering as an example. - Highlights: • Presents a new solution to the RTE called the response matrix DOM (RM/DOM). • Solution representations avoid the instability common in exponential solutions. • Explicit form in terms of matrix hyperbolic functions. • Extreme accuracy through Wynn-epsilon acceleration checked by published benchmarks. • Provides a more transparent numerical evaluation than found previously

  12. The nodal discrete-ordinate transport calculation of anisotropy scattering problem in three-dimensional cartesian geometry

    International Nuclear Information System (INIS)

    Wu Hongchun; Xie Zhongsheng; Zhu Xuehua

    1994-01-01

    The nodal discrete-ordinate transport calculating model of anisotropy scattering problem in three-dimensional cartesian geometry is given. The computing code NOTRAN/3D has been encoded and the satisfied conclusion is gained

  13. Domain decomposition and CMFD acceleration applied to discrete-ordinate methods for the solution of the neutron transport equation in XYZ geometries

    International Nuclear Information System (INIS)

    Masiello, Emiliano; Martin, Brunella; Do, Jean-Michel

    2011-01-01

    A new development for the IDT solver is presented for large reactor core applications in XYZ geometries. The multigroup discrete-ordinate neutron transport equation is solved using a Domain-Decomposition (DD) method coupled with the Coarse-Mesh Finite Differences (CMFD). The later is used for accelerating the DD convergence rate. In particular, the external power iterations are preconditioned for stabilizing the oscillatory behavior of the DD iterative process. A set of critical 2-D and 3-D numerical tests on a single processor will be presented for the analysis of the performances of the method. The results show that the application of the CMFD to the DD can be a good candidate for large 3D full-core parallel applications. (author)

  14. Two-dimensional discrete ordinates photon transport calculations for brachytherapy dosimetry applications

    International Nuclear Information System (INIS)

    Daskalov, G.M.; Baker, R.S.; Little, R.C.; Rogers, D.W.O.; Williamson, J.F.

    2000-01-01

    The DANTSYS discrete ordinates computer code system is applied to quantitative estimation of water kerma rate distributions in the vicinity of discrete photon sources with energies in the 20- to 800-keV range in two-dimensional cylindrical r-z geometry. Unencapsulated sources immersed in cylindrical water phantoms of 40-cm diameter and 40-cm height are modeled in either homogeneous phantoms or shielded by Ti, Fe, and Pb filters with thicknesses of 1 and 2 mean free paths. The obtained dose results are compared with corresponding photon Monte Carlo simulations. A 210-group photon cross-section library for applications in this energy range is developed and applied, together with a general-purpose 42-group library developed at Los Alamos National Laboratory, for DANTSYS calculations. The accuracy of DANTSYS with the 42-group library relative to Monte Carlo exhibits large pointwise fluctuations from -42 to +84%. The major cause for the observed discrepancies is determined to be the inadequacy of the weighting function used for the 42-group library derivation. DANTSYS simulations with a finer 210-group library show excellent accuracy on and off the source transverse plane relative to Monte Carlo kerma calculations, varying from minus4.9 to 3.7%. The P 3 Legendre polynomial expansion of the angular scattering function is shown to be sufficient for accurate calculations. The results demonstrate that DANTSYS is capable of calculating photon doses in very good agreement with Monte Carlo and that the multigroup cross-section library and efficient techniques for mitigation of ray effects are critical for accurate discrete ordinates implementation

  15. Pin cell discontinuity factors in the transient 3-D discrete ordinates code TORT-TD - 237

    International Nuclear Information System (INIS)

    Seubert, A.

    2010-01-01

    This paper describes the application of generalized equivalence theory to the time-dependent 3-D discrete ordinates neutron transport code TORT-TD. The introduction of pin cell discontinuity factors into the discrete ordinates transport equation is described by assuming a linear dependence of the homogenized neutron angular flux within a pin cell which may be discontinuous at the interfaces to adjacent cells. The homogenized flux discontinuity at cell interfaces is expressed by pin cell discontinuity factors which in turn are determined from fuel assembly lattice calculations using HELIOS. Application of TORT-TD to the all rods in state of the PWR MOX/UO 2 Core Transient Benchmark with pin cell homogenized nuclear cross sections demonstrate the potential of pin cell discontinuity factors to reduce pin cell homogenization errors. (authors)

  16. The discrete cones method for two-dimensional neutron transport calculations

    International Nuclear Information System (INIS)

    Watanabe, Y.; Maynard, C.W.

    1986-01-01

    A novel method, the discrete cones method (DC/sub N/), is proposed as an alternative to the discrete ordinates method (S/sub N/) for solutions of the two-dimensional neutron transport equation. The new method utilizes a new concept, discrete cones, which are made by partitioning a unit spherical surface that the direction vector of particles covers. In this method particles in a cone are simultaneously traced instead of those in discrete directions so that an anomaly of the S/sub N/ method, the ray effects, can be eliminated. The DC/sub N/ method has been formulated for X-Y geometry and a program has been creaed by modifying the standard S/sub N/ program TWOTRAN-II. Our sample calculations demonstrate a strong mitigation of the ray effects without a computing cost penalty

  17. Development of parallel 3D discrete ordinates transport program on JASMIN framework

    International Nuclear Information System (INIS)

    Cheng, T.; Wei, J.; Shen, H.; Zhong, B.; Deng, L.

    2015-01-01

    A parallel 3D discrete ordinates radiation transport code JSNT-S is developed, aiming at simulating real-world radiation shielding and reactor physics applications in a reasonable time. Through the patch-based domain partition algorithm, the memory requirement is shared among processors and a space-angle parallel sweeping algorithm is developed based on data-driven algorithm. Acceleration methods such as partial current rebalance are implemented. The correctness is proved through the VENUS-3 and other benchmark models. In the radiation shielding calculation of the Qinshan-II reactor pressure vessel model with 24.3 billion DoF, only 88 seconds is required and the overall parallel efficiency of 44% is achieved on 1536 CPU cores. (author)

  18. Analysis of QUADOS problem on TLD-ALBEDO personal dosemeter responses using discrete ordinates and Monte Carlo methods

    International Nuclear Information System (INIS)

    Kodeli, I.; Tanner, R.

    2005-01-01

    In the scope of QUADOS, a Concerted Action of the European Commission, eight calculational problems were prepared in order to evaluate the use of computational codes for dosimetry in radiation protection and medical physics, and to disseminate 'good practice' throughout the radiation dosimetry community. This paper focuses on the analysis of the P4 problem on the 'TLD-albedo dosemeter: neutron and/or photon response of a four-element TL-dosemeter mounted on a standard ISO slab phantom'. Altogether 17 solutions were received from the participants, 14 of those transported neutrons and 15 photons. Most participants (16 out of 17) used Monte Carlo methods. These calculations are time-consuming, requiring several days of CPU time to perform the whole set of calculations and achieve good statistical precision. The possibility of using deterministic discrete ordinates codes as an alternative to Monte Carlo was therefore investigated and is presented here. In particular the capacity of the adjoint mode calculations is shown. (authors)

  19. On the use of flux limiters in the discrete ordinates method for 3D radiation calculations in absorbing and scattering media

    International Nuclear Information System (INIS)

    Godoy, William F.; DesJardin, Paul E.

    2010-01-01

    The application of flux limiters to the discrete ordinates method (DOM), S N , for radiative transfer calculations is discussed and analyzed for 3D enclosures for cases in which the intensities are strongly coupled to each other such as: radiative equilibrium and scattering media. A Newton-Krylov iterative method (GMRES) solves the final systems of linear equations along with a domain decomposition strategy for parallel computation using message passing libraries in a distributed memory system. Ray effects due to angular discretization and errors due to domain decomposition are minimized until small variations are introduced by these effects in order to focus on the influence of flux limiters on errors due to spatial discretization, known as numerical diffusion, smearing or false scattering. Results are presented for the DOM-integrated quantities such as heat flux, irradiation and emission. A variety of flux limiters are compared to 'exact' solutions available in the literature, such as the integral solution of the RTE for pure absorbing-emitting media and isotropic scattering cases and a Monte Carlo solution for a forward scattering case. Additionally, a non-homogeneous 3D enclosure is included to extend the use of flux limiters to more practical cases. The overall balance of convergence, accuracy, speed and stability using flux limiters is shown to be superior compared to step schemes for any test case.

  20. Application of the 2-D discrete-ordinates method to multiple scattering of laser radiation

    International Nuclear Information System (INIS)

    Zardecki, A.; Gerstl, S.A.W.; Embury, J.F.

    1983-01-01

    The discrete-ordinates finite-element radiation transport code twotran is applied to describe the multiple scattering of a laser beam from a reflecting target. For a model scenario involving a 99% relative humidity rural aerosol we compute the average intensity of the scattered radiation and correction factors to the Beer-Lambert law arising from multiple scattering. As our results indicate, 2-D x-y and r-z geometry modeling can reliably describe a realistic 3-D scenario. Specific results are presented for the two visual ranges of 1.52 and 0.76 km which show that, for sufficiently high aerosol concentrations (e.g., equivalent to V = 0.76 km), the target signature in a distant detector becomes dominated by multiply scattered radiation from interactions of the laser light with the aerosol environment. The merits of the scaling group and the delta-M approximation for the transfer equation are also explored

  1. ASOP, Shield Calculation, 1-D, Discrete Ordinates Transport

    International Nuclear Information System (INIS)

    1993-01-01

    1 - Nature of physical problem solved: ASOP is a shield optimization calculational system based on the one-dimensional discrete ordinates transport program ANISN. It has been used to design optimum shields for space applications of SNAP zirconium-hydride-uranium- fueled reactors and uranium-oxide fueled thermionic reactors and to design beam stops for the ORELA facility. 2 - Method of solution: ASOP generates coefficients of linear equations describing the logarithm of the dose and dose-weight derivatives as functions of position from data obtained in an automated sequence of ANISN calculations. With the dose constrained to a design value and all dose-weight derivatives required to be equal, the linear equations may be solved for a new set of shield dimensions. Since changes in the shield dimensions may cause the linear functions to change, the entire procedure is repeated until convergence is obtained. The detailed calculations of the radiation transport through shield configurations for every step in the procedure distinguish ASOP from other shield optimization computer code systems which rely on multiple component sources and attenuation coefficients to describe the transport. 3 - Restrictions on the complexity of the problem: Problem size is limited only by machine size

  2. Generating Importance Map for Geometry Splitting using Discrete Ordinates Code in Deep Shielding Problem

    International Nuclear Information System (INIS)

    Kim, Jong Woon; Lee, Young Ouk

    2016-01-01

    When we use MCNP code for a deep shielding problem, we prefer to use variance reduction technique such as geometry splitting, or weight window, or source biasing to have relative error within reliable confidence interval. To generate importance map for geometry splitting in MCNP calculation, we should know the track entering number and previous importance on each cells since a new importance is calculated based on these information. If a problem is deep shielding problem such that we have zero tracks entering on a cell, we cannot generate new importance map. In this case, discrete ordinates code can provide information to generate importance map easily. In this paper, we use AETIUS code as a discrete ordinates code. Importance map for MCNP is generated based on a zone average flux of AETIUS calculation. The discretization of space, angle, and energy is not necessary for MCNP calculation. This is the big merit of MCNP code compared to the deterministic code. However, deterministic code (i.e., AETIUS) can provide a rough estimate of the flux throughout a problem relatively quickly. This can help MCNP by providing variance reduction parameters. Recently, ADVANTG code is released. This is an automated tool for generating variance reduction parameters for fixed-source continuous-energy Monte Carlo simulations with MCNP5 v1.60

  3. A parallel algorithm for solving the multidimensional within-group discrete ordinates equations with spatial domain decomposition - 104

    International Nuclear Information System (INIS)

    Zerr, R.J.; Azmy, Y.Y.

    2010-01-01

    A spatial domain decomposition with a parallel block Jacobi solution algorithm has been developed based on the integral transport matrix formulation of the discrete ordinates approximation for solving the within-group transport equation. The new methodology abandons the typical source iteration scheme and solves directly for the fully converged scalar flux. Four matrix operators are constructed based upon the integral form of the discrete ordinates equations. A single differential mesh sweep is performed to construct these operators. The method is parallelized by decomposing the problem domain into several smaller sub-domains, each treated as an independent problem. The scalar flux of each sub-domain is solved exactly given incoming angular flux boundary conditions. Sub-domain boundary conditions are updated iteratively, and convergence is achieved when the scalar flux error in all cells meets a pre-specified convergence criterion. The method has been implemented in a computer code that was then employed for strong scaling studies of the algorithm's parallel performance via a fixed-size problem in tests ranging from one domain up to one cell per sub-domain. Results indicate that the best parallel performance compared to source iterations occurs for optically thick, highly scattering problems, the variety that is most difficult for the traditional SI scheme to solve. Moreover, the minimum execution time occurs when each sub-domain contains a total of four cells. (authors)

  4. Ray effects in the discrete-ordinate solution for surface radiation exchange

    Energy Technology Data Exchange (ETDEWEB)

    Liou, B T [Dept. of Mechanical Engineering, National Cheng Kung Univ., Tainan (Taiwan, Province of China); Wu, C Y [Dept. of Mechanical Engineering, National Cheng Kung Univ., Tainan (Taiwan, Province of China)

    1997-04-01

    A study of the application of the discrete-ordinate method (DOM) with remedy for the ray effects to the solution of surface radiation exchange is presented in this paper. The remedy for the ray effects is achieved by dividing the radiative intensity into the attenuated incident and the medium emitting components. To demonstrate the application of the technique, this work considers radiative heat transfer in a two-dimensional cylindrical enclosure filled with a nearly transparent medium. The results obtained by the present DOM are in excellent agreement with those by the radiosity/irradiation method. (orig.). With 4 figs., 3 tabs. [Deutsch] In der Arbeit wird ein Weg aufgezeigt, wie die Stoerstrahlungseffekte bei Anwendung der Methode der diskreten Ordinaten auf die Berechnung des Energietausches zwischen Oberflaechenstrahlern vermieden werden koennen. Dies laesst sich durch Aufspaltung der Strahlungsintensitaet in die abgeschwaechte einfallende und die vom Medium emittierte Komponente erreichen. Als Beispiel fuer die Anwendung dieses Verfahrens dient der Waermeaustausch durch Strahlung in einem zweidimensionalen zylindrischen Behaeltnis, das mit einem nahezu transparenten Medium befuellt ist. Die mit der modifizierten Methode erhaltenen Ergebnisse stimmen ausgezeichnet mit jenen nach dem klassischen Brutto-Verfahren ueberein. (orig.)

  5. An analytical discrete ordinates solution for a nodal model of a two-dimensional neutron transport problem

    International Nuclear Information System (INIS)

    Filho, J. F. P.; Barichello, L. B.

    2013-01-01

    In this work, an analytical discrete ordinates method is used to solve a nodal formulation of a neutron transport problem in x, y-geometry. The proposed approach leads to an important reduction in the order of the associated eigenvalue systems, when combined with the classical level symmetric quadrature scheme. Auxiliary equations are proposed, as usually required for nodal methods, to express the unknown fluxes at the boundary introduced as additional unknowns in the integrated equations. Numerical results, for the problem defined by a two-dimensional region with a spatially constant and isotropically emitting source, are presented and compared with those available in the literature. (authors)

  6. A Deep Penetration Problem Calculation Using AETIUS:An Easy Modeling Discrete Ordinates Transport Code UsIng Unstructured Tetrahedral Mesh, Shared Memory Parallel

    Science.gov (United States)

    KIM, Jong Woon; LEE, Young-Ouk

    2017-09-01

    As computing power gets better and better, computer codes that use a deterministic method seem to be less useful than those using the Monte Carlo method. In addition, users do not like to think about space, angles, and energy discretization for deterministic codes. However, a deterministic method is still powerful in that we can obtain a solution of the flux throughout the problem, particularly as when particles can barely penetrate, such as in a deep penetration problem with small detection volumes. Recently, a new state-of-the-art discrete-ordinates code, ATTILA, was developed and has been widely used in several applications. ATTILA provides the capabilities to solve geometrically complex 3-D transport problems by using an unstructured tetrahedral mesh. Since 2009, we have been developing our own code by benchmarking ATTILA. AETIUS is a discrete ordinates code that uses an unstructured tetrahedral mesh such as ATTILA. For pre- and post- processing, Gmsh is used to generate an unstructured tetrahedral mesh by importing a CAD file (*.step) and visualizing the calculation results of AETIUS. Using a CAD tool, the geometry can be modeled very easily. In this paper, we describe a brief overview of AETIUS and provide numerical results from both AETIUS and a Monte Carlo code, MCNP5, in a deep penetration problem with small detection volumes. The results demonstrate the effectiveness and efficiency of AETIUS for such calculations.

  7. BALTORO a general purpose code for coupling discrete ordinates and Monte-Carlo radiation transport calculations

    International Nuclear Information System (INIS)

    Zazula, J.M.

    1983-01-01

    The general purpose code BALTORO was written for coupling the three-dimensional Monte-Carlo /MC/ with the one-dimensional Discrete Ordinates /DO/ radiation transport calculations. The quantity of a radiation-induced /neutrons or gamma-rays/ nuclear effect or the score from a radiation-yielding nuclear effect can be analysed in this way. (author)

  8. Intercomparison of the finite difference and nodal discrete ordinates and surface flux transport methods for a LWR pool-reactor benchmark problem in X-Y geometry

    International Nuclear Information System (INIS)

    O'Dell, R.D.; Stepanek, J.; Wagner, M.R.

    1983-01-01

    The aim of the present work is to compare and discuss the three of the most advanced two dimensional transport methods, the finite difference and nodal discrete ordinates and surface flux method, incorporated into the transport codes TWODANT, TWOTRAN-NODAL, MULTIMEDIUM and SURCU. For intercomparison the eigenvalue and the neutron flux distribution are calculated using these codes in the LWR pool reactor benchmark problem. Additionally the results are compared with some results obtained by French collision probability transport codes MARSYAS and TRIDENT. Because the transport solution of this benchmark problem is close to its diffusion solution some results obtained by the finite element diffusion code FINELM and the finite difference diffusion code DIFF-2D are included

  9. Timing comparison of two-dimensional discrete-ordinates codes for criticality calculations

    International Nuclear Information System (INIS)

    Miller, W.F. Jr.; Alcouffe, R.E.; Bosler, G.E.; Brinkley, F.W. Jr.; O'dell, R.D.

    1979-01-01

    The authors compare two-dimensional discrete-ordinates neutron transport computer codes to solve reactor criticality problems. The fundamental interest is in determining which code requires the minimum Central Processing Unit (CPU) time for a given numerical model of a reasonably realistic fast reactor core and peripherals. The computer codes considered are the most advanced available and, in three cases, are not officially released. The conclusion, based on the study of four fast reactor core models, is that for this class of problems the diffusion synthetic accelerated version of TWOTRAN, labeled TWOTRAN-DA, is superior to the other codes in terms of CPU requirements

  10. Radiative transfer equation accounting for rotational Raman scattering and its solution by the discrete-ordinates method

    International Nuclear Information System (INIS)

    Rozanov, Vladimir V.; Vountas, Marco

    2014-01-01

    Rotational Raman scattering of solar light in Earth's atmosphere leads to the filling-in of Fraunhofer and telluric lines observed in the reflected spectrum. The phenomenological derivation of the inelastic radiative transfer equation including rotational Raman scattering is presented. The different forms of the approximate radiative transfer equation with first-order rotational Raman scattering terms are obtained employing the Cabannes, Rayleigh, and Cabannes–Rayleigh scattering models. The solution of these equations is considered in the framework of the discrete-ordinates method using rigorous and approximate approaches to derive particular integrals. An alternative forward-adjoint technique is suggested as well. A detailed description of the model including the exact spectral matching and a binning scheme that significantly speeds up the calculations is given. The considered solution techniques are implemented in the radiative transfer software package SCIATRAN and a specified benchmark setup is presented to enable readers to compare with own results transparently. -- Highlights: • We derived the radiative transfer equation accounting for rotational Raman scattering. • Different approximate radiative transfer approaches with first order scattering were used. • Rigorous and approximate approaches are shown to derive particular integrals. • An alternative forward-adjoint technique is suggested as well. • An additional spectral binning scheme which speeds up the calculations is presented

  11. A parallel algorithm for solving the integral form of the discrete ordinates equations

    International Nuclear Information System (INIS)

    Zerr, R. J.; Azmy, Y. Y.

    2009-01-01

    The integral form of the discrete ordinates equations involves a system of equations that has a large, dense coefficient matrix. The serial construction methodology is presented and properties that affect the execution times to construct and solve the system are evaluated. Two approaches for massively parallel implementation of the solution algorithm are proposed and the current results of one of these are presented. The system of equations May be solved using two parallel solvers-block Jacobi and conjugate gradient. Results indicate that both methods can reduce overall wall-clock time for execution. The conjugate gradient solver exhibits better performance to compete with the traditional source iteration technique in terms of execution time and scalability. The parallel conjugate gradient method is synchronous, hence it does not increase the number of iterations for convergence compared to serial execution, and the efficiency of the algorithm demonstrates an apparent asymptotic decline. (authors)

  12. ANISN-L, a CDC-7600 code which solves the one-dimensional, multigroup, time dependent transport equation by the method of discrete ordinates

    Energy Technology Data Exchange (ETDEWEB)

    Wilcox, T. P.

    1973-09-20

    The code ANISN-L solves the one-dimensional, multigroup, time-independent Boltzmann transport equation by the method of discrete ordinates. In problems involving a fissionable system, it can calculate the system multiplication or alpha. In such cases, it is also capable of determining isotopic concentrations, radii, zone widths, or buckling in order to achieve a given multiplication or alpha. The code may also calculate fluxes caused by a specified fixed source. Neutron, gamma, and coupled neutron--gamma problems may be solved in either the forward or adjoint (backward) modes. Cross sections describing upscatter, as well as the usual downscatter, may be employed. This report describes the use of ANISN-L; this is a revised version of ANISN which handles both large and small problems efficiently on CDC-7600 computers. (RWR)

  13. Exponential characteristics spatial quadrature for discrete ordinates radiation transport in slab geometry

    International Nuclear Information System (INIS)

    Mathews, K.; Sjoden, G.; Minor, B.

    1994-01-01

    The exponential characteristic spatial quadrature for discrete ordinates neutral particle transport in slab geometry is derived and compared with current methods. It is similar to the linear characteristic (or, in slab geometry, the linear nodal) quadrature but differs by assuming an exponential distribution of the scattering source within each cell, S(x) = a exp(bx), whose parameters are root-solved to match the known (from the previous iteration) average and first moment of the source over the cell. Like the linear adaptive method, the exponential characteristic method is positive and nonlinear but more accurate and more readily extended to other cell shapes. The nonlinearity has not interfered with convergence. The authors introduce the ''exponential moment functions,'' a generalization of the functions used by Walters in the linear nodal method, and use them to avoid numerical ill-conditioning. The method exhibits O(Δx 4 ) truncation error on fine enough meshes; the error is insensitive to mesh size for coarse meshes. In a shielding problem, it is accurate to 10% using 16-mfp-thick cells; conventional methods err by 8 to 15 orders of magnitude. The exponential characteristic method is computationally more costly per cell than current methods but can be accurate with very thick cells, leading to increased computational efficiency on appropriate problems

  14. The discrete cones methods for two-dimensional neutral particle transport problems with voids

    International Nuclear Information System (INIS)

    Watanabe, Y.; Maynard, C.W.

    1983-01-01

    One of the most widely applied deterministic methods for time-independent, two-dimensional neutron transport calculations is the discrete ordinates method (DSN). The DSN solution, however, fails to be accurate in a void due to the ray effect. In order to circumvent this drawback, the authors have been developing a novel approximation: the discrete cones method (DCN), where a group of particles in a cone are simultaneously traced instead of particles in discrete directions for the DSN method. Programs, which apply to the DSN method in a non-vacuum region and the DCN method in a void, have been written for transport calculations in X-Y coordinates. The solutions for test problems demonstrate mitigation of the ray effect in voids without loosing the computational efficiency of the DSN method

  15. The TORT three-dimensional discrete ordinates neutron/photon transport code (TORT version 3)

    Energy Technology Data Exchange (ETDEWEB)

    Rhoades, W.A.; Simpson, D.B.

    1997-10-01

    TORT calculates the flux or fluence of neutrons and/or photons throughout three-dimensional systems due to particles incident upon the system`s external boundaries, due to fixed internal sources, or due to sources generated by interaction with the system materials. The transport process is represented by the Boltzman transport equation. The method of discrete ordinates is used to treat the directional variable, and a multigroup formulation treats the energy dependence. Anisotropic scattering is treated using a Legendre expansion. Various methods are used to treat spatial dependence, including nodal and characteristic procedures that have been especially adapted to resist numerical distortion. A method of body overlay assists in material zone specification, or the specification can be generated by an external code supplied by the user. Several special features are designed to concentrate machine resources where they are most needed. The directional quadrature and Legendre expansion can vary with energy group. A discontinuous mesh capability has been shown to reduce the size of large problems by a factor of roughly three in some cases. The emphasis in this code is a robust, adaptable application of time-tested methods, together with a few well-tested extensions.

  16. Preparing the generalized Harvey–Shack rough surface scattering method for use with the discrete ordinates method

    DEFF Research Database (Denmark)

    Johansen, Villads Egede

    2015-01-01

    The paper shows how to implement the generalized Harvey–Shack (GHS) method for isotropic rough surfaces discretized in a polar coordinate system and approximated using Fourier series. This is particularly relevant for the use of the GHS method as a boundary condition for radiative transfer proble...

  17. Analysis of Massively Parallel Discrete-Ordinates Transport Sweep Algorithms with Collisions

    International Nuclear Information System (INIS)

    Bailey, T.S.; Falgout, R.D.

    2008-01-01

    We present theoretical scaling models for a variety of discrete-ordinates sweep algorithms. In these models, we pay particular attention to the way each algorithm handles collisions. A collision is defined as a processor having multiple angles with ready to be swept during one stage of the sweep. The models also take into account how subdomains are assigned to processors and how angles are grouped during the sweep. We describe a data driven algorithm that resolves collisions efficiently during the sweep as well as other algorithms that have been designed to avoid collisions completely. Our models are validated using the ARGES and AMTRAN transport codes. We then use the models to study and predict scaling trends in all of the sweep algorithms

  18. C5 Benchmark Problem with Discrete Ordinate Radiation Transport Code DENOVO

    Energy Technology Data Exchange (ETDEWEB)

    Yesilyurt, Gokhan [ORNL; Clarno, Kevin T [ORNL; Evans, Thomas M [ORNL; Davidson, Gregory G [ORNL; Fox, Patricia B [ORNL

    2011-01-01

    The C5 benchmark problem proposed by the Organisation for Economic Co-operation and Development/Nuclear Energy Agency was modeled to examine the capabilities of Denovo, a three-dimensional (3-D) parallel discrete ordinates (S{sub N}) radiation transport code, for problems with no spatial homogenization. Denovo uses state-of-the-art numerical methods to obtain accurate solutions to the Boltzmann transport equation. Problems were run in parallel on Jaguar, a high-performance supercomputer located at Oak Ridge National Laboratory. Both the two-dimensional (2-D) and 3-D configurations were analyzed, and the results were compared with the reference MCNP Monte Carlo calculations. For an additional comparison, SCALE/KENO-V.a Monte Carlo solutions were also included. In addition, a sensitivity analysis was performed for the optimal angular quadrature and mesh resolution for both the 2-D and 3-D infinite lattices of UO{sub 2} fuel pin cells. Denovo was verified with the C5 problem. The effective multiplication factors, pin powers, and assembly powers were found to be in good agreement with the reference MCNP and SCALE/KENO-V.a Monte Carlo calculations.

  19. Slab geometry spatial discretization schemes with infinite-order convergence

    International Nuclear Information System (INIS)

    Adams, M.L.; Martin, W.R.

    1985-01-01

    Spatial discretization schemes for the slab geometry discrete ordinates transport equation have received considerable attention in the past several years, with particular interest shown in developing methods that are more computationally efficient that standard schemes. Here the authors apply to the discrete ordinates equations a spectral method that is significantly more efficient than previously proposed schemes for high-accuracy calculations of homogeneous problems. This is a direct consequence of the exponential (infinite-order) convergence of spectral methods for problems with every smooth solutions. For heterogeneous problems where smooth solutions do not exist and exponential convergence is not observed with spectral methods, a spectral element method is proposed which does exhibit exponential convergence

  20. Discrete ordinates solution of coupled conductive radiative heat transfer in a two-layer slab with Fresnel interfaces subject to diffuse and obliquely collimated irradiation

    International Nuclear Information System (INIS)

    Muresan, Cristian; Vaillon, Rodolphe; Menezo, Christophe; Morlot, Rodolphe

    2004-01-01

    The coupled conductive radiative heat transfer in a two-layer slab with Fresnel interfaces subject to diffuse and obliquely collimated irradiation is solved. The collimated and diffuse components problems are treated separately. The solution for diffuse radiation is obtained by using a composite discrete ordinates method and includes the development of adaptive directional quadratures to overcome the difficulties usually encountered at the interfaces. The complete radiation numerical model is validated against the predictions obtained by using the Monte Carlo method

  1. Spectral nodal methodology for multigroup slab-geometry discrete ordinates neutron transport problems with linearly anisotropic scattering

    Energy Technology Data Exchange (ETDEWEB)

    Oliva, Amaury M.; Filho, Hermes A.; Silva, Davi M.; Garcia, Carlos R., E-mail: aoliva@iprj.uerj.br, E-mail: halves@iprj.uerj.br, E-mail: davijmsilva@yahoo.com.br, E-mail: cgh@instec.cu [Universidade do Estado do Rio de Janeiro (UERJ), Nova Friburgo, RJ (Brazil). Instituto Politecnico. Departamento de Modelagem Computacional; Instituto Superior de Tecnologias y Ciencias Aplicadas (InSTEC), La Habana (Cuba)

    2017-07-01

    In this paper, we propose a numerical methodology for the development of a method of the spectral nodal class that will generate numerical solutions free from spatial truncation errors. This method, denominated Spectral Deterministic Method (SDM), is tested as an initial study of the solutions (spectral analysis) of neutron transport equations in the discrete ordinates (S{sub N}) formulation, in one-dimensional slab geometry, multigroup approximation, with linearly anisotropic scattering, considering homogeneous and heterogeneous domains with fixed source. The unknowns in the methodology are the cell-edge, and cell average angular fluxes, the numerical values calculated for these quantities coincide with the analytic solution of the equations. These numerical results are shown and compared with the traditional ne- mesh method Diamond Difference (DD) and the coarse-mesh method spectral Green's function (SGF) to illustrate the method's accuracy and stability. The solution algorithms problems are implemented in a computer simulator made in C++ language, the same that was used to generate the results of the reference work. (author)

  2. Augmenting Ordinal Methods of Attribute Weight Approximation

    DEFF Research Database (Denmark)

    Daneilson, Mats; Ekenberg, Love; He, Ying

    2014-01-01

    of the obstacles and methods for introducing so-called surrogate weights have proliferated in the form of ordinal ranking methods for criteria weights. Considering the decision quality, one main problem is that the input information allowed in ordinal methods is sometimes too restricted. At the same time, decision...... makers often possess more background information, for example, regarding the relative strengths of the criteria, and might want to use that. We propose combined methods for facilitating the elicitation process and show how this provides a way to use partial information from the strength of preference...

  3. Description of a neutron field perturbed by a probe using coupled Monte Carlo and discrete ordinates radiation transport calculations

    International Nuclear Information System (INIS)

    Zazula, J.M.

    1984-01-01

    This work concerns calculation of a neutron response, caused by a neutron field perturbed by materials surrounding the source or the detector. Solution of a problem is obtained using coupling of the Monte Carlo radiation transport computation for the perturbed region and the discrete ordinates transport computation for the unperturbed system. (author). 62 refs

  4. Approximate albedo boundary conditions for energy multigroup X,Y-geometry discrete ordinates nuclear global calculations

    Energy Technology Data Exchange (ETDEWEB)

    Silva, Davi J.M.; Nunes, Carlos E.A.; Alves Filho, Hermes; Barros, Ricardo C., E-mail: davijmsilva@yahoo.com.br, E-mail: ceanunes@yahoo.com.br, E-mail: rcbarros@pq.cnpq.br [Secretaria Municipal de Educacao de Itaborai, RJ (Brazil); Universidade Estacio de Sa (UNESA), Rio de Janeiro, RJ (Brazil); Universidade do Estado do Rio de Janeiro (UERJ), Novra Friburgo, RJ (Brazil). Instituto Politecnico. Departamento de Modelagem Computacional

    2017-11-01

    Discussed here is the accuracy of approximate albedo boundary conditions for energy multigroup discrete ordinates (S{sub N}) eigenvalue problems in two-dimensional rectangular geometry for criticality calculations in neutron fission reacting systems, such as nuclear reactors. The multigroup (S{sub N}) albedo matrix substitutes approximately the non-multiplying media around the core, e.g., baffle and reflector, as we neglect the transverse leakage terms within these non-multiplying regions. Numerical results to a typical model problem are given to illustrate the accuracy versus the computer running time. (author)

  5. Mimetic discretization methods

    CERN Document Server

    Castillo, Jose E

    2013-01-01

    To help solve physical and engineering problems, mimetic or compatible algebraic discretization methods employ discrete constructs to mimic the continuous identities and theorems found in vector calculus. Mimetic Discretization Methods focuses on the recent mimetic discretization method co-developed by the first author. Based on the Castillo-Grone operators, this simple mimetic discretization method is invariably valid for spatial dimensions no greater than three. The book also presents a numerical method for obtaining corresponding discrete operators that mimic the continuum differential and

  6. Advanced quadrature sets and acceleration and preconditioning techniques for the discrete ordinates method in parallel computing environments

    Science.gov (United States)

    Longoni, Gianluca

    In the nuclear science and engineering field, radiation transport calculations play a key-role in the design and optimization of nuclear devices. The linear Boltzmann equation describes the angular, energy and spatial variations of the particle or radiation distribution. The discrete ordinates method (S N) is the most widely used technique for solving the linear Boltzmann equation. However, for realistic problems, the memory and computing time require the use of supercomputers. This research is devoted to the development of new formulations for the SN method, especially for highly angular dependent problems, in parallel environments. The present research work addresses two main issues affecting the accuracy and performance of SN transport theory methods: quadrature sets and acceleration techniques. New advanced quadrature techniques which allow for large numbers of angles with a capability for local angular refinement have been developed. These techniques have been integrated into the 3-D SN PENTRAN (Parallel Environment Neutral-particle TRANsport) code and applied to highly angular dependent problems, such as CT-Scan devices, that are widely used to obtain detailed 3-D images for industrial/medical applications. In addition, the accurate simulation of core physics and shielding problems with strong heterogeneities and transport effects requires the numerical solution of the transport equation. In general, the convergence rate of the solution methods for the transport equation is reduced for large problems with optically thick regions and scattering ratios approaching unity. To remedy this situation, new acceleration algorithms based on the Even-Parity Simplified SN (EP-SSN) method have been developed. A new stand-alone code system, PENSSn (Parallel Environment Neutral-particle Simplified SN), has been developed based on the EP-SSN method. The code is designed for parallel computing environments with spatial, angular and hybrid (spatial/angular) domain

  7. On the adequacy of Cartesian geometry discrete ordinates solutions for assembly calculations

    International Nuclear Information System (INIS)

    Schunert, S.; Azmy, Y. Y.

    2009-01-01

    The current generation of lattice codes employs the method of Collision Probabilities (CP), the Method of Characteristics (MOC) or methods derived thereof to solve the two-dimensional multigroup transport equation on the assembly level. We compare the attainable solution accuracy of the lattice code DRAGON to the accuracy of the Discrete Ordinates (DO) code DORT on the basis of the two-dimensional GE-13 assembly in order to determine if the DO on Cartesian meshes is suitable as flux solver in future lattice codes. If DO exhibits high accuracy for assembly configurations, the next question is at what computational expense compared to traditional assembly codes. For this purpose DORT and DRAGON are required to converge to a reference solution, obtained by a multigroup MCNP calculation, with increasing angular quadrature order and decreasing spatial cell size; additionally for DRAGON the reference solution must be approached with increasing tracking density. The convergence of the two codes is judged via the multiplication factor, the pin wise relative error in the fission production rate, it's RMS and the maximum of it's absolute value over all pins. Additionally the computational cost of the obtained solutions is judged via the user CPU time. Although the multiplication factor computed by both codes converges with refinement of the employed meshes, the maximum deviation error of the fission production rate in the central region of the assembly remains unsatisfactorily high for CP and MOC. (authors)

  8. An energy recondensation method using the discrete generalized multigroup energy expansion theory

    International Nuclear Information System (INIS)

    Zhu Lei; Forget, Benoit

    2011-01-01

    Highlights: → Discrete-generalized multigroup method was implemented as a recondensation scheme. → Coarse group cross-sections were recondensed from core-level solution. → Neighboring effect of reflector and MOX bundle was improved. → Methodology was shown to be fully consistent when a flat angular flux approximation is used. - Abstract: In this paper, the discrete generalized multigroup (DGM) method was used to recondense the coarse group cross-sections using the core level solution, thus providing a correction for neighboring effect found at the core level. This approach was tested using a discrete ordinates implementation in both 1-D and 2-D. Results indicate that 2 or 3 iterations can substantially improve the flux and fission density errors associated with strong interfacial spectral changes as found in the presence of strong absorbers, reflector of mixed-oxide fuel. The methodology is also proven to be fully consistent with the multigroup methodology as long as a flat-flux approximation is used spatially.

  9. Discrete ordinate theory of radiative transfer. 2: Scattering from maritime haze

    Science.gov (United States)

    Kattawar, G. W.; Plass, G. N.; Catchings, F. E.

    1971-01-01

    Discrete ordinate theory was used to calculate the reflected and transmitted radiance of photons which have interacted with plane parallel maritime haze layers. The results are presented for three solar zenith angles, three values of the surface albedo, and a range of optical thicknesses from very thin to very thick. The diffuse flux at the lower boundary and the cloud albedo were tabulated. The forward peak and other features in the single scattered phase function caused the radiance in many cases to be very different from that for Rayleigh scattering. The variation of the radiance with both the zenith or nadir angle and the azimuthal angle is more marked, and the relative limb darkening under very thick layers is greater, for haze than for Rayleigh scattering. The downward diffuse flux at the lower boundary for A = O is always greater and the cloud albedo is always less for haze than for Rayleigh layers.

  10. Exponential characteristic spatial quadrature for discrete ordinates radiation transport with rectangular cells

    International Nuclear Information System (INIS)

    Minor, B.; Mathews, K.

    1995-01-01

    The exponential characteristic (EC) spatial quadrature for discrete ordinates neutral particle transport previously introduced in slab geometry is extended here to x-y geometry with rectangular cells. The method is derived and compared with current methods. It is similar to the linear characteristic (LC) quadrature (a linear-linear moments method) but differs by assuming an exponential distribution of the scattering source within each cell, S(x) = a exp(bx + cy), whose parameters are rootsolved to match the known (from the previous iteration) spatial average and first moments of the source over the cell. Similarly, EC assumes exponential distributions of flux along cell edges through which particles enter the cell, with parameters chosen to match the average and first moments of flux, as passed from the adjacent, upstream cells (or as determined by boundary conditions). Like the linear adaptive (LA) method, EC is positive and nonlinear. It is more accurate than LA and does not require subdivision of cells. The nonlinearity has not interfered with convergence. The exponential moment functions, which were introduced with the slab geometry method, are extended to arbitrary dimensions (numbers of arguments) and used to avoid numerical ill conditioning. As in slab geometry, the method approaches O(Δx 4 ) global truncation error on fine-enough meshes, while the error is insensitive to mesh size for coarse meshes. Performance of the method is compared with that of the step characteristic, LC, linear nodal, step adaptive, and LA schemes. The EC method is a strong performer with scattering ratios ranging from 0 to 0.9 (the range tested), particularly so for lower scattering ratios. As in slab geometry, EC is computationally more costly per cell than current methods but can be accurate with very thick cells, leading to increased computational efficiency on appropriate problems

  11. Program to solve the multigroup discrete ordinates transport equation in (x,y,z) geometry

    International Nuclear Information System (INIS)

    Lathrop, K.D.

    1976-04-01

    Numerical formulations and programming algorithms are given for the THREETRAN computer program which solves the discrete ordinates, multigroup transport equation in (x,y,z) geometry. An efficient, flexible, and general data-handling strategy is derived to make use of three hierarchies of storage: small core memory, large core memory, and disk file. Data management, input instructions, and sample problem output are described. A six-group, S 4 , 18 502 mesh point, 2 800 zone, k/sub eff/ calculation of the ZPPR-4 critical assembly required 144 min of CDC-7600 time to execute to a convergence tolerance of 5 x 10 -4 and gave results in good qualitative agreement with experiment and other calculations. 6 references

  12. Open Method of Co-Ordination for Demoi-Cracy?

    DEFF Research Database (Denmark)

    Borrás, Susana; Radaelli, Claudio

    2014-01-01

    Under which conditions does the open method of co-ordination match the standards for demoi-cracy? To answer this question, we need some explicit standards about demoi-cracy. In fact, open co-ordination serves three different but interrelated purposes in European Union policy: to facilitate...... convergence; to support learning processes; and to encourage exploration of policy innovation. By intersecting standards and purposes, we find open co-ordination is neither inherently ‘good’ nor ‘bad’ for demoi-cracy, as it depends on how it has been put into practice. Therefore, we qualify the answer...

  13. The CNCSN: one, two- and three-dimensional coupled neutral and charged particle discrete ordinates code package

    International Nuclear Information System (INIS)

    Voloschenko, A.M.; Gukov, S.V.; Kryuchkov, V.P.; Dubinin, A.A.; Sumaneev, O.V.

    2005-01-01

    The CNCSN package is composed of the following codes: -) KATRIN-2.0: a three-dimensional neutral and charged particle transport code; -) KASKAD-S-2.5: a two-dimensional neutral and charged particle transport code; -) ROZ-6.6: a one-dimensional neutral and charged particle transport code; -) ARVES-2.5: a preprocessor for the working macroscopic cross-section format FMAC-M for transport calculations; -) MIXERM: a utility code for preparing mixtures on the base of multigroup cross-section libraries in ANISN format; -) CEPXS-BFP: a version of the Sandia National Lab. multigroup coupled electron-photon cross-section generating code CEPXS, adapted for solving the charged particles transport in the Boltzmann-Fokker-Planck formulation with the use of discrete ordinate method; -) SADCO-2.4: Institute for High-Energy Physics modular system for generating coupled nuclear data libraries to provide high-energy particles transport calculations by multigroup method; -) KATRIF: the post-processor for the KATRIN code; -) KASF: the post-processor for the KASKAD-S code; and ROZ6F: the post-processor for the ROZ-6 code. The coding language is Fortran-90

  14. Coupling of discrete ordinates methods by transmission of boundary conditions in solving the neutron transport equation in slab geometry; Couplage de discretisations aux ordonnees discretes d`equations de transport 1D par passage de conditions frontieres

    Energy Technology Data Exchange (ETDEWEB)

    Bal, G. [Departement MMN, Service IMA, Direction des Etudes et Recherches, Electricite de France (EDF), 92 - Clamart (France)

    1995-10-01

    Neutron transport in nuclear reactors is quite well modelled by the linear Boltzmann transport equation. Its solution is relatively easy, but unfortunately too expensive to achieve whole core computations. Thus, we have to simplify it, for example by homogenizing some physical characteristics. However, the solution may then be inaccurate. Moreover, in strongly homogeneous areas, the error may be too big. Then we would like to deal with such an inconvenient by solving the equation accurately on this area, but more coarsely away from it, so that the computation is not too expensive. This problem is the subject of a thesis. We present here some results obtained for slab geometry. The couplings between the fine and coarse discretization regions could be conceived in a number of approaches. Here, we only deal with the coupling at crossing the interface between two sub-domains. In the first section, we present the coupling of discrete ordinate methods for solving the homogeneous, isotropic and mono-kinetic equation. Coupling operators are defined and shown to be optimal. The second and the third sections are devoted to an extension of the previous results when the equation is non-homogeneous, anisotropic and multigroup (under some restrictive assumptions). Some numerical results are given in the case of isotropic and mono-kinetic equations. (author) 15 refs.

  15. The time-dependent 3D discrete ordinates code TORT-TD with thermal-hydraulic feedback by ATHLET models

    International Nuclear Information System (INIS)

    Seubert, A.; Velkov, K.; Langenbuch, S.

    2008-01-01

    This paper describes the time-dependent 3D discrete ordinates transport code TORT-TD. Thermal-hydraulic feedback is considered by coupling TORT-TD with the thermal-hydraulics system code ATHLET. The coupled code TORT-TD/ATHLET allows 3D pin-by-pin analyses of transients in few energy groups and anisotropic scattering by solving the time-dependent transport equation using the unconditionally stable implicit method. The nuclear cross sections are interpolated between pre-calculated table values of fuel temperature, moderator density and boron concentration. For verification of the implementation, selected test cases have been calculated by TORT-TD/ATHLET. They include a control rod ejection transient in a small PWR fuel assembly arrangement and a local boron concentration change in a single PWR fuel assembly. In the latter, special attention has been paid to study the influence of the thermal-hydraulic feedback modelling in ATHLET. The results obtained for a control rod ejection accident in a PWR quarter core demonstrate the applicability of TORT-TD/ATHLET. (authors)

  16. High-order discrete ordinate transport in hexagonal geometry: A new capability in ERANOS

    International Nuclear Information System (INIS)

    Le Tellier, R.; Suteau, C.; Fournier, D.; Ruggieri, J.M.

    2010-01-01

    This paper presents the implementation of an arbitrary order discontinuous Galerkin scheme within the framework of a discrete ordinate solver of the neutron transport equation for nuclear reactor calculations. More precisely, it deals with non-conforming spatial meshes for the 2 D and 3 D modeling of core geometries based on hexagonal assemblies. This work aims at improving the capabilities of the ERANOS code system dedicated to fast reactor analysis and design. Both the angular quadrature and spatial scheme peculiarities for hexagonal geometries are presented. A particular focus is set on the spatial non-conforming mesh and variable order capabilities of this scheme in anticipation to the development of spatial adaptiveness algorithms. These features are illustrated on a 3 D numerical benchmark with comparison to a Monte Carlo reference and a 2 D benchmark that shows the potential of this scheme for both h-and p-adaptation.

  17. A generalized nodal finite element formalism for discrete ordinates equations in slab geometry Part I: Theory in the continuous moment case

    International Nuclear Information System (INIS)

    Hennart, J.P.; Valle, E. del.

    1995-01-01

    A generalized nodal finite element formalism is presented, which covers virtually all known finit difference approximation to the discrete ordinates equations in slab geometry. This paper (Part 1) presents the theory of the so called open-quotes continuous moment methodsclose quotes, which include such well-known methods as the open-quotes diamond differenceclose quotes and the open-quotes characteristicclose quotes schemes. In a second paper (hereafter referred to as Part II), the authors will present the theory of the open-quotes discontinuous moment methodsclose quotes, consisting in particular of the open-quotes linear discontinuousclose quotes scheme as well as of an entire new class of schemes. Corresponding numerical results are available for all these schemes and will be presented in a third paper (Part III). 12 refs

  18. Comparison of discrete ordinate and Monte Carlo simulations of polarized radiative transfer in two coupled slabs with different refractive indices.

    Science.gov (United States)

    Cohen, D; Stamnes, S; Tanikawa, T; Sommersten, E R; Stamnes, J J; Lotsberg, J K; Stamnes, K

    2013-04-22

    A comparison is presented of two different methods for polarized radiative transfer in coupled media consisting of two adjacent slabs with different refractive indices, each slab being a stratified medium with no change in optical properties except in the direction of stratification. One of the methods is based on solving the integro-differential radiative transfer equation for the two coupled slabs using the discrete ordinate approximation. The other method is based on probabilistic and statistical concepts and simulates the propagation of polarized light using the Monte Carlo approach. The emphasis is on non-Rayleigh scattering for particles in the Mie regime. Comparisons with benchmark results available for a slab with constant refractive index show that both methods reproduce these benchmark results when the refractive index is set to be the same in the two slabs. Computed results for test cases with coupling (different refractive indices in the two slabs) show that the two methods produce essentially identical results for identical input in terms of absorption and scattering coefficients and scattering phase matrices.

  19. A coarse-mesh diffusion synthetic acceleration of the scattering source iteration scheme for one-speed slab-geometry discrete ordinates problems

    International Nuclear Information System (INIS)

    Santos, Frederico P.; Alves Filho, Hermes; Barros, Ricardo C.; Xavier, Vinicius S.

    2011-01-01

    The scattering source iterative (SI) scheme is traditionally applied to converge fine-mesh numerical solutions to fixed-source discrete ordinates (S N ) neutron transport problems. The SI scheme is very simple to implement under a computational viewpoint. However, the SI scheme may show very slow convergence rate, mainly for diffusive media (low absorption) with several mean free paths in extent. In this work we describe an acceleration technique based on an improved initial guess for the scattering source distribution within the slab. In other words, we use as initial guess for the fine-mesh scattering source, the coarse-mesh solution of the neutron diffusion equation with special boundary conditions to account for the classical S N prescribed boundary conditions, including vacuum boundary conditions. Therefore, we first implement a spectral nodal method that generates coarse-mesh diffusion solution that is completely free from spatial truncation errors, then we reconstruct this coarse-mesh solution within each spatial cell of the discretization grid, to further yield the initial guess for the fine-mesh scattering source in the first S N transport sweep (μm > 0 and μm < 0, m = 1:N) across the spatial grid. We consider a number of numerical experiments to illustrate the efficiency of the offered diffusion synthetic acceleration (DSA) technique. (author)

  20. Spectral collocation method with a flexible angular discretization scheme for radiative transfer in multi-layer graded index medium

    Science.gov (United States)

    Wei, Linyang; Qi, Hong; Sun, Jianping; Ren, Yatao; Ruan, Liming

    2017-05-01

    The spectral collocation method (SCM) is employed to solve the radiative transfer in multi-layer semitransparent medium with graded index. A new flexible angular discretization scheme is employed to discretize the solid angle domain freely to overcome the limit of the number of discrete radiative direction when adopting traditional SN discrete ordinate scheme. Three radial basis function interpolation approaches, named as multi-quadric (MQ), inverse multi-quadric (IMQ) and inverse quadratic (IQ) interpolation, are employed to couple the radiative intensity at the interface between two adjacent layers and numerical experiments show that MQ interpolation has the highest accuracy and best stability. Variable radiative transfer problems in double-layer semitransparent media with different thermophysical properties are investigated and the influence of these thermophysical properties on the radiative transfer procedure in double-layer semitransparent media is also analyzed. All the simulated results show that the present SCM with the new angular discretization scheme can predict the radiative transfer in multi-layer semitransparent medium with graded index efficiently and accurately.

  1. Applying Multivariate Discrete Distributions to Genetically Informative Count Data.

    Science.gov (United States)

    Kirkpatrick, Robert M; Neale, Michael C

    2016-03-01

    We present a novel method of conducting biometric analysis of twin data when the phenotypes are integer-valued counts, which often show an L-shaped distribution. Monte Carlo simulation is used to compare five likelihood-based approaches to modeling: our multivariate discrete method, when its distributional assumptions are correct, when they are incorrect, and three other methods in common use. With data simulated from a skewed discrete distribution, recovery of twin correlations and proportions of additive genetic and common environment variance was generally poor for the Normal, Lognormal and Ordinal models, but good for the two discrete models. Sex-separate applications to substance-use data from twins in the Minnesota Twin Family Study showed superior performance of two discrete models. The new methods are implemented using R and OpenMx and are freely available.

  2. 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.

  3. A coarse-mesh diffusion synthetic acceleration of the source iteration scheme for one-speed discrete ordinates transport calculations in Slab geometry

    International Nuclear Information System (INIS)

    Santos, Frederico P.; Xavier, Vinicius S.; Alves Filho, Hermes; Barros, Ricardo C.

    2011-01-01

    The scattering source iterative (SI) scheme is traditionally applied to converge fine-mesh numerical solutions to fixed-source discrete ordinates (S N ) neutron transport problems. The SI scheme is very simple to implement under a computational viewpoint. However, the SI scheme may show very slow convergence rate, mainly for diffusive media (low absorption) with several mean free paths in extent. In this work we describe an acceleration technique based on an improved initial guess for the scattering source distribution within the slab. In other words, we use as initial guess for the fine-mesh scattering source, the coarse-mesh solution of the neutron diffusion equation with special boundary conditions to account for the classical S N prescribed boundary conditions, including vacuum boundary conditions. Therefore, we first implement a spectral nodal method that generates coarse-mesh diffusion solution that is completely free from spatial truncation errors, then we reconstruct this coarse-mesh solution within each spatial cell of the discretization grid, to further yield the initial guess for the fine-mesh scattering source in the first S N transport sweep (μm > 0 and μm < 0, m = 1:N) across the spatial grid. We consider a number of numerical experiments to illustrate the efficiency of the offered diffusion synthetic acceleration (DSA) technique. (author)

  4. Verification of three dimensional triangular prismatic discrete ordinates transport code ENSEMBLE-TRIZ by comparison with Monte Carlo code GMVP

    International Nuclear Information System (INIS)

    Homma, Y.; Moriwaki, H.; Ikeda, K.; Ohdi, S.

    2013-01-01

    This paper deals with the verification of the 3 dimensional triangular prismatic discrete ordinates transport calculation code ENSEMBLE-TRIZ by comparison with the multi-group Monte Carlo calculation code GMVP in a large fast breeder reactor. The reactor is a 750 MWe electric power sodium cooled reactor. Nuclear characteristics are calculated at the beginning of cycle of an initial core and at the beginning and the end of cycle of an equilibrium core. According to the calculations, the differences between the two methodologies are smaller than 0.0002 Δk in the multiplication factor, relatively about 1% in the control rod reactivity, and 1% in the sodium void reactivity. (authors)

  5. Modeling of radiant heat transfers in non-grey gases using the discrete ordinate method in association with a narrow bands statistical model; Modelisation des transferts radiatifs dans des gaz non gris par la methode des ordonnees discretes associee a un modele statistique a bandes etroites

    Energy Technology Data Exchange (ETDEWEB)

    Miranda, A.B. de; Delmas, A; Sacadura, J F [Institut National des Sciences Appliquees (INSA), 69 - Villeurbanne (France)

    1997-12-31

    A formulation based on the use of the discrete ordinate method applied to the integral form of the radiant heat transfer equation is proposed for non-grey gases. The correlations between transmittances are neglected and no explicit wall reflexion is considered. The configuration analyzed consists in a flat layer of non-isothermal steam-nitrogen mixture. Cavity walls are grey with diffuse reflexion and emission. A narrow band statistical model is used to represent the radiative properties of the gas. The distribution of the radiative source term inside the cavity is calculated along two temperature profiles in a uniform steam concentration. Results obtained using this simplified approach are in good agreement with those found in the literature for the same temperature and concentration distributions. This preliminary study seems to indicate that the algorithm based on the integration of radiant heat transfer along the luminance path is less sensitive to de-correlation effects than formulations based on the differential form the the radiant heat transfer. Thus, a more systematic study of the influence of the neglecting of correlations on the integral approach is analyzed in this work. (J.S.) 16 refs.

  6. Modeling of radiant heat transfers in non-grey gases using the discrete ordinate method in association with a narrow bands statistical model; Modelisation des transferts radiatifs dans des gaz non gris par la methode des ordonnees discretes associee a un modele statistique a bandes etroites

    Energy Technology Data Exchange (ETDEWEB)

    Miranda, A.B. de; Delmas, A.; Sacadura, J.F. [Institut National des Sciences Appliquees (INSA), 69 - Villeurbanne (France)

    1996-12-31

    A formulation based on the use of the discrete ordinate method applied to the integral form of the radiant heat transfer equation is proposed for non-grey gases. The correlations between transmittances are neglected and no explicit wall reflexion is considered. The configuration analyzed consists in a flat layer of non-isothermal steam-nitrogen mixture. Cavity walls are grey with diffuse reflexion and emission. A narrow band statistical model is used to represent the radiative properties of the gas. The distribution of the radiative source term inside the cavity is calculated along two temperature profiles in a uniform steam concentration. Results obtained using this simplified approach are in good agreement with those found in the literature for the same temperature and concentration distributions. This preliminary study seems to indicate that the algorithm based on the integration of radiant heat transfer along the luminance path is less sensitive to de-correlation effects than formulations based on the differential form the the radiant heat transfer. Thus, a more systematic study of the influence of the neglecting of correlations on the integral approach is analyzed in this work. (J.S.) 16 refs.

  7. International Conference eXtended Discretization MethodS

    CERN Document Server

    Benvenuti, Elena

    2016-01-01

    This book gathers selected contributions on emerging research work presented at the International Conference eXtended Discretization MethodS (X-DMS), held in Ferrara in September 2015. It highlights the most relevant advances made at the international level in the context of expanding classical discretization methods, like finite elements, to the numerical analysis of a variety of physical problems. The improvements are intended to achieve higher computational efficiency and to account for special features of the solution directly in the approximation space and/or in the discretization procedure. The methods described include, among others, partition of unity methods (meshfree, XFEM, GFEM), virtual element methods, fictitious domain methods, and special techniques for static and evolving interfaces. The uniting feature of all contributions is the direct link between computational methodologies and their application to different engineering areas.

  8. Simulating Ordinal Data

    Science.gov (United States)

    Ferrari, Pier Alda; Barbiero, Alessandro

    2012-01-01

    The increasing use of ordinal variables in different fields has led to the introduction of new statistical methods for their analysis. The performance of these methods needs to be investigated under a number of experimental conditions. Procedures to simulate from ordinal variables are then required. In this article, we deal with simulation from…

  9. Determination of point isotropic buildup factors of gamma rays including incoherent and coherent scattering for aluminum, iron, lead, and water by discrete ordinates method

    International Nuclear Information System (INIS)

    Kitsos, S.; Assad, A.; Diop, C.M.; Nimal, J.C.

    1994-01-01

    Exposure and energy absorption buildup factors for aluminum, iron, lead, and water are calculated by the SNID discrete ordinates code for an isotropic point source in a homogeneous medium. The calculation of the buildup factors takes into account the effects of both bound-electron Compton (incoherent) and coherent (Rayleigh) scattering. A comparison with buildup factors from the literature shows that these two effects greatly increase the buildup factors for energies below a few hundred kilo-electron-volts, and thus the new results are improved relative to the experiment. This greater accuracy is due to the increase in the linear attenuation coefficient, which leads to the calculation of the buildup factors for a mean free path with a smaller shield thickness. On the other hand, for the same shield thickness, exposure increases when only incoherent scattering is included and decreases when only coherent scattering is included, so that the exposure finally decreases when both effects are included. Great care must also be taken when checking the approximations for gamma-ray deep-penetration transport calculations, as well as for the cross-section treatment and origin

  10. Normal scheme for solving the transport equation independently of spatial discretization

    International Nuclear Information System (INIS)

    Zamonsky, O.M.

    1993-01-01

    To solve the discrete ordinates neutron transport equation, a general order nodal scheme is used, where nodes are allowed to have different orders of approximation and the whole system reaches a final order distribution. Independence in the election of system discretization and order of approximation is obtained without loss of accuracy. The final equations and the iterative method to reach a converged order solution were implemented in a two-dimensional computer code to solve monoenergetic, isotropic scattering, external source problems. Two benchmark problems were solved using different automatic selection order methods. Results show accurate solutions without spatial discretization, regardless of the initial selection of distribution order. (author)

  11. Solution of neutron transport equation using Daubechies' wavelet expansion in the angular discretization

    International Nuclear Information System (INIS)

    Cao Liangzhi; Wu Hongchun; Zheng Youqi

    2008-01-01

    Daubechies' wavelet expansion is introduced to discretize the angular variables of the neutron transport equation when the neutron angular flux varies very acutely with the angular directions. An improvement is made by coupling one-dimensional wavelet expansion and discrete ordinate method to make two-dimensional angular discretization efficient and stable. The angular domain is divided into several subdomains for treating the vacuum boundary condition exactly in the unstructured geometry. A set of wavelet equations coupled with each other is obtained in each subdomain. An iterative method is utilized to decouple the wavelet moments. The numerical results of several benchmark problems demonstrate that the wavelet expansion method can provide more accurate results by lower-order expansion than other angular discretization methods

  12. Monte Carlo and discrete-ordinate simulations of irradiances in the coupled atmosphere-ocean system.

    Science.gov (United States)

    Gjerstad, Karl Idar; Stamnes, Jakob J; Hamre, Børge; Lotsberg, Jon K; Yan, Banghua; Stamnes, Knut

    2003-05-20

    We compare Monte Carlo (MC) and discrete-ordinate radiative-transfer (DISORT) simulations of irradiances in a one-dimensional coupled atmosphere-ocean (CAO) system consisting of horizontal plane-parallel layers. The two models have precisely the same physical basis, including coupling between the atmosphere and the ocean, and we use precisely the same atmospheric and oceanic input parameters for both codes. For a plane atmosphere-ocean interface we find agreement between irradiances obtained with the two codes to within 1%, both in the atmosphere and the ocean. Our tests cover case 1 water, scattering by density fluctuations both in the atmosphere and in the ocean, and scattering by particulate matter represented by a one-parameter Henyey-Greenstein (HG) scattering phase function. The CAO-MC code has an advantage over the CAO-DISORT code in that it can handle surface waves on the atmosphere-ocean interface, but the CAO-DISORT code is computationally much faster. Therefore we use CAO-MC simulations to study the influence of ocean surface waves and propose a way to correct the results of the CAO-DISORT code so as to obtain fast and accurate underwater irradiances in the presence of surface waves.

  13. Monte Carlo and discrete-ordinate simulations of spectral radiances in a coupled air-tissue system.

    Science.gov (United States)

    Hestenes, Kjersti; Nielsen, Kristian P; Zhao, Lu; Stamnes, Jakob J; Stamnes, Knut

    2007-04-20

    We perform a detailed comparison study of Monte Carlo (MC) simulations and discrete-ordinate radiative-transfer (DISORT) calculations of spectral radiances in a 1D coupled air-tissue (CAT) system consisting of horizontal plane-parallel layers. The MC and DISORT models have the same physical basis, including coupling between the air and the tissue, and we use the same air and tissue input parameters for both codes. We find excellent agreement between radiances obtained with the two codes, both above and in the tissue. Our tests cover typical optical properties of skin tissue at the 280, 540, and 650 nm wavelengths. The normalized volume scattering function for internal structures in the skin is represented by the one-parameter Henyey-Greenstein function for large particles and the Rayleigh scattering function for small particles. The CAT-DISORT code is found to be approximately 1000 times faster than the CAT-MC code. We also show that the spectral radiance field is strongly dependent on the inherent optical properties of the skin tissue.

  14. Development of a discrete-ordinate approximation of the neutron transport equation for coupled xy-R-geometry

    International Nuclear Information System (INIS)

    Maertens, H.D.

    1982-01-01

    The inhomogenious structure of modern heavy water reactor fuel elements result in a strong spacial dependence of the neutron flux. The flux distribution can be calculated in detail by numerical methods, which describe exactly the geometrical heterogeniety and take into account the neutron flux anisotropy by higher transport theoretical approximations. Starting from the discrete ordinate method an approximation of the neutron transport equation has been developed, allowing for a cylindrical representation of the fuel-elements in a rectangular array of rods. The discretisation of the space variables, is based on the finite-difference approximation, defining a rectangular lattice in a two-dimensional cartesian coordinate system, which can be cut and replaced by circular mesh elements of a partially one-dimensional cylindrical coordinate system at arbitrary space points. To couple the two spacial regions the outer circle line of a cylindrical geometry is approximated in the cartesian system by a polygon with n >= 8. A cylindrical geometry is approximated in the cartesian system by a polygon with n>=8. A cylindrical geometry is thus enclosed by a system of two-dimensional rectangular, triangular and trapezoid mesh elements. The directional distribution of the neutron flux is conserved when switching from the xy-system to the cylindrical coordinate system. The angle discretisation by balanced sets of squares (EQsub(n)) allows a simple definition of transfer-coefficients for the redistribution of the neutron flux due to coordinate transformations. The procedure is verified and tested by selected problems. Possible applications and limits are discussed. (orig.) [de

  15. An extended step characteristic method for solving the transport equation in general geometries

    International Nuclear Information System (INIS)

    DeHart, M.D.; Pevey, R.E.; Parish, T.A.

    1994-01-01

    A method for applying the discrete ordinates method to solve the Boltzmann transport equation on arbitrary two-dimensional meshes has been developed. The finite difference approach normally used to approximate spatial derivatives in extrapolating angular fluxes across a cell is replaced by direct solution of the characteristic form of the transport equation for each discrete direction. Thus, computational cells are not restricted to the geometrical shape of a mesh element characteristic of a given coordinate system. However, in terms of the treatment of energy and angular dependencies, this method resembles traditional discrete ordinates techniques. By using the method developed here, a general two-dimensional space can be approximated by an irregular mesh comprised of arbitrary polygons. Results for a number of test problems have been compared with solutions obtained from traditional methods, with good agreement. Comparisons include benchmarks against analytical results for problems with simple geometry, as well as numerical results obtained from traditional discrete ordinates methods by applying the ANISN and TWOTRAN-II computer programs

  16. Scalable parallel prefix solvers for discrete ordinates transport

    International Nuclear Information System (INIS)

    Pautz, S.; Pandya, T.; Adams, M.

    2009-01-01

    The well-known 'sweep' algorithm for inverting the streaming-plus-collision term in first-order deterministic radiation transport calculations has some desirable numerical properties. However, it suffers from parallel scaling issues caused by a lack of concurrency. The maximum degree of concurrency, and thus the maximum parallelism, grows more slowly than the problem size for sweeps-based solvers. We investigate a new class of parallel algorithms that involves recasting the streaming-plus-collision problem in prefix form and solving via cyclic reduction. This method, although computationally more expensive at low levels of parallelism than the sweep algorithm, offers better theoretical scalability properties. Previous work has demonstrated this approach for one-dimensional calculations; we show how to extend it to multidimensional calculations. Notably, for multiple dimensions it appears that this approach is limited to long-characteristics discretizations; other discretizations cannot be cast in prefix form. We implement two variants of the algorithm within the radlib/SCEPTRE transport code library at Sandia National Laboratories and show results on two different massively parallel systems. Both the 'forward' and 'symmetric' solvers behave similarly, scaling well to larger degrees of parallelism then sweeps-based solvers. We do observe some issues at the highest levels of parallelism (relative to the system size) and discuss possible causes. We conclude that this approach shows good potential for future parallel systems, but the parallel scalability will depend heavily on the architecture of the communication networks of these systems. (authors)

  17. Preparation and crystal structure of carbonyltris (diethyldithiocarbamato) technetium (III): an unexpected source of co-ordinated carbon monoxide

    International Nuclear Information System (INIS)

    Baldas, J.; Bonnyman, J.; Pojer, P.M.; Williams, G.A.

    1981-10-01

    Tc(S 2 CNEt 2 ) 3 CO has been prepared by the reduction of NH 4 TcO 4 with formamidinesulphinic acid in the presence of NaS 2 CNEt 2 . It is suggested that the co-ordinated carbon monoxide is formed after co-ordination of formamidinesulphinic acid, or some decomposition product, with technetium. The crystal structure of Tc(S 2 CNEt 2 ) 3 CO has been determined by single-crystal X-ray diffraction methods at 17 deg. C. Diffractometry has provided significant Bragg intensities for 2045 independent reflections and the structure has been refined by full-matrix least-squares methods to R 0.049. The compound is isostructural with the rhenium analogue and consists of discrete Tc(S 2 CNEt 2 ) 3 CO molecules, each containing a terminal linear CO group. The technetium atom has a seven co-ordinate environment which is best described as a distorted pentagonal bipyramid

  18. General Purpose Fortran Program for Discrete-Ordinate-Method Radiative Transfer in Scattering and Emitting Layered Media: An Update of DISORT

    Science.gov (United States)

    Tsay, Si-Chee; Stamnes, Knut; Wiscombe, Warren; Laszlo, Istvan; Einaudi, Franco (Technical Monitor)

    2000-01-01

    This update reports a state-of-the-art discrete ordinate algorithm for monochromatic unpolarized radiative transfer in non-isothermal, vertically inhomogeneous, but horizontally homogeneous media. The physical processes included are Planckian thermal emission, scattering with arbitrary phase function, absorption, and surface bidirectional reflection. The system may be driven by parallel or isotropic diffuse radiation incident at the top boundary, as well as by internal thermal sources and thermal emission from the boundaries. Radiances, fluxes, and mean intensities are returned at user-specified angles and levels. DISORT has enjoyed considerable popularity in the atmospheric science and other communities since its introduction in 1988. Several new DISORT features are described in this update: intensity correction algorithms designed to compensate for the 8-M forward-peak scaling and obtain accurate intensities even in low orders of approximation; a more general surface bidirectional reflection option; and an exponential-linear approximation of the Planck function allowing more accurate solutions in the presence of large temperature gradients. DISORT has been designed to be an exemplar of good scientific software as well as a program of intrinsic utility. An extraordinary effort has been made to make it numerically well-conditioned, error-resistant, and user-friendly, and to take advantage of robust existing software tools. A thorough test suite is provided to verify the program both against published results, and for consistency where there are no published results. This careful attention to software design has been just as important in DISORT's popularity as its powerful algorithmic content.

  19. Investigation of radiation effects in Hiroshima and Nagasaki using a general Monte Carlo-discrete ordinates coupling scheme

    International Nuclear Information System (INIS)

    Cramer, S.N.; Slater, C.O.

    1990-01-01

    A general adjoint Monte Carlo-forward discrete ordinates radiation transport calculational scheme has been created to study the effects of the radiation environment in Hiroshima and Nagasaki due to the bombing of these two cities. Various such studies for comparison with physical data have progressed since the end of World War II with advancements in computing machinery and computational methods. These efforts have intensified in the last several years with the U.S.-Japan joint reassessment of nuclear weapons dosimetry in Hiroshima and Nagasaki. Three principal areas of investigation are: (1) to determine by experiment and calculation the neutron and gamma-ray energy and angular spectra and total yield of the two weapons; (2) using these weapons descriptions as source terms, to compute radiation effects at several locations in the two cities for comparison with experimental data collected at various times after the bombings and thus validate the source terms; and (3) to compute radiation fields at the known locations of fatalities and surviving individuals at the time of the bombings and thus establish an absolute cause-and-effect relationship between the radiation received and the resulting injuries to these individuals and any of their descendants as indicated by their medical records. It is in connection with the second and third items, the determination of the radiation effects and the dose received by individuals, that the current study is concerned

  20. Deteksi Pemalsuan Citra dengan Teknik Copy-Move Menggunakan Metode Ordinal Measure dari Koefisien Discrete Cosine Transform

    Directory of Open Access Journals (Sweden)

    Zulfan

    2016-07-01

    Full Text Available This article discusses a new method for the detection of forgery images generated by copy-move technique. Copy-move technique is one of image forgery techniques which taking a particular object from its original image and add it on that image for the purpose of increasing the number of or changing the same object in the original image. This study aims to detect the forged image generated by the copy-move techniques and copy-move forged image that has been modified by the rotation operation and histogram equalization. Detection feature used is Ordinal Measure of Discrete Cosine Transform coefficient (OM-DCT. Detection starts with division of the image into a block size of BXB (B = 16x16, 32x32 and 64x64 and two-dimensional DCT was performed to each of blocks. The feature distance from the original to the fake image, was calculated by the Euclidian distance and each feature has a distance of less than or equal to the threshold value (T according to the observations will be marked as a forged part. The results show that there are blocks detected on the copy-move image, whether on the unmodified copy-move forge image or those which modified by the rotation operation and histogram equalization. The number of blocks that are found in the copy-move object varies according to the size of the detection block used.

  1. New ordinances

    International Nuclear Information System (INIS)

    Reuter, H.

    1980-01-01

    Based on extensive preliminary work of the responsible Federal Minister of Labour and Social Affairs, the 'Ordinance to Replace Ordinances under Article 24 of the Irading and Industrial Code' has been issued by the Federal Government on February 27, 1980. This new ordinance also contains the new versions of the Steam Boiler Ordinance, the Pressure Gas Ordinance, the Lift Ordinance, the Ordinance on Electrical Installations in Rooms with High Explosion Hazards, the Acetylene Ordinance, and the Ordinance on Combustible Liquids. Accordingly, these new ordinances all have the same date of issue. Coming into force on July 1, 1980, they will replace six ordinances for plants to be licensed. The same applies to the pertinent general administrative regulations. (orig.) [de

  2. Applications of the Discrete ordinates of Oak ridge System (DOORS) package to Nuclear Engineering problems

    Energy Technology Data Exchange (ETDEWEB)

    Azmy, Y.Y. [The Pennsylvania State University, 229 Reber Building, University Park, PA 16802 (United States)]. e-mail: yya3@psu.edu

    2004-07-01

    Particle transport problems are notorious for their difficulty. This fact requires that production level computer codes designed to address realistic engineering problems possess three important features: (i) high computational efficiency as measured by solution accuracy for a fixed computational cost; (ii) a wide variety of options to enhance robustness of the transport solver; and (iii) a broad collection of support codes that extend the reach of the transport solver to a wide variety of applications. The Discrete Ordinates of Oak Ridge System (DOORS) code package was designed with these features in mind. In this paper, capabilities of member codes in the DOORS package are overviewed with particular emphasis on two newly developed peripheral codes: BOT3P the mesh-generation and visualization code package, and GipGui the graphical user interface for the cross section manipulation code, GIP. Two large applications are used to illustrate the tight coupling between the peripheral codes and the DORT and TORT transport solvers in two and three dimensional geometries, respectively. These are: (i) criticality calculations for the C5G7MOX core benchmark; and (ii) dose distribution calculations for the Target Service Cell (TSC) of the Spallation Neutron Source (SNS). (Author)

  3. Applications of the Discrete ordinates of Oak ridge System (DOORS) package to Nuclear Engineering problems

    International Nuclear Information System (INIS)

    Azmy, Y.Y.

    2004-01-01

    Particle transport problems are notorious for their difficulty. This fact requires that production level computer codes designed to address realistic engineering problems possess three important features: (i) high computational efficiency as measured by solution accuracy for a fixed computational cost; (ii) a wide variety of options to enhance robustness of the transport solver; and (iii) a broad collection of support codes that extend the reach of the transport solver to a wide variety of applications. The Discrete Ordinates of Oak Ridge System (DOORS) code package was designed with these features in mind. In this paper, capabilities of member codes in the DOORS package are overviewed with particular emphasis on two newly developed peripheral codes: BOT3P the mesh-generation and visualization code package, and GipGui the graphical user interface for the cross section manipulation code, GIP. Two large applications are used to illustrate the tight coupling between the peripheral codes and the DORT and TORT transport solvers in two and three dimensional geometries, respectively. These are: (i) criticality calculations for the C5G7MOX core benchmark; and (ii) dose distribution calculations for the Target Service Cell (TSC) of the Spallation Neutron Source (SNS). (Author)

  4. A piecewise bi-linear discontinuous finite element spatial discretization of the Sn transport equation

    International Nuclear Information System (INIS)

    Bailey, Teresa S.; Warsa, James S.; Chang, Jae H.; Adams, Marvin L.

    2011-01-01

    We present a new spatial discretization of the discrete-ordinates transport equation in two dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretization that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems. (author)

  5. A Piecewise Bi-Linear Discontinuous Finite Element Spatial Discretization of the Sn Transport Equation

    International Nuclear Information System (INIS)

    Bailey, T.S.; Chang, J.H.; Warsa, J.S.; Adams, M.L.

    2010-01-01

    We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretizations that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems.

  6. A Piecewise Bi-Linear Discontinuous Finite Element Spatial Discretization of the Sn Transport Equation

    Energy Technology Data Exchange (ETDEWEB)

    Bailey, T S; Chang, J H; Warsa, J S; Adams, M L

    2010-12-22

    We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretizations that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems.

  7. A posteriori error estimator and AMR for discrete ordinates nodal transport methods

    International Nuclear Information System (INIS)

    Duo, Jose I.; Azmy, Yousry Y.; Zikatanov, Ludmil T.

    2009-01-01

    In the development of high fidelity transport solvers, optimization of the use of available computational resources and access to a tool for assessing quality of the solution are key to the success of large-scale nuclear systems' simulation. In this regard, error control provides the analyst with a confidence level in the numerical solution and enables for optimization of resources through Adaptive Mesh Refinement (AMR). In this paper, we derive an a posteriori error estimator based on the nodal solution of the Arbitrarily High Order Transport Method of the Nodal type (AHOT-N). Furthermore, by making assumptions on the regularity of the solution, we represent the error estimator as a function of computable volume and element-edges residuals. The global L 2 error norm is proved to be bound by the estimator. To lighten the computational load, we present a numerical approximation to the aforementioned residuals and split the global norm error estimator into local error indicators. These indicators are used to drive an AMR strategy for the spatial discretization. However, the indicators based on forward solution residuals alone do not bound the cell-wise error. The estimator and AMR strategy are tested in two problems featuring strong heterogeneity and highly transport streaming regime with strong flux gradients. The results show that the error estimator indeed bounds the global error norms and that the error indicator follows the cell-error's spatial distribution pattern closely. The AMR strategy proves beneficial to optimize resources, primarily by reducing the number of unknowns solved for to achieve prescribed solution accuracy in global L 2 error norm. Likewise, AMR achieves higher accuracy compared to uniform refinement when resolving sharp flux gradients, for the same number of unknowns

  8. Derivation of new 3D discrete ordinate equations

    International Nuclear Information System (INIS)

    Ahrens, C. D.

    2012-01-01

    The Sn equations have been the workhorse of deterministic radiation transport calculations for many years. Here we derive two new angular discretizations of the 3D transport equation. The first set of equations, derived using Lagrange interpolation and collocation, retains the classical Sn structure, with the main difference being how the scattering source is calculated. Because of the formal similarity with the classical S n equations, it should be possible to modify existing computer codes to take advantage of the new formulation. In addition, the new S n-like equations correctly capture delta function scattering. The second set of equations, derived using a Galerkin technique, does not retain the classical Sn structure because the streaming term is not diagonal. However, these equations can be cast into a form similar to existing methods developed to reduce ray effects. Numerical investigation of both sets of equations is under way. (authors)

  9. A more efficient implementation of the discrete-ordinates method for an approximate model of particle transport in a duct

    International Nuclear Information System (INIS)

    Ganapol, B.D.

    2015-01-01

    Highlights: • Method of doubling solution for the pipe problem. • Uses convergence acceleration. • Fully discretized solution. • Improvement over ADO. - Abstract: We consider transport of light, neutrons, or any uncharged particles in a straight duct of circular cross section. This problem first came to fashion some 30 years ago when Pomraning and Prinja formulated their so called “pipe problem”. In the years to follow, investigators applied essentially every known method of numerical solution, including MMRW’s Wiener–Hopf – except possibly one. This presentation concerns that particular numerical solution, which arguably seems to be the most efficient of all.

  10. Direct Discrete Method for Neutronic Calculations

    International Nuclear Information System (INIS)

    Vosoughi, Naser; Akbar Salehi, Ali; Shahriari, Majid

    2002-01-01

    The objective of this paper is to introduce a new direct method for neutronic calculations. This method which is named Direct Discrete Method, is simpler than the neutron Transport equation and also more compatible with physical meaning of problems. This method is based on physic of problem and with meshing of the desired geometry, writing the balance equation for each mesh intervals and with notice to the conjunction between these mesh intervals, produce the final discrete equations series without production of neutron transport differential equation and mandatory passing from differential equation bridge. We have produced neutron discrete equations for a cylindrical shape with two boundary conditions in one group energy. The correction of the results from this method are tested with MCNP-4B code execution. (authors)

  11. TIMEX: a time-dependent explicit discrete ordinates program for the solution of multigroup transport equations with delayed neutrons

    International Nuclear Information System (INIS)

    Hill, T.R.; Reed, W.H.

    1976-01-01

    TIMEX solves the time-dependent, one-dimensional multigroup transport equation with delayed neutrons in plane, cylindrical, spherical, and two-angle plane geometries. Both regular and adjoint, inhomogeneous and homogeneous problems subject to vacuum, reflective, periodic, white, albedo or inhomogeneous boundary flux conditions are solved. General anisotropic scattering is allowed and anisotropic inhomogeneous sources are permitted. The discrete ordinates approximation for the angular variable is used with the diamond (central) difference approximation for the angular extrapolation in curved geometries. A linear discontinuous finite element representation for the angular flux in each spatial mesh cell is used. The time variable is differenced by an explicit technique that is unconditionally stable so that arbitrarily large time steps can be taken. Because no iteration is performed the method is exceptionally fast in terms of computing time per time step. Two acceleration methods, exponential extrapolation and rebalance, are utilized to improve the accuracy of the time differencing scheme. Variable dimensioning is used so that any combination of problem parameters leading to a container array less than MAXCOR can be accommodated. The running time for TIMEX is highly problem-dependent, but varies almost linearly with the total number of unknowns and time steps. Provision is made for creation of standard interface output files for angular fluxes and angle-integrated fluxes. Five interface units (use of interface units is optional), five output units, and two system input/output units are required. A large bulk memory is desirable, but may be replaced by disk, drum, or tape storage. 13 tables, 9 figures

  12. Pin cell discontinuity factors in the transient 3-D discrete ordinates code TORT-TD

    International Nuclear Information System (INIS)

    Seubert, A.

    2010-01-01

    Even with the rapid increase of computing power, whole core transient and accident analyses based on the direct solution of the 3-D neutron transport equation with a large number of energy groups and a detailed heterogeneous description of the core still remain computationally challenging. Current industrial methods for reactor core calculations therefore involve a two step approach in which lattice (assembly) depletion transport methods are used to prepare energy collapsed and fuel assembly or pin cell homogenized cross sections for subsequent whole core transport calculations. Spatial homogenization, in principal, requires the knowledge of both the actual boundary condition (local core environment) of the fuel assembly and the exact heterogeneous flux distribution (reference solution) of the whole core problem within that fuel assembly. Since, in particular, the latter is not known a priori, an infinite medium (zero net current) condition is used in the lattice calculations. It is well known that this approximation may lead to undesirable errors in cores in which large flux gradients are present across the fuel assemblies. This is the case in cores that have high heterogeneity and/or strong local absorbers, e.g. PWRs with partial MOX loading and inserted control rod clusters. There are two major approaches to mitigate spatial homogenization errors, superhomogenization (SPH) factors, and discontinuity factors within the scope of equivalence theory (ET) and generalized equivalence theory (GET). Although discontinuity factors are usually applied at the level of fuel assembly node size (assembly discontinuity factors, ADF), the methodology can be extended to pin cell homogenized whole core calculations involving pin cell discontinuity factors (PDF). There are also further developments for both the diffusion and the simplified transport (SP3) equation. In this paper, PDFs are introduced into the time-dependent 3-D discrete ordinates code TORT-TD in order to reduce the

  13. Acceleration methods and models in Sn calculations

    International Nuclear Information System (INIS)

    Sbaffoni, M.M.; Abbate, M.J.

    1984-01-01

    In some neutron transport problems solved by the discrete ordinate method, it is relatively common to observe some particularities as, for example, negative fluxes generation, slow and insecure convergences and solution instabilities. The commonly used models for neutron flux calculation and acceleration methods included in the most used codes were analyzed, in face of their use in problems characterized by a strong upscattering effect. Some special conclusions derived from this analysis are presented as well as a new method to perform the upscattering scaling for solving the before mentioned problems in this kind of cases. This method has been included in the DOT3.5 code (two dimensional discrete ordinates radiation transport code) generating a new version of wider application. (Author) [es

  14. Application of an efficient Bayesian discretization method to biomedical data

    Directory of Open Access Journals (Sweden)

    Gopalakrishnan Vanathi

    2011-07-01

    Full Text Available Abstract Background Several data mining methods require data that are discrete, and other methods often perform better with discrete data. We introduce an efficient Bayesian discretization (EBD method for optimal discretization of variables that runs efficiently on high-dimensional biomedical datasets. The EBD method consists of two components, namely, a Bayesian score to evaluate discretizations and a dynamic programming search procedure to efficiently search the space of possible discretizations. We compared the performance of EBD to Fayyad and Irani's (FI discretization method, which is commonly used for discretization. Results On 24 biomedical datasets obtained from high-throughput transcriptomic and proteomic studies, the classification performances of the C4.5 classifier and the naïve Bayes classifier were statistically significantly better when the predictor variables were discretized using EBD over FI. EBD was statistically significantly more stable to the variability of the datasets than FI. However, EBD was less robust, though not statistically significantly so, than FI and produced slightly more complex discretizations than FI. Conclusions On a range of biomedical datasets, a Bayesian discretization method (EBD yielded better classification performance and stability but was less robust than the widely used FI discretization method. The EBD discretization method is easy to implement, permits the incorporation of prior knowledge and belief, and is sufficiently fast for application to high-dimensional data.

  15. Co-ordinating Product Developing Activities

    DEFF Research Database (Denmark)

    Terkelsen, Søren Bendix

    1996-01-01

    The paper contains a presentation of research methods to be used in case studies in product development and a presentation on how to deal with Design Co-ordination according to litterature......The paper contains a presentation of research methods to be used in case studies in product development and a presentation on how to deal with Design Co-ordination according to litterature...

  16. Coupling of a discrete ordinate 3-D radiant heat transfer model with the PHOENICS fluid mechanics software; Couplage d`un modele radiatif tridimensionnel aux ordonnees discretes au logiciel de mecanique des fluides phoenics

    Energy Technology Data Exchange (ETDEWEB)

    Muller, J [IRSID, Institut de Recherches Siderurgie, 57 - Maizieres-les-Metz (France)

    1997-12-31

    Radiant heat transfer is the main solution retained in many iron and steel metallurgy installations (re-heating and annealing furnaces etc..). Today, it has become important to dispose of performing radiant heat transfer models in heat transfer and fluid mechanics simulation softwares, and well adapted to multidimensional industrial problems. This work presents the discrete ordinate radiant heat transfer model developed at the IRSID (the French institute of research in iron and steel metallurgy) and coupled with the PHOENICS heat transfer-fluid mechanics software. Three modeling approaches are presented concerning the radiative properties of gases (H{sub 2}O-CO{sub 2}). A ``weighted grey gases sum`` model gives satisfactory results for several 1-D validation cases. (J.S.) 20 refs.

  17. Coupling of a discrete ordinate 3-D radiant heat transfer model with the PHOENICS fluid mechanics software; Couplage d`un modele radiatif tridimensionnel aux ordonnees discretes au logiciel de mecanique des fluides phoenics

    Energy Technology Data Exchange (ETDEWEB)

    Muller, J. [IRSID, Institut de Recherches Siderurgie, 57 - Maizieres-les-Metz (France)

    1996-12-31

    Radiant heat transfer is the main solution retained in many iron and steel metallurgy installations (re-heating and annealing furnaces etc..). Today, it has become important to dispose of performing radiant heat transfer models in heat transfer and fluid mechanics simulation softwares, and well adapted to multidimensional industrial problems. This work presents the discrete ordinate radiant heat transfer model developed at the IRSID (the French institute of research in iron and steel metallurgy) and coupled with the PHOENICS heat transfer-fluid mechanics software. Three modeling approaches are presented concerning the radiative properties of gases (H{sub 2}O-CO{sub 2}). A ``weighted grey gases sum`` model gives satisfactory results for several 1-D validation cases. (J.S.) 20 refs.

  18. Systematization of Accurate Discrete Optimization Methods

    Directory of Open Access Journals (Sweden)

    V. A. Ovchinnikov

    2015-01-01

    Full Text Available The object of study of this paper is to define accurate methods for solving combinatorial optimization problems of structural synthesis. The aim of the work is to systemize the exact methods of discrete optimization and define their applicability to solve practical problems.The article presents the analysis, generalization and systematization of classical methods and algorithms described in the educational and scientific literature.As a result of research a systematic presentation of combinatorial methods for discrete optimization described in various sources is given, their capabilities are described and properties of the tasks to be solved using the appropriate methods are specified.

  19. Methodology for solving the equation of transport ordered discrete TORT code in the reactor IPEN/MB-01; Metodologia para resolver la ecuacion del transporte con el codigo de Ordenadas Discretas TORT en el reactor IPEN/MB-01

    Energy Technology Data Exchange (ETDEWEB)

    Bernal, A.; Abarca, A.; Barrachina, T.; Miro, R.; Verdu, G.

    2013-07-01

    The resolution of the neutron transport equation in steady state in pool-type nuclear reactors, is normally achieved through 2 different numerical methods: Monte Carlo (stochastic) and discrete ordinates (deterministic). The discrete ordinates method solves the neutron transport equation for a set of specific addresses, obtaining a set of equations and solutions for each direction, where the solution for each direction is the angular flux. With the aim of treating energy dependence, used energy multigroup approximation, thus obtaining a set of equations that depends on the number of energy groups considered.

  20. TDTORT: Time-Dependent, 3-D, Discrete Ordinates, Neutron Transport Code System with Delayed Neutrons

    International Nuclear Information System (INIS)

    2002-01-01

    1 - Description of program or function: TDTORT solves the time-dependent, three-dimensional neutron transport equation with explicit representation of delayed neutrons to estimate the fission yield from fissionable material transients. This release includes a modified version of TORT from the C00650MFMWS01 DOORS3.1 code package plus the time-dependent TDTORT code. GIP is also included for cross-section preparation. TORT calculates the flux or fluence of particles due to particles incident upon the system from extraneous sources or generated internally as a result of interaction with the system in two- or three-dimensional geometric systems. The principle application is to the deep-penetration transport of neutrons and photons. Reactor eigenvalue problems can also be solved. Numerous printed edits of the results are available, and results can be transferred to output files for subsequent analysis. TDTORT reads ANISN-format cross-section libraries, which are not included in the package. Users may choose from several available in RSICC's data library collection which can be identified by the keyword 'ANISN FORMAT'. 2 - Methods:The time-dependent spatial flux is expressed as a product of a space-, energy-, and angle-dependent shape function, which is usually slowly varying in time and a purely time-dependent amplitude function. The shape equation is solved for the shape using TORT; and the result is used to calculate the point kinetics parameters (e.g., reactivity) by using their inner product definitions, which are then used to solve the time-dependent amplitude and precursor equations. The amplitude function is calculated by solving the kinetics equations using the LSODE solver. When a new shape calculation is needed, the flux is calculated using the newly computed amplitude function. The Boltzmann transport equation is solved using the method of discrete ordinates to treat the directional variable and weighted finite-difference methods, in addition to Linear Nodal

  1. Acceleration of Multidimensional Discrete Ordinates Methods Via Adjacent-Cell Preconditioners

    International Nuclear Information System (INIS)

    Azmy, Y.Y.

    2000-01-01

    The adjacent-cell preconditioner (AP) formalism originally derived in slab geometry is extended to multidimensional Cartesian geometry for generic fixed-weight, weighted diamond difference neutron transport methods. This is accomplished for the thick-cell regime (KAP) and thin-cell regime (NAP). A spectral analysis of the resulting acceleration schemes demonstrates their excellent spectral properties for model problem configurations, characterized by a uniform mesh of infinite extent and homogeneous material composition, each in its own cell-size regime. Thus, the spectral radius of KAP vanishes as the computational cell size approaches infinity, but it exceeds unity for very thin cells, thereby implying instability. In contrast, NAP is stable and robust for all cell sizes, but its spectral radius vanishes more slowly as the cell size increases. For this reason, and to avoid potential complication in the case of cells that are thin in one dimension and thick in another, NAP is adopted in the remainder of this work. The most important feature of AP for practical implementation in production level codes is that it is cell centered, reducing the size of the algebraic system comprising the acceleration stage compared to face-centered schemes. Boundary conditions for finite extent problems and a mixing formula across material and cell-size discontinuity are derived and used to implement NAP in a test code, AHOT, and a production code, TORT. Numerical testing for algebraically linear iterative schemes for the cases embodied in Burre's Suite of Test Problems demonstrates the high efficiency of the new method in reducing the number of iterations required to achieve convergence, especially for optically thick cells where acceleration is most needed. Also, for algebraically nonlinear (adaptive) methods, AP generally performs better than the partial current rebalance method in TORT and the diffusion synthetic acceleration method in TWODANT. Finally, application of the AP

  2. The influence of boundary conditions on resonant frequencies of cavities in 3-D FDTD algorithm using non-orthogonal co-ordinates

    Energy Technology Data Exchange (ETDEWEB)

    Zhao, L.; Tong, L.S. [Southeast Univ., Nanjing (China). Research Inst. of Electronics; Carter, R.G. [Lancaster Univ. (United Kingdom). Engineering Dept.

    1994-09-01

    The 3-dimensional finite-difference time-domain method in non-orthogonal co-ordinates (non-standard FDTD) is used to calculate the frequencies of resonators. The numerical boundary conditions of the method are presented. The Influences of boundary conditions and discrete meshes on the numerical accuracy are investigated. The authors present the nonstandard FDTD method using the boundary-orthogonal mesh and equivalent dielectric constant so that the error is reduced from 8.66% to 3.0% for the cylindrical cavity loaded by a dielectric button.

  3. Probabilistic Power Flow Method Considering Continuous and Discrete Variables

    Directory of Open Access Journals (Sweden)

    Xuexia Zhang

    2017-04-01

    Full Text Available This paper proposes a probabilistic power flow (PPF method considering continuous and discrete variables (continuous and discrete power flow, CDPF for power systems. The proposed method—based on the cumulant method (CM and multiple deterministic power flow (MDPF calculations—can deal with continuous variables such as wind power generation (WPG and loads, and discrete variables such as fuel cell generation (FCG. In this paper, continuous variables follow a normal distribution (loads or a non-normal distribution (WPG, and discrete variables follow a binomial distribution (FCG. Through testing on IEEE 14-bus and IEEE 118-bus power systems, the proposed method (CDPF has better accuracy compared with the CM, and higher efficiency compared with the Monte Carlo simulation method (MCSM.

  4. Discretization vs. Rounding Error in Euler's Method

    Science.gov (United States)

    Borges, Carlos F.

    2011-01-01

    Euler's method for solving initial value problems is an excellent vehicle for observing the relationship between discretization error and rounding error in numerical computation. Reductions in stepsize, in order to decrease discretization error, necessarily increase the number of steps and so introduce additional rounding error. The problem is…

  5. Biomedical applications of two- and three-dimensional deterministic radiation transport methods

    International Nuclear Information System (INIS)

    Nigg, D.W.

    1992-01-01

    Multidimensional deterministic radiation transport methods are routinely used in support of the Boron Neutron Capture Therapy (BNCT) Program at the Idaho National Engineering Laboratory (INEL). Typical applications of two-dimensional discrete-ordinates methods include neutron filter design, as well as phantom dosimetry. The epithermal-neutron filter for BNCT that is currently available at the Brookhaven Medical Research Reactor (BMRR) was designed using such methods. Good agreement between calculated and measured neutron fluxes was observed for this filter. Three-dimensional discrete-ordinates calculations are used routinely for dose-distribution calculations in three-dimensional phantoms placed in the BMRR beam, as well as for treatment planning verification for live canine subjects. Again, good agreement between calculated and measured neutron fluxes and dose levels is obtained

  6. Digital Resonant Controller based on Modified Tustin Discretization Method

    Directory of Open Access Journals (Sweden)

    STOJIC, D.

    2016-11-01

    Full Text Available Resonant controllers are used in power converter voltage and current control due to their simplicity and accuracy. However, digital implementation of resonant controllers introduces problems related to zero and pole mapping from the continuous to the discrete time domain. Namely, some discretization methods introduce significant errors in the digital controller resonant frequency, resulting in the loss of the asymptotic AC reference tracking, especially at high resonant frequencies. The delay compensation typical for resonant controllers can also be compromised. Based on the existing analysis, it can be concluded that the Tustin discretization with frequency prewarping represents a preferable choice from the point of view of the resonant frequency accuracy. However, this discretization method has a shortcoming in applications that require real-time frequency adaptation, since complex trigonometric evaluation is required for each frequency change. In order to overcome this problem, in this paper the modified Tustin discretization method is proposed based on the Taylor series approximation of the frequency prewarping function. By comparing the novel discretization method with commonly used two-integrator-based proportional-resonant (PR digital controllers, it is shown that the resulting digital controller resonant frequency and time delay compensation errors are significantly reduced for the novel controller.

  7. Co-ordination properties of diglycol-amide (DGA) to trivalent curium and lanthanides studied by XAS, XRD and XPS methods

    International Nuclear Information System (INIS)

    Yaita, T.; Hirata, M.; Narita, H.; Tachimori, S.; Yamamoto, H.; Edelstein, N.M.; Bucher, J.J.; Shuh, D.K.; Rao, L.

    2001-01-01

    Co-ordination properties of diglycol-amide (DGA) to trivalent curium and to the trivalent lanthanides were studied by the EXAFS, the XRD and the XPS methods. The structural determinations by both the crystal XRD and the solution EXAFS methods showed that the DGA co-ordinated to the trivalent lanthanide ion in a tridentate fashion: co-ordination of three oxygen atoms of each ligand to the metal ion. The bond distances of Er-O (carbonyl) and Er-O (ether) in the Er-DGA complex were 2.35 Angstrom, and 2.46 Angstrom, respectively, while the atom distances of Cm-O (carbonyl) and Cm-O (ether) in the Cm-DGA complex were 2.42 Angstrom and 3.94 Angstrom, respectively from the EXAFS data for the Cm-DGA complex. Accordingly, the DGA would behave only as a semi-tridentate in the co-ordination to trivalent curium in solution. We determined the valence band structures of the Er-DGA complex by the XPS in order to clarify the bond properties of the complex, and assigned the XPS spectrum by using the DV-DS molecular orbital calculation method. (authors)

  8. The discontinuous finite element method for solving Eigenvalue problems of transport equations

    International Nuclear Information System (INIS)

    Yang, Shulin; Wang, Ruihong

    2011-01-01

    In this paper, the multigroup transport equations for solving the eigenvalues λ and K_e_f_f under two dimensional cylindrical coordinate are discussed. Aimed at the equations, the discretizing way combining discontinuous finite element method (DFE) with discrete ordinate method (SN) is developed, and the iterative algorithms and steps are studied. The numerical results show that the algorithms are efficient. (author)

  9. A Low Complexity Discrete Radiosity Method

    OpenAIRE

    Chatelier , Pierre Yves; Malgouyres , Rémy

    2006-01-01

    International audience; Rather than using Monte Carlo sampling techniques or patch projections to compute radiosity, it is possible to use a discretization of a scene into voxels and perform some discrete geometry calculus to quickly compute visibility information. In such a framework , the radiosity method may be as precise as a patch-based radiosity using hemicube computation for form-factors, but it lowers the overall theoretical complexity to an O(N log N) + O(N), where the O(N) is largel...

  10. Finite element method for solving neutron transport problems

    International Nuclear Information System (INIS)

    Ferguson, J.M.; Greenbaum, A.

    1984-01-01

    A finite element method is introduced for solving the neutron transport equations. Our method falls into the category of Petrov-Galerkin solution, since the trial space differs from the test space. The close relationship between this method and the discrete ordinate method is discussed, and the methods are compared for simple test problems

  11. Solution of the within-group multidimensional discrete ordinates transport equations on massively parallel architectures

    Science.gov (United States)

    Zerr, Robert Joseph

    2011-12-01

    The integral transport matrix method (ITMM) has been used as the kernel of new parallel solution methods for the discrete ordinates approximation of the within-group neutron transport equation. The ITMM abandons the repetitive mesh sweeps of the traditional source iterations (SI) scheme in favor of constructing stored operators that account for the direct coupling factors among all the cells and between the cells and boundary surfaces. The main goals of this work were to develop the algorithms that construct these operators and employ them in the solution process, determine the most suitable way to parallelize the entire procedure, and evaluate the behavior and performance of the developed methods for increasing number of processes. This project compares the effectiveness of the ITMM with the SI scheme parallelized with the Koch-Baker-Alcouffe (KBA) method. The primary parallel solution method involves a decomposition of the domain into smaller spatial sub-domains, each with their own transport matrices, and coupled together via interface boundary angular fluxes. Each sub-domain has its own set of ITMM operators and represents an independent transport problem. Multiple iterative parallel solution methods have investigated, including parallel block Jacobi (PBJ), parallel red/black Gauss-Seidel (PGS), and parallel GMRES (PGMRES). The fastest observed parallel solution method, PGS, was used in a weak scaling comparison with the PARTISN code. Compared to the state-of-the-art SI-KBA with diffusion synthetic acceleration (DSA), this new method without acceleration/preconditioning is not competitive for any problem parameters considered. The best comparisons occur for problems that are difficult for SI DSA, namely highly scattering and optically thick. SI DSA execution time curves are generally steeper than the PGS ones. However, until further testing is performed it cannot be concluded that SI DSA does not outperform the ITMM with PGS even on several thousand or tens of

  12. Methods in nuclear reactors calculations

    International Nuclear Information System (INIS)

    Velarde, G.

    1966-01-01

    Studies are made of the neutron transport equation corresponding to the the real and virtual reactors, as well as the starting hypotheses. Methods are developed to solve the transport equation in slab geometry, and P l ; B l ; M l ; S n and discrete ordinates approximations. (Author)

  13. Comparative study of discretization methods of microarray data for inferring transcriptional regulatory networks

    Directory of Open Access Journals (Sweden)

    Ji Wei

    2010-10-01

    Full Text Available Abstract Background Microarray data discretization is a basic preprocess for many algorithms of gene regulatory network inference. Some common discretization methods in informatics are used to discretize microarray data. Selection of the discretization method is often arbitrary and no systematic comparison of different discretization has been conducted, in the context of gene regulatory network inference from time series gene expression data. Results In this study, we propose a new discretization method "bikmeans", and compare its performance with four other widely-used discretization methods using different datasets, modeling algorithms and number of intervals. Sensitivities, specificities and total accuracies were calculated and statistical analysis was carried out. Bikmeans method always gave high total accuracies. Conclusions Our results indicate that proper discretization methods can consistently improve gene regulatory network inference independent of network modeling algorithms and datasets. Our new method, bikmeans, resulted in significant better total accuracies than other methods.

  14. Second Ordinance amending the Radiation Protection Ordinance

    International Nuclear Information System (INIS)

    1989-01-01

    The amendment of the Radiation Protection Ordinance brings about the following changes: (1) Introduction of the concept of effective dose, reduction of limits for partial body dose, adoption of the radiotoxicity values of radionuclides as established by the EC Basis Standards; (2) introduction of a working-life-related dose limit of 400 mSv; (3) supplementing provisions for the protection of the population, particularly by the standard procedure for radioecological impact assessment and determination of dose factors; (4) supplementing provisions on the use of radioactive substances in medicine and medical research; (5) supplementing provisions on health physics monitoring; (6) provisions for improving the supervision and controls in the transport of radioactive substances; (7) definition of activities and their assignment to the provisions of the Radiation Protection Ordinance; (8) revision of the waste management provisions of the Radiation Protection Ordinance. (HP) [de

  15. 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)

  16. Multilevel Fast Multipole Method for Higher Order Discretizations

    DEFF Research Database (Denmark)

    Borries, Oscar Peter; Meincke, Peter; Jorgensen, Erik

    2014-01-01

    The multi-level fast multipole method (MLFMM) for a higher order (HO) discretization is demonstrated on high-frequency (HF) problems, illustrating for the first time how an efficient MLFMM for HO can be achieved even for very large groups. Applying several novel ideas, beneficial to both lower...... order and higher order discretizations, results from a low-memory, high-speed MLFMM implementation of a HO hierarchical discretization are shown. These results challenge the general view that the benefits of HO and HF-MLFMM cannot be combined....

  17. Coarse-mesh rebalance methods compatible with the spherical harmonic fictitious source in neutron transport calculations

    International Nuclear Information System (INIS)

    Miller, W.F. Jr.

    1975-10-01

    The coarse-mesh rebalance method, based on neutron conservation, is used in discrete ordinates neutron transport codes to accelerate convergence of the within-group scattering source. Though very powerful for this application, the method is ineffective in accelerating the iteration on the discrete-ordinates-to-spherical-harmonics fictitious sources used for ray-effect elimination. This is largely because this source makes a minimum contribution to the neutron balance equation. The traditional rebalance approach is derived in a variational framework and compared with new rebalance approaches tailored to be compatible with the fictitious source. The new approaches are compared numerically to determine their relative advantages. It is concluded that there is little incentive to use the new methods. (3 tables, 5 figures)

  18. X-ray Ordinance

    International Nuclear Information System (INIS)

    Kramer, R.; Zerlett, G.

    1983-01-01

    This commentary, presented as volume 2 of the Deutsches Strahlenschutzrecht (German legislation on radiation protection) deals with the legal provisions of the ordinance on the protection against harmful effects of X-radiation (X-ray Ordinance - RoeV), of March 1, 1973 (announced in BGBl.I, page 173), as amended by the ordinance on the protection against harmful effects of ionizing radiation, of October 13, 1976 (announced in BGBl. I, page 2905). Thus volume 2 completes the task started with volume 1, namely to present a comprehensive view and account of the body of laws governing radiation protection, a task which was thought useful as developments in the FRG led to regulations being split up into the X-ray Ordinance, and the Radiation Protection Ordinance. In order to present a well-balanced commentary on the X-ray Ordinance, it was necessary to discuss the provisions both from the legal and the medical point of view. This edition takes into account the Fourth Public Notice of the BMA (Fed. Min. of Labour and Social Affairs) concerning the implementation of the X-ray Ordinance of January 4, 1982, as well as court decisions and literature published in this field, until September 1982. In addition, the judgment of the Federal Constitutional Court, dated October 19, 1982, concerning the voidness of the law on government liability, and two decisions by the Federal High Court, dated November 23, 1982, concerning the right to have insight into medical reports - of great significance in practice - have been considered. This commentary therefore is up to date with current developments. (orig.) [de

  19. Neutron distribution modeling based on integro-probabilistic approach of discrete ordinates method

    International Nuclear Information System (INIS)

    Khromov, V.V.; Kryuchkov, E.F.; Tikhomirov, G.V.

    1992-01-01

    In this paper is described the universal nodal method for the neutron distribution calculation in reactor and shielding problems, based on using of influence functions and factors of local-integrated volume and surface neutron sources in phase subregions. This method permits to avoid the limited capabilities of collision-probability method concerning with the detailed calculation of angular neutron flux dependence, scattering anisotropy and empty channels. The proposed method may be considered as modification of S n - method with advantage of ray-effects elimination. There are presented the description of method theory and algorithm following by the examples of method applications for calculation of neutron distribution in three-dimensional model of fusion reactor blanket and in highly heterogeneous reactor with empty channel

  20. A spectral nodal method for discrete ordinates problems in x,y geometry

    International Nuclear Information System (INIS)

    Barros, R.C. de; Larsen, E.W.

    1991-06-01

    A new nodal method is proposed for the solution of S N problems in x- y-geometry. This method uses the Spectral Green's Function (SGF) scheme for solving the one-dimensional transverse-integrated nodal transport equations with no spatial truncation error. Thus, the only approximations in the x, y-geometry nodal method occur in the transverse leakage terms, as in diffusion theory. We approximate these leakage terms using a flat or constant approximation, and we refer to the resulting method as the SGF-Constant Nodal (SGF-CN) method. We show in numerical calculations that the SGF-CN method is much more accurate than other well-known transport nodal methods for coarse-mesh deep-penetration S N problems, even though the transverse leakage terms are approximated rather simply. (author)

  1. Ordinance on the Protection against X-Radiation Hazards (X-Ray Ordinance)

    International Nuclear Information System (INIS)

    1987-01-01

    The ordinance refers to X-ray equipment and to stray radiation sources which generate X-radiation of at least 5 keV by means of accelerated electrons, and for this purpose apply an acceleration energy not exceeding 3 MeV. The ordinance does not apply to stray radiation sources which are used for the generation of ionizing particle radiation and thus are subject to the provisions of the Radiation Protection Ordinance. (orig./PW) [de

  2. Rational function approximation method for discrete ordinates problems in slab geometry

    International Nuclear Information System (INIS)

    Leal, Andre Luiz do C.; Barros, Ricardo C.

    2009-01-01

    In this work we use rational function approaches to obtain the transfer functions that appear in the spectral Green's function (SGF) auxiliary equations for one-speed isotropic scattering SN equations in one-dimensional Cartesian geometry. For this task we use the computation of the Pade approximants to compare the results with the standard SGF method's applied to deep penetration problems in homogeneous domains. This work is a preliminary investigation of a new proposal for handling leakage terms that appear in the two transverse integrated one-dimensional SN equations in the exponential SGF method (SGF-ExpN). Numerical results are presented to illustrate the rational function approximation accuracy. (author)

  3. Semi-supervised learning for ordinal Kernel Discriminant Analysis.

    Science.gov (United States)

    Pérez-Ortiz, M; Gutiérrez, P A; Carbonero-Ruz, M; Hervás-Martínez, C

    2016-12-01

    Ordinal classification considers those classification problems where the labels of the variable to predict follow a given order. Naturally, labelled data is scarce or difficult to obtain in this type of problems because, in many cases, ordinal labels are given by a user or expert (e.g. in recommendation systems). Firstly, this paper develops a new strategy for ordinal classification where both labelled and unlabelled data are used in the model construction step (a scheme which is referred to as semi-supervised learning). More specifically, the ordinal version of kernel discriminant learning is extended for this setting considering the neighbourhood information of unlabelled data, which is proposed to be computed in the feature space induced by the kernel function. Secondly, a new method for semi-supervised kernel learning is devised in the context of ordinal classification, which is combined with our developed classification strategy to optimise the kernel parameters. The experiments conducted compare 6 different approaches for semi-supervised learning in the context of ordinal classification in a battery of 30 datasets, showing (1) the good synergy of the ordinal version of discriminant analysis and the use of unlabelled data and (2) the advantage of computing distances in the feature space induced by the kernel function. Copyright © 2016 Elsevier Ltd. All rights reserved.

  4. Iterative discrete ordinates solution of the equation for surface-reflected radiance

    Science.gov (United States)

    Radkevich, Alexander

    2017-11-01

    This paper presents a new method of numerical solution of the integral equation for the radiance reflected from an anisotropic surface. The equation relates the radiance at the surface level with BRDF and solutions of the standard radiative transfer problems for a slab with no reflection on its surfaces. It is also shown that the kernel of the equation satisfies the condition of the existence of a unique solution and the convergence of the successive approximations to that solution. The developed method features two basic steps: discretization on a 2D quadrature, and solving the resulting system of algebraic equations with successive over-relaxation method based on the Gauss-Seidel iterative process. Presented numerical examples show good coincidence between the surface-reflected radiance obtained with DISORT and the proposed method. Analysis of contributions of the direct and diffuse (but not yet reflected) parts of the downward radiance to the total solution is performed. Together, they represent a very good initial guess for the iterative process. This fact ensures fast convergence. The numerical evidence is given that the fastest convergence occurs with the relaxation parameter of 1 (no relaxation). An integral equation for BRDF is derived as inversion of the original equation. The potential of this new equation for BRDF retrievals is analyzed. The approach is found not viable as the BRDF equation appears to be an ill-posed problem, and it requires knowledge the surface-reflected radiance on the entire domain of both Sun and viewing zenith angles.

  5. Radiation protection Ordinance

    International Nuclear Information System (INIS)

    1976-06-01

    This Ordinance lays down the licensing system for activities in Switzerland involving possible exposure to radiation, with the exception of nuclear installations, fuels and radioactive waste which, under the 1959 Atomic Energy Act, are subject to licensing. The Ordinance applies to the production, handling, use, storage, transport, disposal, import and export of radioactive substances and devices and articles containing them; and generally to any activity involving hazards caused by ionizing radiation. The Federal Public Health Office is the competent authority for granting licences. Provision is also made for the administrative conditions to be complied with for obtaining such licences as well as for technical measures required when engaged in work covered by the Ordinance. This consolidated version of the Ordinance contains all the successive amendments up to 26 September 1988. (NEA) [fr

  6. Anatomical localization of electrophysiological recording sites by co-ordinate transformation.

    Science.gov (United States)

    Sinex, D G

    1997-07-18

    A method for estimating the anatomical locations of the units recorded in electrophysiological mapping experiments is described. A total of three locations must be marked by dye injections or electrolytic lesions and identified in tissue sections. From those locations, equations are derived to translate, scale, and rotate the three-dimensional co-ordinates of the recording sites, so that they are correct for a second, three-dimensional co-ordinate system based on the anatomy of the mapped structure. There is no limit to the number of recording sites that can be localized. This differs from methods that require a dye injection or lesion to be made at the exact location at which a particular unit was recorded. The accuracy of the transformed co-ordinates is limited by the accuracy with which the co-ordinates can be measured: in test measurements and in the experiments for which this algorithm was developed, the computed co-ordinates were typically accurate to within 100 microns or less.

  7. The Second Ordinance for Amendment of the Radiation Protection Ordinance

    International Nuclear Information System (INIS)

    Czajka, D.

    1989-01-01

    This Second Ordinance for Amendment of the Radiation Protection Ordinance has modified the most important legal provisions supplementing the Atomic Energy Act. But looking closer at the revised version of the Ordinance, many an amendment turns out to be just a new facade on the old brickwork. The article critically reviews the most important amendments, stating that the main principles have remained untouched, and discussing the modification of limiting values, the definition of regulatory scopes, the new meaning of the term 'wastes containing nuclear fuel', and the regulatory scope of provisions governing radioactive substances and their medical applications. (orig./RST) [de

  8. Overstatement in happiness reporting with ordinal, bounded scale.

    Science.gov (United States)

    Tanaka, Saori C; Yamada, Katsunori; Kitada, Ryo; Tanaka, Satoshi; Sugawara, Sho K; Ohtake, Fumio; Sadato, Norihiro

    2016-02-18

    There are various methods by which people can express subjective evaluations quantitatively. For example, happiness can be measured on a scale from 1 to 10, and has been suggested as a measure of economic policy. However, there is resistance to these types of measurement from economists, who often regard welfare to be a cardinal, unbounded quantity. It is unclear whether there are differences between subjective evaluation reported on ordinal, bounded scales and on cardinal, unbounded scales. To answer this question, we developed functional magnetic resonance imaging experimental tasks for reporting happiness from monetary gain and the perception of visual stimulus. Subjects tended to report higher values when they used ordinal scales instead of cardinal scales. There were differences in neural activation between ordinal and cardinal reporting scales. The posterior parietal area showed greater activation when subjects used an ordinal scale instead of a cardinal scale. Importantly, the striatum exhibited greater activation when asked to report happiness on an ordinal scale than when asked to report on a cardinal scale. The finding that ordinal (bounded) scales are associated with higher reported happiness and greater activation in the reward system shows that overstatement bias in happiness data must be considered.

  9. Discrete gradient methods for solving variational image regularisation models

    International Nuclear Information System (INIS)

    Grimm, V; McLachlan, Robert I; McLaren, David I; Quispel, G R W; Schönlieb, C-B

    2017-01-01

    Discrete gradient methods are well-known methods of geometric numerical integration, which preserve the dissipation of gradient systems. In this paper we show that this property of discrete gradient methods can be interesting in the context of variational models for image processing, that is where the processed image is computed as a minimiser of an energy functional. Numerical schemes for computing minimisers of such energies are desired to inherit the dissipative property of the gradient system associated to the energy and consequently guarantee a monotonic decrease of the energy along iterations, avoiding situations in which more computational work might lead to less optimal solutions. Under appropriate smoothness assumptions on the energy functional we prove that discrete gradient methods guarantee a monotonic decrease of the energy towards stationary states, and we promote their use in image processing by exhibiting experiments with convex and non-convex variational models for image deblurring, denoising, and inpainting. (paper)

  10. Discrete linear canonical transform computation by adaptive method.

    Science.gov (United States)

    Zhang, Feng; Tao, Ran; Wang, Yue

    2013-07-29

    The linear canonical transform (LCT) describes the effect of quadratic phase systems on a wavefield and generalizes many optical transforms. In this paper, the computation method for the discrete LCT using the adaptive least-mean-square (LMS) algorithm is presented. The computation approaches of the block-based discrete LCT and the stream-based discrete LCT using the LMS algorithm are derived, and the implementation structures of these approaches by the adaptive filter system are considered. The proposed computation approaches have the inherent parallel structures which make them suitable for efficient VLSI implementations, and are robust to the propagation of possible errors in the computation process.

  11. Diamond difference method with hybrid angular quadrature applied to neutron transport problems

    International Nuclear Information System (INIS)

    Zani, Jose H.; Barros, Ricardo C.; Alves Filho, Hermes

    2005-01-01

    In this work we presents the results for the calculations of the disadvantage factor in thermal nuclear reactor physics. We use the one-group discrete ordinates (S N ) equations to mathematically model the flux distributions in slab lattices. We apply the diamond difference method with source iteration iterative scheme to numerically solve the discretized systems equations. We used special interface conditions to describe the method with hybrid angular quadrature. We show numerical results to illustrate the accuracy of the hybrid method. (author)

  12. Influence of discretization method on the digital control system performance

    Directory of Open Access Journals (Sweden)

    Futás József

    2003-12-01

    Full Text Available The design of control system can be divided into two steps. First the process or plant have to be convert into mathematical model form, so that its behavior can be analyzed. Then an appropriate controller have to be design in order to get the desired response of the controlled system. In the continuous time domain the system is represented by differential equations. Replacing a continuous system into discrete time form is always an approximation of the continuous system. The different discretization methods give different digital controller performance. The methods presented on the paper are Step Invariant or Zero Order Hold (ZOH Method, Matched Pole-Zero Method, Backward difference Method and Bilinear transformation. The above mentioned discretization methods are used in developing PI position controller of a dc motor. The motor model was converted by the ZOH method. The performances of the different methods are compared and the results are presented.

  13. Solving the discrete KdV equation with homotopy analysis method

    International Nuclear Information System (INIS)

    Zou, L.; Zong, Z.; Wang, Z.; He, L.

    2007-01-01

    In this Letter, we apply the homotopy analysis method to differential-difference equations. We take the discrete KdV equation as an example, and successfully obtain double periodic wave solutions and solitary wave solutions. It illustrates the validity and the great potential of the homotopy analysis method in solving discrete KdV equation. Comparisons are made between the results of the proposed method and exact solutions. The results reveal that the proposed method is very effective and convenient

  14. An Efficient Approach for Identifying Stable Lobes with Discretization Method

    Directory of Open Access Journals (Sweden)

    Baohai Wu

    2013-01-01

    Full Text Available This paper presents a new approach for quick identification of chatter stability lobes with discretization method. Firstly, three different kinds of stability regions are defined: absolute stable region, valid region, and invalid region. Secondly, while identifying the chatter stability lobes, three different regions within the chatter stability lobes are identified with relatively large time intervals. Thirdly, stability boundary within the valid regions is finely calculated to get exact chatter stability lobes. The proposed method only needs to test a small portion of spindle speed and cutting depth set; about 89% computation time is savedcompared with full discretization method. It spends only about10 minutes to get exact chatter stability lobes. Since, based on discretization method, the proposed method can be used for different immersion cutting including low immersion cutting process, the proposed method can be directly implemented in the workshop to promote machining parameters selection efficiency.

  15. Proposed Ordinance for the Regulation of Cable Television. Working Draft.

    Science.gov (United States)

    Chicago City Council, IL.

    A model ordinance is proposed for the regulation of cable television in the city of Chicago. It defines the language of the ordinance, sets forth the method of granting franchises, and describes the terms of the franchises. The duties of a commission to regulate cable television are listed and the method of selecting commission members is…

  16. Ordinal measures for iris recognition.

    Science.gov (United States)

    Sun, Zhenan; Tan, Tieniu

    2009-12-01

    Images of a human iris contain rich texture information useful for identity authentication. A key and still open issue in iris recognition is how best to represent such textural information using a compact set of features (iris features). In this paper, we propose using ordinal measures for iris feature representation with the objective of characterizing qualitative relationships between iris regions rather than precise measurements of iris image structures. Such a representation may lose some image-specific information, but it achieves a good trade-off between distinctiveness and robustness. We show that ordinal measures are intrinsic features of iris patterns and largely invariant to illumination changes. Moreover, compactness and low computational complexity of ordinal measures enable highly efficient iris recognition. Ordinal measures are a general concept useful for image analysis and many variants can be derived for ordinal feature extraction. In this paper, we develop multilobe differential filters to compute ordinal measures with flexible intralobe and interlobe parameters such as location, scale, orientation, and distance. Experimental results on three public iris image databases demonstrate the effectiveness of the proposed ordinal feature models.

  17. Ordinal Log-Linear Models for Contingency Tables

    Directory of Open Access Journals (Sweden)

    Brzezińska Justyna

    2016-12-01

    Full Text Available A log-linear analysis is a method providing a comprehensive scheme to describe the association for categorical variables in a contingency table. The log-linear model specifies how the expected counts depend on the levels of the categorical variables for these cells and provide detailed information on the associations. The aim of this paper is to present theoretical, as well as empirical, aspects of ordinal log-linear models used for contingency tables with ordinal variables. We introduce log-linear models for ordinal variables: linear-by-linear association, row effect model, column effect model and RC Goodman’s model. Algorithm, advantages and disadvantages will be discussed in the paper. An empirical analysis will be conducted with the use of R.

  18. A residual Monte Carlo method for discrete thermal radiative diffusion

    International Nuclear Information System (INIS)

    Evans, T.M.; Urbatsch, T.J.; Lichtenstein, H.; Morel, J.E.

    2003-01-01

    Residual Monte Carlo methods reduce statistical error at a rate of exp(-bN), where b is a positive constant and N is the number of particle histories. Contrast this convergence rate with 1/√N, which is the rate of statistical error reduction for conventional Monte Carlo methods. Thus, residual Monte Carlo methods hold great promise for increased efficiency relative to conventional Monte Carlo methods. Previous research has shown that the application of residual Monte Carlo methods to the solution of continuum equations, such as the radiation transport equation, is problematic for all but the simplest of cases. However, the residual method readily applies to discrete systems as long as those systems are monotone, i.e., they produce positive solutions given positive sources. We develop a residual Monte Carlo method for solving a discrete 1D non-linear thermal radiative equilibrium diffusion equation, and we compare its performance with that of the discrete conventional Monte Carlo method upon which it is based. We find that the residual method provides efficiency gains of many orders of magnitude. Part of the residual gain is due to the fact that we begin each timestep with an initial guess equal to the solution from the previous timestep. Moreover, fully consistent non-linear solutions can be obtained in a reasonable amount of time because of the effective lack of statistical noise. We conclude that the residual approach has great potential and that further research into such methods should be pursued for more general discrete and continuum systems

  19. Albedo boundary conditions for global calculations of thermal nuclear reactors with the model of discrete ordinates to two energy groups

    International Nuclear Information System (INIS)

    Nunes, Carlos Eduardo de Araujo

    2011-01-01

    As neutron fission events do not take place in the non-multiplying regions of nuclear reactors, e.g., moderator, reflector, and structural core, these regions do not generate power and the computational efficiency of nuclear reactor global calculations can hence be improved by eliminating the explicit numerical calculations within the non-multiplying regions around the active domain. Discussed here is the computational efficiency of approximate discrete ordinates (SN) albedo boundary conditions for two-energy group eigenvalue problems in X, Y geometry. Albedo, the Latin word for w hiteness , was originally defined as the fraction of incident light reflected diffusely by a surface. This Latin word has remained the usual scientific term in astronomy and in this dissertation this concept is extended for the reflection of neutrons. The non-standard SN albedo substitutes approximately the reflector region around the active domain, as we neglect the transverse leakage terms within the non-multiplying reflector. Should the problem have no transverse leakage terms, i.e., one dimensional slab geometry, then the offered albedo boundary conditions are exact. By computational efficiency we mean analyzing the accuracy of the numerical results versus the CPU execution time of each run for a given model problem. Numerical results to two 1/4 symmetric test problems are shown to illustrate this efficiency analysis. (author)

  20. Angular discretization errors in transport theory

    International Nuclear Information System (INIS)

    Nelson, P.; Yu, F.

    1992-01-01

    Elements of the information-based complexity theory are computed for several types of information and associated algorithms for angular approximations in the setting of a on-dimensional model problem. For point-evaluation information, the local and global radii of information are computed, a (trivial) optimal algorithm is determined, and the local and global error of a discrete ordinates algorithm are shown to be infinite. For average cone-integral information, the local and global radii of information are computed, the local and global error tends to zero as the underlying partition is indefinitely refined. A central algorithm for such information and an optimal partition (of given cardinality) are described. It is further shown that the analytic first-collision source method has zero error (for the purely absorbing model problem). Implications of the restricted problem domains suitable for the various types of information are discussed

  1. New formulation of the discrete element method

    Science.gov (United States)

    Rojek, Jerzy; Zubelewicz, Aleksander; Madan, Nikhil; Nosewicz, Szymon

    2018-01-01

    A new original formulation of the discrete element method based on the soft contact approach is presented in this work. The standard DEM has heen enhanced by the introduction of the additional (global) deformation mode caused by the stresses in the particles induced by the contact forces. Uniform stresses and strains are assumed for each particle. The stresses are calculated from the contact forces. The strains are obtained using an inverse constitutive relationship. The strains allow us to obtain deformed particle shapes. The deformed shapes (ellipses) are taken into account in contact detection and evaluation of the contact forces. A simple example of a uniaxial compression of a rectangular specimen, discreti.zed with equal sized particles is simulated to verify the DDEM algorithm. The numerical example shows that a particle deformation changes the particle interaction and the distribution of forces in the discrete element assembly. A quantitative study of micro-macro elastic properties proves the enhanced capabilities of the DDEM as compared to standard DEM.

  2. Numerical Method for Darcy Flow Derived Using Discrete Exterior Calculus

    Science.gov (United States)

    Hirani, A. N.; Nakshatrala, K. B.; Chaudhry, J. H.

    2015-05-01

    We derive a numerical method for Darcy flow, and also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is one of its discretizations on simplicial complexes such as triangle and tetrahedral meshes. DEC is a coordinate invariant discretization, in that it does not depend on the embedding of the simplices or the whole mesh. We start by rewriting the governing equations of Darcy flow using the language of exterior calculus. This yields a formulation in terms of flux differential form and pressure. The numerical method is then derived by using the framework provided by DEC for discretizing differential forms and operators that act on forms. We also develop a discretization for a spatially dependent Hodge star that varies with the permeability of the medium. This also allows us to address discontinuous permeability. The matrix representation for our discrete non-homogeneous Hodge star is diagonal, with positive diagonal entries. The resulting linear system of equations for flux and pressure are saddle type, with a diagonal matrix as the top left block. The performance of the proposed numerical method is illustrated on many standard test problems. These include patch tests in two and three dimensions, comparison with analytically known solutions in two dimensions, layered medium with alternating permeability values, and a test with a change in permeability along the flow direction. We also show numerical evidence of convergence of the flux and the pressure. A convergence experiment is included for Darcy flow on a surface. A short introduction to the relevant parts of smooth and discrete exterior calculus is included in this article. We also include a discussion of the boundary condition in terms of exterior calculus.

  3. Neutronics analysis of the International Thermonuclear Experimental Reactor (ITER) MCNP ''Benchmark CAD Model'' with the ATTILA discrete ordinance code

    International Nuclear Information System (INIS)

    Youssef, M.Z.; Feder, R.; Davis, I.

    2007-01-01

    The ITER IT has adopted the newly developed FEM, 3-D, and CAD-based Discrete Ordinates code, ATTILA for the neutronics studies contingent on its success in predicting key neutronics parameters and nuclear field according to the stringent QA requirements set forth by the Management and Quality Program (MQP). ATTILA has the advantage of providing a full flux and response functions mapping everywhere in one run where components subjected to excessive radiation level and strong streaming paths can be identified. The ITER neutronics community had agreed to use a standard CAD model of ITER (40 degree sector, denoted ''Benchmark CAD Model'') to compare results for several responses selected for calculation benchmarking purposes to test the efficiency and accuracy of the CAD-MCNP approach developed by each party. Since ATTILA seems to lend itself as a powerful design tool with minimal turnaround time, it was decided to benchmark this model with ATTILA as well and compare the results to those obtained with the CAD MCNP calculations. In this paper we report such comparison for five responses, namely: (1) Neutron wall load on the surface of the 18 shield blanket module (SBM), (2) Neutron flux and nuclear heating rate in the divertor cassette, (3) nuclear heating rate in the winding pack of the inner leg of the TF coil, (4) Radial flux profile across dummy port plug and shield plug placed in the equatorial port, and (5) Flux at seven point locations situated behind the equatorial port plug. (orig.)

  4. Sensitivity of Particle Size in Discrete Element Method to Particle Gas Method (DEM_PGM) Coupling in Underbody Blast Simulations

    Science.gov (United States)

    2016-06-12

    Particle Size in Discrete Element Method to Particle Gas Method (DEM_PGM) Coupling in Underbody Blast Simulations Venkatesh Babu, Kumar Kulkarni, Sanjay...buried in soil viz., (1) coupled discrete element & particle gas methods (DEM-PGM) and (2) Arbitrary Lagrangian-Eulerian (ALE), are investigated. The...DEM_PGM and identify the limitations/strengths compared to the ALE method. Discrete Element Method (DEM) can model individual particle directly, and

  5. The discrete adjoint method for parameter identification in multibody system dynamics.

    Science.gov (United States)

    Lauß, Thomas; Oberpeilsteiner, Stefan; Steiner, Wolfgang; Nachbagauer, Karin

    2018-01-01

    The adjoint method is an elegant approach for the computation of the gradient of a cost function to identify a set of parameters. An additional set of differential equations has to be solved to compute the adjoint variables, which are further used for the gradient computation. However, the accuracy of the numerical solution of the adjoint differential equation has a great impact on the gradient. Hence, an alternative approach is the discrete adjoint method , where the adjoint differential equations are replaced by algebraic equations. Therefore, a finite difference scheme is constructed for the adjoint system directly from the numerical time integration method. The method provides the exact gradient of the discretized cost function subjected to the discretized equations of motion.

  6. A dynamic discretization method for reliability inference in Dynamic Bayesian Networks

    International Nuclear Information System (INIS)

    Zhu, Jiandao; Collette, Matthew

    2015-01-01

    The material and modeling parameters that drive structural reliability analysis for marine structures are subject to a significant uncertainty. This is especially true when time-dependent degradation mechanisms such as structural fatigue cracking are considered. Through inspection and monitoring, information such as crack location and size can be obtained to improve these parameters and the corresponding reliability estimates. Dynamic Bayesian Networks (DBNs) are a powerful and flexible tool to model dynamic system behavior and update reliability and uncertainty analysis with life cycle data for problems such as fatigue cracking. However, a central challenge in using DBNs is the need to discretize certain types of continuous random variables to perform network inference while still accurately tracking low-probability failure events. Most existing discretization methods focus on getting the overall shape of the distribution correct, with less emphasis on the tail region. Therefore, a novel scheme is presented specifically to estimate the likelihood of low-probability failure events. The scheme is an iterative algorithm which dynamically partitions the discretization intervals at each iteration. Through applications to two stochastic crack-growth example problems, the algorithm is shown to be robust and accurate. Comparisons are presented between the proposed approach and existing methods for the discretization problem. - Highlights: • A dynamic discretization method is developed for low-probability events in DBNs. • The method is compared to existing approaches on two crack growth problems. • The method is shown to improve on existing methods for low-probability events

  7. Atomic Energy Act and ordinances. 8. ed.

    International Nuclear Information System (INIS)

    Anon.

    1978-01-01

    The new issue of the text contains the Atomic Energy Act (AtG) in its new wording of the announcement of 31 Oct 76, the new wording of the ordinances put in effect in 1977: Atomic procedure ordinance (AtVfV), radiation protection ordinance (SSU), and atomic financial security ordinance (AtDeckV); furthermore the x-ray ordinance (RoeV) of 1978 in its wording which has been changed by the radiation protection ordinance. Also printed are the cost ordinance (AtKostV) of 1971, the food irradiation ordinance (LebensmBestrV) in the wording of 1975 and the medicine ordinance (ArzneimV) in the wording of 1971. An addition was made by adding to the liability laws the Paris agreement (PUE) on the liability towards third persons in the field of nuclear energy in the wording of the announcement of 5 Feb 76. (orig./HP) [de

  8. Discrete Lattice effect of various forcing methods of body force on immersed Boundary-Lattice Boltzmann method

    Energy Technology Data Exchange (ETDEWEB)

    Son, Sung Wan; Ha, Man Yeong; Yoon, Hyun Sik [Pusan National University, Busan (Korea, Republic of); Jeong, Hae Kwon [POSCO, Pohang (Korea, Republic of); Balachandar, S. [University of Florida, Florida (United States)

    2013-02-15

    We investigate the discrete lattice effect of various forcing methods in the lattice Boltzmann method (LBM) to include the body force obtained from the immersed boundary method (IBM). In the immersed boundary lattice Boltzmann method (IB-LBM), the LBM needs a forcing method to involve the body force on a forcing point near the immersed boundary that is calculated by IBM. The proper forcing method in LBM is derived to include the body force, which appears to resolve problems such as multiphase flow, non-ideal gas behavior, etc. Many researchers have adopted different forcing methods in LBM to involve the body force from IBM, even when they solved similar problems. However, it is necessary to evaluate the discrete lattice effect, which originates from different forcing methods in LBM, to include the effect of the body force from IBM on the results. Consequently, in this study, a rigorous analysis of the discrete lattice effect for different forcing methods in IB-LBM is performed by solving various problems.

  9. Discrete Lattice effect of various forcing methods of body force on immersed Boundary-Lattice Boltzmann method

    International Nuclear Information System (INIS)

    Son, Sung Wan; Ha, Man Yeong; Yoon, Hyun Sik; Jeong, Hae Kwon; Balachandar, S.

    2013-01-01

    We investigate the discrete lattice effect of various forcing methods in the lattice Boltzmann method (LBM) to include the body force obtained from the immersed boundary method (IBM). In the immersed boundary lattice Boltzmann method (IB-LBM), the LBM needs a forcing method to involve the body force on a forcing point near the immersed boundary that is calculated by IBM. The proper forcing method in LBM is derived to include the body force, which appears to resolve problems such as multiphase flow, non-ideal gas behavior, etc. Many researchers have adopted different forcing methods in LBM to involve the body force from IBM, even when they solved similar problems. However, it is necessary to evaluate the discrete lattice effect, which originates from different forcing methods in LBM, to include the effect of the body force from IBM on the results. Consequently, in this study, a rigorous analysis of the discrete lattice effect for different forcing methods in IB-LBM is performed by solving various problems.

  10. Multivariate normal maximum likelihood with both ordinal and continuous variables, and data missing at random.

    Science.gov (United States)

    Pritikin, Joshua N; Brick, Timothy R; Neale, Michael C

    2018-04-01

    A novel method for the maximum likelihood estimation of structural equation models (SEM) with both ordinal and continuous indicators is introduced using a flexible multivariate probit model for the ordinal indicators. A full information approach ensures unbiased estimates for data missing at random. Exceeding the capability of prior methods, up to 13 ordinal variables can be included before integration time increases beyond 1 s per row. The method relies on the axiom of conditional probability to split apart the distribution of continuous and ordinal variables. Due to the symmetry of the axiom, two similar methods are available. A simulation study provides evidence that the two similar approaches offer equal accuracy. A further simulation is used to develop a heuristic to automatically select the most computationally efficient approach. Joint ordinal continuous SEM is implemented in OpenMx, free and open-source software.

  11. To the development of numerical methods in problems of radiation transport

    International Nuclear Information System (INIS)

    Germogenova, T.A.

    1990-01-01

    Review of studies on the development of numerical methods and the discrete ordinate method in particular, used for solution of radiation protection physics problems is given. Consideration is given to the problems, which arise when calculating fields of penetrating radiation and when studying processes of charged-particle transport and cascade processes, generated by high-energy primary radiation

  12. Cluster analysis of European Y-chromosomal STR haplotypes using the discrete Laplace method

    DEFF Research Database (Denmark)

    Andersen, Mikkel Meyer; Eriksen, Poul Svante; Morling, Niels

    2014-01-01

    The European Y-chromosomal short tandem repeat (STR) haplotype distribution has previously been analysed in various ways. Here, we introduce a new way of analysing population substructure using a new method based on clustering within the discrete Laplace exponential family that models the probabi......The European Y-chromosomal short tandem repeat (STR) haplotype distribution has previously been analysed in various ways. Here, we introduce a new way of analysing population substructure using a new method based on clustering within the discrete Laplace exponential family that models...... the probability distribution of the Y-STR haplotypes. Creating a consistent statistical model of the haplotypes enables us to perform a wide range of analyses. Previously, haplotype frequency estimation using the discrete Laplace method has been validated. In this paper we investigate how the discrete Laplace...... method can be used for cluster analysis to further validate the discrete Laplace method. A very important practical fact is that the calculations can be performed on a normal computer. We identified two sub-clusters of the Eastern and Western European Y-STR haplotypes similar to results of previous...

  13. From Discrete Space-Time to Minkowski Space: Basic Mechanisms, Methods and Perspectives

    Science.gov (United States)

    Finster, Felix

    This survey article reviews recent results on fermion systems in discrete space-time and corresponding systems in Minkowski space. After a basic introduction to the discrete setting, we explain a mechanism of spontaneous symmetry breaking which leads to the emergence of a discrete causal structure. As methods to study the transition between discrete space-time and Minkowski space, we describe a lattice model for a static and isotropic space-time, outline the analysis of regularization tails of vacuum Dirac sea configurations, and introduce a Lorentz invariant action for the masses of the Dirac seas. We mention the method of the continuum limit, which allows to analyze interacting systems. Open problems are discussed.

  14. Privacy Data Decomposition and Discretization Method for SaaS Services

    Directory of Open Access Journals (Sweden)

    Changbo Ke

    2017-01-01

    Full Text Available In cloud computing, user functional requirements are satisfied through service composition. However, due to the process of interaction and sharing among SaaS services, user privacy data tends to be illegally disclosed to the service participants. In this paper, we propose a privacy data decomposition and discretization method for SaaS services. First, according to logic between the data, we classify the privacy data into discrete privacy data and continuous privacy data. Next, in order to protect the user privacy information, continuous data chains are decomposed into discrete data chain, and discrete data chains are prevented from being synthesized into continuous data chains. Finally, we propose a protection framework for privacy data and demonstrate its correctness and feasibility with experiments.

  15. Analysis of Ordinal Categorical Data

    CERN Document Server

    Agresti, Alan

    2012-01-01

    Statistical science's first coordinated manual of methods for analyzing ordered categorical data, now fully revised and updated, continues to present applications and case studies in fields as diverse as sociology, public health, ecology, marketing, and pharmacy. Analysis of Ordinal Categorical Data, Second Edition provides an introduction to basic descriptive and inferential methods for categorical data, giving thorough coverage of new developments and recent methods. Special emphasis is placed on interpretation and application of methods including an integrated comparison of the available st

  16. Baecklund transformations for discrete Painleve equations: Discrete PII-PV

    International Nuclear Information System (INIS)

    Sakka, A.; Mugan, U.

    2006-01-01

    Transformation properties of discrete Painleve equations are investigated by using an algorithmic method. This method yields explicit transformations which relates the solutions of discrete Painleve equations, discrete P II -P V , with different values of parameters. The particular solutions which are expressible in terms of the discrete analogue of the classical special functions of discrete Painleve equations can also be obtained from these transformations

  17. Computational methods of electron/photon transport

    International Nuclear Information System (INIS)

    Mack, J.M.

    1983-01-01

    A review of computational methods simulating the non-plasma transport of electrons and their attendant cascades is presented. Remarks are mainly restricted to linearized formalisms at electron energies above 1 keV. The effectiveness of various metods is discussed including moments, point-kernel, invariant imbedding, discrete-ordinates, and Monte Carlo. Future research directions and the potential impact on various aspects of science and engineering are indicated

  18. Methods in nuclear reactors calculations; Metodos de calculo en reactores nucleares

    Energy Technology Data Exchange (ETDEWEB)

    Velarde, G

    1966-07-01

    Studies are made of the neutron transport equation corresponding to the the real and virtual reactors, as well as the starting hypotheses. Methods are developed to solve the transport equation in slab geometry, and P{sub l}; B{sub l}; M{sub l}; S{sub n} and discrete ordinates approximations. (Author)

  19. Quantization in rotating co-ordinates revisited

    International Nuclear Information System (INIS)

    Hussain, F.; Qadir, A.

    1982-07-01

    Recent work on quantization in rotating co-ordinates showed that no radiation would be seen by an observer rotating with a constant angular speed. This work used a Galilean-type co-ordinate transformation. We show that the same result holds for a Lorentz-type co-ordinate system, in spite of the fact that the metric has a co-ordinate singularity at rΩ = 1. Further, we are able to define positive and negative energy modes for a particular case of a non-static, non-stationary metric. (author)

  20. Radiation (Safety Control) Ordinance 1978

    International Nuclear Information System (INIS)

    1978-01-01

    This Ordinance provides for the control, regulation, possession, use and transport of radioactive substance and irradiating apparatus. The Director of Health is responsible for administration of the Ordinance, which contains detailed provisions concerning the terms and conditions of licences, duties of licensees, medical examinations, maximum radiation doses, precautions to be taken to avoid exceeding such doses. The Ordinance also lays down a system of record-keeping and registration as well as packaging specifications for the transport of radioactive substances. (NEA) [fr

  1. Ordinal bivariate inequality

    DEFF Research Database (Denmark)

    Sonne-Schmidt, Christoffer Scavenius; Tarp, Finn; Østerdal, Lars Peter Raahave

    This paper introduces a concept of inequality comparisons with ordinal bivariate categorical data. In our model, one population is more unequal than another when they have common arithmetic median outcomes and the first can be obtained from the second by correlationincreasing switches and/or median......-preserving spreads. For the canonical 2x2 case (with two binary indicators), we derive a simple operational procedure for checking ordinal inequality relations in practice. As an illustration, we apply the model to childhood deprivation in Mozambique....

  2. Two split cell numerical methods for solving 2-D non-equilibrium radiation transport equations

    International Nuclear Information System (INIS)

    Feng Tinggui

    2004-11-01

    Two numerically positive methods, the step characteristic integral method and subcell balance method, for solving radiative transfer equations on quadrilateral grids are presented. Numerical examples shows that the schemes presented are feasible on non-rectangle grid computation, and that the computing results by the schemes presented are comparative to that by the discrete ordinate diamond scheme on rectangle grid. (author)

  3. Radiation doses in diagnostic radiology and methods for dose reduction. Report of a co-ordinated research programme (1991-1993)

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    1995-04-01

    It is well recognized that diagnostic radiology is the largest contributor to the collective dose from all man-made sources of radiation. Large differences in radiation doses from the same procedures among different X ray rooms have led to the conclusion that there is a potential for dose reduction. A Co-ordinated Research Programme on Radiation Doses in Diagnostic Radiology and Methods for Dose Reduction, involving Member States with different degrees of development, was launched by the IAEA in co-operation with the CEC. This report summarizes the results of the second and final Research Co-ordination Meeting held in Vienna from 4 to 8 October 1993. 22 refs, 6 figs and tabs.

  4. Radiation doses in diagnostic radiology and methods for dose reduction. Report of a co-ordinated research programme (1991-1993)

    International Nuclear Information System (INIS)

    1995-04-01

    It is well recognized that diagnostic radiology is the largest contributor to the collective dose from all man-made sources of radiation. Large differences in radiation doses from the same procedures among different X ray rooms have led to the conclusion that there is a potential for dose reduction. A Co-ordinated Research Programme on Radiation Doses in Diagnostic Radiology and Methods for Dose Reduction, involving Member States with different degrees of development, was launched by the IAEA in co-operation with the CEC. This report summarizes the results of the second and final Research Co-ordination Meeting held in Vienna from 4 to 8 October 1993. 22 refs, 6 figs and tabs

  5. Recently developed methods in neutral-particle transport calculations: overview

    International Nuclear Information System (INIS)

    Alcouffe, R.E.

    1982-01-01

    It has become increasingly apparent that successful, general methods for the solution of the neutral particle transport equation involve a close connection between the spatial-discretization method used and the source-acceleration method chosen. The first form of the transport equation, angular discretization which is discrete ordinates is considered as well as spatial discretization based upon a mesh arrangement. Characteristic methods are considered briefly in the context of future, desirable developments. The ideal spatial-discretization method is described as having the following attributes: (1) positive-positive boundary data yields a positive angular flux within the mesh including its boundaries; (2) satisfies the particle balance equation over the mesh, that is, the method is conservative; (3) possesses the diffusion limit independent of spatial mesh size, that is, for a linearly isotropic flux assumption, the transport differencing reduces to a suitable diffusion equation differencing; (4) the method is unconditionally acceleratable, i.e., for each mesh size, the method is unconditionally convergent with a source iteration acceleration. It is doubtful that a single method possesses all these attributes for a general problem. Some commonly used methods are outlined and their computational performance and usefulness are compared; recommendations for future development are detailed, which include practical computational considerations

  6. Comparison of calculational methods for liquid metal reactor shields

    International Nuclear Information System (INIS)

    Carter, L.L.; Moore, F.S.; Morford, R.J.; Mann, F.M.

    1985-09-01

    A one-dimensional comparison is made between Monte Carlo (MCNP), discrete ordinances (ANISN), and diffusion theory (MlDX) calculations of neutron flux and radiation damage from the core of the Fast Flux Test Facility (FFTF) out to the reactor vessel. Diffusion theory was found to be reasonably accurate for the calculation of both total flux and radiation damage. However, for large distances from the core, the calculated flux at very high energies is low by an order of magnitude or more when the diffusion theory is used. Particular emphasis was placed in this study on the generation of multitable cross sections for use in discrete ordinates codes that are self-shielded, consistent with the self-shielding employed in the generation of cross sections for use with diffusion theory. The Monte Carlo calculation, with a pointwise representation of the cross sections, was used as the benchmark for determining the limitations of the other two calculational methods. 12 refs., 33 figs

  7. Ordinance on protection from the harmful effects of X-radiation (X-ray Ordinance). As of January 8, 1987. 3. ed.

    International Nuclear Information System (INIS)

    Hinrichs, O.

    1992-01-01

    The German X-ray Ordinance (Roentgenverordnung) contains the main protective provisions applying to the field of X-ray equipment and sources of unwanted X radiation. It thus forms a complement to the German Radiation Protection Ordinance (Strahlenschutzverordnung). The X-ray Ordinance is based, as is the Radiation Protection Ordinance, on the German Nuclear Energy Act (Atomgesetz). It transposes the same Euratom Directives into national law, through which above all the limit values are defined. The current state of the X-ray Ordinance is that of the text promulgated on 8.01.1987 with the subsequent amendments, the last of which was adopted on 19.12.1990. The brochure also reproduces the Official Memorandum to the X-ray Ordinance, as this gives important indications for the legal construction of the Ordinance. (orig./HSCH) [de

  8. Radiation transport calculation methods in BNCT

    International Nuclear Information System (INIS)

    Koivunoro, H.; Seppaelae, T.; Savolainen, S.

    2000-01-01

    Boron neutron capture therapy (BNCT) is used as a radiotherapy for malignant brain tumours. Radiation dose distribution is necessary to determine individually for each patient. Radiation transport and dose distribution calculations in BNCT are more complicated than in conventional radiotherapy. Total dose in BNCT consists of several different dose components. The most important dose component for tumour control is therapeutic boron dose D B . The other dose components are gamma dose D g , incident fast neutron dose D f ast n and nitrogen dose D N . Total dose is a weighted sum of the dose components. Calculation of neutron and photon flux is a complex problem and requires numerical methods, i.e. deterministic or stochastic simulation methods. Deterministic methods are based on the numerical solution of Boltzmann transport equation. Such are discrete ordinates (SN) and spherical harmonics (PN) methods. The stochastic simulation method for calculation of radiation transport is known as Monte Carlo method. In the deterministic methods the spatial geometry is partitioned into mesh elements. In SN method angular integrals of the transport equation are replaced with weighted sums over a set of discrete angular directions. Flux is calculated iteratively for all these mesh elements and for each discrete direction. Discrete ordinates transport codes used in the dosimetric calculations are ANISN, DORT and TORT. In PN method a Legendre expansion for angular flux is used instead of discrete direction fluxes, land the angular dependency comes a property of vector function space itself. Thus, only spatial iterations are required for resulting equations. A novel radiation transport code based on PN method and tree-multigrid technique (TMG) has been developed at VTT (Technical Research Centre of Finland). Monte Carlo method solves the radiation transport by randomly selecting neutrons and photons from a prespecified boundary source and following the histories of selected particles

  9. Memory-Based Specification of Verbal Features for Classifying Animals into Super-Ordinate and Sub-Ordinate Categories

    Directory of Open Access Journals (Sweden)

    Takahiro Soshi

    2017-09-01

    Full Text Available Accumulating evidence suggests that category representations are based on features. Distinguishing features are considered to define categories, because of all-or-none responses for objects in different categories; however, it is unclear how distinguishing features actually classify objects at various category levels. The present study included 75 animals within three classes (mammal, bird, and fish, along with 195 verbal features. Healthy adults participated in memory-based feature-animal matching verification tests. Analyses included a hierarchical clustering analysis, support vector machine, and independent component analysis to specify features effective for classifications. Quantitative and qualitative comparisons for significant features were conducted between super-ordinate and sub-ordinate levels. The number of significant features was larger for super-ordinate than sub-ordinate levels. Qualitatively, the proportion of biological features was larger than cultural/affective features in both the levels, while the proportion of affective features increased at the sub-ordinate level. To summarize, the two types of features differentially function to establish category representations.

  10. Discrete Mathematics

    DEFF Research Database (Denmark)

    Sørensen, John Aasted

    2011-01-01

    The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics......; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...

  11. Awareness on the Implementation of Anti-Smoking Ordinance No. 1S. 2012

    Directory of Open Access Journals (Sweden)

    Rowena E. Mojares

    2014-10-01

    Full Text Available This study aimed to identify the respondent’s profile variable such as gender, age, educational attainment, occupation, and frequency of smoking; to identify the level of awareness of the public on Anti-Smoking Ordinance and to determine the significant difference on the level of awareness in the implementation when grouped according to profile variables. The researchers used the descriptive method of research and utilized two hundred-four (204 respondents. The result showed that the respondents are dominated by male, college graduate and under graduate and most of them are private employees. They agreed that they are aware on the implementation of anti-smoking ordinance no. 1S 2012 because the ordinance was clearly stated, well disseminated, there are authorities prohibiting it and there is a usage of signage. But they agree also that they are less aware about the specific boundary that the ordinance covered, that there is regular monitoring and there is enough number of personnel implementing the ordinance. The researchers recommended that the Pamahalaang Panglunsod may continue to maintain the strict implementation of the Anti-Smoking Ordinance; authorities should specify the boundary covered by the Ordinance and should have enough personnel to implement it,

  12. Improvement of spatial discretization error on the semi-analytic nodal method using the scattered source subtraction method

    International Nuclear Information System (INIS)

    Yamamoto, Akio; Tatsumi, Masahiro

    2006-01-01

    In this paper, the scattered source subtraction (SSS) method is newly proposed to improve the spatial discretization error of the semi-analytic nodal method with the flat-source approximation. In the SSS method, the scattered source is subtracted from both side of the diffusion or the transport equation to make spatial variation of the source term to be small. The same neutron balance equation is still used in the SSS method. Since the SSS method just modifies coefficients of node coupling equations (those used in evaluation for the response of partial currents), its implementation is easy. Validity of the present method is verified through test calculations that are carried out in PWR multi-assemblies configurations. The calculation results show that the SSS method can significantly improve the spatial discretization error. Since the SSS method does not have any negative impact on execution time, convergence behavior and memory requirement, it will be useful to reduce the spatial discretization error of the semi-analytic nodal method with the flat-source approximation. (author)

  13. Ordinal Bivariate Inequality

    DEFF Research Database (Denmark)

    Sonne-Schmidt, Christoffer Scavenius; Tarp, Finn; Østerdal, Lars Peter Raahave

    2016-01-01

    This paper introduces a concept of inequality comparisons with ordinal bivariate categorical data. In our model, one population is more unequal than another when they have common arithmetic median outcomes and the first can be obtained from the second by correlation-increasing switches and....../or median-preserving spreads. For the canonical 2 × 2 case (with two binary indicators), we derive a simple operational procedure for checking ordinal inequality relations in practice. As an illustration, we apply the model to childhood deprivation in Mozambique....

  14. Tree Ordination as Invented Tradition

    Directory of Open Access Journals (Sweden)

    Avery Morrow

    2012-01-01

    Full Text Available The symbolic ordination of trees as monks in Thailand is widely perceived in Western scholarship to be proof of the power of Buddhism to spur ecological thought. However, a closer analysis of tree ordination demonstrates that it is not primarily about Buddhist teaching, but rather is an invented tradition based on the sanctity of Thai Buddhist symbols as well as those of spirit worship and the monarchy. Tree ordinations performed by non-Buddhist minorities in Thailand do not demonstrate a religious commitment but rather a political one.

  15. Two linearization methods for atmospheric remote sensing

    International Nuclear Information System (INIS)

    Doicu, A.; Trautmann, T.

    2009-01-01

    We present two linearization methods for a pseudo-spherical atmosphere and general viewing geometries. The first approach is based on an analytical linearization of the discrete ordinate method with matrix exponential and incorporates two models for matrix exponential calculation: the matrix eigenvalue method and the Pade approximation. The second method referred to as the forward-adjoint approach is based on the adjoint radiative transfer for a pseudo-spherical atmosphere. We provide a compact description of the proposed methods as well as a numerical analysis of their accuracy and efficiency.

  16. The large discretization step method for time-dependent partial differential equations

    Science.gov (United States)

    Haras, Zigo; Taasan, Shlomo

    1995-01-01

    A new method for the acceleration of linear and nonlinear time dependent calculations is presented. It is based on the Large Discretization Step (LDS) approximation, defined in this work, which employs an extended system of low accuracy schemes to approximate a high accuracy discrete approximation to a time dependent differential operator. Error bounds on such approximations are derived. These approximations are efficiently implemented in the LDS methods for linear and nonlinear hyperbolic equations, presented here. In these algorithms the high and low accuracy schemes are interpreted as the same discretization of a time dependent operator on fine and coarse grids, respectively. Thus, a system of correction terms and corresponding equations are derived and solved on the coarse grid to yield the fine grid accuracy. These terms are initialized by visiting the fine grid once in many coarse grid time steps. The resulting methods are very general, simple to implement and may be used to accelerate many existing time marching schemes.

  17. A Photon Free Method to Solve Radiation Transport Equations

    International Nuclear Information System (INIS)

    Chang, B

    2006-01-01

    The multi-group discrete-ordinate equations of radiation transfer is solved for the first time by Newton's method. It is a photon free method because the photon variables are eliminated from the radiation equations to yield a N group XN direction smaller but equivalent system of equations. The smaller set of equations can be solved more efficiently than the original set of equations. Newton's method is more stable than the Semi-implicit Linear method currently used by conventional radiation codes

  18. Report of the first research co-ordination meeting on the co-ordinated research programme: Rapid instrumental and separation methods for monitoring radionuclides in food and environmental samples, Central Laboratory for Radiological Protection, Warsaw, Poland 4-8 September 1989

    International Nuclear Information System (INIS)

    1989-09-01

    Concern about the release of radionuclides to the environment, especially to the foodchain, has been heightened by recent nuclear incidents. The assessment of any release of radioactivity demands rapid, reliable and practical techniques. In the intermediate and late post-accident period, where the interest is in food control rather then evacuation and sheltering, rapid methods would be useful for screening purposes as well as providing timely information and easing sample workload minimizing sample overloads. In the first research co-ordination meeting on the co-ordinated research program ''Rapid.... samples'', the specifications for the time required for sample preparation, separation, and analysis and the accuracy desired were outlined. Considerable attention was given to the need to develop rapid method for sample preparation and dissolution. Emphasis was placed on achieving the development of rapid methods with the minimum sacrifice in reliability, practicality and economy

  19. Parametric methods outperformed non-parametric methods in comparisons of discrete numerical variables

    Directory of Open Access Journals (Sweden)

    Sandvik Leiv

    2011-04-01

    Full Text Available Abstract Background The number of events per individual is a widely reported variable in medical research papers. Such variables are the most common representation of the general variable type called discrete numerical. There is currently no consensus on how to compare and present such variables, and recommendations are lacking. The objective of this paper is to present recommendations for analysis and presentation of results for discrete numerical variables. Methods Two simulation studies were used to investigate the performance of hypothesis tests and confidence interval methods for variables with outcomes {0, 1, 2}, {0, 1, 2, 3}, {0, 1, 2, 3, 4}, and {0, 1, 2, 3, 4, 5}, using the difference between the means as an effect measure. Results The Welch U test (the T test with adjustment for unequal variances and its associated confidence interval performed well for almost all situations considered. The Brunner-Munzel test also performed well, except for small sample sizes (10 in each group. The ordinary T test, the Wilcoxon-Mann-Whitney test, the percentile bootstrap interval, and the bootstrap-t interval did not perform satisfactorily. Conclusions The difference between the means is an appropriate effect measure for comparing two independent discrete numerical variables that has both lower and upper bounds. To analyze this problem, we encourage more frequent use of parametric hypothesis tests and confidence intervals.

  20. Atomic Energy Law with ordinances. 9. ed.

    International Nuclear Information System (INIS)

    Anon.

    1982-01-01

    The revised edition of the text is due to a variety of major changes in, and amendments to, the German Atomic Energy Law. This book includes the current version of the Atomic Energy Law which has been changed several times, the 1982-version of the ordinace concerning procedures laid down in the Atomic Energy Law, the 1976 radiation protection ordinance together with recent amendments, the 1973 X-ray ordinance, the 1977 financial security ordinance laid down in the Atomic Energy Law, the 1981 ordinance concerning costs, the ordinance concerning performance in anticipation of ultimate disposal. The book is a compilation of the basic Atomic Energy Law which is needed mostly for imminent practical requirements. (orig./HSCH) [de

  1. Discrete variational methods and their application to electronic structures

    International Nuclear Information System (INIS)

    Ellis, D.E.

    1987-01-01

    Some general concepts concerning Discrete Variational methods are developed and applied to problems of determination of eletronic spectra, charge densities and bonding of free molecules, surface-chemisorbed species and bulk solids. (M.W.O.) [pt

  2. A scalar flux - oriented method for the transport equation in slab geometry

    International Nuclear Information System (INIS)

    Budd, C.

    1981-01-01

    A new method for solving the neutron transport equation is described. An unusual feature of this method is that it deals principally with scalar fluxes rather than angular fluxes. An alternative approach in slab geometry promises to be cheaper to run and does not suffer from many of the problems of the discrete ordinates method. It also appears possible to extend the method to several dimensions and this is discussed. (U.K.)

  3. Comparison of calculational methods for EBT reactor nucleonics

    International Nuclear Information System (INIS)

    Henninger, R.J.; Seed, T.J.; Soran, P.D.; Dudziak, D.J.

    1980-01-01

    Nucleonic calculations for a preliminary conceptual design of the first wall/blanket/shield/coil assembly for an EBT reactor are described. Two-dimensional Monte Carlo, and one- and two-dimensional discrete-ordinates calculations are compared. Good agreement for the calculated values of tritium breeding and nuclear heating is seen. We find that the three methods are all useful and complementary as a design of this type evolves

  4. Discrete-ordinate method with matrix exponential for a pseudo-spherical atmosphere: Vector case

    International Nuclear Information System (INIS)

    Doicu, A.; Trautmann, T.

    2009-01-01

    The paper is devoted to the extension of the matrix-exponential formalism for the scalar radiative transfer to the vector case. Using basic results of the theory of matrix-exponential functions we provide a compact and versatile formulation of the vector radiative transfer. As in the scalar case, we operate with the concept of the layer equation incorporating the level values of the Stokes vector. The matrix exponentials which enter in the expression of the layer equation are computed by using the matrix eigenvalue method and the Pade approximation. A discussion of the computational efficiency of the proposed method for both an aerosol-loaded atmosphere as well as a cloudy atmosphere is also provided

  5. Discrete Element Modeling

    Energy Technology Data Exchange (ETDEWEB)

    Morris, J; Johnson, S

    2007-12-03

    The Distinct Element Method (also frequently referred to as the Discrete Element Method) (DEM) is a Lagrangian numerical technique where the computational domain consists of discrete solid elements which interact via compliant contacts. This can be contrasted with Finite Element Methods where the computational domain is assumed to represent a continuum (although many modern implementations of the FEM can accommodate some Distinct Element capabilities). Often the terms Discrete Element Method and Distinct Element Method are used interchangeably in the literature, although Cundall and Hart (1992) suggested that Discrete Element Methods should be a more inclusive term covering Distinct Element Methods, Displacement Discontinuity Analysis and Modal Methods. In this work, DEM specifically refers to the Distinct Element Method, where the discrete elements interact via compliant contacts, in contrast with Displacement Discontinuity Analysis where the contacts are rigid and all compliance is taken up by the adjacent intact material.

  6. Social Host Ordinances and Policies. Prevention Update

    Science.gov (United States)

    Higher Education Center for Alcohol, Drug Abuse, and Violence Prevention, 2011

    2011-01-01

    Social host liability laws (also known as teen party ordinances, loud or unruly gathering ordinances, or response costs ordinances) target the location in which underage drinking takes place. Social host liability laws hold noncommercial individuals responsible for underage drinking events on property they own, lease, or otherwise control. They…

  7. Analysis of a discrete element method and coupling with a compressible fluid flow method

    International Nuclear Information System (INIS)

    Monasse, L.

    2011-01-01

    This work aims at the numerical simulation of compressible fluid/deformable structure interactions. In particular, we have developed a partitioned coupling algorithm between a Finite Volume method for the compressible fluid and a Discrete Element method capable of taking into account fractures in the solid. A survey of existing fictitious domain methods and partitioned algorithms has led to choose an Embedded Boundary method and an explicit coupling scheme. We first showed that the Discrete Element method used for the solid yielded the correct macroscopic behaviour and that the symplectic time-integration scheme ensured the preservation of energy. We then developed an explicit coupling algorithm between a compressible inviscid fluid and an un-deformable solid. Mass, momentum and energy conservation and consistency properties were proved for the coupling scheme. The algorithm was then extended to the coupling with a deformable solid, in the form of a semi implicit scheme. Finally, we applied this method to unsteady inviscid flows around moving structures: comparisons with existing numerical and experimental results demonstrate the excellent accuracy of our method. (author) [fr

  8. A systematic method for constructing time discretizations of integrable lattice systems: local equations of motion

    International Nuclear Information System (INIS)

    Tsuchida, Takayuki

    2010-01-01

    We propose a new method for discretizing the time variable in integrable lattice systems while maintaining the locality of the equations of motion. The method is based on the zero-curvature (Lax pair) representation and the lowest-order 'conservation laws'. In contrast to the pioneering work of Ablowitz and Ladik, our method allows the auxiliary dependent variables appearing in the stage of time discretization to be expressed locally in terms of the original dependent variables. The time-discretized lattice systems have the same set of conserved quantities and the same structures of the solutions as the continuous-time lattice systems; only the time evolution of the parameters in the solutions that correspond to the angle variables is discretized. The effectiveness of our method is illustrated using examples such as the Toda lattice, the Volterra lattice, the modified Volterra lattice, the Ablowitz-Ladik lattice (an integrable semi-discrete nonlinear Schroedinger system) and the lattice Heisenberg ferromagnet model. For the modified Volterra lattice, we also present its ultradiscrete analogue.

  9. Ordinal Comparison of Multidimensional Deprivation

    DEFF Research Database (Denmark)

    Sonne-Schmidt, Christoffer Scavenius; Tarp, Finn; Østerdal, Lars Peter

    This paper develops an ordinal method of comparison of multidimensional inequality. In our model, population distribution g is more unequal than f when the distributions have common median and can be obtained from f  by one or more shifts in population density that increase inequality. For our be...... benchmark 2x2 case (i.e. the case of two binary outcome variables), we derive an empirical method for making inequality comparisons. As an illustration, we apply the model to childhood poverty in Mozambique....

  10. Processing ordinality and quantity: the case of developmental dyscalculia.

    Directory of Open Access Journals (Sweden)

    Orly Rubinsten

    Full Text Available In contrast to quantity processing, up to date, the nature of ordinality has received little attention from researchers despite the fact that both quantity and ordinality are embodied in numerical information. Here we ask if there are two separate core systems that lie at the foundations of numerical cognition: (1 the traditionally and well accepted numerical magnitude system but also (2 core system for representing ordinal information. We report two novel experiments of ordinal processing that explored the relation between ordinal and numerical information processing in typically developing adults and adults with developmental dyscalculia (DD. Participants made "ordered" or "non-ordered" judgments about 3 groups of dots (non-symbolic numerical stimuli; in Experiment 1 and 3 numbers (symbolic task: Experiment 2. In contrast to previous findings and arguments about quantity deficit in DD participants, when quantity and ordinality are dissociated (as in the current tasks, DD participants exhibited a normal ratio effect in the non-symbolic ordinal task. They did not show, however, the ordinality effect. Ordinality effect in DD appeared only when area and density were randomized, but only in the descending direction. In the symbolic task, the ordinality effect was modulated by ratio and direction in both groups. These findings suggest that there might be two separate cognitive representations of ordinal and quantity information and that linguistic knowledge may facilitate estimation of ordinal information.

  11. Processing ordinality and quantity: the case of developmental dyscalculia.

    Science.gov (United States)

    Rubinsten, Orly; Sury, Dana

    2011-01-01

    In contrast to quantity processing, up to date, the nature of ordinality has received little attention from researchers despite the fact that both quantity and ordinality are embodied in numerical information. Here we ask if there are two separate core systems that lie at the foundations of numerical cognition: (1) the traditionally and well accepted numerical magnitude system but also (2) core system for representing ordinal information. We report two novel experiments of ordinal processing that explored the relation between ordinal and numerical information processing in typically developing adults and adults with developmental dyscalculia (DD). Participants made "ordered" or "non-ordered" judgments about 3 groups of dots (non-symbolic numerical stimuli; in Experiment 1) and 3 numbers (symbolic task: Experiment 2). In contrast to previous findings and arguments about quantity deficit in DD participants, when quantity and ordinality are dissociated (as in the current tasks), DD participants exhibited a normal ratio effect in the non-symbolic ordinal task. They did not show, however, the ordinality effect. Ordinality effect in DD appeared only when area and density were randomized, but only in the descending direction. In the symbolic task, the ordinality effect was modulated by ratio and direction in both groups. These findings suggest that there might be two separate cognitive representations of ordinal and quantity information and that linguistic knowledge may facilitate estimation of ordinal information.

  12. Discrete Curvatures and Discrete Minimal Surfaces

    KAUST Repository

    Sun, Xiang

    2012-06-01

    This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads to great interest in studying discrete surfaces. With the rich smooth surface theory in hand, one would hope that this elegant theory can still be applied to the discrete counter part. Such a generalization, however, is not always successful. While discrete surfaces have the advantage of being finite dimensional, thus easier to treat, their geometric properties such as curvatures are not well defined in the classical sense. Furthermore, the powerful calculus tool can hardly be applied. The methods in this thesis, including angular defect formula, cotangent formula, parallel meshes, relative geometry etc. are approaches based on offset meshes or generalized offset meshes. As an important application, we discuss discrete minimal surfaces and discrete Koenigs meshes.

  13. A generalized endogenous grid method for discrete-continuous choice

    OpenAIRE

    John Rust; Bertel Schjerning; Fedor Iskhakov

    2012-01-01

    This paper extends Carroll's endogenous grid method (2006 "The method of endogenous gridpoints for solving dynamic stochastic optimization problems", Economic Letters) for models with sequential discrete and continuous choice. Unlike existing generalizations, we propose solution algorithm that inherits both advantages of the original method, namely it avoids all root finding operations, and also efficiently deals with restrictions on the continuous decision variable. To further speed up the s...

  14. Discrete Data Qualification System and Method Comprising Noise Series Fault Detection

    Science.gov (United States)

    Fulton, Christopher; Wong, Edmond; Melcher, Kevin; Bickford, Randall

    2013-01-01

    A Sensor Data Qualification (SDQ) function has been developed that allows the onboard flight computers on NASA s launch vehicles to determine the validity of sensor data to ensure that critical safety and operational decisions are not based on faulty sensor data. This SDQ function includes a novel noise series fault detection algorithm for qualification of the output data from LO2 and LH2 low-level liquid sensors. These sensors are positioned in a launch vehicle s propellant tanks in order to detect propellant depletion during a rocket engine s boost operating phase. This detection capability can prevent the catastrophic situation where the engine operates without propellant. The output from each LO2 and LH2 low-level liquid sensor is a discrete valued signal that is expected to be in either of two states, depending on whether the sensor is immersed (wet) or exposed (dry). Conventional methods for sensor data qualification, such as threshold limit checking, are not effective for this type of signal due to its discrete binary-state nature. To address this data qualification challenge, a noise computation and evaluation method, also known as a noise fault detector, was developed to detect unreasonable statistical characteristics in the discrete data stream. The method operates on a time series of discrete data observations over a moving window of data points and performs a continuous examination of the resulting observation stream to identify the presence of anomalous characteristics. If the method determines the existence of anomalous results, the data from the sensor is disqualified for use by other monitoring or control functions.

  15. The endogenous grid method for discrete-continuous dynamic choice models with (or without) taste shocks

    DEFF Research Database (Denmark)

    Iskhakov, Fedor; Jørgensen, Thomas H.; Rust, John

    2017-01-01

    We present a fast and accurate computational method for solving and estimating a class of dynamic programming models with discrete and continuous choice variables. The solution method we develop for structural estimation extends the endogenous grid-point method (EGM) to discrete-continuous (DC) p...

  16. Integrable discretizations and self-adaptive moving mesh method for a coupled short pulse equation

    International Nuclear Information System (INIS)

    Feng, Bao-Feng; Chen, Junchao; Chen, Yong; Maruno, Ken-ichi; Ohta, Yasuhiro

    2015-01-01

    In the present paper, integrable semi-discrete and fully discrete analogues of a coupled short pulse (CSP) equation are constructed. The key to the construction are the bilinear forms and determinant structure of the solutions of the CSP equation. We also construct N-soliton solutions for the semi-discrete and fully discrete analogues of the CSP equations in the form of Casorati determinants. In the continuous limit, we show that the fully discrete CSP equation converges to the semi-discrete CSP equation, then further to the continuous CSP equation. Moreover, the integrable semi-discretization of the CSP equation is used as a self-adaptive moving mesh method for numerical simulations. The numerical results agree with the analytical results very well. (paper)

  17. Computational methods for high-energy source shielding

    International Nuclear Information System (INIS)

    Armstrong, T.W.; Cloth, P.; Filges, D.

    1983-01-01

    The computational methods for high-energy radiation transport related to shielding of the SNQ-spallation source are outlined. The basic approach is to couple radiation-transport computer codes which use Monte Carlo methods and discrete ordinates methods. A code system is suggested that incorporates state-of-the-art radiation-transport techniques. The stepwise verification of that system is briefly summarized. The complexity of the resulting code system suggests a more straightforward code specially tailored for thick shield calculations. A short guide line to future development of such a Monte Carlo code is given

  18. About local fractional three-dimensional compressible Navier-Stokes equations in Cantor-type cylindrical co-ordinate system

    Directory of Open Access Journals (Sweden)

    Gao Guo-Ping

    2016-01-01

    Full Text Available In this article, we investigate the local fractional 3-D compressible Navier-Stokes equation via local fractional derivative. We use the Cantor-type cylindrical co-ordinate method to transfer 3-D compressible Navier-Stokes equation from the Cantorian co-ordinate system to the Cantor-type cylindrical co-ordinate system.

  19. Improved Multilevel Fast Multipole Method for Higher-Order discretizations

    DEFF Research Database (Denmark)

    Borries, Oscar Peter; Meincke, Peter; Jorgensen, Erik

    2014-01-01

    The Multilevel Fast Multipole Method (MLFMM) allows for a reduced computational complexity when solving electromagnetic scattering problems. Combining this with the reduced number of unknowns provided by Higher-Order discretizations has proven to be a difficult task, with the general conclusion b...

  20. A guide to practical radiation protection in medicine. X-Ray Ordinance. Radiation Protection Ordinance. Practice-oriented hints, comments, text compilation

    International Nuclear Information System (INIS)

    Fiebich, M.; Nischelsky, J.E.; Pfeiff, H.; Westermann, K.

    2003-01-01

    This loose-leaf collection has been compiled for users who have to implement the X-ray Ordinance and the Radiation Protection Ordinance at their place of work. It presents all acts, ordinances, safety guides, regulations and recommendations of relevance in connection with the above two ordinances, as well as practical instructions and the full text of technical codes. Radiation protection officers and other persons in charge of radiation protection will find the references, information and advice needed to solve problems encountered. (orig.) [de

  1. A Krylov Subspace Method for Unstructured Mesh SN Transport Computation

    International Nuclear Information System (INIS)

    Yoo, Han Jong; Cho, Nam Zin; Kim, Jong Woon; Hong, Ser Gi; Lee, Young Ouk

    2010-01-01

    Hong, et al., have developed a computer code MUST (Multi-group Unstructured geometry S N Transport) for the neutral particle transport calculations in three-dimensional unstructured geometry. In this code, the discrete ordinates transport equation is solved by using the discontinuous finite element method (DFEM) or the subcell balance methods with linear discontinuous expansion. In this paper, the conventional source iteration in the MUST code is replaced by the Krylov subspace method to reduce computing time and the numerical test results are given

  2. A parametric level-set method for partially discrete tomography

    NARCIS (Netherlands)

    A. Kadu (Ajinkya); T. van Leeuwen (Tristan); K.J. Batenburg (Joost)

    2017-01-01

    textabstractThis paper introduces a parametric level-set method for tomographic reconstruction of partially discrete images. Such images consist of a continuously varying background and an anomaly with a constant (known) grey-value. We express the geometry of the anomaly using a level-set function,

  3. The new German radiation protection ordinance

    International Nuclear Information System (INIS)

    Pfeffer, W.; Weimer, G.

    2003-01-01

    According to European law, the Basic Safety Standards (BSS) published by the European Council in 1996 and the Council Directive on health protection of individuals against dangers of ionising radiation in relation to medical exposure had to be transferred into national law within due time. In 2001 the new Ordinance for the Implementation of the Euratom Guidelines on Radiation Protection] was published, which replaces the old Radiation Protection Ordinance. The new German Ordinance adapts the European Directive to German law, covering the general principles but even giving more details in many fields of radiation protection. The BSS scope certainly is much broader than the prescriptions important for the field of radiation protection in nuclear power plants. According to the scope of this workshop on occupational exposure in nuclear power plants - and as the BSS most probably will be quite familiar to all of you - after a short general overview on relevant contents of the German Ordinance, this presentation will focus on the main issues important in the operation of NPP and especially on some areas which may give rise to necessary changes caused by the new Ordinance. (A.L.B.)

  4. A constrained Delaunay discretization method for adaptively meshing highly discontinuous geological media

    Science.gov (United States)

    Wang, Yang; Ma, Guowei; Ren, Feng; Li, Tuo

    2017-12-01

    A constrained Delaunay discretization method is developed to generate high-quality doubly adaptive meshes of highly discontinuous geological media. Complex features such as three-dimensional discrete fracture networks (DFNs), tunnels, shafts, slopes, boreholes, water curtains, and drainage systems are taken into account in the mesh generation. The constrained Delaunay triangulation method is used to create adaptive triangular elements on planar fractures. Persson's algorithm (Persson, 2005), based on an analogy between triangular elements and spring networks, is enriched to automatically discretize a planar fracture into mesh points with varying density and smooth-quality gradient. The triangulated planar fractures are treated as planar straight-line graphs (PSLGs) to construct piecewise-linear complex (PLC) for constrained Delaunay tetrahedralization. This guarantees the doubly adaptive characteristic of the resulted mesh: the mesh is adaptive not only along fractures but also in space. The quality of elements is compared with the results from an existing method. It is verified that the present method can generate smoother elements and a better distribution of element aspect ratios. Two numerical simulations are implemented to demonstrate that the present method can be applied to various simulations of complex geological media that contain a large number of discontinuities.

  5. The Method of Lines Solution of the Regularized Long-Wave Equation Using Runge-Kutta Time Discretization Method

    Directory of Open Access Journals (Sweden)

    H. O. Bakodah

    2013-01-01

    Full Text Available A method of lines approach to the numerical solution of nonlinear wave equations typified by the regularized long wave (RLW is presented. The method developed uses a finite differences discretization to the space. Solution of the resulting system was obtained by applying fourth Runge-Kutta time discretization method. Using Von Neumann stability analysis, it is shown that the proposed method is marginally stable. To test the accuracy of the method some numerical experiments on test problems are presented. Test problems including solitary wave motion, two-solitary wave interaction, and the temporal evaluation of a Maxwellian initial pulse are studied. The accuracy of the present method is tested with and error norms and the conservation properties of mass, energy, and momentum under the RLW equation.

  6. A practical discrete-adjoint method for high-fidelity compressible turbulence simulations

    International Nuclear Information System (INIS)

    Vishnampet, Ramanathan; Bodony, Daniel J.; Freund, Jonathan B.

    2015-01-01

    Methods and computing hardware advances have enabled accurate predictions of complex compressible turbulence phenomena, such as the generation of jet noise that motivates the present effort. However, limited understanding of underlying physical mechanisms restricts the utility of such predictions since they do not, by themselves, indicate a route to design improvements. Gradient-based optimization using adjoints can circumvent the flow complexity to guide designs, though this is predicated on the availability of a sufficiently accurate solution of the forward and adjoint systems. These are challenging to obtain, since both the chaotic character of the turbulence and the typical use of discretizations near their resolution limits in order to efficiently represent its smaller scales will amplify any approximation errors made in the adjoint formulation. Formulating a practical exact adjoint that avoids such errors is especially challenging if it is to be compatible with state-of-the-art simulation methods used for the turbulent flow itself. Automatic differentiation (AD) can provide code to calculate a nominally exact adjoint, but existing general-purpose AD codes are inefficient to the point of being prohibitive for large-scale turbulence simulations. Here, we analyze the compressible flow equations as discretized using the same high-order workhorse methods used for many high-fidelity compressible turbulence simulations, and formulate a practical space–time discrete-adjoint method without changing the basic discretization. A key step is the definition of a particular discrete analog of the continuous norm that defines our cost functional; our selection leads directly to an efficient Runge–Kutta-like scheme, though it would be just first-order accurate if used outside the adjoint formulation for time integration, with finite-difference spatial operators for the adjoint system. Its computational cost only modestly exceeds that of the flow equations. We confirm that

  7. Criticality calculation by the LTSN method

    International Nuclear Information System (INIS)

    Batistela, Claudia H.F.; Vilhena, Marco T. de; Borges, Volnei

    1997-01-01

    This work evaluates criticality parameters (multiplication factor and critical thickness) by the LTS N method in unidimensional slabs homogeneous and heterogeneous considering one-group model and isotropic scattering. The idea of the LTS N method encompasses the following steps: application of the Laplace transform into a set of discrete ordinates equations, analytical solution of the algebraic linear system for the transformed angular fluxes and their reconstruction by the Heaviside expansion technique. The novel feature of the proposed method is based upon the criticality parameters determination by solving a transcendental equation. Numerical results are reported. 12 refs., 2 tabs

  8. Formal methods for discrete-time dynamical systems

    CERN Document Server

    Belta, Calin; Aydin Gol, Ebru

    2017-01-01

    This book bridges fundamental gaps between control theory and formal methods. Although it focuses on discrete-time linear and piecewise affine systems, it also provides general frameworks for abstraction, analysis, and control of more general models. The book is self-contained, and while some mathematical knowledge is necessary, readers are not expected to have a background in formal methods or control theory. It rigorously defines concepts from formal methods, such as transition systems, temporal logics, model checking and synthesis. It then links these to the infinite state dynamical systems through abstractions that are intuitive and only require basic convex-analysis and control-theory terminology, which is provided in the appendix. Several examples and illustrations help readers understand and visualize the concepts introduced throughout the book.

  9. Discrete Mathematics

    DEFF Research Database (Denmark)

    Sørensen, John Aasted

    2011-01-01

    ; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics...... to new problems. Relations and functions: Define a product set; define and apply equivalence relations; construct and apply functions. Apply these concepts to new problems. Natural numbers and induction: Define the natural numbers; apply the principle of induction to verify a selection of properties...

  10. Application of network methods for understanding evolutionary dynamics in discrete habitats.

    Science.gov (United States)

    Greenbaum, Gili; Fefferman, Nina H

    2017-06-01

    In populations occupying discrete habitat patches, gene flow between habitat patches may form an intricate population structure. In such structures, the evolutionary dynamics resulting from interaction of gene-flow patterns with other evolutionary forces may be exceedingly complex. Several models describing gene flow between discrete habitat patches have been presented in the population-genetics literature; however, these models have usually addressed relatively simple settings of habitable patches and have stopped short of providing general methodologies for addressing nontrivial gene-flow patterns. In the last decades, network theory - a branch of discrete mathematics concerned with complex interactions between discrete elements - has been applied to address several problems in population genetics by modelling gene flow between habitat patches using networks. Here, we present the idea and concepts of modelling complex gene flows in discrete habitats using networks. Our goal is to raise awareness to existing network theory applications in molecular ecology studies, as well as to outline the current and potential contribution of network methods to the understanding of evolutionary dynamics in discrete habitats. We review the main branches of network theory that have been, or that we believe potentially could be, applied to population genetics and molecular ecology research. We address applications to theoretical modelling and to empirical population-genetic studies, and we highlight future directions for extending the integration of network science with molecular ecology. © 2017 John Wiley & Sons Ltd.

  11. Application of direct discrete method (DDM) to multigroup neutron transport problems

    International Nuclear Information System (INIS)

    Vosoughi, Naser; Salehi, Ali Akbar; Shahriari, Majid

    2003-01-01

    The Direct Discrete Method (DDM), which produced excellent results for one-group neutron transport problems, has been developed for multigroup energy. A multigroup neutron transport discrete equation has been produced for a cylindrical shape fuel element with and without associated coolant regions with two boundary conditions. The calculations are illustrated for two-group energy by graphs showing the fast and thermal fluxes. The validity of the results are tested against the results obtained by the ANISN code. (author)

  12. Overview of Existing Wind Energy Ordinances

    Energy Technology Data Exchange (ETDEWEB)

    Oteri, F.

    2008-12-01

    Due to increased energy demand in the United States, rural communities with limited or no experience with wind energy now have the opportunity to become involved in this industry. Communities with good wind resources may be approached by entities with plans to develop the resource. Although these opportunities can create new revenue in the form of construction jobs and land lease payments, they also create a new responsibility on the part of local governments to ensure that ordinances will be established to aid the development of safe facilities that will be embraced by the community. The purpose of this report is to educate and engage state and local governments, as well as policymakers, about existing large wind energy ordinances. These groups will have a collection of examples to utilize when they attempt to draft a new large wind energy ordinance in a town or county without existing ordinances.

  13. Co-ordinated research programme on applications of stable isotope tracers in human nutrition research

    International Nuclear Information System (INIS)

    1992-01-01

    This document provides a very brief report on the final Research Co-ordination Meeting of this Co-ordinated Research Project (CRP): the final report on the CRP will be published by the IAEA in the IAEA-TECDOC series. The present document contains a detailed proposal for a new Co-ordinated Research Programme on ''Stable Isotope Tracer Techniques for Studies on Protein-Energy Interactions'', and a brief series of notes on stable isotopic methods for investigating protein and amino-acid metabolism in man. Refs

  14. Spatial Representation of Ordinal Information

    Directory of Open Access Journals (Sweden)

    Meng eZhang

    2016-04-01

    Full Text Available Right hand responds faster than left hand when shown larger numbers and vice-versa when shown smaller numbers (the SNARC effect. Accumulating evidence suggests that the SNARC effect may not be exclusive for numbers and can be extended to other ordinal sequences (e.g., months or letters in the alphabet as well. In this study, we tested the SNARC effect with a non-numerically ordered sequence: The Chinese notations for the color spectrum (Red, Orange, Yellow, Green, Blue, Indigo, and Violet. Chinese color word sequence reserves relatively weak ordinal information, because each element color in the sequence normally appears in non-sequential contexts, making it ideal to test the spatial organization of sequential information that was stored in the long-term memory. This study found a reliable SNARC-like effect for Chinese color words (deciding whether the presented color word was before or after the reference color word green, suggesting that, without access to any quantitative information or exposure to any previous training, ordinal representation can still activate a sense of space. The results support that weak ordinal information without quantitative magnitude encoded in the long-term memory can activate spatial representation in a comparison task.

  15. Spatial Representation of Ordinal Information.

    Science.gov (United States)

    Zhang, Meng; Gao, Xuefei; Li, Baichen; Yu, Shuyuan; Gong, Tianwei; Jiang, Ting; Hu, Qingfen; Chen, Yinghe

    2016-01-01

    Right hand responds faster than left hand when shown larger numbers and vice-versa when shown smaller numbers (the SNARC effect). Accumulating evidence suggests that the SNARC effect may not be exclusive for numbers and can be extended to other ordinal sequences (e.g., months or letters in the alphabet) as well. In this study, we tested the SNARC effect with a non-numerically ordered sequence: the Chinese notations for the color spectrum (Red, Orange, Yellow, Green, Blue, Indigo, and Violet). Chinese color word sequence reserves relatively weak ordinal information, because each element color in the sequence normally appears in non-sequential contexts, making it ideal to test the spatial organization of sequential information that was stored in the long-term memory. This study found a reliable SNARC-like effect for Chinese color words (deciding whether the presented color word was before or after the reference color word "green"), suggesting that, without access to any quantitative information or exposure to any previous training, ordinal representation can still activate a sense of space. The results support that weak ordinal information without quantitative magnitude encoded in the long-term memory can activate spatial representation in a comparison task.

  16. Modelling of Granular Materials Using the Discrete Element Method

    DEFF Research Database (Denmark)

    Ullidtz, Per

    1997-01-01

    With the Discrete Element Method it is possible to model materials that consists of individual particles where a particle may role or slide on other particles. This is interesting because most of the deformation in granular materials is due to rolling or sliding rather that compression of the gra...

  17. Splitting Method for Solving the Coarse-Mesh Discretized Low-Order Quasi-Diffusion Equations

    International Nuclear Information System (INIS)

    Hiruta, Hikaru; Anistratov, Dmitriy Y.; Adams, Marvin L.

    2005-01-01

    In this paper, the development is presented of a splitting method that can efficiently solve coarse-mesh discretized low-order quasi-diffusion (LOQD) equations. The LOQD problem can reproduce exactly the transport scalar flux and current. To solve the LOQD equations efficiently, a splitting method is proposed. The presented method splits the LOQD problem into two parts: (a) the D problem that captures a significant part of the transport solution in the central parts of assemblies and can be reduced to a diffusion-type equation and (b) the Q problem that accounts for the complicated behavior of the transport solution near assembly boundaries. Independent coarse-mesh discretizations are applied: the D problem equations are approximated by means of a finite element method, whereas the Q problem equations are discretized using a finite volume method. Numerical results demonstrate the efficiency of the methodology presented. This methodology can be used to modify existing diffusion codes for full-core calculations (which already solve a version of the D problem) to account for transport effects

  18. Cable Television Report and Suggested Ordinance.

    Science.gov (United States)

    League of California Cities, Sacramento.

    Guidelines and suggested ordinances for cable television regulation by local governments are comprehensively discussed in this report. The emphasis is placed on franchising the cable operator. Seventeen legal aspects of franchising are reviewed, and an exemplary ordinance is presented. In addition, current statistics about cable franchising in…

  19. Estimating Ordinal Reliability for Likert-Type and Ordinal Item Response Data: A Conceptual, Empirical, and Practical Guide

    Science.gov (United States)

    Gadermann, Anne M.; Guhn, Martin; Zumbo, Bruno D.

    2012-01-01

    This paper provides a conceptual, empirical, and practical guide for estimating ordinal reliability coefficients for ordinal item response data (also referred to as Likert, Likert-type, ordered categorical, or rating scale item responses). Conventionally, reliability coefficients, such as Cronbach's alpha, are calculated using a Pearson…

  20. Amendments to ordinances in Radiation Protection Law; Novellierung der strahlenschutzrechtlichen Verordnungen

    Energy Technology Data Exchange (ETDEWEB)

    Heller, W.

    2007-05-15

    The last major reform of the German Radiation Protection Ordinance took place on July 26, 2001. The 'First Ordinance Amending Ordinances in Radiation Protection Law' now proposed is to cover primarily the necessary changes and supplements resulting from experience in the execution of the ordinances. They mainly relate to these issues: (1) the scope of application of the Radiation Protection Ordinance and of the x-ray Ordinance in medical research (2) the scope of application of the Radiation Protection Ordinance and the -ray Ordinance in unjustified types of activities (3) electronic communication ('e-government') (4) changes in the provisions about permits and announcements in the Radiation Protection Ordinance (5) new clearance levels in the Radiation Protection Ordinance (6) cross-border transports of 'NORM' materials (7) other changes in the scope of application of the Radiation Protection Ordinance (8) other changes in the x-ray area. (orig.)

  1. Application of methods of discrete mathematics at modular synthesis of mechatronic devices

    OpenAIRE

    Nikiforov, S.; Nikiforov, B.; Mandarov, E.; Rabdanova, N.

    2010-01-01

    The article is devoted to application of methods of discrete mathematics (the theory of counts, the method of matrix code and others) and synthesis of executive mechanisms of mechatronic handling devices

  2. Comparison of the methods for discrete approximation of the fractional-order operator

    Directory of Open Access Journals (Sweden)

    Zborovjan Martin

    2003-12-01

    Full Text Available In this paper we will present some alternative types of discretization methods (discrete approximation for the fractional-order (FO differentiator and their application to the FO dynamical system described by the FO differential equation (FDE. With analytical solution and numerical solution by power series expansion (PSE method are compared two effective methods - the Muir expansion of the Tustin operator and continued fraction expansion method (CFE with the Tustin operator and the Al-Alaoui operator. Except detailed mathematical description presented are also simulation results. From the Bode plots of the FO differentiator and FDE and from the solution in the time domain we can see, that the CFE is a more effective method according to the PSE method, but there are some restrictions for the choice of the time step. The Muir expansion is almost unusable.

  3. Ordinance on nuclear third party liability (ORCN)

    International Nuclear Information System (INIS)

    1983-12-01

    The Ordinance exempts from the application of the 1983 Act on Nuclear Third Party Liability some substances with low radiation effects. It determines the amount of private insurance cover and defines the risks that insurers may exclude from cover. It establishes a special fund for nuclear damage made up of contributions from the nuclear operators. Specifications are given on the amount of the contributions and their conditions, as well as on administration of the fund. The Ordinance repeals the Ordinance of 13 June 1960 on funds for delayed atomic damage, the Order of 19 December 1960 on contributions to the fund for delayed atomic damage and the Ordinance of 30 November 1981 on cover for third party liability resulting from nuclear power plant operation [fr

  4. Representation of discrete Steklov-Poincare operator arising in domain decomposition methods in wavelet basis

    Energy Technology Data Exchange (ETDEWEB)

    Jemcov, A.; Matovic, M.D. [Queen`s Univ., Kingston, Ontario (Canada)

    1996-12-31

    This paper examines the sparse representation and preconditioning of a discrete Steklov-Poincare operator which arises in domain decomposition methods. A non-overlapping domain decomposition method is applied to a second order self-adjoint elliptic operator (Poisson equation), with homogeneous boundary conditions, as a model problem. It is shown that the discrete Steklov-Poincare operator allows sparse representation with a bounded condition number in wavelet basis if the transformation is followed by thresholding and resealing. These two steps combined enable the effective use of Krylov subspace methods as an iterative solution procedure for the system of linear equations. Finding the solution of an interface problem in domain decomposition methods, known as a Schur complement problem, has been shown to be equivalent to the discrete form of Steklov-Poincare operator. A common way to obtain Schur complement matrix is by ordering the matrix of discrete differential operator in subdomain node groups then block eliminating interface nodes. The result is a dense matrix which corresponds to the interface problem. This is equivalent to reducing the original problem to several smaller differential problems and one boundary integral equation problem for the subdomain interface.

  5. Discrete variational derivative method a structure-preserving numerical method for partial differential equations

    CERN Document Server

    Furihata, Daisuke

    2010-01-01

    Nonlinear Partial Differential Equations (PDEs) have become increasingly important in the description of physical phenomena. Unlike Ordinary Differential Equations, PDEs can be used to effectively model multidimensional systems. The methods put forward in Discrete Variational Derivative Method concentrate on a new class of ""structure-preserving numerical equations"" which improves the qualitative behaviour of the PDE solutions and allows for stable computing. The authors have also taken care to present their methods in an accessible manner, which means that the book will be useful to engineer

  6. The spectral volume method as applied to transport problems

    International Nuclear Information System (INIS)

    McClarren, Ryan G.

    2011-01-01

    We present a new spatial discretization for transport problems: the spectral volume method. This method, rst developed by Wang for computational fluid dynamics, divides each computational cell into several sub-cells and enforces particle balance on each of these sub-cells. Also, these sub-cells are used to build a polynomial reconstruction in the cell. The idea of dividing cells into many cells is a generalization of the simple corner balance and other similar schemes. The spectral volume method preserves particle conservation and preserves the asymptotic diffusion limit. We present results from the method on two transport problems in slab geometry using discrete ordinates and second through sixth order spectral volume schemes. The numerical results demonstrate the accuracy and preservation of the diffusion limit of the spectral volume method. Future work will explore possible bene ts of the scheme for high-performance computing and for resolving diffusive boundary layers. (author)

  7. Ordinal convolutional neural networks for predicting RDoC positive valence psychiatric symptom severity scores.

    Science.gov (United States)

    Rios, Anthony; Kavuluru, Ramakanth

    2017-11-01

    The CEGS N-GRID 2016 Shared Task in Clinical Natural Language Processing (NLP) provided a set of 1000 neuropsychiatric notes to participants as part of a competition to predict psychiatric symptom severity scores. This paper summarizes our methods, results, and experiences based on our participation in the second track of the shared task. Classical methods of text classification usually fall into one of three problem types: binary, multi-class, and multi-label classification. In this effort, we study ordinal regression problems with text data where misclassifications are penalized differently based on how far apart the ground truth and model predictions are on the ordinal scale. Specifically, we present our entries (methods and results) in the N-GRID shared task in predicting research domain criteria (RDoC) positive valence ordinal symptom severity scores (absent, mild, moderate, and severe) from psychiatric notes. We propose a novel convolutional neural network (CNN) model designed to handle ordinal regression tasks on psychiatric notes. Broadly speaking, our model combines an ordinal loss function, a CNN, and conventional feature engineering (wide features) into a single model which is learned end-to-end. Given interpretability is an important concern with nonlinear models, we apply a recent approach called locally interpretable model-agnostic explanation (LIME) to identify important words that lead to instance specific predictions. Our best model entered into the shared task placed third among 24 teams and scored a macro mean absolute error (MMAE) based normalized score (100·(1-MMAE)) of 83.86. Since the competition, we improved our score (using basic ensembling) to 85.55, comparable with the winning shared task entry. Applying LIME to model predictions, we demonstrate the feasibility of instance specific prediction interpretation by identifying words that led to a particular decision. In this paper, we present a method that successfully uses wide features and

  8. General method to find the attractors of discrete dynamic models of biological systems

    Science.gov (United States)

    Gan, Xiao; Albert, Réka

    2018-04-01

    Analyzing the long-term behaviors (attractors) of dynamic models of biological networks can provide valuable insight. We propose a general method that can find the attractors of multilevel discrete dynamical systems by extending a method that finds the attractors of a Boolean network model. The previous method is based on finding stable motifs, subgraphs whose nodes' states can stabilize on their own. We extend the framework from binary states to any finite discrete levels by creating a virtual node for each level of a multilevel node, and describing each virtual node with a quasi-Boolean function. We then create an expanded representation of the multilevel network, find multilevel stable motifs and oscillating motifs, and identify attractors by successive network reduction. In this way, we find both fixed point attractors and complex attractors. We implemented an algorithm, which we test and validate on representative synthetic networks and on published multilevel models of biological networks. Despite its primary motivation to analyze biological networks, our motif-based method is general and can be applied to any finite discrete dynamical system.

  9. General method to find the attractors of discrete dynamic models of biological systems.

    Science.gov (United States)

    Gan, Xiao; Albert, Réka

    2018-04-01

    Analyzing the long-term behaviors (attractors) of dynamic models of biological networks can provide valuable insight. We propose a general method that can find the attractors of multilevel discrete dynamical systems by extending a method that finds the attractors of a Boolean network model. The previous method is based on finding stable motifs, subgraphs whose nodes' states can stabilize on their own. We extend the framework from binary states to any finite discrete levels by creating a virtual node for each level of a multilevel node, and describing each virtual node with a quasi-Boolean function. We then create an expanded representation of the multilevel network, find multilevel stable motifs and oscillating motifs, and identify attractors by successive network reduction. In this way, we find both fixed point attractors and complex attractors. We implemented an algorithm, which we test and validate on representative synthetic networks and on published multilevel models of biological networks. Despite its primary motivation to analyze biological networks, our motif-based method is general and can be applied to any finite discrete dynamical system.

  10. On three-dimensional incompressible Navier-Stokes fluid on cantor sets in spherical Cantor type co-ordinate system

    Directory of Open Access Journals (Sweden)

    Meng Zhi-Jun

    2016-01-01

    Full Text Available This paper addresses the systems of the incompressible Navier-Stokes equations on Cantor sets without the external force involving the fractal heat-conduction problem vial local fractional derivative. The spherical Cantor type co-ordinate method is used to transfer the incompressible Navier-Stokes equation from the Cantorian co-ordinate system into the spherical Cantor type co-ordinate system.

  11. Non-proportional odds multivariate logistic regression of ordinal family data.

    Science.gov (United States)

    Zaloumis, Sophie G; Scurrah, Katrina J; Harrap, Stephen B; Ellis, Justine A; Gurrin, Lyle C

    2015-03-01

    Methods to examine whether genetic and/or environmental sources can account for the residual variation in ordinal family data usually assume proportional odds. However, standard software to fit the non-proportional odds model to ordinal family data is limited because the correlation structure of family data is more complex than for other types of clustered data. To perform these analyses we propose the non-proportional odds multivariate logistic regression model and take a simulation-based approach to model fitting using Markov chain Monte Carlo methods, such as partially collapsed Gibbs sampling and the Metropolis algorithm. We applied the proposed methodology to male pattern baldness data from the Victorian Family Heart Study. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  12. Radiation Ordinance 1983 (No. 58 of 1983) (Australian Capital Territory)

    International Nuclear Information System (INIS)

    1983-01-01

    This Ordinance provides for the safe use, transportation and disposal of radioactive materials and irradiating apparatus. It repeals the Fluoroscopes Ordinance of 1958. Radioactive materials whose radioactivity does not exceed levels as set out in a Schedule to the Ordinance are exempted from application of the Ordinance. (NEA) [fr

  13. Wielandt method applied to the diffusion equations discretized by finite element nodal methods

    International Nuclear Information System (INIS)

    Mugica R, A.; Valle G, E. del

    2003-01-01

    Nowadays the numerical methods of solution to the diffusion equation by means of algorithms and computer programs result so extensive due to the great number of routines and calculations that should carry out, this rebounds directly in the execution times of this programs, being obtained results in relatively long times. This work shows the application of an acceleration method of the convergence of the classic method of those powers that it reduces notably the number of necessary iterations for to obtain reliable results, what means that the compute times they see reduced in great measure. This method is known in the literature like Wielandt method and it has incorporated to a computer program that is based on the discretization of the neutron diffusion equations in plate geometry and stationary state by polynomial nodal methods. In this work the neutron diffusion equations are described for several energy groups and their discretization by means of those called physical nodal methods, being illustrated in particular the quadratic case. It is described a model problem widely described in the literature which is solved for the physical nodal grade schemes 1, 2, 3 and 4 in three different ways: to) with the classic method of the powers, b) method of the powers with the Wielandt acceleration and c) method of the powers with the Wielandt modified acceleration. The results for the model problem as well as for two additional problems known as benchmark problems are reported. Such acceleration method can also be implemented to problems of different geometry to the proposal in this work, besides being possible to extend their application to problems in 2 or 3 dimensions. (Author)

  14. An iterative method to invert the LTSn matrix

    Energy Technology Data Exchange (ETDEWEB)

    Cardona, A.V.; Vilhena, M.T. de [UFRGS, Porto Alegre (Brazil)

    1996-12-31

    Recently Vilhena and Barichello proposed the LTSn method to solve, analytically, the Discrete Ordinates Problem (Sn problem) in transport theory. The main feature of this method consist in the application of the Laplace transform to the set of Sn equations and solve the resulting algebraic system for the transport flux. Barichello solve the linear system containing the parameter s applying the definition of matrix invertion exploiting the structure of the LTSn matrix. In this work, it is proposed a new scheme to invert the LTSn matrix, decomposing it in blocks and recursively inverting this blocks.

  15. Multigroup discrete ordinates solution of Boltzmann-Fokker-Planck equations and cross section library development of ion transport

    International Nuclear Information System (INIS)

    Prinja, A.K.

    1995-08-01

    We have developed and successfully implemented a two-dimensional bilinear discontinuous in space and time, used in conjunction with the S N angular approximation, to numerically solve the time dependent, one-dimensional, one-speed, slab geometry, (ion) transport equation. Numerical results and comparison with analytical solutions have shown that the bilinear-discontinuous (BLD) scheme is third-order accurate in the space ad time dimensions independently. Comparison of the BLD results with diamond-difference methods indicate that the BLD method is both quantitavely and qualitatively superior to the DD scheme. We note that the form of the transport operator is such that these conclusions carry over to energy dependent problems that include the constant-slowing-down-approximation term, and to multiple space dimensions or combinations thereof. An optimized marching or inversion scheme or a parallel algorithm should be investigated to determine if the increased accuracy can compensate for the extra overhead required for a BLD solution, and then could be compared to other discretization methods such as nodal or characteristic schemes

  16. Infrared and visual image fusion method based on discrete cosine transform and local spatial frequency in discrete stationary wavelet transform domain

    Science.gov (United States)

    Jin, Xin; Jiang, Qian; Yao, Shaowen; Zhou, Dongming; Nie, Rencan; Lee, Shin-Jye; He, Kangjian

    2018-01-01

    In order to promote the performance of infrared and visual image fusion and provide better visual effects, this paper proposes a hybrid fusion method for infrared and visual image by the combination of discrete stationary wavelet transform (DSWT), discrete cosine transform (DCT) and local spatial frequency (LSF). The proposed method has three key processing steps. Firstly, DSWT is employed to decompose the important features of the source image into a series of sub-images with different levels and spatial frequencies. Secondly, DCT is used to separate the significant details of the sub-images according to the energy of different frequencies. Thirdly, LSF is applied to enhance the regional features of DCT coefficients, and it can be helpful and useful for image feature extraction. Some frequently-used image fusion methods and evaluation metrics are employed to evaluate the validity of the proposed method. The experiments indicate that the proposed method can achieve good fusion effect, and it is more efficient than other conventional image fusion methods.

  17. Discrete nodal integral transport-theory method for multidimensional reactor physics and shielding calculations

    International Nuclear Information System (INIS)

    Lawrence, R.D.; Dorning, J.J.

    1980-01-01

    A coarse-mesh discrete nodal integral transport theory method has been developed for the efficient numerical solution of multidimensional transport problems of interest in reactor physics and shielding applications. The method, which is the discrete transport theory analogue and logical extension of the nodal Green's function method previously developed for multidimensional neutron diffusion problems, utilizes the same transverse integration procedure to reduce the multidimensional equations to coupled one-dimensional equations. This is followed by the conversion of the differential equations to local, one-dimensional, in-node integral equations by integrating back along neutron flight paths. One-dimensional and two-dimensional transport theory test problems have been systematically studied to verify the superior computational efficiency of the new method

  18. Amendment of Atomic Ordinance

    International Nuclear Information System (INIS)

    1987-10-01

    This amendment to the 1984 Ordinance on definitions and licences in the atomic energy field aims essentially to ensure that the commitments under the Treaty on the Non-Proliferation of Nuclear Weapons are complied with in Switzerland. The goods and articles involving uranium enrichment by the gas centrifuge process and nuclear fuel reprocessing as specified by the competent international bodies, are henceforth included in the goods subject to notification or licensing listed in the Annex to the Ordinance. Also, it is provided that a construction and an operating licence for a nuclear installation may be granted simultaneously in cases where safe operating conditions can be fully assessed. (NEA) [fr

  19. Confidence intervals for distinguishing ordinal and disordinal interactions in multiple regression.

    Science.gov (United States)

    Lee, Sunbok; Lei, Man-Kit; Brody, Gene H

    2015-06-01

    Distinguishing between ordinal and disordinal interaction in multiple regression is useful in testing many interesting theoretical hypotheses. Because the distinction is made based on the location of a crossover point of 2 simple regression lines, confidence intervals of the crossover point can be used to distinguish ordinal and disordinal interactions. This study examined 2 factors that need to be considered in constructing confidence intervals of the crossover point: (a) the assumption about the sampling distribution of the crossover point, and (b) the possibility of abnormally wide confidence intervals for the crossover point. A Monte Carlo simulation study was conducted to compare 6 different methods for constructing confidence intervals of the crossover point in terms of the coverage rate, the proportion of true values that fall to the left or right of the confidence intervals, and the average width of the confidence intervals. The methods include the reparameterization, delta, Fieller, basic bootstrap, percentile bootstrap, and bias-corrected accelerated bootstrap methods. The results of our Monte Carlo simulation study suggest that statistical inference using confidence intervals to distinguish ordinal and disordinal interaction requires sample sizes more than 500 to be able to provide sufficiently narrow confidence intervals to identify the location of the crossover point. (c) 2015 APA, all rights reserved).

  20. A hierarchical model for ordinal matrix factorization

    DEFF Research Database (Denmark)

    Paquet, Ulrich; Thomson, Blaise; Winther, Ole

    2012-01-01

    This paper proposes a hierarchical probabilistic model for ordinal matrix factorization. Unlike previous approaches, we model the ordinal nature of the data and take a principled approach to incorporating priors for the hidden variables. Two algorithms are presented for inference, one based...

  1. An application of multigrid methods for a discrete elastic model for epitaxial systems

    International Nuclear Information System (INIS)

    Caflisch, R.E.; Lee, Y.-J.; Shu, S.; Xiao, Y.-X.; Xu, J.

    2006-01-01

    We apply an efficient and fast algorithm to simulate the atomistic strain model for epitaxial systems, recently introduced by Schindler et al. [Phys. Rev. B 67, 075316 (2003)]. The discrete effects in this lattice statics model are crucial for proper simulation of the influence of strain for thin film epitaxial growth, but the size of the atomistic systems of interest is in general quite large and hence the solution of the discrete elastic equations is a considerable numerical challenge. In this paper, we construct an algebraic multigrid method suitable for efficient solution of the large scale discrete strain model. Using this method, simulations are performed for several representative physical problems, including an infinite periodic step train, a layered nanocrystal, and a system of quantum dots. The results demonstrate the effectiveness and robustness of the method and show that the method attains optimal convergence properties, regardless of the problem size, the geometry and the physical parameters. The effects of substrate depth and of invariance due to traction-free boundary conditions are assessed. For a system of quantum dots, the simulated strain energy density supports the observations that trench formation near the dots provides strain relief

  2. A comparison of three methods of assessing differential item functioning (DIF) in the Hospital Anxiety Depression Scale: ordinal logistic regression, Rasch analysis and the Mantel chi-square procedure.

    Science.gov (United States)

    Cameron, Isobel M; Scott, Neil W; Adler, Mats; Reid, Ian C

    2014-12-01

    It is important for clinical practice and research that measurement scales of well-being and quality of life exhibit only minimal differential item functioning (DIF). DIF occurs where different groups of people endorse items in a scale to different extents after being matched by the intended scale attribute. We investigate the equivalence or otherwise of common methods of assessing DIF. Three methods of measuring age- and sex-related DIF (ordinal logistic regression, Rasch analysis and Mantel χ(2) procedure) were applied to Hospital Anxiety Depression Scale (HADS) data pertaining to a sample of 1,068 patients consulting primary care practitioners. Three items were flagged by all three approaches as having either age- or sex-related DIF with a consistent direction of effect; a further three items identified did not meet stricter criteria for important DIF using at least one method. When applying strict criteria for significant DIF, ordinal logistic regression was slightly less sensitive. Ordinal logistic regression, Rasch analysis and contingency table methods yielded consistent results when identifying DIF in the HADS depression and HADS anxiety scales. Regardless of methods applied, investigators should use a combination of statistical significance, magnitude of the DIF effect and investigator judgement when interpreting the results.

  3. An exact and consistent adjoint method for high-fidelity discretization of the compressible flow equations

    Science.gov (United States)

    Subramanian, Ramanathan Vishnampet Ganapathi

    Methods and computing hardware advances have enabled accurate predictions of complex compressible turbulence phenomena, such as the generation of jet noise that motivates the present effort. However, limited understanding of underlying physical mechanisms restricts the utility of such predictions since they do not, by themselves, indicate a route to design improvement. Gradient-based optimization using adjoints can circumvent the flow complexity to guide designs. Such methods have enabled sensitivity analysis and active control of turbulence at engineering flow conditions by providing gradient information at computational cost comparable to that of simulating the flow. They accelerate convergence of numerical design optimization algorithms, though this is predicated on the availability of an accurate gradient of the discretized flow equations. This is challenging to obtain, since both the chaotic character of the turbulence and the typical use of discretizations near their resolution limits in order to efficiently represent its smaller scales will amplify any approximation errors made in the adjoint formulation. Formulating a practical exact adjoint that avoids such errors is especially challenging if it is to be compatible with state-of-the-art simulation methods used for the turbulent flow itself. Automatic differentiation (AD) can provide code to calculate a nominally exact adjoint, but existing general-purpose AD codes are inefficient to the point of being prohibitive for large-scale turbulence simulations. We analyze the compressible flow equations as discretized using the same high-order workhorse methods used for many high-fidelity compressible turbulence simulations, and formulate a practical space--time discrete-adjoint method without changing the basic discretization. A key step is the definition of a particular discrete analog of the continuous norm that defines our cost functional; our selection leads directly to an efficient Runge--Kutta-like scheme

  4. Discrete Particle Method for Simulating Hypervelocity Impact Phenomena

    Directory of Open Access Journals (Sweden)

    Erkai Watson

    2017-04-01

    Full Text Available In this paper, we introduce a computational model for the simulation of hypervelocity impact (HVI phenomena which is based on the Discrete Element Method (DEM. Our paper constitutes the first application of DEM to the modeling and simulating of impact events for velocities beyond 5 kms-1. We present here the results of a systematic numerical study on HVI of solids. For modeling the solids, we use discrete spherical particles that interact with each other via potentials. In our numerical investigations we are particularly interested in the dynamics of material fragmentation upon impact. We model a typical HVI experiment configuration where a sphere strikes a thin plate and investigate the properties of the resulting debris cloud. We provide a quantitative computational analysis of the resulting debris cloud caused by impact and a comprehensive parameter study by varying key parameters of our model. We compare our findings from the simulations with recent HVI experiments performed at our institute. Our findings are that the DEM method leads to very stable, energy–conserving simulations of HVI scenarios that map the experimental setup where a sphere strikes a thin plate at hypervelocity speed. Our chosen interaction model works particularly well in the velocity range where the local stresses caused by impact shock waves markedly exceed the ultimate material strength.

  5. 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.

  6. Why Overlearned Sequences are Special: Distinct Neural Networks for Ordinal Sequences

    Directory of Open Access Journals (Sweden)

    Vani ePariyadath

    2012-12-01

    Full Text Available Several observations suggest that overlearned ordinal categories (e.g., letters, numbers, weekdays, months are processed differently than non-ordinal categories in the brain. In synesthesia, for example, anomalous perceptual experiences are most often triggered by members of ordinal categories (Rich et al., 2005; Eagleman, 2009. In semantic dementia, the processing of ordinal stimuli appears to be preserved relative to non-ordinal ones (Cappelletti et al., 2001. Moreover, ordinal stimuli often map onto unconscious spatial representations, as observed in the SNARC effect (Dehaene et al, 1993; Fias, 1996. At present, little is known about the neural representation of ordinal categories. Using functional neuroimaging, we show that words in ordinal categories are processed in a fronto-temporo-parietal network biased toward the right hemisphere. This differs from words in non-ordinal categories (such as names of furniture, animals, cars and fruit, which show an expected bias toward the left hemisphere. Further, we find that increased predictability of stimulus order correlates with smaller regions of BOLD activation, a phenomenon we term prediction suppression. Our results provide new insights into the processing of ordinal stimuli, and suggest a new anatomical framework for understanding the patterns seen in synesthesia, unconscious spatial representation, and semantic dementia.

  7. Discrete calculus methods for counting

    CERN Document Server

    Mariconda, Carlo

    2016-01-01

    This book provides an introduction to combinatorics, finite calculus, formal series, recurrences, and approximations of sums. Readers will find not only coverage of the basic elements of the subjects but also deep insights into a range of less common topics rarely considered within a single book, such as counting with occupancy constraints, a clear distinction between algebraic and analytical properties of formal power series, an introduction to discrete dynamical systems with a thorough description of Sarkovskii’s theorem, symbolic calculus, and a complete description of the Euler-Maclaurin formulas and their applications. Although several books touch on one or more of these aspects, precious few cover all of them. The authors, both pure mathematicians, have attempted to develop methods that will allow the student to formulate a given problem in a precise mathematical framework. The aim is to equip readers with a sound strategy for classifying and solving problems by pursuing a mathematically rigorous yet ...

  8. The Full—Discrete Mixed Finite Element Methods for Nonlinear Hyperbolic Equations

    Institute of Scientific and Technical Information of China (English)

    YanpingCHEN; YunqingHUANG

    1998-01-01

    This article treats mixed finite element methods for second order nonlinear hyperbolic equations.A fully discrete scheme is presented and improved L2-error estimates are established.The convergence of both the function value andthe flux is demonstrated.

  9. Ordinance of 8 February 1984 on the radioactivity of timepieces

    International Nuclear Information System (INIS)

    1984-01-01

    This Ordinance regulates the approval of radioluminescent timepieces (wristwatches, fob-watches, alarm-clocks, clocks, etc.) imported or made in Switzerland. Such timepieces must comply with conditions in particular regarding their maximum radioactivity as laid down by the Ordinance and are subject to controls by the Federal Office of Public Health. The Ordinance, which came into force on 1 March 1984, replaces a similar Ordinance of 18 April 1968. (NEA) [fr

  10. Modeling and evaluating repeatability and reproducibility of ordinal classifications

    NARCIS (Netherlands)

    de Mast, J.; van Wieringen, W.N.

    2010-01-01

    This paper argues that currently available methods for the assessment of the repeatability and reproducibility of ordinal classifications are not satisfactory. The paper aims to study whether we can modify a class of models from Item Response Theory, well established for the study of the reliability

  11. Frequency domain optical tomography using a conjugate gradient method without line search

    International Nuclear Information System (INIS)

    Kim, Hyun Keol; Charette, Andre

    2007-01-01

    A conjugate gradient method without line search (CGMWLS) is presented. This method is used to retrieve the local maps of absorption and scattering coefficients inside the tissue-like test medium, with the synthetic data. The forward problem is solved with a discrete-ordinates finite-difference method based on the frequency domain formulation of radiative transfer equation. The inversion results demonstrate that the CGMWLS can retrieve simultaneously the spatial distributions of optical properties inside the medium within a reasonable accuracy, by reducing cross-talk between absorption and scattering coefficients

  12. Discrete fourier transform (DFT) analysis for applications using iterative transform methods

    Science.gov (United States)

    Dean, Bruce H. (Inventor)

    2012-01-01

    According to various embodiments, a method is provided for determining aberration data for an optical system. The method comprises collecting a data signal, and generating a pre-transformation algorithm. The data is pre-transformed by multiplying the data with the pre-transformation algorithm. A discrete Fourier transform of the pre-transformed data is performed in an iterative loop. The method further comprises back-transforming the data to generate aberration data.

  13. Economic and ordinal benefits of Hydrogen Energy Technology

    International Nuclear Information System (INIS)

    Giannantoni, C.; Zoli, M.

    2009-01-01

    A method for assessing economic, environmental and energy investments is particularly suited for hydrogen technologies, because it makes it possible to calculate business returns, negative externalities and, above all, the economic benefits to the citizens: the monetizable positive externalities and the ordinal benefits, i.e. those which cannot be reduced to a simple monetary value. [it

  14. Rate My Stake: Interpretation of Ordinal Stake Ratings

    Science.gov (United States)

    Patricia Lebow; Grant Kirker

    2014-01-01

    Ordinal rating systems are commonly employed to evaluate biodeterioration of wood exposed outdoors over long periods of time. The purpose of these ratings is to compare the durability of test systems to nondurable wood products or known durable wood products. There are many reasons why these systems have evolved as the chosen method of evaluation, including having an...

  15. Discrete method for design of flow distribution in manifolds

    International Nuclear Information System (INIS)

    Wang, Junye; Wang, Hualin

    2015-01-01

    Flow in manifold systems is encountered in designs of various industrial processes, such as fuel cells, microreactors, microchannels, plate heat exchanger, and radial flow reactors. The uniformity of flow distribution in manifold is a key indicator for performance of the process equipment. In this paper, a discrete method for a U-type arrangement was developed to evaluate the uniformity of the flow distribution and the pressure drop and then was used for direct comparisons between the U-type and the Z-type. The uniformity of the U-type is generally better than that of the Z-type in most of cases for small ζ and large M. The U-type and the Z-type approach each other as ζ increases or M decreases. However, the Z-type is more sensitive to structures than the U-type and approaches uniform flow distribution faster than the U-type as M decreases or ζ increases. This provides a simple yet powerful tool for the designers to evaluate and select a flow arrangement and offers practical measures for industrial applications. - Highlights: • Discrete methodology of flow field designs in manifolds with U-type arrangements. • Quantitative comparison between U-type and Z-type arrangements. • Discrete solution of flow distribution with varying flow coefficients. • Practical measures and guideline to design of manifold systems.

  16. Visual grading characteristics and ordinal regression analysis during optimisation of CT head examinations.

    Science.gov (United States)

    Zarb, Francis; McEntee, Mark F; Rainford, Louise

    2015-06-01

    To evaluate visual grading characteristics (VGC) and ordinal regression analysis during head CT optimisation as a potential alternative to visual grading assessment (VGA), traditionally employed to score anatomical visualisation. Patient images (n = 66) were obtained using current and optimised imaging protocols from two CT suites: a 16-slice scanner at the national Maltese centre for trauma and a 64-slice scanner in a private centre. Local resident radiologists (n = 6) performed VGA followed by VGC and ordinal regression analysis. VGC alone indicated that optimised protocols had similar image quality as current protocols. Ordinal logistic regression analysis provided an in-depth evaluation, criterion by criterion allowing the selective implementation of the protocols. The local radiology review panel supported the implementation of optimised protocols for brain CT examinations (including trauma) in one centre, achieving radiation dose reductions ranging from 24 % to 36 %. In the second centre a 29 % reduction in radiation dose was achieved for follow-up cases. The combined use of VGC and ordinal logistic regression analysis led to clinical decisions being taken on the implementation of the optimised protocols. This improved method of image quality analysis provided the evidence to support imaging protocol optimisation, resulting in significant radiation dose savings. • There is need for scientifically based image quality evaluation during CT optimisation. • VGC and ordinal regression analysis in combination led to better informed clinical decisions. • VGC and ordinal regression analysis led to dose reductions without compromising diagnostic efficacy.

  17. Shielding analyses: the rabbit vs the turtle?

    International Nuclear Information System (INIS)

    Broadhead, B.L.

    1996-01-01

    This paper compares solutions using Monte Carlo and discrete- ordinates methods applied to two actual shielding situations in order to make some general observations concerning the efficiency and advantages/disadvantages of the two approaches. The discrete- ordinates solutions are performed using two-dimensional geometries, while the Monte Carlo approaches utilize three-dimensional geometries with both multigroup and point cross-section data

  18. A discrete optimization method for nuclear fuel management

    International Nuclear Information System (INIS)

    Argaud, J.P.

    1993-01-01

    Nuclear fuel management can be seen as a large discrete optimization problem under constraints, and optimization methods on such problems are numerically costly. After an introduction of the main aspects of nuclear fuel management, this paper presents a new way to treat the combinatorial problem by using information included in the gradient of optimized cost function. A new search process idea is to choose, by direct observation of the gradient, the more interesting changes in fuel loading patterns. An example is then developed to illustrate an operating mode of the method. Finally, connections with classical simulated annealing and genetic algorithms are described as an attempt to improve search processes. 16 refs., 2 figs

  19. Multi-objective optimization design method of radiation shielding

    International Nuclear Information System (INIS)

    Yang Shouhai; Wang Weijin; Lu Daogang; Chen Yixue

    2012-01-01

    Due to the shielding design goals of diversification and uncertain process of many factors, it is necessary to develop an optimization design method of intelligent shielding by which the shielding scheme selection will be achieved automatically and the uncertainties of human impact will be reduced. For economical feasibility to achieve a radiation shielding design for automation, the multi-objective genetic algorithm optimization of screening code which combines the genetic algorithm and discrete-ordinate method was developed to minimize the costs, size, weight, and so on. This work has some practical significance for gaining the optimization design of shielding. (authors)

  20. Comparison of two ordinal prediction models

    DEFF Research Database (Denmark)

    Kattan, Michael W; Gerds, Thomas A

    2015-01-01

    system (i.e. old or new), such as the level of evidence for one or more factors included in the system or the general opinions of expert clinicians. However, given the major objective of estimating prognosis on an ordinal scale, we argue that the rival staging system candidates should be compared...... on their ability to predict outcome. We sought to outline an algorithm that would compare two rival ordinal systems on their predictive ability. RESULTS: We devised an algorithm based largely on the concordance index, which is appropriate for comparing two models in their ability to rank observations. We...... demonstrate our algorithm with a prostate cancer staging system example. CONCLUSION: We have provided an algorithm for selecting the preferred staging system based on prognostic accuracy. It appears to be useful for the purpose of selecting between two ordinal prediction models....

  1. A Novel Method for Detection of Epilepsy in Short and Noisy EEG Signals Using Ordinal Pattern Analysis

    Directory of Open Access Journals (Sweden)

    Iman Veisi

    2010-03-01

    Full Text Available Introduction: In this paper, a novel complexity measure is proposed to detect dynamical changes in nonlinear systems using ordinal pattern analysis of time series data taken from the system. Epilepsy is considered as a dynamical change in nonlinear and complex brain system. The ability of the proposed measure for characterizing the normal and epileptic EEG signals when the signal is short or is contaminated with noise is investigated and compared with some traditional chaos-based measures. Materials and Methods: In the proposed method, the phase space of the time series is reconstructed and then partitioned using ordinal patterns. The partitions can be labeled using a set of symbols. Therefore, the state trajectory is converted to a symbol sequence. A finite state machine is then constructed to model the sequence. A new complexity measure is proposed to detect dynamical changes using the state transition matrix of the state machine. The proposed complexity measure was applied to detect epilepsy in short and noisy EEG signals and the results were compared with some chaotic measures. Results: The results indicate that this complexity measure can distinguish normal and epileptic EEG signals with an accuracy of more than 97% for clean EEG and more than 75% for highly noised EEG signals. Discussion and Conclusion: The complexity measure can be computed in a very fast and easy way and, unlike traditional chaotic measures, is robust with respect to noise corrupting the data. This measure is also capable of dynamical change detection in short time series data.

  2. Radiation Protection Ordinance 1989. Supplement with Radiation Protection Register Ordinance, general administration regulation pursuant to Sect. 45 Radiation Protection Ordinance, general administration regulation pursuant to Sect. 62 sub-sect. radiation passport

    International Nuclear Information System (INIS)

    Veith, H.M.

    1990-01-01

    The addendum contains regulations issued supplementary to the Radiation Protection Ordinance: The Radiation Protection Register as of April 3, 1990 including the law on the setting up of a Federal Office on Radiation Protection; the general administration regulation pursuant to Sect. 45 Radiation Protection Ordinance as of February 21, 1990; the general administration regulation pursuant to Sect. 62 sub-sect. 2 Radiation Protection Ordinance as of May 3, 1990 (AVV Radiation passport). The volume contains, apart from the legal texts, the appropriate decision by the Bundesrat, the official explanation from the Bundestag Publications as well as a comprehensive introduction into the new legal matter. (orig.) [de

  3. Applications of discrete element method in modeling of grain postharvest operations

    Science.gov (United States)

    Grain kernels are finite and discrete materials. Although flowing grain can behave like a continuum fluid at times, the discontinuous behavior exhibited by grain kernels cannot be simulated solely with conventional continuum-based computer modeling such as finite-element or finite-difference methods...

  4. Report of the second research co-ordination meeting on the co-ordinated research programme: rapid instrumental and separation methods for monitoring radionuclides in food and environmental samples

    International Nuclear Information System (INIS)

    1992-10-01

    The purpose of this Second Research Co-ordinated Meeting (12-16 August 1991) on Rapid Instrumental and Separation Methods for Monitoring Radionuclides in Food and Environmental Samples is to discuss the progress of the programmes since the First Research Co-ordination Meeting, discuss how to validate the methodologies developed (e.g. reference samples, intercomparisons), and outline a schedule for CRP completion by the end of 1992. Radioactive contamination of the environment after a nuclear accident, such as had occurred at Chernobyl, is of serious concern to government officials and members of the general public. In 1990/1991 the Agency was asked to organize the International Chernobyl Project to assess the situation in the USSR. A network of laboratories was organized to carry out the environmental assessment needed for this project. The following recommendations are based on the experience gained by many of the laboratories involved in this project. 1. Maintain a network of analytical laboratories with special skills and experience to provide assessments of radionuclide contamination in the environment in case of a radiological emergency. 2. Methodologies for assessment of contamination in the environment should take into consideration potential trajectories, radioecology, and food chain parameters. 3. Focus on areas of representative sample collection, is situ instrumental and chemical analysis, as well as advanced streamlined laboratory analyses which will facilitate the timeline of an assessment. 4. Conduct intercomparison and testing of technologies, employing standard reference materials and procedures, and field measurements at significantly contaminated area. 5. Conduct training of Member State laboratory personnel through fellowships, special courses, and workshops. 5 refs

  5. Efficient methods for time-absorption (α) eigenvalue calculations

    International Nuclear Information System (INIS)

    Hill, T.R.

    1983-01-01

    The time-absorption eigenvalue (α) calculation is one of the options found in most discrete-ordinates transport codes. Several methods have been developed at Los Alamos to improve the efficiency of this calculation. Two procedures, based on coarse-mesh rebalance, to accelerate the α eigenvalue search are derived. A hybrid scheme to automatically choose the more-effective rebalance method is described. The α rebalance scheme permits some simple modifications to the iteration strategy that eliminates many unnecessary calculations required in the standard search procedure. For several fast supercritical test problems, these methods resulted in convergence with one-fifth the number of iterations required for the conventional eigenvalue search procedure

  6. Ordinal-Measure Based Shape Correspondence

    Directory of Open Access Journals (Sweden)

    Faouzi Alaya Cheikh

    2002-04-01

    Full Text Available We present a novel approach to shape similarity estimation based on distance transformation and ordinal correlation. The proposed method operates in three steps: object alignment, contour to multilevel image transformation, and similarity evaluation. This approach is suitable for use in shape classification, content-based image retrieval and performance evaluation of segmentation algorithms. The two latter applications are addressed in this papers. Simulation results show that in both applications our proposed measure performs quite well in quantifying shape similarity. The scores obtained using this technique reflect well the correspondence between object contours as humans perceive it.

  7. Discrete exterior calculus discretization of incompressible Navier–Stokes equations over surface simplicial meshes

    KAUST Repository

    Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

    2016-01-01

    A conservative discretization of incompressible Navier–Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a

  8. Knowledge of the ordinal position of list items in pigeons.

    Science.gov (United States)

    Scarf, Damian; Colombo, Michael

    2011-10-01

    Ordinal knowledge is a fundamental aspect of advanced cognition. It is self-evident that humans represent ordinal knowledge, and over the past 20 years it has become clear that nonhuman primates share this ability. In contrast, evidence that nonprimate species represent ordinal knowledge is missing from the comparative literature. To address this issue, in the present experiment we trained pigeons on three 4-item lists and then tested them with derived lists in which, relative to the training lists, the ordinal position of the items was either maintained or changed. Similar to the findings with human and nonhuman primates, our pigeons performed markedly better on the maintained lists compared to the changed lists, and displayed errors consistent with the view that they used their knowledge of ordinal position to guide responding on the derived lists. These findings demonstrate that the ability to acquire ordinal knowledge is not unique to the primate lineage. (PsycINFO Database Record (c) 2011 APA, all rights reserved).

  9. Hybrid SN Laplace Transform Method For Slab Lattice Calculations

    International Nuclear Information System (INIS)

    Segatto, Cynthia F.; Vilhena, Marco T.; Zani, Jose H.; Barros, Ricardo C.

    2008-01-01

    In typical lattice cells where a highly absorbing, small fuel element is embedded in the moderator, a large weakly absorbing medium, high-order transport methods become unnecessary. In this paper we describe a hybrid discrete ordinates (S N ) method for slab lattice calculations. This hybrid S N method combines the convenience of a low-order S N method in the moderator with a high-order S N method in the fuel. We use special fuel-moderator interface conditions based on an approximate angular flux interpolation analytical method and the Laplace transform (LTS N ) numerical method to calculate the neutron flux distribution and the thermal disadvantage factor. We present numerical results for a range of typical model problems. (authors)

  10. Discrete event simulation of crop operations in sweet pepper in support of work method innovation

    NARCIS (Netherlands)

    Ooster, van 't Bert; Aantjes, Wiger; Melamed, Z.

    2017-01-01

    Greenhouse Work Simulation, GWorkS, is a model that simulates crop operations in greenhouses for the purpose of analysing work methods. GWorkS is a discrete event model that approaches reality as a discrete stochastic dynamic system. GWorkS was developed and validated using cut-rose as a case

  11. Spectral element method for vector radiative transfer equation

    International Nuclear Information System (INIS)

    Zhao, J.M.; Liu, L.H.; Hsu, P.-F.; Tan, J.Y.

    2010-01-01

    A spectral element method (SEM) is developed to solve polarized radiative transfer in multidimensional participating medium. The angular discretization is based on the discrete-ordinates approach, and the spatial discretization is conducted by spectral element approach. Chebyshev polynomial is used to build basis function on each element. Four various test problems are taken as examples to verify the performance of the SEM. The effectiveness of the SEM is demonstrated. The h and the p convergence characteristics of the SEM are studied. The convergence rate of p-refinement follows the exponential decay trend and is superior to that of h-refinement. The accuracy and efficiency of the higher order approximation in the SEM is well demonstrated for the solution of the VRTE. The predicted angular distribution of brightness temperature and Stokes vector by the SEM agree very well with the benchmark solutions in references. Numerical results show that the SEM is accurate, flexible and effective to solve multidimensional polarized radiative transfer problems.

  12. Ordinance on measures for preparation of a radioactive waste repository (Ordinance on preparatory measures) of 24 October 1979

    International Nuclear Information System (INIS)

    1981-01-01

    This Ordinance contains details concerning the special procedure provided for under Section 10(2) of the Federal Order of 6th October 1978 concerning the Atomic Energy Act whereby the Federal Council must grant permission before preparations for the construction of radioactive waste repositories may be undertaken. The Ordinance defines the preparatory measures, which include maps and plans of the area, a geological report, etc. (NEA) [fr

  13. Lanthanide co-ordination frameworks: Opportunities and diversity

    International Nuclear Information System (INIS)

    Hill, Robert J.; Long, De-Liang; Hubberstey, Peter; Schroeder, Martin; Champness, Neil R.

    2005-01-01

    Significant successes have been made over recent years in preparing co-ordination framework polymers that show macroscopic material properties, but in the vast majority of cases this has been achieved with d-block metal-based systems. Lanthanide co-ordination frameworks also offer attractive properties in terms of their potential applications as luminescent, non-linear optical and porous materials. However, lanthanide-based systems have been far less studied to date than their d-block counterparts. One possible reason for this is that the co-ordination spheres of lanthanide cations are more difficult to control and, in the absence of design strategies for lanthanide co-ordination frameworks, it is significantly more difficult to target materials with specific properties. However, this article highlights some of the exciting possibilities that have emerged from the earliest investigations in this field with new topological families of compounds being discovered from relatively simple framework components, including unusual eight, seven and five-connected framework systems. Our own research, as well as others, is leading to a much greater appreciation of the factors that control framework formation and the resultant observed topologies of these polymers. As this understanding develops targeting particular framework types will become more straightforward and the development of designed polyfunctional materials more accessible. Thus, it can be seen that lanthanide co-ordination frameworks have the potential to open up previously unexplored directions for materials chemistry. This article focuses on the underlying concepts for the construction of these enticing and potentially highly important materials

  14. The new X-ray ordinance: what's new?

    International Nuclear Information System (INIS)

    Reichow, H.

    2000-01-01

    The augmented requirements for the minimisation of the radiation dose in medical exposure and the experiences gained from the implementation of the ordinance in force call for more extensive measures for reducing radiation, for quality assurance and expertise in radiological protection. In future physicians, dentists, veterinarians and other people using X-rays will have to bring their necessary expert knowledge regarding radiological protection up to date at regular intervals, and prove that they have done so. To protect the public against radiation exposure from targeted use, the limit value of the effective dose is reduced to 1 mSv in the calendar year. The dose level for the protection of people professionally exposed to radiation is reduced to 20 mSv. The further development of information technology and digital imaging demands that appropriate framework conditions be laid down in response to the changing requirements for radiation protection such as those in telemedicine and in digital recording and documentation possibilities in radiology. The draft further clarifies the distinction between the Radiological Protection Ordinance and the X-Ray Ordinance in relation to accelerators, in which electrons are accelerated with the aim of producing ionizing radiation, and reduces the limit energy from 3 MeV to 1 MeV. It is discussed to remove the X-ray therapy from the X-ray Ordinance and to insert it into the Radiological Protection Ordinance, in order to conform to the higher protection requirements in X-ray therapy. (orig.) [de

  15. Time Discretization Techniques

    KAUST Repository

    Gottlieb, S.; Ketcheson, David I.

    2016-01-01

    The time discretization of hyperbolic partial differential equations is typically the evolution of a system of ordinary differential equations obtained by spatial discretization of the original problem. Methods for this time evolution include

  16. Dynamic modeling method for infrared smoke based on enhanced discrete phase model

    Science.gov (United States)

    Zhang, Zhendong; Yang, Chunling; Zhang, Yan; Zhu, Hongbo

    2018-03-01

    The dynamic modeling of infrared (IR) smoke plays an important role in IR scene simulation systems and its accuracy directly influences the system veracity. However, current IR smoke models cannot provide high veracity, because certain physical characteristics are frequently ignored in fluid simulation; simplifying the discrete phase as a continuous phase and ignoring the IR decoy missile-body spinning. To address this defect, this paper proposes a dynamic modeling method for IR smoke, based on an enhanced discrete phase model (DPM). A mathematical simulation model based on an enhanced DPM is built and a dynamic computing fluid mesh is generated. The dynamic model of IR smoke is then established using an extended equivalent-blackbody-molecule model. Experiments demonstrate that this model realizes a dynamic method for modeling IR smoke with higher veracity.

  17. Revision without ordinals

    NARCIS (Netherlands)

    Rivello, Edoardo

    2013-01-01

    We show that Herzberger’s and Gupta’s revision theories of truth can be recast in purely inductive terms, without any appeal neither to the transfinite ordinal numbers nor to the axiom of Choice. The result is presented in an abstract and general setting, emphasising both its validity for a wide

  18. Adaptive Discrete Hypergraph Matching.

    Science.gov (United States)

    Yan, Junchi; Li, Changsheng; Li, Yin; Cao, Guitao

    2018-02-01

    This paper addresses the problem of hypergraph matching using higher-order affinity information. We propose a solver that iteratively updates the solution in the discrete domain by linear assignment approximation. The proposed method is guaranteed to converge to a stationary discrete solution and avoids the annealing procedure and ad-hoc post binarization step that are required in several previous methods. Specifically, we start with a simple iterative discrete gradient assignment solver. This solver can be trapped in an -circle sequence under moderate conditions, where is the order of the graph matching problem. We then devise an adaptive relaxation mechanism to jump out this degenerating case and show that the resulting new path will converge to a fixed solution in the discrete domain. The proposed method is tested on both synthetic and real-world benchmarks. The experimental results corroborate the efficacy of our method.

  19. The Pakistan atomic energy commission ordinance, 1965 ordinance no. XVII of 1965

    International Nuclear Information System (INIS)

    1983-01-01

    This act, entitled Pakistan Atomic Energy Commission ordinance 1965, allows amendments incorporated under PAEC (amendment) act 1974 upto August 1983. The amendments relates to regulations concerned with the composition and functions of the commission and some miscellaneous rules. (A.B.)

  20. Collection of laws and ordinances concerning regulation of atomic energy, 1991 edition

    International Nuclear Information System (INIS)

    1990-01-01

    This is the collection of the laws and ordinances on the regulation of atomic energy, 1991 edition, published under the supervision of Nuclear Safety Bureau, Science and Technology Agency. First, the abbreviated indication of the laws and ordinances is shown. The contents are those as of September 30, 1990. 12 basic laws and ordinances, 45 laws and ordinances on the regulation of nuclear raw materials, nuclear fuel materials and nuclear reactors, 26 laws and ordinances on the prevention of the radiation injuries due to radioisotopes and others, and 29 related laws and ordinances are collected in this book. (K.I.)

  1. Bilinear nodal transport method in weighted diamond difference form

    International Nuclear Information System (INIS)

    Azmy, Y.Y.

    1987-01-01

    Nodal methods have been developed and implemented for the numerical solution of the discrete ordinates neutron transport equation. Numerical testing of these methods and comparison of their results to those obtained by conventional methods have established the high accuracy of nodal methods. Furthermore, it has been suggested that the linear-linear approximation is the most computationally efficient, practical nodal approximation. Indeed, this claim has been substantiated by comparing the accuracy in the solution, and the CPU time required to achieve convergence to that solution by several nodal approximations, as well as the diamond difference scheme. Two types of linear-linear nodal methods have been developed in the literature: analytic linear-linear (NLL) methods, in which the transverse-leakage terms are derived analytically, and approximate linear-linear (PLL) methods, in which these terms are approximated. In spite of their higher accuracy, NLL methods result in very complicated discrete-variable equations that exhibit a high degree of coupling, thus requiring special solution algorithms. On the other hand, the sacrificed accuracy in PLL methods is compensated for by the simple discrete-variable equations and diamond-difference-like solution algorithm. In this paper the authors outline the development of an NLL nodal method, the bilinear method, which can be written in a weighted diamond difference form with one spatial weight per dimension that is analytically derived rather than preassigned in an ad hoc fashion

  2. A Fully Discrete Galerkin Method for a Nonlinear Space-Fractional Diffusion Equation

    Directory of Open Access Journals (Sweden)

    Yunying Zheng

    2011-01-01

    Full Text Available The spatial transport process in fractal media is generally anomalous. The space-fractional advection-diffusion equation can be used to characterize such a process. In this paper, a fully discrete scheme is given for a type of nonlinear space-fractional anomalous advection-diffusion equation. In the spatial direction, we use the finite element method, and in the temporal direction, we use the modified Crank-Nicolson approximation. Here the fractional derivative indicates the Caputo derivative. The error estimate for the fully discrete scheme is derived. And the numerical examples are also included which are in line with the theoretical analysis.

  3. Discrete Element Method simulations of standing jumps in granular flows down inclines

    Directory of Open Access Journals (Sweden)

    Méjean Ségolène

    2017-01-01

    Full Text Available This paper describes a numerical set-up which uses Discrete Element Method to produce standing jumps in flows of dry granular materials down a slope in two dimensions. The grain-scale force interactions are modeled by a visco-elastic normal force and an elastic tangential force with a Coulomb threshold. We will show how it is possible to reproduce all the shapes of the jumps observed in a previous laboratory study: diffuse versus steep jumps and compressible versus incompressible jumps. Moreover, we will discuss the additional measurements that can be done thanks to discrete element modelling.

  4. Modeling of asphalt by means of discrete element method – an initial study

    DEFF Research Database (Denmark)

    Feng, Huan; Hededal, Ole; Stang, Henrik

    of conducting time-consuming and lab-costly procedures. The use of numerical models, capable of reducing greatly the testing cost, has shown great potential in characterizing asphalt-aggregate mixtures for both material evaluation and structural design purposes, [1],[2]. Discrete element method (DEM) is one...... – will be applied. The work presented here will focus on the discrete element method as a tool for modelling composite materials, i.e. determination of a representative volume; boundary conditions; characterisation of the components mastic (binder + filler) and aggregates; and establishment of virtual test samples....... Results from initial tests will be presented and the future development of the model towards characterising asphalt from its composition will be outlined....

  5. A new high accuracy non-polynomial tension spline method for the solution of one dimensional wave equation in polar co-ordinates

    Directory of Open Access Journals (Sweden)

    Venu Gopal

    2014-07-01

    Full Text Available In this paper, we propose a new three-level implicit nine point compact finite difference formulation of O(k2 + h4 based on non-polynomial tension spline approximation in r-direction and finite difference approximation in t-direction for the numerical solution of one dimensional wave equation in polar co-ordinates. We describe the mathematical formulation procedure in details and also discuss the stability of the method. Numerical results are provided to justify the usefulness of the proposed method.

  6. Urban Runoff: Model Ordinances for Erosion and Sediment Control

    Science.gov (United States)

    The model ordinance in this section borrows language from the erosion and sediment control ordinance features that might help prevent erosion and sedimentation and protect natural resources more fully.

  7. Positivity for Convective Semi-discretizations

    KAUST Repository

    Fekete, Imre

    2017-04-19

    We propose a technique for investigating stability properties like positivity and forward invariance of an interval for method-of-lines discretizations, and apply the technique to study positivity preservation for a class of TVD semi-discretizations of 1D scalar hyperbolic conservation laws. This technique is a generalization of the approach suggested in Khalsaraei (J Comput Appl Math 235(1): 137–143, 2010). We give more relaxed conditions on the time-step for positivity preservation for slope-limited semi-discretizations integrated in time with explicit Runge–Kutta methods. We show that the step-size restrictions derived are sharp in a certain sense, and that many higher-order explicit Runge–Kutta methods, including the classical 4th-order method and all non-confluent methods with a negative Butcher coefficient, cannot generally maintain positivity for these semi-discretizations under any positive step size. We also apply the proposed technique to centered finite difference discretizations of scalar hyperbolic and parabolic problems.

  8. The impact of ordinate scaling on the visual analysis of single-case data.

    Science.gov (United States)

    Dart, Evan H; Radley, Keith C

    2017-08-01

    Visual analysis is the primary method for detecting the presence of treatment effects in graphically displayed single-case data and it is often referred to as the "gold standard." Although researchers have developed standards for the application of visual analysis (e.g., Horner et al., 2005), over- and underestimation of effect size magnitude is not uncommon among analysts. Several characteristics have been identified as potential contributors to these errors; however, researchers have largely focused on characteristics of the data itself (e.g., autocorrelation), paying less attention to characteristics of the graphic display which are largely in control of the analyst (e.g., ordinate scaling). The current study investigated the impact that differences in ordinate scaling, a graphic display characteristic, had on experts' accuracy in judgments regarding the magnitude of effect present in single-case percentage data. 32 participants were asked to evaluate eight ABAB data sets (2 each presenting null, small, moderate, and large effects) along with three iterations of each (32 graphs in total) in which only the ordinate scale was manipulated. Results suggest that raters are less accurate in their detection of treatment effects as the ordinate scale is constricted. Additionally, raters were more likely to overestimate the size of a treatment effect when the ordinate scale was constricted. Copyright © 2017 Society for the Study of School Psychology. Published by Elsevier Ltd. All rights reserved.

  9. Predicting multi-level drug response with gene expression profile in multiple myeloma using hierarchical ordinal regression.

    Science.gov (United States)

    Zhang, Xinyan; Li, Bingzong; Han, Huiying; Song, Sha; Xu, Hongxia; Hong, Yating; Yi, Nengjun; Zhuang, Wenzhuo

    2018-05-10

    Multiple myeloma (MM), like other cancers, is caused by the accumulation of genetic abnormalities. Heterogeneity exists in the patients' response to treatments, for example, bortezomib. This urges efforts to identify biomarkers from numerous molecular features and build predictive models for identifying patients that can benefit from a certain treatment scheme. However, previous studies treated the multi-level ordinal drug response as a binary response where only responsive and non-responsive groups are considered. It is desirable to directly analyze the multi-level drug response, rather than combining the response to two groups. In this study, we present a novel method to identify significantly associated biomarkers and then develop ordinal genomic classifier using the hierarchical ordinal logistic model. The proposed hierarchical ordinal logistic model employs the heavy-tailed Cauchy prior on the coefficients and is fitted by an efficient quasi-Newton algorithm. We apply our hierarchical ordinal regression approach to analyze two publicly available datasets for MM with five-level drug response and numerous gene expression measures. Our results show that our method is able to identify genes associated with the multi-level drug response and to generate powerful predictive models for predicting the multi-level response. The proposed method allows us to jointly fit numerous correlated predictors and thus build efficient models for predicting the multi-level drug response. The predictive model for the multi-level drug response can be more informative than the previous approaches. Thus, the proposed approach provides a powerful tool for predicting multi-level drug response and has important impact on cancer studies.

  10. Recent advances in the spectral green's function method for monoenergetic slab-geometry fixed-source adjoint transport problems in S{sub N} formulation

    Energy Technology Data Exchange (ETDEWEB)

    Curbelo, Jesus P.; Alves Filho, Hermes; Barros, Ricardo C., E-mail: jperez@iprj.uerj.br, E-mail: halves@iprj.uerj.br, E-mail: rcbarros@pq.cnpq.br [Universidade do Estado do Rio de Janeiro (UERJ), Nova Friburgo, RJ (Brazil). Instituto Politecnico. Programa de Pos-Graduacao em Modelagem Computacional; Hernandez, Carlos R.G., E-mail: cgh@instec.cu [Instituto Superior de Tecnologias y Ciencias Aplicadas (InSTEC), La Habana (Cuba)

    2015-07-01

    The spectral Green's function (SGF) method is a numerical method that is free of spatial truncation errors for slab-geometry fixed-source discrete ordinates (S{sub N}) adjoint problems. The method is based on the standard spatially discretized adjoint S{sub N} balance equations and a nonstandard adjoint auxiliary equation expressing the node-average adjoint angular flux, in each discretization node, as a weighted combination of the node-edge outgoing adjoint fluxes. The auxiliary equation contains parameters which act as Green's functions for the cell-average adjoint angular flux. These parameters are determined by means of a spectral analysis which yields the local general solution of the S{sub N} equations within each node of the discretization grid. In this work a number of advances in the SGF adjoint method are presented: the method is extended to adjoint S{sub N} problems considering linearly anisotropic scattering and non-zero prescribed boundary conditions for the forward source-detector problem. Numerical results to typical model problems are considered to illustrate the efficiency and accuracy of the o offered method. (author)

  11. Atomic ordinance - amendment of 28 october 1987

    International Nuclear Information System (INIS)

    1987-10-01

    This Ordinance amends certain provisions of the 1984 Ordinance on licences for the construction and operation of nuclear installations, import, export and transit of nuclear fuel, as well as the export of nuclear reactors, equipment and technical data. The Order also amends the provisions on the delivery procedure for these licences and makes minor amendments to the 1983 Order on nuclear third party liability [fr

  12. A two-dimensional discontinuous heterogeneous finite element method for neutron transport calculations

    International Nuclear Information System (INIS)

    Masiello, E.; Sanchez, R.

    2007-01-01

    A discontinuous heterogeneous finite element method is presented and discussed. The method is intended for realistic numerical pin-by-pin lattice calculations when an exact representation of the geometric shape of the pins is made without need for homogenization. The method keeps the advantages of conventional discrete ordinate methods, such as fast execution together with the possibility to deal with a large number of spatial meshes, while minimizing the need for geometric modeling. It also provides a complete factorization in space, angle, and energy for the discretized matrices and minimizes, thus, storage requirements. An angular multigrid acceleration technique has also been developed to speed up the rate of convergence of the inner iterations. A particular aspect of this acceleration is the introduction of boundary restriction and prolongation operators that minimize oscillatory behavior and enhance positivity. Numerical tests are presented that show the high precision of the method and the efficiency of the angular multigrid acceleration. (authors)

  13. Overcurrent protection co-ordination. A modern approach for modern devices

    Energy Technology Data Exchange (ETDEWEB)

    Hindle, P. [GEC Alsthom Engineering Systems Ltd., Whetstone (United Kingdom); Sanderson, J.V.H. [Power Engineering Consultants Ltd., Cheshire (United Kingdom)

    1995-12-31

    A modern approach to relay co-ordination that takes advantage of the improved performance of modern protective relays and circuits was proposed. The proposed method dealt with a mixture of new and old equipment and was most useful when implemented using common spreadsheet software. The suggested approach justified reduced time margins for relay co-ordination in many difficult applications. Other established approaches were reviewed. A discussion of fixed and variable time margin allowances was presented. The formulation of an equation to determine the required upstream relay operating time was explained, with sample calculations. Relay performance standards and modern protective equipment were discussed. It was concluded that modern relays and circuit breakers are much more advanced than designs of the recent past. The method described allowed significant reductions in margins which enabled modern relays to operate faster. While calculations for the procedures were said to be tedious to perform by hand, they can be easily done with spreadsheet software. 10 refs., 4 figs.

  14. A high-order method for the integration of the Galerkin semi-discretized nuclear reactor kinetics equations

    International Nuclear Information System (INIS)

    Vargas, L.

    1988-01-01

    The numerical approximate solution of the space-time nuclear reactor kinetics equation is investigated using a finite-element discretization of the space variable and a high order integration scheme for the resulting semi-discretized parabolic equation. The Galerkin method with spatial piecewise polynomial Lagrange basis functions are used to obtained a continuous time semi-discretized form of the space-time reactor kinetics equation. A temporal discretization is then carried out with a numerical scheme based on the Iterated Defect Correction (IDC) method using piecewise quadratic polynomials or exponential functions. The kinetics equations are thus solved with in a general finite element framework with respect to space as well as time variables in which the order of convergence of the spatial and temporal discretizations is consistently high. A computer code GALFEM/IDC is developed, to implement the numerical schemes described above. This issued to solve a one space dimensional benchmark problem. The results of the numerical experiments confirm the theoretical arguments and show that the convergence is very fast and the overall procedure is quite efficient. This is due to the good asymptotic properties of the numerical scheme which is of third order in the time interval

  15. The German Radiation Protection Ordinance (StrlSchV). 3. ed.

    International Nuclear Information System (INIS)

    Hinrichs, O.

    1992-01-01

    The German Radiation Protection Ordinance constitutes the central statutory instrument containing the main protective provisions for all fields of application of radioactive materials and ionizing radiation, with the exception of the field covered by the X-ray Ordinance. The current text of the Ordinance is that promulgated on 30.06.1989 with the subsequent amendments, as last amended through the Unification Treaty (Einigungsvertrag) of 23.09.1990. The Radiation Protection Ordinance was adopted on the basis of the German Nuclear Energy Act (Atomgesetz), which contains, inter alia, the necessary empowerments to issue statutory ordinances. Further fields containing relevant protective provisions are, above all, the law of dangerous substances (which concerns the transport of radioactive materials), the law of pharmaceutical products and the law of foodstuffs. The whole regulatory package is a part of EC and Euratom law. The limit values of the Euratom Directives were transposed into the Radiation Protection Ordinance. In order to reduce the bulk of the Ordinance, the legislator has only included the limit values for the most important radionuclides, and has made provision for the separate promulgation of the other limit values. In order to enhance the practical use of the book, the provisions governing the radiation pass, which are regulated in a separate administrative instruction, are also reproduced. (orig./HSCH) [de

  16. Discrete exterior calculus discretization of incompressible Navier–Stokes equations over surface simplicial meshes

    KAUST Repository

    Mohamed, Mamdouh S.

    2016-02-11

    A conservative discretization of incompressible Navier–Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.

  17. Discrete exterior calculus discretization of incompressible Navier-Stokes equations over surface simplicial meshes

    Science.gov (United States)

    Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

    2016-05-01

    A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.

  18. Quadratic Finite Element Method for 1D Deterministic Transport

    International Nuclear Information System (INIS)

    Tolar, D R Jr.; Ferguson, J M

    2004-01-01

    In the discrete ordinates, or SN, numerical solution of the transport equation, both the spatial ((und r)) and angular ((und (Omega))) dependences on the angular flux ψ(und r),(und (Omega))are modeled discretely. While significant effort has been devoted toward improving the spatial discretization of the angular flux, we focus on improving the angular discretization of ψ(und r),(und (Omega)). Specifically, we employ a Petrov-Galerkin quadratic finite element approximation for the differencing of the angular variable (μ) in developing the one-dimensional (1D) spherical geometry S N equations. We develop an algorithm that shows faster convergence with angular resolution than conventional S N algorithms

  19. An approach to solve group-decision-making problems with ordinal interval numbers.

    Science.gov (United States)

    Fan, Zhi-Ping; Liu, Yang

    2010-10-01

    The ordinal interval number is a form of uncertain preference information in group decision making (GDM), while it is seldom discussed in the existing research. This paper investigates how the ranking order of alternatives is determined based on preference information of ordinal interval numbers in GDM problems. When ranking a large quantity of ordinal interval numbers, the efficiency and accuracy of the ranking process are critical. A new approach is proposed to rank alternatives using ordinal interval numbers when every ranking ordinal in an ordinal interval number is thought to be uniformly and independently distributed in its interval. First, we give the definition of possibility degree on comparing two ordinal interval numbers and the related theory analysis. Then, to rank alternatives, by comparing multiple ordinal interval numbers, a collective expectation possibility degree matrix on pairwise comparisons of alternatives is built, and an optimization model based on this matrix is constructed. Furthermore, an algorithm is also presented to rank alternatives by solving the model. Finally, two examples are used to illustrate the use of the proposed approach.

  20. Standardized methods to verify absorbed dose in irradiated food for insect control. Proceedings of a final research co-ordination meeting

    International Nuclear Information System (INIS)

    2001-03-01

    Irradiation to control insect infestation of food is increasingly accepted and applied, especially as a phytosanitary treatment of food as an alternative to fumigation. However, unlike other processes for insect control, irradiation does not always result in immediate insect death. Thus, it is conceivable that fresh and dried fruits and tree nuts, which have been correctly irradiated to meet insect disinfestation/quarantine requirements, may still contain live insects at the time of importation. There is, however, a movement by plant quarantine authorities away from inspecting to ensure the absence of live insects in imported consignments towards examining through administrative procedures that a treatment required by law has been given. Nevertheless, there is a need to provide plant quarantine inspectors with a reliable objective method to verify that a minimum absorbed dose of radiation was given to supplement administrative procedures. Such an objective method is expected to bolster the confidence of the inspectors in clearing the consignment without delay and to facilitate trade in irradiated commodities. The Joint FAO/IAEA Division of Nuclear Techniques in Food and Agriculture initiated a co-ordinated research project (CRP) in 1994 to generate data on the verification of absorbed dose of irradiation in fresh, dried fruits and tree nuts for insect disinfestation/quarantine purposes. A standardized label dose indicator available commercially was used to verify the minimum/maximum absorbed dose of the irradiated commodities for these purposes as required by regulations in certain countries. It appears that such a label dose indicator with certain modifications could be made available to assist national authorities and the food industry to verify the absorbed dose of irradiation to facilitate trade in such irradiated commodities. This TECDOC reports on the accomplishments of this co-ordinated research project and includes the papers presented by the participants

  1. Compliance to two city convenience store ordinance requirements

    Science.gov (United States)

    Menéndez, Cammie K Chaumont; Amandus, Harlan E; Wu, Nan; Hendricks, Scott A

    2015-01-01

    Background Robbery-related homicides and assaults are the leading cause of death in retail businesses. Robbery reduction approaches focus on compliance to Crime Prevention Through Environmental Design (CPTED) guidelines. Purpose We evaluated the level of compliance to CPTED guidelines specified by convenience store safety ordinances effective in 2010 in Dallas and Houston, Texas, USA. Methods Convenience stores were defined as businesses less than 10 000 square feet that sell grocery items. Store managers were interviewed for store ordinance requirements from August to November 2011, in a random sample of 594 (289 in Dallas, 305 in Houston) convenience stores that were open before and after the effective dates of their city’s ordinance. Data were collected in 2011 and analysed in 2012–2014. Results Overall, 9% of stores were in full compliance, although 79% reported being registered with the police departments as compliant. Compliance was consistently significantly higher in Dallas than in Houston for many requirements and by store type. Compliance was lower among single owner-operator stores compared with corporate/franchise stores. Compliance to individual requirements was lowest for signage and visibility. Conclusions Full compliance to the required safety measures is consistent with industry ‘best practices’ and evidence-based workplace violence prevention research findings. In Houston and Dallas compliance was higher for some CPTED requirements but not the less costly approaches that are also the more straightforward to adopt. PMID:26337569

  2. Co-ordinated action between youth-care and sports: facilitators and barriers.

    Science.gov (United States)

    Hermens, Niels; de Langen, Lisanne; Verkooijen, Kirsten T; Koelen, Maria A

    2017-07-01

    In the Netherlands, youth-care organisations and community sports clubs are collaborating to increase socially vulnerable youths' participation in sport. This is rooted in the idea that sports clubs are settings for youth development. As not much is known about co-ordinated action involving professional care organisations and community sports clubs, this study aims to generate insight into facilitators of and barriers to successful co-ordinated action between these two organisations. A cross-sectional study was conducted using in-depth semi-structured qualitative interview data. In total, 23 interviews were held at five locations where co-ordinated action between youth-care and sports takes place. Interviewees were youth-care workers, representatives from community sports clubs, and Care Sport Connectors who were assigned to encourage and manage the co-ordinated action. Using inductive coding procedures, this study shows that existing and good relationships, a boundary spanner, care workers' attitudes, knowledge and competences of the participants, organisational policies and ambitions, and some elements external to the co-ordinated action were reported to be facilitators or barriers. In addition, the participants reported that the different facilitators and barriers influenced the success of the co-ordinated action at different stages of the co-ordinated action. Future research is recommended to further explore the role of boundary spanners in co-ordinated action involving social care organisations and community sports clubs, and to identify what external elements (e.g. events, processes, national policies) are turning points in the formation, implementation and continuation of such co-ordinated action. © 2017 John Wiley & Sons Ltd.

  3. Is Best-Worst Scaling Suitable for Health State Valuation? A Comparison with Discrete Choice Experiments.

    Science.gov (United States)

    Krucien, Nicolas; Watson, Verity; Ryan, Mandy

    2017-12-01

    Health utility indices (HUIs) are widely used in economic evaluation. The best-worst scaling (BWS) method is being used to value dimensions of HUIs. However, little is known about the properties of this method. This paper investigates the validity of the BWS method to develop HUI, comparing it to another ordinal valuation method, the discrete choice experiment (DCE). Using a parametric approach, we find a low level of concordance between the two methods, with evidence of preference reversals. BWS responses are subject to decision biases, with significant effects on individuals' preferences. Non parametric tests indicate that BWS data has lower stability, monotonicity and continuity compared to DCE data, suggesting that the BWS provides lower quality data. As a consequence, for both theoretical and technical reasons, practitioners should be cautious both about using the BWS method to measure health-related preferences, and using HUI based on BWS data. Given existing evidence, it seems that the DCE method is a better method, at least because its limitations (and measurement properties) have been extensively researched. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

  4. Ordinance on the transport of dangerous goods by road (SDR)

    International Nuclear Information System (INIS)

    1985-04-01

    This Ordinance regulates the transport of dangerous goods by road and replaces a similar Ordinance of 1972. The dangerous goods are listed in Annex A and the special provisions to be complied with for their transport are contained in Annex B. Radioactive materials, categorized as Class IVb, are included in the goods covered by the Ordinance. The Ordinance which entered into force on 1 May 1985 was amended on 9 April 1987 on a minor point and on 27 November 1989 so as to provide for special training for drivers of vehicles carrying such goods. This latter amendment entered into force on 1 January 1990. (NEA) [fr

  5. Using high-order methods on adaptively refined block-structured meshes - discretizations, interpolations, and filters.

    Energy Technology Data Exchange (ETDEWEB)

    Ray, Jaideep; Lefantzi, Sophia; Najm, Habib N.; Kennedy, Christopher A.

    2006-01-01

    Block-structured adaptively refined meshes (SAMR) strive for efficient resolution of partial differential equations (PDEs) solved on large computational domains by clustering mesh points only where required by large gradients. Previous work has indicated that fourth-order convergence can be achieved on such meshes by using a suitable combination of high-order discretizations, interpolations, and filters and can deliver significant computational savings over conventional second-order methods at engineering error tolerances. In this paper, we explore the interactions between the errors introduced by discretizations, interpolations and filters. We develop general expressions for high-order discretizations, interpolations, and filters, in multiple dimensions, using a Fourier approach, facilitating the high-order SAMR implementation. We derive a formulation for the necessary interpolation order for given discretization and derivative orders. We also illustrate this order relationship empirically using one and two-dimensional model problems on refined meshes. We study the observed increase in accuracy with increasing interpolation order. We also examine the empirically observed order of convergence, as the effective resolution of the mesh is increased by successively adding levels of refinement, with different orders of discretization, interpolation, or filtering.

  6. Amendment of the Ordinance on the export and transit of goods

    International Nuclear Information System (INIS)

    1989-12-01

    This Ordinance amends the Annex of the Ordinance of 7 March 1983 on the export and transit of dangerous goods which lists the nuclear items, ie nuclear reactors, equipment and materials subject to export restrictions. The Ordinance came into force on 1 January 1990 (NEA) [fr

  7. Sub-cell balanced nodal expansion methods using S4 eigenfunctions for multi-group SN transport problems in slab geometry

    International Nuclear Information System (INIS)

    Hong, Ser Gi; Lee, Deokjung

    2015-01-01

    A highly accurate S 4 eigenfunction-based nodal method has been developed to solve multi-group discrete ordinate neutral particle transport problems with a linearly anisotropic scattering in slab geometry. The new method solves the even-parity form of discrete ordinates transport equation with an arbitrary S N order angular quadrature using two sub-cell balance equations and the S 4 eigenfunctions of within-group transport equation. The four eigenfunctions from S 4 approximation have been chosen as basis functions for the spatial expansion of the angular flux in each mesh. The constant and cubic polynomial approximations are adopted for the scattering source terms from other energy groups and fission source. A nodal method using the conventional polynomial expansion and the sub-cell balances was also developed to be used for demonstrating the high accuracy of the new methods. Using the new methods, a multi-group eigenvalue problem has been solved as well as fixed source problems. The numerical test results of one-group problem show that the new method has third-order accuracy as mesh size is finely refined and it has much higher accuracies for large meshes than the diamond differencing method and the nodal method using sub-cell balances and polynomial expansion of angular flux. For multi-group problems including eigenvalue problem, it was demonstrated that the new method using the cubic polynomial approximation of the sources could produce very accurate solutions even with large mesh sizes. (author)

  8. A simple method of chaos control for a class of chaotic discrete-time systems

    International Nuclear Information System (INIS)

    Jiang Guoping; Zheng Weixing

    2005-01-01

    In this paper, a simple method is proposed for chaos control for a class of discrete-time chaotic systems. The proposed method is built upon the state feedback control and the characteristic of ergodicity of chaos. The feedback gain matrix of the controller is designed using a simple criterion, so that control parameters can be selected via the pole placement technique of linear control theory. The new controller has a feature that it only uses the state variable for control and does not require the target equilibrium point in the feedback path. Moreover, the proposed control method cannot only overcome the so-called 'odd eigenvalues number limitation' of delayed feedback control, but also control the chaotic systems to the specified equilibrium points. The effectiveness of the proposed method is demonstrated by a two-dimensional discrete-time chaotic system

  9. Compatible Spatial Discretizations for Partial Differential Equations

    Energy Technology Data Exchange (ETDEWEB)

    Arnold, Douglas, N, ed.

    2004-11-25

    From May 11--15, 2004, the Institute for Mathematics and its Applications held a hot topics workshop on Compatible Spatial Discretizations for Partial Differential Equations. The numerical solution of partial differential equations (PDE) is a fundamental task in science and engineering. The goal of the workshop was to bring together a spectrum of scientists at the forefront of the research in the numerical solution of PDEs to discuss compatible spatial discretizations. We define compatible spatial discretizations as those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. A wide variety of discretization methods applied across a wide range of scientific and engineering applications have been designed to or found to inherit or mimic intrinsic spatial structure and reproduce fundamental properties of the solution of the continuous PDE model at the finite dimensional level. A profusion of such methods and concepts relevant to understanding them have been developed and explored: mixed finite element methods, mimetic finite differences, support operator methods, control volume methods, discrete differential forms, Whitney forms, conservative differencing, discrete Hodge operators, discrete Helmholtz decomposition, finite integration techniques, staggered grid and dual grid methods, etc. This workshop seeks to foster communication among the diverse groups of researchers designing, applying, and studying such methods as well as researchers involved in practical solution of large scale problems that may benefit from advancements in such discretizations; to help elucidate the relations between the different methods and concepts; and to generally advance our understanding in the area of compatible spatial discretization methods for PDE. Particular points of emphasis included: + Identification of intrinsic properties of PDE models that are critical for the fidelity of numerical

  10. Constructing ordinal partition transition networks from multivariate time series.

    Science.gov (United States)

    Zhang, Jiayang; Zhou, Jie; Tang, Ming; Guo, Heng; Small, Michael; Zou, Yong

    2017-08-10

    A growing number of algorithms have been proposed to map a scalar time series into ordinal partition transition networks. However, most observable phenomena in the empirical sciences are of a multivariate nature. We construct ordinal partition transition networks for multivariate time series. This approach yields weighted directed networks representing the pattern transition properties of time series in velocity space, which hence provides dynamic insights of the underling system. Furthermore, we propose a measure of entropy to characterize ordinal partition transition dynamics, which is sensitive to capturing the possible local geometric changes of phase space trajectories. We demonstrate the applicability of pattern transition networks to capture phase coherence to non-coherence transitions, and to characterize paths to phase synchronizations. Therefore, we conclude that the ordinal partition transition network approach provides complementary insight to the traditional symbolic analysis of nonlinear multivariate time series.

  11. 1984 Ordinance on nuclear activities (1984:14)

    International Nuclear Information System (INIS)

    1984-01-01

    This Supplementary Ordinance on Nuclear Activities (1984:14) sets out a regulatory regime for the conveyance out of Sweden of equipment or material that has been specially designed or prepared for the processing, use or production of nuclear substances or which is otherwise of essential importance for the production of nuclear devices. The Annex to the Ordinance sets out the list of such equipment or material whose export is subject to Government authorisation. (NEA) [fr

  12. An ordinal model of the McGurk illusion

    DEFF Research Database (Denmark)

    Andersen, Tobias

    2011-01-01

    Audiovisual information is integrated in speech perception. One manifestation of this is the McGurk illusion in which watching the articulating face alters the auditory phonetic percept. Understanding this phenomenon fully requires a computational model with predictive power. Here, we describe...... model it also employed 30 free parameters where the ordinal model needed only 14. Testing the predictive power of the models using a form of cross-validation we found that, although both models performed rather poorly, the ordinal model performed better than the FLMP. Based on these findings we suggest...... that ordinal models generally have greater predictive power because they are constrained by a priori information about the adjacency of phonetic categories....

  13. Ordinance of 30 June 1976 on radiation protection

    International Nuclear Information System (INIS)

    1976-01-01

    This Ordinance on radiation protection lays down the licensing system for activities in Switzerland involving possible exposure to radiation, with the exception of nuclear installations, fuels and radioactive waste which, under the 1959 Atomic Energy Act, are subject to licensing. The Ordinance applies to the production, handling, use, storage, transport, disposal, import and export of radioactive substances and devices and articles containing them; and generally to any activity involving hazards caused by ionizing radiation. The Federal Public Health Service is the competent authority for granting licences. Provision is also made for the administrative conditions to be complied with for obtaining such licences as well as for technical measures required when engaged in work covered by the Ordinance. (NEA) [fr

  14. The Design Co-ordination Framework: key elements for effective product development

    DEFF Research Database (Denmark)

    Andreasen, Mogens Myrup; Bowen, J.; Storm, T.

    1997-01-01

    This paper proposes a Design Co-ordination Framework (DCF) i.e. a concept for an ideal DC system with the abilities to support co-ordination of various complex aspects of product development. A set of frames, modelling key elements of co-ordination, which reflect the states of design, plans, orga...

  15. Research on a Hierarchical Dynamic Automatic Voltage Control System Based on the Discrete Event-Driven Method

    Directory of Open Access Journals (Sweden)

    Yong Min

    2013-06-01

    Full Text Available In this paper, concepts and methods of hybrid control systems are adopted to establish a hierarchical dynamic automatic voltage control (HD-AVC system, realizing the dynamic voltage stability of power grids. An HD-AVC system model consisting of three layers is built based on the hybrid control method and discrete event-driven mechanism. In the Top Layer, discrete events are designed to drive the corresponding control block so as to avoid solving complex multiple objective functions, the power system’s characteristic matrix is formed and the minimum amplitude eigenvalue (MAE is calculated through linearized differential-algebraic equations. MAE is applied to judge the system’s voltage stability and security and construct discrete events. The Middle Layer is responsible for management and operation, which is also driven by discrete events. Control values of the control buses are calculated based on the characteristics of power systems and the sensitivity method. Then control values generate control strategies through the interface block. In the Bottom Layer, various control devices receive and implement the control commands from the Middle Layer. In this way, a closed-loop power system voltage control is achieved. Computer simulations verify the validity and accuracy of the HD-AVC system, and verify that the proposed HD-AVC system is more effective than normal voltage control methods.

  16. Colorimetric determination of nitrate plus nitrite in water by enzymatic reduction, automated discrete analyzer methods

    Science.gov (United States)

    Patton, Charles J.; Kryskalla, Jennifer R.

    2011-01-01

    This report documents work at the U.S. Geological Survey (USGS) National Water Quality Laboratory (NWQL) to validate enzymatic reduction, colorimetric determinative methods for nitrate + nitrite in filtered water by automated discrete analysis. In these standard- and low-level methods (USGS I-2547-11 and I-2548-11), nitrate is reduced to nitrite with nontoxic, soluble nitrate reductase rather than toxic, granular, copperized cadmium used in the longstanding USGS automated continuous-flow analyzer methods I-2545-90 (NWQL laboratory code 1975) and I-2546-91 (NWQL laboratory code 1979). Colorimetric reagents used to determine resulting nitrite in aforementioned enzymatic- and cadmium-reduction methods are identical. The enzyme used in these discrete analyzer methods, designated AtNaR2 by its manufacturer, is produced by recombinant expression of the nitrate reductase gene from wall cress (Arabidopsis thaliana) in the yeast Pichia pastoris. Unlike other commercially available nitrate reductases we evaluated, AtNaR2 maintains high activity at 37°C and is not inhibited by high-phenolic-content humic acids at reaction temperatures in the range of 20°C to 37°C. These previously unrecognized AtNaR2 characteristics are essential for successful performance of discrete analyzer nitrate + nitrite assays (henceforth, DA-AtNaR2) described here.

  17. Fracture Failure of Reinforced Concrete Slabs Subjected to Blast Loading Using the Combined Finite-Discrete Element Method

    Directory of Open Access Journals (Sweden)

    Z. M. Jaini

    Full Text Available Abstract Numerical modeling of fracture failure is challenging due to various issues in the constitutive law and the transition of continuum to discrete bodies. Therefore, this study presents the application of the combined finite-discrete element method to investigate the fracture failure of reinforced concrete slabs subjected to blast loading. In numerical modeling, the interaction of non-uniform blast loading on the concrete slab was modeled using the incorporation of the finite element method with a crack rotating approach and the discrete element method to model crack, fracture onset and its post-failures. A time varying pressure-time history based on the mapping method was adopted to define blast loading. The Mohr-Coulomb with Rankine cut-off and von-Mises criteria were applied for concrete and steel reinforcement respectively. The results of scabbing, spalling and fracture show a reliable prediction of damage and fracture.

  18. Measuring Patient Preferences: An Overview of Methods with a Focus on Discrete Choice Experiments.

    Science.gov (United States)

    Hazlewood, Glen S

    2018-05-01

    There is increasing recognition of the importance of patient preferences and methodologies to measure them. In this article, methods to quantify patient preferences are reviewed, with a focus on discrete choice experiments. In a discrete choice experiment, patients are asked to choose between 2 or more treatments. The results can be used to quantify the relative importance of treatment outcomes and/or other considerations relevant to medical decision making. Conducting and interpreting a discrete choice experiment requires multiple steps and an understanding of the potential biases that can arise, which we review in this article with examples in rheumatic diseases. Copyright © 2018 Elsevier Inc. All rights reserved.

  19. How can the co-ordinate transformation method of beam matching be extended to include separately labelled collimators?

    Science.gov (United States)

    Morgan-Fletcher, S; McKenzie, A L

    1996-03-01

    The problem of matching radiation beams was tackled by Siddon in 1980 using co-ordinate transformations. Since then, the need to distinguish between individual collimators in prescriptions of treatment set-up, brought about by the widespread use of 3-D treatment planning systems and asymmetric fields, as well as a reversal of the rotation sense in the turntable co-ordinate system proposed by the International Electrotechnical Commission, have made it necessary to revisit this particular problem. This paper builds upon Siddon's general equations for the particular case of matching beams, and derives expressions for calculating treatment-unit settings which may be used in a computer program without the need to perform matrix manipulation. The expression treat the individual collimator jaws separately.

  20. An experimental test of CSR theory using a globally calibrated ordination method.

    Science.gov (United States)

    Li, Yuanzhi; Shipley, Bill

    2017-01-01

    Can CSR theory, in conjunction with a recently proposed globally calibrated CSR ordination ("StrateFy"), using only three easily measured leaf traits (leaf area, specific leaf area and leaf dry matter content) predict the functional signature of herbaceous vegetation along experimentally manipulated gradients of soil fertility and disturbance? To determine this, we grew 37 herbaceous species in mixture for five years in 24 experimental mesocosms differing in factorial levels of soil resources (stress) and density-independent mortality (disturbance). We measured 16 different functional traits and then ordinated the resulting vegetation within the CSR triangle using StrateFy. We then calculated community-weighted mean (CWM) values of the competitor (CCWM), stress-tolerator (SCWM) and ruderal (RCWM) scores for each mesocosm. We found a significant increase in SCWM from low to high stress mesocosms, and an increase in RCWM from lowly to highly disturbed mesocosms. However, CCWM did not decline significantly as intensity of stress or disturbance increased, as predicted by CSR theory. This last result likely arose because our herbaceous species were relatively poor competitors in global comparisons and thus no strong competitors in our species pool were selectively favoured in low stress and low disturbed mesocosms. Variation in the 13 other traits, not used by StrateFy, largely argeed with the predictions of CSR theory. StrateFy worked surprisingly well in our experimental study except for the C-dimension. Despite loss of some precision, it has great potential applicability in future studies due to its simplicity and generality.

  1. A novel method for computation of the discrete Fourier transform over characteristic two finite field of even extension degree

    OpenAIRE

    Fedorenko, Sergei V.

    2011-01-01

    A novel method for computation of the discrete Fourier transform over a finite field with reduced multiplicative complexity is described. If the number of multiplications is to be minimized, then the novel method for the finite field of even extension degree is the best known method of the discrete Fourier transform computation. A constructive method of constructing for a cyclic convolution over a finite field is introduced.

  2. The expert knowledge as defined by the X-ray Ordinance

    International Nuclear Information System (INIS)

    1991-01-01

    Persons applying within their role responsibility X-rays in medicine or veterinary medicine, or persons with a responsibility as radiation protection officer or according to section 24, sub-sec. (3) Radiation Protection Ordinance have to give proof of the required expert knowledge (section 3, sub-sec. (2), no. 3, section 4, sub-sec. (1) no. 3, section 13, sub-sec. (4), section 23 no.s. 1 and 3 of the X-ray Ordinance). In addition, persons applying X-rays under the supervision and responsibility of a medical specialist or dentist, have to acquire the knowledge in radiation protection as defined by section 23, no. 2 and 4 X-ray Ordinance. As to the application of X-rays in veterinary medicine, the expert knowledge required is defined in section 3, sub-sec. (2) no. 3, section 4, sub-sec. 1 no. 3, section 13, sub-sec. (4), section 29 sub-sec. (1) no. 4 of the X-ray Ordinance. The knowledge to be acquired in radiation protection is given in section 29, sub-sec. (1) no. 3 of the X-ray Ordinance. The radiation protection officer or persons responsible for radiation protection have to give proof of their expert knowledge within the course of the licensing or notification procedure in accordance with sections 3 and 4 of the X-ray Ordinance, or in the course of the procedure for appointment of a radiation protection officier in accordance with section 13, sub-sec. (3) of the X-ray Ordinance. (orig.) [de

  3. Numerical Evaluation of P-Multigrid Method for the Solution of Discontinuous Galerkin Discretizations of Diffusive Equations

    Science.gov (United States)

    Atkins, H. L.; Helenbrook, B. T.

    2005-01-01

    This paper describes numerical experiments with P-multigrid to corroborate analysis, validate the present implementation, and to examine issues that arise in the implementations of the various combinations of relaxation schemes, discretizations and P-multigrid methods. The two approaches to implement P-multigrid presented here are equivalent for most high-order discretization methods such as spectral element, SUPG, and discontinuous Galerkin applied to advection; however it is discovered that the approach that mimics the common geometric multigrid implementation is less robust, and frequently unstable when applied to discontinuous Galerkin discretizations of di usion. Gauss-Seidel relaxation converges 40% faster than block Jacobi, as predicted by analysis; however, the implementation of Gauss-Seidel is considerably more expensive that one would expect because gradients in most neighboring elements must be updated. A compromise quasi Gauss-Seidel relaxation method that evaluates the gradient in each element twice per iteration converges at rates similar to those predicted for true Gauss-Seidel.

  4. New methods and techniques for decontamination in maintenance or decommissioning operations. Results of a co-ordinated research programme 1994-1998

    International Nuclear Information System (INIS)

    1998-06-01

    Decontamination of nuclear facilities is a subject of increasing importance as the nuclear community considers the issues related to the decommissioning of surplus or obsolete facilities and making modifications to operational facilities, or conducts the necessary inspections and maintenance to permit continued efficient and safe operation of existing facilities. Previous co-ordinated research programmes (CRP) conducted respectively from 1984 to 1987, and from 1989 to 1993, highlighted the role of decontamination within the overall domain of decommissioning. Having recognized technological progress in decontamination and the large potential for optimization, the CRP on New Methods and Techniques for Optimization of Decontamination for Maintenance or Decommissioning was launched and conducted by the IAEA from 1994 to 1998. Concluding reports that summarized the work undertaken under the aegis of the CRP were presented at the third and final Research Co-ordination Meeting (RCM) held in Mol, Belgium, 12-16 January 1998 and are collected in this Technical Document. Operating experience in real-scale applications, lessons learned, key results in laboratory scale or pilot scale research, and validation of mathematical models, are among the most significant achievements of the CRP and have been highlighted

  5. On simulation of no-slip condition in the method of discrete vortices

    Science.gov (United States)

    Shmagunov, O. A.

    2017-10-01

    When modeling flows of an incompressible fluid, it is convenient sometimes to use the method of discrete vortices (MDV), where the continuous vorticity field is approximated by a set of discrete vortex elements moving in the velocity field. The vortex elements have a clear physical interpretation, they do not require the construction of grids and are automatically adaptive, since they concentrate in the regions of greatest interest and successfully describe the flows of a non-viscous fluid. The possibility of using MDV in simulating flows of a viscous fluid was considered in the previous papers using the examples of flows past bodies with sharp edges with the no-penetration condition at solid boundaries. However, the appearance of vorticity on smooth boundaries requires the no-slip condition to be met when MDV is realized, which substantially complicates the initially simple method. In this connection, an approach is considered that allows solving the problem by simple means.

  6. Rain Scattering and Co-ordinate Distance Calculation

    Directory of Open Access Journals (Sweden)

    M. Hajny

    1998-12-01

    Full Text Available Calculations of scattered field on the rain objects are based on using of Multiple MultiPole (MMP numerical method. Both bi-static scattering function and bi-static scattering cross section are calculated in the plane parallel to Earth surface. The co-ordination area was determined using the simple model of scattering volume [1]. Calculation for frequency 9.595 GHz and antenna elevation of 25° was done. Obtained results are compared with calculation in accordance to ITU-R recommendation.

  7. Improved stochastic approximation methods for discretized parabolic partial differential equations

    Science.gov (United States)

    Guiaş, Flavius

    2016-12-01

    We present improvements of the stochastic direct simulation method, a known numerical scheme based on Markov jump processes which is used for approximating solutions of ordinary differential equations. This scheme is suited especially for spatial discretizations of evolution partial differential equations (PDEs). By exploiting the full path simulation of the stochastic method, we use this first approximation as a predictor and construct improved approximations by Picard iterations, Runge-Kutta steps, or a combination. This has as consequence an increased order of convergence. We illustrate the features of the improved method at a standard benchmark problem, a reaction-diffusion equation modeling a combustion process in one space dimension (1D) and two space dimensions (2D).

  8. Radiation transport benchmarks for simple geometries with void regions using the spherical harmonics method

    International Nuclear Information System (INIS)

    Kobayashi, K.

    2009-01-01

    In 2001, an international cooperation on the 3D radiation transport benchmarks for simple geometries with void region was performed under the leadership of E. Sartori of OECD/NEA. There were contributions from eight institutions, where 6 contributions were by the discrete ordinate method and only two were by the spherical harmonics method. The 3D spherical harmonics program FFT3 by the finite Fourier transformation method has been improved for this presentation, and benchmark solutions for the 2D and 3D simple geometries with void region by the FFT2 and FFT3 are given showing fairly good accuracy. (authors)

  9. Using GIS to check co-ordinates of genebank accessions

    NARCIS (Netherlands)

    Hijmans, R.J.; Schreuder, M.; Cruz, de la J.; Guarino, L.

    1999-01-01

    The geographic co-ordinates of the locations where germplasm accessions have been collected are usually documented in genebank databases. However, the co-ordinate data are often incomplete and may contain errors. This paper describes procedures to check for errors, to determine the cause of these

  10. Analysis of the morphology of oral structures from 3-D co-ordinate data.

    Science.gov (United States)

    Jovanovski, V; Lynch, E

    2000-01-01

    A non-intrusive method is described which can be used to determine the forms of oral structures. It is based on the digitising of standard replicas with a co-ordinate-measuring machine. Supporting software permits a mathematical model of the surface to be reconstructed and visualised from captured three-dimensional co-ordinates. A series of surface data sets can be superposed into a common reference frame without the use of extrinsic markers, allowing changes in the shapes of oral structures to be quantified accurately over an extended period of time. The system has found numerous applications.

  11. Expert knowledge as defined by the X-Ray Ordinance

    International Nuclear Information System (INIS)

    1987-01-01

    The radiation protection officer or any person responsible for radiation safety have to give proof of their expert knowledge in accordance with sections 3, 4 of the X-Ray Ordinance. Proof of expert knowledge has to be furnished within the procedure of appointment (sec. 13, sub-sec. (3) X-Ray Ordinance). The directive defines the scope of the expert knowledge required, and the scope of expert knowledge persons must have, or acquire, who are responsible for radiation protection within the preview of sec. 23, no. 2, 4 and sec. 29, sub-sec. 1, no. 3 of the X-Ray Ordinance. (orig./HP) [de

  12. Numerical discretization-based estimation methods for ordinary differential equation models via penalized spline smoothing with applications in biomedical research.

    Science.gov (United States)

    Wu, Hulin; Xue, Hongqi; Kumar, Arun

    2012-06-01

    Differential equations are extensively used for modeling dynamics of physical processes in many scientific fields such as engineering, physics, and biomedical sciences. Parameter estimation of differential equation models is a challenging problem because of high computational cost and high-dimensional parameter space. In this article, we propose a novel class of methods for estimating parameters in ordinary differential equation (ODE) models, which is motivated by HIV dynamics modeling. The new methods exploit the form of numerical discretization algorithms for an ODE solver to formulate estimating equations. First, a penalized-spline approach is employed to estimate the state variables and the estimated state variables are then plugged in a discretization formula of an ODE solver to obtain the ODE parameter estimates via a regression approach. We consider three different order of discretization methods, Euler's method, trapezoidal rule, and Runge-Kutta method. A higher-order numerical algorithm reduces numerical error in the approximation of the derivative, which produces a more accurate estimate, but its computational cost is higher. To balance the computational cost and estimation accuracy, we demonstrate, via simulation studies, that the trapezoidal discretization-based estimate is the best and is recommended for practical use. The asymptotic properties for the proposed numerical discretization-based estimators are established. Comparisons between the proposed methods and existing methods show a clear benefit of the proposed methods in regards to the trade-off between computational cost and estimation accuracy. We apply the proposed methods t an HIV study to further illustrate the usefulness of the proposed approaches. © 2012, The International Biometric Society.

  13. Collection of stand data for ordination | AJ | African Journal of Range ...

    African Journals Online (AJOL)

    African Journal of Range and Forage Science ... Four field stand tables for collecting data for the ordination of species and stands in Mopani Veld are described. The type of ... Keywords: surveys|trees|relative densities|relative frequency parameters|canopy spreads|bushveld|Savanna Biome|methods|data capture|Mopani ...

  14. Rigid Body Motion Calculated From Spatial Co-ordinates of Markers ...

    African Journals Online (AJOL)

    In this paper, we present a unified method for calculating spatial coordinates of markers for a rigid body motion such as in bones. Kinematical analysis of bone movement in cadaveric specimens or living objects had been developed. Here, we show how spatial co-ordinates of markers in or on bone can be calculated from ...

  15. Local zoning ordinances -- how they limit or restrict mining

    International Nuclear Information System (INIS)

    Ingram, H.

    1991-01-01

    Local regulation of mining by zoning has taken place for a long period of time. The delegation to local municipalities of land use planning, zoning and nuisance abatement authority which may affect mining by state governments has been consistently upheld by appellate courts as valid exercises of the police power. Recently, mine operators and mineral owners have been confronted by efforts of local municipalities, often initiated by anti-mining citizen's groups, to impose more stringent restrictions on mining activities within their borders. In some situations, existing ordinances are being enforced for the first time, in others, new ordinances have been adopted without much awareness or involvement by the public. Enforced to the letter, these ordinances can sterilize large blocks of mineable reserves open-quotes operatingclose quotes or performance standards in excess of SMCRA-based regulatory requirements. It is fair to say that investigation of the potential impacts of local zoning and other related ordinances is essential in the planning for the expansion of existing operations or for new operations. There may be new rules in the game. This paper identifies problem areas in typical open-quotes modernclose quotes ordinances and discusses legal and constitutional issues which may arise by their enforcement in coal producing regions

  16. Nucleonic analysis of a preliminary design for the ETF neutral-beam-injector duct shielding

    International Nuclear Information System (INIS)

    Urban, W.T.; Seed, T.J.; Dudziak, D.J.

    1980-01-01

    A nucleonic analysis of the Engineering Test Facility Neutral-Beam-Injector duct shielding has been made using a hybrid Monte Carlo/discrete-ordinates method. This method used Monte Carlo to determine internal and external boundary surface sources for a subsequent discrete-ordinates calculation of the neutron and gamma-ray transport through the shield. The analysis also included determination of the energy and angular distribution of neutrons and gamma rays entering the duct from the torus plasma chamber. Confidence in the hybrid method and the results obtained were provided through a comparison with three-dimensional Monte Carlo results

  17. An assessment of the effects of a cadmium discharge ordinance

    International Nuclear Information System (INIS)

    Moser, J.H.; Schultz, J.L.

    1982-01-01

    The problem facing the MMSD was high levels of cadmium in Milorganite fertilizer. The cause was determined to be discharges from industry, primarily electroplaters. The solution was the cooperative development of an ordinance to limit the discharge of cadmium. Because the dischargers acted responsibly to comply with the ordinance, the ordinance succeeded in achieving its objective of significantly reducing the cadmium loading to the municipal sewerage system and subsequently reducing the cadmium concentration in Milorganite fertilizer

  18. Discrete control systems

    CERN Document Server

    Okuyama, Yoshifumi

    2014-01-01

    Discrete Control Systems establishes a basis for the analysis and design of discretized/quantized control systemsfor continuous physical systems. Beginning with the necessary mathematical foundations and system-model descriptions, the text moves on to derive a robust stability condition. To keep a practical perspective on the uncertain physical systems considered, most of the methods treated are carried out in the frequency domain. As part of the design procedure, modified Nyquist–Hall and Nichols diagrams are presented and discretized proportional–integral–derivative control schemes are reconsidered. Schemes for model-reference feedback and discrete-type observers are proposed. Although single-loop feedback systems form the core of the text, some consideration is given to multiple loops and nonlinearities. The robust control performance and stability of interval systems (with multiple uncertainties) are outlined. Finally, the monograph describes the relationship between feedback-control and discrete ev...

  19. Exact analysis of discrete data

    CERN Document Server

    Hirji, Karim F

    2005-01-01

    Researchers in fields ranging from biology and medicine to the social sciences, law, and economics regularly encounter variables that are discrete or categorical in nature. While there is no dearth of books on the analysis and interpretation of such data, these generally focus on large sample methods. When sample sizes are not large or the data are otherwise sparse, exact methods--methods not based on asymptotic theory--are more accurate and therefore preferable.This book introduces the statistical theory, analysis methods, and computation techniques for exact analysis of discrete data. After reviewing the relevant discrete distributions, the author develops the exact methods from the ground up in a conceptually integrated manner. The topics covered range from univariate discrete data analysis, a single and several 2 x 2 tables, a single and several 2 x K tables, incidence density and inverse sampling designs, unmatched and matched case -control studies, paired binary and trinomial response models, and Markov...

  20. Conservative, unconditionally stable discretization methods for Hamiltonian equations, applied to wave motion in lattice equations modeling protein molecules

    Science.gov (United States)

    LeMesurier, Brenton

    2012-01-01

    A new approach is described for generating exactly energy-momentum conserving time discretizations for a wide class of Hamiltonian systems of DEs with quadratic momenta, including mechanical systems with central forces; it is well-suited in particular to the large systems that arise in both spatial discretizations of nonlinear wave equations and lattice equations such as the Davydov System modeling energetic pulse propagation in protein molecules. The method is unconditionally stable, making it well-suited to equations of broadly “Discrete NLS form”, including many arising in nonlinear optics. Key features of the resulting discretizations are exact conservation of both the Hamiltonian and quadratic conserved quantities related to continuous linear symmetries, preservation of time reversal symmetry, unconditional stability, and respecting the linearity of certain terms. The last feature allows a simple, efficient iterative solution of the resulting nonlinear algebraic systems that retain unconditional stability, avoiding the need for full Newton-type solvers. One distinction from earlier work on conservative discretizations is a new and more straightforward nearly canonical procedure for constructing the discretizations, based on a “discrete gradient calculus with product rule” that mimics the essential properties of partial derivatives. This numerical method is then used to study the Davydov system, revealing that previously conjectured continuum limit approximations by NLS do not hold, but that sech-like pulses related to NLS solitons can nevertheless sometimes arise.

  1. First ordinance amending the Ordinance on Rail Transport of Dangerous Goods (1. Amendment Ordinance Rail Transport of Dangerous Goods). As of June 22, 1983

    International Nuclear Information System (INIS)

    1983-01-01

    This Amendment which came into force on September 1, 1983 brings about modifications of many items of the original Ordinance on Rail Transport of Dangerous Goods and its supplement, as of August 29, 1979. (HSCH) [de

  2. Collections of laws and ordinances concerning radiation injury prevention as of July 24, 1981

    International Nuclear Information System (INIS)

    Tsuruta, Takao

    1981-01-01

    There are laws, government and ministerial ordinances and notifications, each of them bears a definite role, and the contents of the legal regulation on a certain range of matter are determined by their close interrelation and mutual supplementation. Many laws and ordinances concerning atomic energy also form a legal system under such mutual relation. The Atomic Energy Act is positioned at its top, and the main part related to radiation injury prevention comprises a law, two ordinances, a regulation and a notification. Such relationship of individual laws and ordinances is mostly shown in lower rank laws and ordinances. In Chapter 1 of this book, the Atomic Energy Act and the government ordinance concerning the definition of nuclear fuel materials, nuclear raw materials, nuclear reactors and radiation are described. In Chapter 2, the law concerning prevention of radiation injuries due to radiactive isotopes and others, the ordinances and eight notifications closely related to them are collected. In Chapter 3, other related laws and ordinances are gathered. To understand the laws and ordinances synthetically and systematically, the provisions of different laws and ordinances, which are mutually related, are arranged together showing their relation. (Kako, I.)

  3. 2D co-ordinate transformation based on a spike timing-dependent plasticity learning mechanism.

    Science.gov (United States)

    Wu, QingXiang; McGinnity, Thomas Martin; Maguire, Liam; Belatreche, Ammar; Glackin, Brendan

    2008-11-01

    In order to plan accurate motor actions, the brain needs to build an integrated spatial representation associated with visual stimuli and haptic stimuli. Since visual stimuli are represented in retina-centered co-ordinates and haptic stimuli are represented in body-centered co-ordinates, co-ordinate transformations must occur between the retina-centered co-ordinates and body-centered co-ordinates. A spiking neural network (SNN) model, which is trained with spike-timing-dependent-plasticity (STDP), is proposed to perform a 2D co-ordinate transformation of the polar representation of an arm position to a Cartesian representation, to create a virtual image map of a haptic input. Through the visual pathway, a position signal corresponding to the haptic input is used to train the SNN with STDP synapses such that after learning the SNN can perform the co-ordinate transformation to generate a representation of the haptic input with the same co-ordinates as a visual image. The model can be applied to explain co-ordinate transformation in spiking neuron based systems. The principle can be used in artificial intelligent systems to process complex co-ordinate transformations represented by biological stimuli.

  4. Some improvements in the discrete ordinate method of B.G. Carlson for solving the neutron transport equation

    Energy Technology Data Exchange (ETDEWEB)

    Askew, J R; Brissenden, R J [Technical Assessments and Services Division, Atomic Energy Establishment, Winfrith, Dorchester, Dorset (United Kingdom)

    1963-08-15

    This report gives an account of the DSN method for simulating neutron transport, together with methods of solution developed to deal with problems in the physics of thermal reactors, for which previously available computer programmes were unsatisfactory. The methods described are those incorporated in the programmes WINFRITH DSN written in FORTRAN language for the IBM 7090 and STRETCH computers. (author)

  5. Ordinance on the Implementation of Atomic Safety and Radiation Protection

    International Nuclear Information System (INIS)

    1984-01-01

    In execution of the new Atomic Energy Act the Ordinance on the Implementation of Atomic Safety and Radiation Protection was put into force on 1 February 1985. It takes into account all forms of peaceful nuclear energy and ionizing radiation uses in nuclear installations, irradiation facilities and devices in research, industries, and health services, and in radioactive isotope production and laboratories. It covers all aspects of safety and protection and defines atomic safety as nuclear safety and nuclear safeguards and physical protection of nuclear materials and facilities, whereas radiation protection includes the total of requirements, measures, means and methods necessary to protect man and the environment from the detrimental effects of ionizing radiation. It has been based on ICRP Recommendation No. 26 and the IAEA's Basic Safety Standards and supersedes the Radiation Protection Ordinance of 1969

  6. Space discretization in SN methods: Features, improvements and convergence patterns

    International Nuclear Information System (INIS)

    Coppa, G.G.M.; Lapenta, G.; Ravetto, P.

    1990-01-01

    A comparative analysis of the space discretization schemes currently used in S N methods is performed and special attention is devoted to direct integration techniques. Some improvements are proposed in one- and two-dimensional applications, which are based on suitable choices for the spatial variation of the collision source. A study of the convergence pattern is carried out for eigenvalue calculations within the space asymptotic approximation by means of both analytical and numerical investigations. (orig.) [de

  7. Space in Numerical and Ordinal Information: A Common Construct?

    Directory of Open Access Journals (Sweden)

    Philipp Alexander Schroeder

    2017-12-01

    Full Text Available Space is markedly involved in numerical processing, both explicitly in instrumental learning and implicitly in mental operations on numbers. Besides action decisions, action generations, and attention, the response-related effect of numerical magnitude or ordinality on space is well documented in the Spatial-Numerical Associations of Response Codes (SNARC effect. Here, right- over left-hand responses become relatively faster with increasing magnitude positions. However, SNARC-like behavioral signatures in non-numerical tasks with ordinal information were also observed and inspired new models integrating seemingly spatial effects of ordinal and numerical metrics. To examine this issue further, we report a comparison between numerical SNARC and ordinal SNARC-like effects to investigate group-level characteristics and individual-level deductions from generalized views, i.e., convergent validity. Participants solved order-relevant (before/after classification and order-irrelevant tasks (font color classification with numerical stimuli 1-5, comprising both magnitude and order information, and with weekday stimuli, comprising only ordinal information. A small correlation between magnitude- and order-related SNARCs was observed, but effects are not pronounced in order-irrelevant color judgments. On the group level, order-relevant spatial-numerical associations were best accounted for by a linear magnitude predictor, whereas the SNARC effect for weekdays was categorical. Limited by the representativeness of these tasks and analyses, results are inconsistent with a single amodal cognitive mechanism that activates space in mental processing of cardinal and ordinal information alike. A possible resolution to maintain a generalized view is proposed by discriminating different spatial activations, possibly mediated by visuospatial and verbal working memory, and by relating results to findings from embodied numerical cognition.

  8. Multi-dimensional, fully-implicit, spectral method for the Vlasov-Maxwell equations with exact conservation laws in discrete form

    Science.gov (United States)

    Delzanno, G. L.

    2015-11-01

    A spectral method for the numerical solution of the multi-dimensional Vlasov-Maxwell equations is presented. The plasma distribution function is expanded in Fourier (for the spatial part) and Hermite (for the velocity part) basis functions, leading to a truncated system of ordinary differential equations for the expansion coefficients (moments) that is discretized with an implicit, second order accurate Crank-Nicolson time discretization. The discrete non-linear system is solved with a preconditioned Jacobian-Free Newton-Krylov method. It is shown analytically that the Fourier-Hermite method features exact conservation laws for total mass, momentum and energy in discrete form. Standard tests involving plasma waves and the whistler instability confirm the validity of the conservation laws numerically. The whistler instability test also shows that we can step over the fastest time scale in the system without incurring in numerical instabilities. Some preconditioning strategies are presented, showing that the number of linear iterations of the Krylov solver can be drastically reduced and a significant gain in performance can be obtained.

  9. Finite Discrete Gabor Analysis

    DEFF Research Database (Denmark)

    Søndergaard, Peter Lempel

    2007-01-01

    frequency bands at certain times. Gabor theory can be formulated for both functions on the real line and for discrete signals of finite length. The two theories are largely the same because many aspects come from the same underlying theory of locally compact Abelian groups. The two types of Gabor systems...... can also be related by sampling and periodization. This thesis extends on this theory by showing new results for window construction. It also provides a discussion of the problems associated to discrete Gabor bases. The sampling and periodization connection is handy because it allows Gabor systems...... on the real line to be well approximated by finite and discrete Gabor frames. This method of approximation is especially attractive because efficient numerical methods exists for doing computations with finite, discrete Gabor systems. This thesis presents new algorithms for the efficient computation of finite...

  10. Metal selective co-ordinative self-assembly of π-donors

    Indian Academy of Sciences (India)

    Metal selective co-ordinative nanostructures were constructed by the supramolecular ... observed an anomalous binding of metal ion to the core sulphur groups causing redox changes in the TTF ... attention on metal-assisted co-ordinative self-assembly ..... M TTF-Py in 1:1 CHCl3: MeCN and (c) photographs showing visual.

  11. Comparative study of the discrete velocity and lattice Boltzmann methods for rarefied gas flows through irregular channels.

    Science.gov (United States)

    Su, Wei; Lindsay, Scott; Liu, Haihu; Wu, Lei

    2017-08-01

    Rooted from the gas kinetics, the lattice Boltzmann method (LBM) is a powerful tool in modeling hydrodynamics. In the past decade, it has been extended to simulate rarefied gas flows beyond the Navier-Stokes level, either by using the high-order Gauss-Hermite quadrature, or by introducing the relaxation time that is a function of the gas-wall distance. While the former method, with a limited number of discrete velocities (e.g., D2Q36), is accurate up to the early transition flow regime, the latter method (especially the multiple relaxation time (MRT) LBM), with the same discrete velocities as those used in simulating hydrodynamics (i.e., D2Q9), is accurate up to the free-molecular flow regime in the planar Poiseuille flow. This is quite astonishing in the sense that less discrete velocities are more accurate. In this paper, by solving the Bhatnagar-Gross-Krook kinetic equation accurately via the discrete velocity method, we find that the high-order Gauss-Hermite quadrature cannot describe the large variation in the velocity distribution function when the rarefaction effect is strong, but the MRT-LBM can capture the flow velocity well because it is equivalent to solving the Navier-Stokes equations with an effective shear viscosity. Since the MRT-LBM has only been validated in simple channel flows, and for complex geometries it is difficult to find the effective viscosity, it is necessary to assess its performance for the simulation of rarefied gas flows. Our numerical simulations based on the accurate discrete velocity method suggest that the accuracy of the MRT-LBM is reduced significantly in the simulation of rarefied gas flows through the rough surface and porous media. Our simulation results could serve as benchmarking cases for future development of the LBM for modeling and simulation of rarefied gas flows in complex geometries.

  12. Comparative study of the discrete velocity and lattice Boltzmann methods for rarefied gas flows through irregular channels

    Science.gov (United States)

    Su, Wei; Lindsay, Scott; Liu, Haihu; Wu, Lei

    2017-08-01

    Rooted from the gas kinetics, the lattice Boltzmann method (LBM) is a powerful tool in modeling hydrodynamics. In the past decade, it has been extended to simulate rarefied gas flows beyond the Navier-Stokes level, either by using the high-order Gauss-Hermite quadrature, or by introducing the relaxation time that is a function of the gas-wall distance. While the former method, with a limited number of discrete velocities (e.g., D2Q36), is accurate up to the early transition flow regime, the latter method (especially the multiple relaxation time (MRT) LBM), with the same discrete velocities as those used in simulating hydrodynamics (i.e., D2Q9), is accurate up to the free-molecular flow regime in the planar Poiseuille flow. This is quite astonishing in the sense that less discrete velocities are more accurate. In this paper, by solving the Bhatnagar-Gross-Krook kinetic equation accurately via the discrete velocity method, we find that the high-order Gauss-Hermite quadrature cannot describe the large variation in the velocity distribution function when the rarefaction effect is strong, but the MRT-LBM can capture the flow velocity well because it is equivalent to solving the Navier-Stokes equations with an effective shear viscosity. Since the MRT-LBM has only been validated in simple channel flows, and for complex geometries it is difficult to find the effective viscosity, it is necessary to assess its performance for the simulation of rarefied gas flows. Our numerical simulations based on the accurate discrete velocity method suggest that the accuracy of the MRT-LBM is reduced significantly in the simulation of rarefied gas flows through the rough surface and porous media. Our simulation results could serve as benchmarking cases for future development of the LBM for modeling and simulation of rarefied gas flows in complex geometries.

  13. 40 CFR 35.935-16 - Sewer use ordinance and evaluation/rehabilitation program.

    Science.gov (United States)

    2010-07-01

    ... 40 Protection of Environment 1 2010-07-01 2010-07-01 false Sewer use ordinance and evaluation...-Clean Water Act § 35.935-16 Sewer use ordinance and evaluation/rehabilitation program. (a) The grantee... sewer use ordinance, and the grantee is complying with the sewer system evaluation and rehabilitation...

  14. Optimized waveform relaxation domain decomposition method for discrete finite volume non stationary convection diffusion equation

    International Nuclear Information System (INIS)

    Berthe, P.M.

    2013-01-01

    In the context of nuclear waste repositories, we consider the numerical discretization of the non stationary convection diffusion equation. Discontinuous physical parameters and heterogeneous space and time scales lead us to use different space and time discretizations in different parts of the domain. In this work, we choose the discrete duality finite volume (DDFV) scheme and the discontinuous Galerkin scheme in time, coupled by an optimized Schwarz waveform relaxation (OSWR) domain decomposition method, because this allows the use of non-conforming space-time meshes. The main difficulty lies in finding an upwind discretization of the convective flux which remains local to a sub-domain and such that the multi domain scheme is equivalent to the mono domain one. These difficulties are first dealt with in the one-dimensional context, where different discretizations are studied. The chosen scheme introduces a hybrid unknown on the cell interfaces. The idea of up winding with respect to this hybrid unknown is extended to the DDFV scheme in the two-dimensional setting. The well-posedness of the scheme and of an equivalent multi domain scheme is shown. The latter is solved by an OSWR algorithm, the convergence of which is proved. The optimized parameters in the Robin transmission conditions are obtained by studying the continuous or discrete convergence rates. Several test-cases, one of which inspired by nuclear waste repositories, illustrate these results. (author) [fr

  15. Applications of the discrete element method in mechanical engineering

    International Nuclear Information System (INIS)

    Fleissner, Florian; Gaugele, Timo; Eberhard, Peter

    2007-01-01

    Compared to other fields of engineering, in mechanical engineering, the Discrete Element Method (DEM) is not yet a well known method. Nevertheless, there is a variety of simulation problems where the method has obvious advantages due to its meshless nature. For problems where several free bodies can collide and break after having been largely deformed, the DEM is the method of choice. Neighborhood search and collision detection between bodies as well as the separation of large solids into smaller particles are naturally incorporated in the method. The main DEM algorithm consists of a relatively simple loop that basically contains the three substeps contact detection, force computation and integration. However, there exists a large variety of different algorithms to choose the substeps to compose the optimal method for a given problem. In this contribution, we describe the dynamics of particle systems together with appropriate numerical integration schemes and give an overview over different types of particle interactions that can be composed to adapt the method to fit to a given simulation problem. Surface triangulations are used to model complicated, non-convex bodies in contact with particle systems. The capabilities of the method are finally demonstrated by means of application examples

  16. A Semi-Discrete Landweber-Kaczmarz Method for Cone Beam Tomography and Laminography Exploiting Geometric Prior Information

    Science.gov (United States)

    Vogelgesang, Jonas; Schorr, Christian

    2016-12-01

    We present a semi-discrete Landweber-Kaczmarz method for solving linear ill-posed problems and its application to Cone Beam tomography and laminography. Using a basis function-type discretization in the image domain, we derive a semi-discrete model of the underlying scanning system. Based on this model, the proposed method provides an approximate solution of the reconstruction problem, i.e. reconstructing the density function of a given object from its projections, in suitable subspaces equipped with basis function-dependent weights. This approach intuitively allows the incorporation of additional information about the inspected object leading to a more accurate model of the X-rays through the object. Also, physical conditions of the scanning geometry, like flat detectors in computerized tomography as used in non-destructive testing applications as well as non-regular scanning curves e.g. appearing in computed laminography (CL) applications, are directly taken into account during the modeling process. Finally, numerical experiments of a typical CL application in three dimensions are provided to verify the proposed method. The introduction of geometric prior information leads to a significantly increased image quality and superior reconstructions compared to standard iterative methods.

  17. Guidelines for the implementation of the X-ray Ordinance (RoeV). Vol. 2. Recommendations concerning data acquisition and archivation pursuant to paragraph 28 of the X-ray Ordinance passed by the Laender Committee for the X-ray Ordinance, 26/27 January 1989

    International Nuclear Information System (INIS)

    1990-01-01

    The recommendations apply to biomedical radiography and X-ray therapy. They refer to: 1) Patients' personal data as required according to Paragraph 28, sub-sec. 1, X-ray Ordinance. 2) Scope of data to be recorded acc. to Paragraph 28, sub-sec. 2, X-ray Ordinance. 3) Archivation of data acc. to Paragraph 28, sub-sec., 4 + 5, X-ray Ordinance. 4) Passing on of data acc. to Paragraph 28, sub-sec. 6, X-ray Ordinance. 5) Archivation of technical standard data (X-ray equipment specification records). The recommendations' main aim is to provide for radiological protection of the patient and for data showing the radiation doses received by patients. (HP) [de

  18. Few-Group Transport Analysis of the Core-Reflector Problem in Fast Reactor Cores via Equivalent Group Condensation and Local/Global Iteration

    International Nuclear Information System (INIS)

    Won, Jong Hyuck; Cho, Nam Zin

    2011-01-01

    In deterministic neutron transport methods, a process called fine-group to few-group condensation is used to reduce the computational burden. However, recent results on the core-reflector problem in fast reactor cores show that use of a small number of energy groups has limitation to describe neutron flux around core reflector interface. Therefore, researches are still ongoing to overcome this limitation. Recently, the authors proposed I) direct application of equivalently condensed angle-dependent total cross section to discrete ordinates method to overcome the limitation of conventional multi-group approximations, and II) local/global iteration framework in which fine-group discrete ordinates calculation is used in local problems while few-group transport calculation is used in the global problem iteratively. In this paper, an analysis of the core-reflector problem is performed in few-group structure using equivalent angle-dependent total cross section with local/global iteration. Numerical results are obtained under S 12 discrete ordinates-like transport method with scattering cross section up to P1 Legendre expansion

  19. Novel Discrete Element Method for 3D non-spherical granular particles.

    Science.gov (United States)

    Seelen, Luuk; Padding, Johan; Kuipers, Hans

    2015-11-01

    Granular materials are common in many industries and nature. The different properties from solid behavior to fluid like behavior are well known but less well understood. The main aim of our work is to develop a discrete element method (DEM) to simulate non-spherical granular particles. The non-spherical shape of particles is important, as it controls the behavior of the granular materials in many situations, such as static systems of packed particles. In such systems the packing fraction is determined by the particle shape. We developed a novel 3D discrete element method that simulates the particle-particle interactions for a wide variety of shapes. The model can simulate quadratic shapes such as spheres, ellipsoids, cylinders. More importantly, any convex polyhedron can be used as a granular particle shape. These polyhedrons are very well suited to represent non-rounded sand particles. The main difficulty of any non-spherical DEM is the determination of particle-particle overlap. Our model uses two iterative geometric algorithms to determine the overlap. The algorithms are robust and can also determine multiple contact points which can occur for these shapes. With this method we are able to study different applications such as the discharging of a hopper or silo. Another application the creation of a random close packing, to determine the solid volume fraction as a function of the particle shape.

  20. Dimension Reduction and Discretization in Stochastic Problems by Regression Method

    DEFF Research Database (Denmark)

    Ditlevsen, Ove Dalager

    1996-01-01

    The chapter mainly deals with dimension reduction and field discretizations based directly on the concept of linear regression. Several examples of interesting applications in stochastic mechanics are also given.Keywords: Random fields discretization, Linear regression, Stochastic interpolation, ...

  1. Discrete differential geometry. Consistency as integrability

    OpenAIRE

    Bobenko, Alexander I.; Suris, Yuri B.

    2005-01-01

    A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete geometry studies geometric shapes with finite number of elements (such as polyhedra), the discrete differential geometry aims at the development of discrete equivalents of notions and methods of smooth surface theory. Current interest in this field derives not ...

  2. A low noise discrete velocity method for the Boltzmann equation with quantized rotational and vibrational energy

    Science.gov (United States)

    Clarke, Peter; Varghese, Philip; Goldstein, David

    2018-01-01

    A discrete velocity method is developed for gas mixtures of diatomic molecules with both rotational and vibrational energy states. A full quantized model is described, and rotation-translation and vibration-translation energy exchanges are simulated using a Larsen-Borgnakke exchange model. Elastic and inelastic molecular interactions are modeled during every simulated collision to help produce smooth internal energy distributions. The method is verified by comparing simulations of homogeneous relaxation by our discrete velocity method to numerical solutions of the Jeans and Landau-Teller equations, and to direct simulation Monte Carlo. We compute the structure of a 1D shock using this method, and determine how the rotational energy distribution varies with spatial location in the shock and with position in velocity space.

  3. Rapid instrumental and separation methods for monitoring radionuclides in food and environmental samples. Final report on an IAEA co-ordinated research programme

    International Nuclear Information System (INIS)

    1995-01-01

    The Co-ordinated Research Programme (CRP) on Rapid Instrumental and Separation Methods for Monitoring Radionuclides in Food and Environmental Samples was established by the Agency following a Consultants' Meeting on the same topic, which was held 5-9 September 1988 in Vienna. It was completed in 1992. At various times during its course it encompassed 15 participants from 14 countries. The scope of work and objectives of the CRP were established at the Consultants' Meeting. It was agreed that the CRP should focus on the development of rapid methods for the determination of radionuclides in food and environmental samples during the intermediate and late post-accident phases. The rapid methods developed during the course of the CRP were intended to permit a timely and accurate determination of radionuclides at concentrations at least one order of magnitude below those specified for Derived Intervention Levels (DILs) for food by the WHO/FAO and the IAEA. Research Co-ordination meetings were held in Warsaw, Poland in September 1989 and in Vienna, Austria in 1991. Reports of the meetings are available from the Agency on Request. This document comprises copies of final reports from the participants and selected contributions presented by the participants at the meetings. The contributions were selected on the basis of being able to stand alone, without further explanation. Where there was an overlap in the information presented by a participant at both meetings, the most complete contribution was selected

  4. Rapid instrumental and separation methods for monitoring radionuclides in food and environmental samples. Final report on an IAEA co-ordinated research programme

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    1995-07-01

    The Co-ordinated Research Programme (CRP) on Rapid Instrumental and Separation Methods for Monitoring Radionuclides in Food and Environmental Samples was established by the Agency following a Consultants' Meeting on the same topic, which was held 5-9 September 1988 in Vienna. It was completed in 1992. At various times during its course it encompassed 15 participants from 14 countries. The scope of work and objectives of the CRP were established at the Consultants' Meeting. It was agreed that the CRP should focus on the development of rapid methods for the determination of radionuclides in food and environmental samples during the intermediate and late post-accident phases. The rapid methods developed during the course of the CRP were intended to permit a timely and accurate determination of radionuclides at concentrations at least one order of magnitude below those specified for Derived Intervention Levels (DILs) for food by the WHO/FAO and the IAEA. Research Co-ordination meetings were held in Warsaw, Poland in September 1989 and in Vienna, Austria in 1991. Reports of the meetings are available from the Agency on Request. This document comprises copies of final reports from the participants and selected contributions presented by the participants at the meetings. The contributions were selected on the basis of being able to stand alone, without further explanation. Where there was an overlap in the information presented by a participant at both meetings, the most complete contribution was selected.

  5. Solving Hammerstein Type Integral Equation by New Discrete Adomian Decomposition Methods

    Directory of Open Access Journals (Sweden)

    Huda O. Bakodah

    2013-01-01

    Full Text Available New discrete Adomian decomposition methods are presented by using some identified Clenshaw-Curtis quadrature rules. We investigate two mixed quadrature rules one of precision five and the other of precision seven. The first rule is formed by using the Fejér second rule of precision three and Simpson rule of precision three, while the second rule is formed by using the Fejér second rule of precision five and the Boole rule of precision five. Our methods were applied to a nonlinear integral equation of the Hammerstein type and some examples are given to illustrate the validity of our methods.

  6. Inferring network structure in non-normal and mixed discrete-continuous genomic data.

    Science.gov (United States)

    Bhadra, Anindya; Rao, Arvind; Baladandayuthapani, Veerabhadran

    2018-03-01

    Inferring dependence structure through undirected graphs is crucial for uncovering the major modes of multivariate interaction among high-dimensional genomic markers that are potentially associated with cancer. Traditionally, conditional independence has been studied using sparse Gaussian graphical models for continuous data and sparse Ising models for discrete data. However, there are two clear situations when these approaches are inadequate. The first occurs when the data are continuous but display non-normal marginal behavior such as heavy tails or skewness, rendering an assumption of normality inappropriate. The second occurs when a part of the data is ordinal or discrete (e.g., presence or absence of a mutation) and the other part is continuous (e.g., expression levels of genes or proteins). In this case, the existing Bayesian approaches typically employ a latent variable framework for the discrete part that precludes inferring conditional independence among the data that are actually observed. The current article overcomes these two challenges in a unified framework using Gaussian scale mixtures. Our framework is able to handle continuous data that are not normal and data that are of mixed continuous and discrete nature, while still being able to infer a sparse conditional sign independence structure among the observed data. Extensive performance comparison in simulations with alternative techniques and an analysis of a real cancer genomics data set demonstrate the effectiveness of the proposed approach. © 2017, The International Biometric Society.

  7. Matrix formulations of radiative transfer including the polarization effect in a coupled atmosphere-ocean system

    International Nuclear Information System (INIS)

    Ota, Yoshifumi; Higurashi, Akiko; Nakajima, Teruyuki; Yokota, Tatsuya

    2010-01-01

    A vector radiative transfer model has been developed for a coupled atmosphere-ocean system. The radiative transfer scheme is based on the discrete ordinate and matrix operator methods. The reflection/transmission matrices and source vectors are obtained for each atmospheric or oceanic layer through the discrete ordinate solution. The vertically inhomogeneous system is constructed using the matrix operator method, which combines the radiative interaction between the layers. This radiative transfer scheme is flexible for a vertically inhomogeneous system including the oceanic layers as well as the ocean surface. Compared with the benchmark results, the computational error attributable to the radiative transfer scheme has been less than 0.1% in the case of eight discrete ordinate directions. Furthermore, increasing the number of discrete ordinate directions has produced computations with higher accuracy. Based on our radiative transfer scheme, simulations of sun glint radiation have been presented for wavelengths of 670 nm and 1.6 μm. Results of simulations have shown reasonable characteristics of the sun glint radiation such as the strongly peaked, but slightly smoothed radiation by the rough ocean surface and depolarization through multiple scattering by the aerosol-loaded atmosphere. The radiative transfer scheme of this paper has been implemented to the numerical model named Pstar as one of the OpenCLASTR/STAR radiative transfer code systems, which are widely applied to many radiative transfer problems, including the polarization effect.

  8. A discrete fibre dispersion method for excluding fibres under compression in the modelling of fibrous tissues.

    Science.gov (United States)

    Li, Kewei; Ogden, Ray W; Holzapfel, Gerhard A

    2018-01-01

    Recently, micro-sphere-based methods derived from the angular integration approach have been used for excluding fibres under compression in the modelling of soft biological tissues. However, recent studies have revealed that many of the widely used numerical integration schemes over the unit sphere are inaccurate for large deformation problems even without excluding fibres under compression. Thus, in this study, we propose a discrete fibre dispersion model based on a systematic method for discretizing a unit hemisphere into a finite number of elementary areas, such as spherical triangles. Over each elementary area, we define a representative fibre direction and a discrete fibre density. Then, the strain energy of all the fibres distributed over each elementary area is approximated based on the deformation of the representative fibre direction weighted by the corresponding discrete fibre density. A summation of fibre contributions over all elementary areas then yields the resultant fibre strain energy. This treatment allows us to exclude fibres under compression in a discrete manner by evaluating the tension-compression status of the representative fibre directions only. We have implemented this model in a finite-element programme and illustrate it with three representative examples, including simple tension and simple shear of a unit cube, and non-homogeneous uniaxial extension of a rectangular strip. The results of all three examples are consistent and accurate compared with the previously developed continuous fibre dispersion model, and that is achieved with a substantial reduction of computational cost. © 2018 The Author(s).

  9. Co-ordination of heterovalent cation impurities in molten salts

    International Nuclear Information System (INIS)

    Andreoni, W.; Rovere, M.; Tosi, M.P.

    1982-01-01

    The local liquid structure around heterovalent cation impurities in molten chlorides is discussed in relation to spectroscopic data on solutions of transition metal ions. A tightly packed, low co-ordination shell is shown to be favoured by Coulomb ionic interactions for physically reasonable values of the size of the impurity. A competition between these forces and ''crystal field'' interactions favouring octahedral co-ordination is thus to be expected for many transition metal ions, as suggested by Gruen and McBeth. The transition observed for some transition metal ions from higher to lower co-ordination with increasing temperature is attributed primarily to entropy differences, that are roughly estimated in a solid-like model. (author)

  10. Transformation Matrix for Time Discretization Based on Tustin’s Method

    Directory of Open Access Journals (Sweden)

    Yiming Jiang

    2014-01-01

    Full Text Available This paper studies rules in transformation of transfer function through time discretization. A method of using transformation matrix to realize bilinear transform (also known as Tustin’s method is presented. This method can be described as the conversion between the coefficients of transfer functions, which are expressed as transform by certain matrix. For a polynomial of degree n, the corresponding transformation matrix of order n exists and is unique. Furthermore, the transformation matrix can be decomposed into an upper triangular matrix multiplied with another lower triangular matrix. And both have obvious regularity. The proposed method can achieve rapid bilinear transform used in automatic design of digital filter. The result of numerical simulation verifies the correctness of the theoretical results. Moreover, it also can be extended to other similar problems. Example in the last throws light on this point.

  11. Flows about a rotating circular cylinder by the discrete-vortex method

    Science.gov (United States)

    Kimura, Takeyoshi; Tsutahara, Michihisa

    1987-01-01

    A numerical study has been conducted for flows past a rotating circular cylinder at high Reynolds numbers, using the discrete-vortex method. It is noted that the reverse Magnus effect is caused by the retreat of the separation point on the acceleration side. At high rotating speed, the nascent vortices of opposite directions are mixed faster, the wake becomes narrower, and predominating frequencies in the lift force disappear.

  12. Space-Time Discrete KPZ Equation

    Science.gov (United States)

    Cannizzaro, G.; Matetski, K.

    2018-03-01

    We study a general family of space-time discretizations of the KPZ equation and show that they converge to its solution. The approach we follow makes use of basic elements of the theory of regularity structures (Hairer in Invent Math 198(2):269-504, 2014) as well as its discrete counterpart (Hairer and Matetski in Discretizations of rough stochastic PDEs, 2015. arXiv:1511.06937). Since the discretization is in both space and time and we allow non-standard discretization for the product, the methods mentioned above have to be suitably modified in order to accommodate the structure of the models under study.

  13. Optimizing the maximum reported cluster size in the spatial scan statistic for ordinal data.

    Science.gov (United States)

    Kim, Sehwi; Jung, Inkyung

    2017-01-01

    The spatial scan statistic is an important tool for spatial cluster detection. There have been numerous studies on scanning window shapes. However, little research has been done on the maximum scanning window size or maximum reported cluster size. Recently, Han et al. proposed to use the Gini coefficient to optimize the maximum reported cluster size. However, the method has been developed and evaluated only for the Poisson model. We adopt the Gini coefficient to be applicable to the spatial scan statistic for ordinal data to determine the optimal maximum reported cluster size. Through a simulation study and application to a real data example, we evaluate the performance of the proposed approach. With some sophisticated modification, the Gini coefficient can be effectively employed for the ordinal model. The Gini coefficient most often picked the optimal maximum reported cluster sizes that were the same as or smaller than the true cluster sizes with very high accuracy. It seems that we can obtain a more refined collection of clusters by using the Gini coefficient. The Gini coefficient developed specifically for the ordinal model can be useful for optimizing the maximum reported cluster size for ordinal data and helpful for properly and informatively discovering cluster patterns.

  14. An improved Lobatto discrete variable representation by a phase optimisation and variable mapping method

    International Nuclear Information System (INIS)

    Yu, Dequan; Cong, Shu-Lin; Sun, Zhigang

    2015-01-01

    Highlights: • An optimised finite element discrete variable representation method is proposed. • The method is tested by solving one and two dimensional Schrödinger equations. • The method is quite efficient in solving the molecular Schrödinger equation. • It is very easy to generalise the method to multidimensional problems. - Abstract: The Lobatto discrete variable representation (LDVR) proposed by Manoloupolos and Wyatt (1988) has unique features but has not been generally applied in the field of chemical dynamics. Instead, it has popular application in solving atomic physics problems, in combining with the finite element method (FE-DVR), due to its inherent abilities for treating the Coulomb singularity in spherical coordinates. In this work, an efficient phase optimisation and variable mapping procedure is proposed to improve the grid efficiency of the LDVR/FE-DVR method, which makes it not only be competing with the popular DVR methods, such as the Sinc-DVR, but also keep its advantages for treating with the Coulomb singularity. The method is illustrated by calculations for one-dimensional Coulomb potential, and the vibrational states of one-dimensional Morse potential, two-dimensional Morse potential and two-dimensional Henon–Heiles potential, which prove the efficiency of the proposed scheme and promise more general applications of the LDVR/FE-DVR method

  15. An improved Lobatto discrete variable representation by a phase optimisation and variable mapping method

    Energy Technology Data Exchange (ETDEWEB)

    Yu, Dequan [School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024 (China); State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Science, Dalian 116023 (China); Cong, Shu-Lin, E-mail: shlcong@dlut.edu.cn [School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024 (China); Sun, Zhigang, E-mail: zsun@dicp.ac.cn [State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Science, Dalian 116023 (China); Center for Advanced Chemical Physics and 2011 Frontier Center for Quantum Science and Technology, University of Science and Technology of China, 96 Jinzhai Road, Hefei 230026 (China)

    2015-09-08

    Highlights: • An optimised finite element discrete variable representation method is proposed. • The method is tested by solving one and two dimensional Schrödinger equations. • The method is quite efficient in solving the molecular Schrödinger equation. • It is very easy to generalise the method to multidimensional problems. - Abstract: The Lobatto discrete variable representation (LDVR) proposed by Manoloupolos and Wyatt (1988) has unique features but has not been generally applied in the field of chemical dynamics. Instead, it has popular application in solving atomic physics problems, in combining with the finite element method (FE-DVR), due to its inherent abilities for treating the Coulomb singularity in spherical coordinates. In this work, an efficient phase optimisation and variable mapping procedure is proposed to improve the grid efficiency of the LDVR/FE-DVR method, which makes it not only be competing with the popular DVR methods, such as the Sinc-DVR, but also keep its advantages for treating with the Coulomb singularity. The method is illustrated by calculations for one-dimensional Coulomb potential, and the vibrational states of one-dimensional Morse potential, two-dimensional Morse potential and two-dimensional Henon–Heiles potential, which prove the efficiency of the proposed scheme and promise more general applications of the LDVR/FE-DVR method.

  16. Analysis of a HP-refinement method for solving the neutron transport equation using two error estimators

    International Nuclear Information System (INIS)

    Fournier, D.; Le Tellier, R.; Suteau, C.; Herbin, R.

    2011-01-01

    The solution of the time-independent neutron transport equation in a deterministic way invariably consists in the successive discretization of the three variables: energy, angle and space. In the SNATCH solver used in this study, the energy and the angle are respectively discretized with a multigroup approach and the discrete ordinate method. A set of spatial coupled transport equations is obtained and solved using the Discontinuous Galerkin Finite Element Method (DGFEM). Within this method, the spatial domain is decomposed into elements and the solution is approximated by a hierarchical polynomial basis in each one. This approach is time and memory consuming when the mesh becomes fine or the basis order high. To improve the computational time and the memory footprint, adaptive algorithms are proposed. These algorithms are based on an error estimation in each cell. If the error is important in a given region, the mesh has to be refined (h−refinement) or the polynomial basis order increased (p−refinement). This paper is related to the choice between the two types of refinement. Two ways to estimate the error are compared on different benchmarks. Analyzing the differences, a hp−refinement method is proposed and tested. (author)

  17. Application of the Arbitrarily High Order Method to Coupled Electron Photon Transport

    International Nuclear Information System (INIS)

    Duo, Jose Ignacio

    2004-01-01

    This work is about the application of the Arbitrary High Order Nodal Method to coupled electron photon transport.A Discrete Ordinates code was enhanced and validated which permited to evaluate the advantages of using variable spatial development order per particle.The results obtained using variable spatial development and adaptive mesh refinement following an a posteriori error estimator are encouraging.Photon spectra for clinical accelerator target and, dose and charge depositio profiles are simulated in one-dimensional problems using cross section generated with CEPXS code.Our results are in good agreement with ONELD and MCNP codes

  18. In-plane material continuity for the discrete material optimization method

    DEFF Research Database (Denmark)

    Sørensen, Rene; Lund, Erik

    2015-01-01

    When performing discrete material optimization of laminated composite structures, the variation of the in-plane material continuity is typically governed by the size of the finite element discretization. For a fine mesh, this can lead to designs that cannot be manufactured due to the complexity...

  19. Retrieving quasi-phase-matching structure with discrete layer-peeling method

    DEFF Research Database (Denmark)

    Zhang, Q. W.; Zeng, Xianglong; Wang, M.

    2012-01-01

    An approach to reconstruct a quasi-phase-matching grating by using a discrete layer-peeling algorithm is presented. Experimentally measured output spectra of Solc-type filters, based on uniform and chirped QPM structures, are used in the discrete layer-peeling algorithm. The reconstructed QPM...

  20. Shielding calculations in support of the Spallation Neutron Source (SNS) proton beam transport system

    International Nuclear Information System (INIS)

    Johnson, Jeffrey O.; Gallmeier, Franz X.; Popova, Irina

    2002-01-01

    Determining the bulk shielding requirements for accelerator environments is generally an easy task compared to analyzing the radiation transport through the complex shield configurations and penetrations typically associated with the detailed Title II design efforts of a facility. Shielding calculations for penetrations in the SNS accelerator environment are presented based on hybrid Monte Carlo and discrete ordinates particle transport methods. This methodology relies on coupling tools that map boundary surface leakage information from the Monte Carlo calculations to boundary sources for one-, two-, and three-dimensional discrete ordinates calculations. The paper will briefly introduce the coupling tools for coupling MCNPX to the one-, two-, and three-dimensional discrete ordinates codes in the DOORS code suite. The paper will briefly present typical applications of these tools in the design of complex shield configurations and penetrations in the SNS proton beam transport system

  1. Ordinance on the Finnish Centre of Radiation and Nuclear Safety

    International Nuclear Information System (INIS)

    1990-01-01

    This Ordinance was adopted in implementation of the 1983 Act setting up the Finnish Centre for Radiation and Nuclear Safety and the 1987 Nuclear Energy Act and entered into force on 1 November 1990. The Ordinance specifies the tasks of the Centre, as provided under both Acts, and gives it several supplementary responsibilities. In addition to its overall competence in respect of radiation safety, the Centre will carry out research into and supervise the health effects of radiation and maintain a laboratory for national measurements in that field. The Ordinance also sets out the Centre's organisation chart and the staff duties [fr

  2. EPRI-LATTICE: a multigroup neutron transport code for light water reactor lattice physics calculations

    International Nuclear Information System (INIS)

    Jones, D.B.

    1986-01-01

    EPRI-LATTICE is a multigroup neutron transport computer code for the analysis of light water reactor fuel assemblies. It can solve the two-dimensional neutron transport problem by two distinct methods: (a) the method of collision probabilities and (b) the method of discrete ordinates. The code was developed by S. Levy Inc. as an account of work sponsored by the Electric Power Research Institute (EPRI). The collision probabilities calculation in EPRI-LATTICE (L-CP) is based on the same methodology that exists in the lattice codes CPM-2 and EPRI-CPM. Certain extensions have been made to the data representations of the CPM programs to improve the overall accuracy of the calculation. The important extensions include unique representations of scattering matrices and fission fractions (chi) for each composition in the problem. A new capability specifically developed for the EPRI-LATTICE code is a discrete ordinates methodology. The discrete ordinates calculation in EPRI-LATTICE (L-SN) is based on the discrete S/sub n/ methodology that exists in the TWODANT program. In contrast to TWODANT, which utilizes synthetic diffusion acceleration and supports multiple geometries, only the transport equations are solved by L-SN and only the data representations for the two-dimensional geometry are treated

  3. Co-ordination Action on Ocean Energy (CA-OE)

    DEFF Research Database (Denmark)

    Tedd, James; Frigaard, Peter

    In October 2004, the Co-ordination Action on Ocean Energy (CA-OE) was launched, co-financed by the European Commission, under the Renewable Energy Technologies priority within the 6th Framework programme, contract number 502701, chaired by Kim Nielsen, Rambøll, Denmark. The project involves 41...... partners. In general the public is not aware of the development of ocean energy and its exploitation. There is a need to make a united effort from the developers and research community to present the various principles and results in a coordinated manner with public appeal. The main objectives of the Co......-ordination Action on Ocean Energy are: To develop a common knowledge base necessary for coherent research and development policiesTo bring a co-ordinated approach within key areas of ocean energy research and development.To provide a forum for the longer term marketing of promising research developments...

  4. 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.

  5. Rite of Ordination of Fr Karol Wojtyła

    Directory of Open Access Journals (Sweden)

    Szymon Fedorowicz

    2014-06-01

    Full Text Available The article contains the source text of the Polish translation of the rite of ordination of a bishop prepared for the episcopal ordination of Fr. Karol Wojtyła by Franciszek Małaczyński OSB. The text was found in the archives of Jacek Fedorowicz and prepared for publication by his son Szymon Fedorowicz.

  6. Discrete gradients in discrete classical mechanics

    International Nuclear Information System (INIS)

    Renna, L.

    1987-01-01

    A simple model of discrete classical mechanics is given where, starting from the continuous Hamilton equations, discrete equations of motion are established together with a proper discrete gradient definition. The conservation laws of the total discrete momentum, angular momentum, and energy are demonstrated

  7. A 2D Electromechanical Model of Human Atrial Tissue Using the Discrete Element Method

    Directory of Open Access Journals (Sweden)

    Paul Brocklehurst

    2015-01-01

    Full Text Available Cardiac tissue is a syncytium of coupled cells with pronounced intrinsic discrete nature. Previous models of cardiac electromechanics often ignore such discrete properties and treat cardiac tissue as a continuous medium, which has fundamental limitations. In the present study, we introduce a 2D electromechanical model for human atrial tissue based on the discrete element method (DEM. In the model, single-cell dynamics are governed by strongly coupling the electrophysiological model of Courtemanche et al. to the myofilament model of Rice et al. with two-way feedbacks. Each cell is treated as a viscoelastic body, which is physically represented by a clump of nine particles. Cell aggregations are arranged so that the anisotropic nature of cardiac tissue due to fibre orientations can be modelled. Each cell is electrically coupled to neighbouring cells, allowing excitation waves to propagate through the tissue. Cell-to-cell mechanical interactions are modelled using a linear contact bond model in DEM. By coupling cardiac electrophysiology with mechanics via the intracellular Ca2+ concentration, the DEM model successfully simulates the conduction of cardiac electrical waves and the tissue’s corresponding mechanical contractions. The developed DEM model is numerically stable and provides a powerful method for studying the electromechanical coupling problem in the heart.

  8. Applied discrete-time queues

    CERN Document Server

    Alfa, Attahiru S

    2016-01-01

    This book introduces the theoretical fundamentals for modeling queues in discrete-time, and the basic procedures for developing queuing models in discrete-time. There is a focus on applications in modern telecommunication systems. It presents how most queueing models in discrete-time can be set up as discrete-time Markov chains. Techniques such as matrix-analytic methods (MAM) that can used to analyze the resulting Markov chains are included. This book covers single node systems, tandem system and queueing networks. It shows how queues with time-varying parameters can be analyzed, and illustrates numerical issues associated with computations for the discrete-time queueing systems. Optimal control of queues is also covered. Applied Discrete-Time Queues targets researchers, advanced-level students and analysts in the field of telecommunication networks. It is suitable as a reference book and can also be used as a secondary text book in computer engineering and computer science. Examples and exercises are includ...

  9. GGVS. Ordinance on road transport of hazardous materials, including the European agreement on international road transport of hazardous materials (ADR), in their wording. Annexes A and B. Ordinances regarding exceptions from GGVS and from the ordinance on rail transport of hazardous materials, GGVE. Reasons. Selected guidelines. List of materials. 6. rev. and enlarged ed.

    International Nuclear Information System (INIS)

    Ridder, K.

    1990-01-01

    The brochure contains the following texts: (1) Ordinance on road transport of hazardous materials (GGVS), including the European agreement on international road transport of hazardous materials (ADR), as of 1990: Skeleton ordinance, annexes A and B, reasons given for the first version, and for the first amendment in 1988, execution guidelines - RS 002 (guidelines for executing the ordinance on road transport of hazardous materials, with catalogue of penalties), guidelines for drawing up written instructions for the event of accidents - RS 006, guiding principles for the training of vehicle conductors; (2) ordinance regarding exceptions from the ordinance on road transport of hazardous materials; (3) ordinance regarding exceptions from the ordinance on rail transport of hazardous materials; (4) selected guidelines: Technical guidelines TR IBC K 001, TRS 003, TRS 004, TRS 005, TRS 006; (5) listing of materials and objects governed by the ordinance on hazardous materials transport; (6) catalogue of penalties relative to road transport of hazardous materials. (orig./HP) [de

  10. Time Discretization Techniques

    KAUST Repository

    Gottlieb, S.

    2016-10-12

    The time discretization of hyperbolic partial differential equations is typically the evolution of a system of ordinary differential equations obtained by spatial discretization of the original problem. Methods for this time evolution include multistep, multistage, or multiderivative methods, as well as a combination of these approaches. The time step constraint is mainly a result of the absolute stability requirement, as well as additional conditions that mimic physical properties of the solution, such as positivity or total variation stability. These conditions may be required for stability when the solution develops shocks or sharp gradients. This chapter contains a review of some of the methods historically used for the evolution of hyperbolic PDEs, as well as cutting edge methods that are now commonly used.

  11. An error estimate for Tremolieres method for the discretization of parabolic variational inequalities

    International Nuclear Information System (INIS)

    Uko, L.U.

    1990-02-01

    We study a scheme for the time-discretization of parabolic variational inequalities that is often easier to use than the classical method of Rothe. We show that if the data are compatible in a certain sense, then this scheme is of order ≥1/2. (author). 10 refs

  12. Thickness optimization of fiber reinforced laminated composites using the discrete material optimization method

    DEFF Research Database (Denmark)

    Sørensen, Søren Nørgaard; Lund, Erik

    2012-01-01

    This work concerns a novel large-scale multi-material topology optimization method for simultaneous determination of the optimum variable integer thickness and fiber orientation throughout laminate structures with fixed outer geometries while adhering to certain manufacturing constraints....... The conceptual combinatorial/integer problem is relaxed to a continuous problem and solved on basis of the so-called Discrete Material Optimization method, explicitly including the manufacturing constraints as linear constraints....

  13. Discrete Routh reduction

    International Nuclear Information System (INIS)

    Jalnapurkar, Sameer M; Leok, Melvin; Marsden, Jerrold E; West, Matthew

    2006-01-01

    This paper develops the theory of Abelian Routh reduction for discrete mechanical systems and applies it to the variational integration of mechanical systems with Abelian symmetry. The reduction of variational Runge-Kutta discretizations is considered, as well as the extent to which symmetry reduction and discretization commute. These reduced methods allow the direct simulation of dynamical features such as relative equilibria and relative periodic orbits that can be obscured or difficult to identify in the unreduced dynamics. The methods are demonstrated for the dynamics of an Earth orbiting satellite with a non-spherical J 2 correction, as well as the double spherical pendulum. The J 2 problem is interesting because in the unreduced picture, geometric phases inherent in the model and those due to numerical discretization can be hard to distinguish, but this issue does not appear in the reduced algorithm, where one can directly observe interesting dynamical structures in the reduced phase space (the cotangent bundle of shape space), in which the geometric phases have been removed. The main feature of the double spherical pendulum example is that it has a non-trivial magnetic term in its reduced symplectic form. Our method is still efficient as it can directly handle the essential non-canonical nature of the symplectic structure. In contrast, a traditional symplectic method for canonical systems could require repeated coordinate changes if one is evoking Darboux' theorem to transform the symplectic structure into canonical form, thereby incurring additional computational cost. Our method allows one to design reduced symplectic integrators in a natural way, despite the non-canonical nature of the symplectic structure

  14. Understanding advanced statistical methods

    CERN Document Server

    Westfall, Peter

    2013-01-01

    Introduction: Probability, Statistics, and ScienceReality, Nature, Science, and ModelsStatistical Processes: Nature, Design and Measurement, and DataModelsDeterministic ModelsVariabilityParametersPurely Probabilistic Statistical ModelsStatistical Models with Both Deterministic and Probabilistic ComponentsStatistical InferenceGood and Bad ModelsUses of Probability ModelsRandom Variables and Their Probability DistributionsIntroductionTypes of Random Variables: Nominal, Ordinal, and ContinuousDiscrete Probability Distribution FunctionsContinuous Probability Distribution FunctionsSome Calculus-Derivatives and Least SquaresMore Calculus-Integrals and Cumulative Distribution FunctionsProbability Calculation and SimulationIntroductionAnalytic Calculations, Discrete and Continuous CasesSimulation-Based ApproximationGenerating Random NumbersIdentifying DistributionsIntroductionIdentifying Distributions from Theory AloneUsing Data: Estimating Distributions via the HistogramQuantiles: Theoretical and Data-Based Estimate...

  15. On the integration scheme along a trajectory for the characteristics method

    International Nuclear Information System (INIS)

    Le Tellier, Romain; Hebert, Alain

    2006-01-01

    The issue of the integration scheme along a trajectory which appears for all tracking-based transport methods is discussed from the point of view of the method of characteristics. The analogy with the discrete ordinates method in slab geometry is highlighted along with the practical limitation in transposing high-order S N schemes to a trajectory-based method. We derived an example of such a transposition starting from the linear characteristic scheme. This new scheme is compared with the standard flat-source approximation of the step characteristic scheme and with the diamond differencing scheme. The numerical study covers a 1D analytical case, 2D one-group critical and fixed-source benchmarks and finally a realistic multigroup calculation on a BWR-MOX assembly

  16. Ordinance on distribution of iodine tablets to the population

    International Nuclear Information System (INIS)

    1992-01-01

    This Ordinance provides for the organization of supplies of iodine tablets to the population. The tablets will be held in case of occurrences that might endanger the population following an accident provoking the emission of radioactive iodine. The Federal Health Ministry is responsible for organizing the supply to the appropriate bodies for distribution to the population. The Ordinance entered into force on 1 August 1992. (NEA)

  17. Accident prevention ordinance 2.0 Thermal Power Plants

    International Nuclear Information System (INIS)

    Egyptien, H.H.; Fischermann, E.

    This accident prevention ordinance is to cover primarily the very section of a power station where fossil or nuclear energy is converted into thermal energy, e.g. by heating or vaporization of a heat source. In paragraph 1, 40 GJ/h are stipulated as the lower limit of capacity corresponding to about 11 MW. Therefore, the accident prevention ordinance does not only marshal the operation of steam generators in electricity supply utilities but also covers smaller industrial power stations which partly do only meet the company's own requirements. Pipes are only covered as far as they are operated in conjunction with a heat generator. The same applies to coal handling and ash removal facilities. This means that for heat release e.g. in the framework of a district heating grid, the transfer station to the distribution grid is regarded as being a border of the power station and thus a border to the area of application of the accident prevention ordinance. (orig./HP) [de

  18. In-plane Material Filters for the Discrete Material Optimization Method

    DEFF Research Database (Denmark)

    Sørensen, Rene; Lund, Erik

    2015-01-01

    , because the projection filter is a non-linear function of the design variables, the projected variables have to be re-scaled in a final so-called normalization filter. This is done to prevent the optimizer in creating superior, but non-physical pseudo-materials. The method is demonstrated on a series......This paper presents in-plane material filters for the Discrete Material Optimization method used for optimizing laminated composite structures. The filters make it possible for engineers to specify a minimum length scale which governs the minimum size of areas with constant material continuity....... Consequently, engineers can target the available production methods, and thereby increase its manufacturability while the optimizer is free to determine which material to apply together with an optimum location, shape, and size of these areas with constant material continuity. By doing so, engineers no longer...

  19. Positivity for Convective Semi-discretizations

    KAUST Repository

    Fekete, Imre; Ketcheson, David I.; Loczi, Lajos

    2017-01-01

    We propose a technique for investigating stability properties like positivity and forward invariance of an interval for method-of-lines discretizations, and apply the technique to study positivity preservation for a class of TVD semi-discretizations

  20. A Characterization of Ordinal Potential Games

    NARCIS (Netherlands)

    Voorneveld, M.; Norde, H.W.

    1996-01-01

    This note characterizes ordinal potential games by the absence of weak improvement cycles and an order condition on the strategy space.This order condition is automatically satisfied if the strategy space is countable.