A general formulation of the resonance spectrum expansion self-shielding method

ABSTRACT: The resonance spectrum expansion (RSE) self-shielding method was recently proposed by Nagoya and Osaka universities as a powerful alternative to existing approaches. First investigations of the RSE at Polytechnique Montreal show that it can effectively replace the actual subgroup method used for production calculations in DRAGON5. The Japanese implementation of the RSE method is limited to a solution of the Boltzmann transport equation (BTE) with the method of characteristics. We are proposing a new implementation of the RSE method compatible with various types of solutions for the BTE, including the collision probability and the interface current methods. We based our validation study on a subset made up of eight Rowlands pin cell benchmark cases. The absorption rates obtained after self-shielding are compared with exact values obtained using an elastic slowing-down calculation where each resonance is modeled individually in the resolved energy domain. Validation of Rowlands benchmark with effective multiplication factor calculations was also conducted with respect of the SERPENT2 Monte Carlo code. It is shown that the RSE method is compatible with both advanced and legacy energy meshes and performs slightly better than the production subgroup methods actually used

Application of the augmented block Householder Arnoldi method to the calculation of non-fundamental modes of the diffusion equation

The determination of non-fundamental modes of the diffusion equation is required for computing CANDU reactor power distribution from analysis of in-core detector readings. They are also important for understanding subcritical mode instabilities occurring in boiling water reactors. The legacy method for computing these modes is the Hotelling deflation technique based on bi-harmonic decontamination. However, the Hotelling technique becomes unstable as the number of modes increase or as their eigenvalues become closer. Effective and fast alternatives are provided with Implicit Arnoldi Restarted Methods (IRAM). Among them, we investigated the Krylov–Schur method available in the SLEPc library, and we are proposing a custom implementation of the augmented block Householder Arnoldi (ABHA) method, similar to the Open Source implementation of Prof. James Baglama. In our work, the ABHA method is applied to the neutron diffusion equation, discretized with the Raviart–Thomas and Raviart–Thomas-Schneider methods or with the mesh-centered finite difference method

Color calibration of an RGB camera mounted in front of a microscope with strong color distortion

International audienceThis paper aims at showing that performing color calibration of an RGB camera can be achieved even in the case where the optical system before the camera introduces strong color distortion. In the present case, the optical system is a microscope containing a halogen lamp, with a nonuniform irradiance on the viewed surface. The calibration method proposed in this work is based on an existing method, but it is preceded by a three-step preprocessing of the RGB images aiming at extracting relevant color information from the strongly distorted images, taking especially into account the nonuniform irradiance map and the perturbing texture due to the surface topology of the standard color calibration charts when observed at micrometric scale. The proposed color calibration process consists first in computing the average color of the color-chart patches viewed under the microscope; then computing white balance, gamma correction, and saturation enhancement; and finally applying a third-order polynomial regression color calibration transform. Despite the nonusual conditions for color calibration, fairly good performance is achieved from a 48 patch Lambertian color chart, since an average CIE-94 color difference on the color-chart colors lower than 2.5 units is obtained

A Krylov-Schur solution of the eigenvalue problem for the neutron diffusion equation discretized with the Raviart-Thomas method

[EN] Mixed-dual formulations of the finite element method were successfully applied to the neutron diffusion equation, such as the Raviart¿Thomas method in Cartesian geometry and the Raviart¿Thomas¿Schneider in hexagonal geometry. Both methods obtain system matrices which are suitable for solving the eigenvalue problem with the preconditioned power method. This method is very fast and optimized, but only for the calculation of the fundamental mode. However, the determination of non-fundamental modes is important for modal analysis, instabilities, and fluctuations of nuclear reactors. So, effective and fast methods are required for solving eigenvalue problems. The most effective methods are those based on Krylov subspaces projection combined with restart, such as Krylov¿Schur. In this work, a Krylov¿Schur method has been applied to the neutron diffusion equation, discretized with the Raviart¿Thomas and Raviart¿Thomas¿Schneider methods.This work has been partially supported by the Spanish Ministerio de Eduacion Cultura y Deporte [grant number FPU13/01009]; Spanish Ministerio de Ciencia e Innovacion [project number ENE2014-59442-P]; Spanish Ministerio de Economia y Competitividad and the European Fondo Europeo de Desarrollo Regional (FEDER) [project number ENE2015-68353-P (MINECO/FEDER)]; Generalitat Valenciana [project number PROMETEOII/2014/008]; Universitat Politecnica de Valencia [project number UPPTE/2012/118]; Spanish Ministerio de Economia y Competitividad [project number TIN2016-75985-P].Bernal-Garcia, A.; Hébert, A.; Roman, JE.; Miró Herrero, R.; Verdú Martín, GJ. (2017). A Krylov-Schur solution of the eigenvalue problem for the neutron diffusion equation discretized with the Raviart-Thomas method. Journal of Nuclear Science and Technology. 54(10):1085-1094. https://doi.org/10.1080/00223131.2017.1344577S108510945410Hébert, A. (1993). Application of a dual variational formulation to finite element reactor calculations. Annals of Nuclear Energy, 20(12), 823-845. doi:10.1016/0306-4549(93)90076-2Hébert, A. (2008). A Raviart–Thomas–Schneider solution of the diffusion equation in hexagonal geometry. Annals of Nuclear Energy, 35(3), 363-376. doi:10.1016/j.anucene.2007.07.016Hébert, A. (1986). Preconditioning the Power Method for Reactor Calculations. Nuclear Science and Engineering, 94(1), 1-11. doi:10.13182/nse86-a17111Verdú, G., Ginestar, D., Vidal, V., & Muñoz-Cobo, J. L. (1994). 3D λ-modes of the neutron-diffusion equation. Annals of Nuclear Energy, 21(7), 405-421. doi:10.1016/0306-4549(94)90041-8Miró, R., Ginestar, D., Verdú, G., & Hennig, D. (2002). A nodal modal method for the neutron diffusion equation. Application to BWR instabilities analysis. Annals of Nuclear Energy, 29(10), 1171-1194. doi:10.1016/s0306-4549(01)00103-7Hébert A. Applied reactor physics. 2nd ed. Montréal: Presses Internationales Polytechnique; 2016. p. 368–369.Döring, M. G., Kalkkuhl, J. C., & Schröder, W. (1993). Subspace Iteration for Nonsymmetric Eigenvalue Problems Applied to the λ-Eigenvalue Problem. Nuclear Science and Engineering, 115(3), 244-252. doi:10.13182/nse93-a24053Modak, R. S., & Jain, V. K. (1996). Sub-space iteration scheme for the evaluation of λ-modes of finite-differenced multi-group neutron diffusion equations. Annals of Nuclear Energy, 23(3), 229-237. doi:10.1016/0306-4549(95)00015-6Singh, K. P., Modak, R. S., Degweker, S. B., & Singh, K. (2009). Iterative schemes for obtaining dominant alpha-modes of the neutron diffusion equation. Annals of Nuclear Energy, 36(8), 1086-1092. doi:10.1016/j.anucene.2009.05.006Gupta, A., & Modak, R. S. (2011). Evaluation of dominant time-eigenvalues of neutron transport equation by Meyer’s sub-space iterations. Annals of Nuclear Energy, 38(7), 1680-1686. doi:10.1016/j.anucene.2011.02.016Kópházi, J., & Lathouwers, D. (2012). Three-dimensional transport calculation of multiple alpha modes in subcritical systems. Annals of Nuclear Energy, 50, 167-174. doi:10.1016/j.anucene.2012.06.021VERDÚ, G., GINESTAR, D., ROMÁN, J., & VIDAL, V. (2010). 3D Alpha Modes of a Nuclear Power Reactor. Journal of Nuclear Science and Technology, 47(5), 501-514. doi:10.1080/18811248.2010.9711641Lathouwers, D. (2003). Iterative computation of time-eigenvalues of the neutron transport equation. Annals of Nuclear Energy, 30(17), 1793-1806. doi:10.1016/s0306-4549(03)00151-8Warsa, J. S., Wareing, T. A., Morel, J. E., McGhee, J. M., & Lehoucq, R. B. (2004). Krylov Subspace Iterations for Deterministick-Eigenvalue Calculations. Nuclear Science and Engineering, 147(1), 26-42. doi:10.13182/nse04-1Verdu, G., Miro, R., Ginestar, D., & Vidal, V. (1999). The implicit restarted Arnoldi method, an efficient alternative to solve the neutron diffusion equation. Annals of Nuclear Energy, 26(7), 579-593. doi:10.1016/s0306-4549(98)00077-2Lehoucq, R. B., Sorensen, D. C., & Yang, C. (1998). ARPACK Users’ Guide. doi:10.1137/1.9780898719628Boer, B., Lathouwers, D., Kloosterman, J. L., Van Der Hagen, T. H. J. J., & Strydom, G. (2010). Validation of the DALTON-THERMIX Code System with Transient Analyses of the HTR-10 and Application to the PBMR. Nuclear Technology, 170(2), 306-321. doi:10.13182/nt10-a9485Hernandez, V., Roman, J. E., & Vidal, V. (2005). SLEPc. ACM Transactions on Mathematical Software, 31(3), 351-362. doi:10.1145/1089014.1089019Hernández, V., Román, J. E., & Vidal, V. (2003). SLEPc: Scalable Library for Eigenvalue Problem Computations. 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Osteoid Osteoma of the Capitate: A Case Report and Literature Review

Osteoid osteoma is a benign bone tumor that rarely affects the carpal bones. Because of its nonspecific presentation in the wrist, it remains a diagnostic challenge. We report an unusual case of osteoid osteoma in the capitate where the diagnosis was delayed and the presentation was that of an aggressive natured lesion with considerable functional incapacitation. Diagnosis was made by computed tomographic scan of the wrist and surgical excision lead to a dramatic relief of symptoms

Sociologie de la défense et études stratégiques

Alain Joxe, directeur d’études Globalisation, petites guerres cruelles et paix en panne : le débat euro-américain Le séminaire s’est donné tout au long de l’année pour objet une interprétation stratégique de l’attentat du 11 Septembre contre les États-Unis, la proclamation d’une guerre mondiale contre le terrorisme, commençant en Afghanistan, et la multiplication des ripostes américaines sur des théâtres voisins ou connexes, au Moyen-Orient et dans le monde islamique en général. On a cherché,..

Sociologie de la défense et études stratégiques

Alain Joxe, directeur d’études La question centrale posée au cours du séminaire est la suivante : existe-t-il des différences ou des divergences importantes, identifiables et précises, entre les critères stratégiques de sécurité mis en œuvre par les États-Unis et par l’Europe dans les zones de conflits limités ? Quelles sont les racines de ces divergences : politiques, économiques stratégiques culturelles ? Les cours et les exposés de recherches ont traité trois sujets principaux au cours de ..

A Newton solution for the superhomogenization method: The PJFNK-SPH

RÉSUMÉ: This work presents two novel topics regarding the Superhomogenization method: 1) the formalism for the implementation of the method with the linear Boltzmann Transport Equation, and 2) a Newton algorithm for the solution of the nonlinear problem that arises from the method. These new ideas have been implemented in a continuous finite element discretization in the MAMMOTH reactor physics application. The traditional solution strategy for this nonlinear problem uses a Picard, fixed-point iterative process whereas the new implementation relies on MOOSE's Preconditioned Jacobian-Free Newton Krylov method to allow for a direct solution. The PJFNK-SPH can converge problems that were either intractable or very difficult to converge with the traditional iterative approach, including geometries with reflectors and vacuum boundary conditions. This is partly due to the underlying Scalable Nonlinear Equations Solvers in PETSc, which are integral to MOOSE and offer Newton damping, line search and trust region methods. The PJFNK-SPH has been implemented and tested for various discretizations of the transport equation included in the Rattlesnake transport solver. Speedups of five times for diffusion and ten to fifteen times for transport were obtained when compared to the traditional Picard approach. The three test problems cover a wide range of applications including a standard Pressurized Water Reactor lattice with control rods, a Transient Reactor Test facility control rod supercell and a prototype fast-thermal reactor. The reference solutions and initial cross sections were obtained from the Serpent 2 Monte Carlo code. The SPH-corrected cross sections yield eigenvalues that are near exact, relative to reference solutions, for reflected geometries, even with reflector regions. In geometries with vacuum boundary conditions the accuracy is problem dependent and solutions can be within a few to a few hundred pcm. The root mean-square error in the power distribution is below 0.8% of the reference Monte Carlo. There is little benefit from SPH-corrected transport in typical scoping calculations, but for more detailed analyses it can yield superior convergence of the solution in some of the test problems. This PJFNK-SPH approach is currently being used in the modeling of the Transient Test Reactor at Idaho National Laboratory, where full reactor core SPH-corrected cross sections are employed to reduce the homogenization errors in transient or multi-physics calculations. This base implementation of the PJFNK-SPH provides an extremely robust solver and a springboard to further improve the Superhomogenization method in order to better preserve neutron currents, one of the primary deficiencies "of the method. (C) 2017 The Authors. Published by Elsevier Ltd

Influential groups for seeding and sustaining nonlinear contagion in heterogeneous hypergraphs

Contagion phenomena are often the results of multibody interactions—such as superspreading events or social reinforcement—describable as hypergraphs. We develop an approximate master equation framework to study contagions on hypergraphs with a heterogeneous structure in terms of group size (hyperedge cardinality) and of node membership (hyperdegree). By mapping multibody interactions to nonlinear infection rates, we demonstrate the influence of large groups in two ways. First, we characterize the phase transition, which can be continuous or discontinuous with a bistable regime. Our analytical expressions for the critical and tricritical points highlight the influence of the first three moments of the membership distribution. We also show that heterogeneous group sizes and nonlinear contagion promote a mesoscopic localization regime where contagion is sustained by the largest groups, thereby inhibiting bistability. Second, we formulate an optimal seeding problem for hypergraph contagion and compare two strategies: allocating seeds according to node or group properties. We find that, when the contagion is sufficiently nonlinear, groups are more effective seeds than individual hubs