MINARET, A DETERMINISTIC NEUTRON TRANSPORT SOLVER FOR NUCLEAR CORE CALCULATIONS

We present here MINARET a deterministic transport solver for nuclear core calculations to solve the steady state Boltzmann equation. The code follows the multi-group formalism to discretize the energy variable. It uses discrete ordinate method to deal with the angular variable and a DGFEM to solve spatially the Boltzmann equation. The mesh is unstructured in 2D and semi-unstructured in 3D (cylindrical). Curved triangles can be used to fit the exact geometry. For the curved elements, two different sets of basis functions can be used. Transport solver is accelerated with a DSA method. Diffusion and SPN calculations are made possible by skipping the transport sweep in the source iteration. The transport calculations are parallelized with respect to the angular directions. Numerical results are presented for simple geometries and for the C5G7 Benchmark, JHR reactor and the ESFR (in 2D and 3D). Straight and curved finite element results are compared

MINARET or the quest towards the use of time-dependent neutron transport solvers for nuclear core calculations on a regular basis

International audienceThe present paper deals with the resolution of the time-dependent neutron transport equation that is involved in the field of nuclear safety studies. Through the presentation of the newly implemented kinetic module in the MINARET solver [24] (developed at CEA in the framework of the APOLLO3\registered $$ project), we aim first of all at presenting a brief and comprehensive overview of the most widespread resolution techniques employed nowadays in neutron transport industrial codes. Given that the main obstacle in the use of this type of accurate solver on a regular basis relies in the long computing times, MINARET has been used in the present work as a support to rigorously quantify the efficiency of the most common sequential and parallel acceleration techniques that are currently used in this field. An important part of the paper will be devoted to study the performances of an acceleration method that has never been considered before in the resolution of this equation, which is the parallelization of the time variable. In this regard, the parareal in time algorithm (a domain decomposition method for the time variable, [20]) has been implemented to explore its potentialities in this particular application

Parareal in time 3D numerical solver for the LWR Benchmark neutron diffusion transient model

We present a parareal in time algorithm for the simulation of neutron diffusion transient model. The method is made efficient by means of a coarse solver defined with large time steps and steady control rods model. Using finite element for the space discretization, our implementation provides a good scalability of the algorithm. Numerical results show the efficiency of the parareal method on large light water reactor transient model corresponding to the Langenbuch-Maurer-Werner (LMW) benchmark [1]

Bank tellers : eight women on the financial front lines

This study examines the working lives of eight female bank tellers in Fredericton, New Brunswick. It considers three questions: (1) how do tellers define, and relate to, their jobs which are subject to considerable change and are of doubtful security? (2) how do the bank tellers cope with the daily demands of the job? (3) how do the bank tellers justify their involvement in their work roles, and to what degree do these justifications result in feelings of satisfaction with their jobs? The thesis considers how the bank tellers handle their occupational roles within a job that is undergoing significant change and possible elimination. A Goffmanesque approach focuses upon the role-playing activities of bank tellers in their interactions with clients. Added to the analysis are the effects of technological innovations on the interviewees' work demands. Among the main findings this study found that several tellers drew a comparison between telling in the past and present. Two distinct views of bank telling also emerged from the sample; bank telling as a profession and bank telling as an insecure, part-time job. Finally, many of the tellers described how bank telling is perceived to be more prestigious than it actually is. The significance of this latter finding arises from the fact that, for those who work as tellers, it is an insecure job characterized by low pay, high targets and on-going training. These findings extend the application of Goffman's approach by pointing out how tellers interpret their performance and thereby deal with role demands that offer little in the way of job satisfaction nor job security

Extension of the Discrete-Ordinates Transport Solver IDT to Regular Two-Dimensional Triangular Meshes

In this work, the Integro-Differential Transport solver (IDT), which is one of the transport solvers available in the APOLLO3(R) lattice code, has been extended to handle 2D unstructured meshes. In particular, the previously implemented method of short characteristics (MoSC) used to solve for the spatial variable in the framework of an SN approach has been extended to triangular cells which represent the natural discretization for calculating the hexagonal lattices present in fast reactors. The coefficients of the collision-probability matrices have been evaluated by means of a split-cell algorithm, specialized for dealing with different orientations of the triangle with respect to each discrete ordinate of the SN sweeping. A new sweeping routine for unstructured meshes has been added to IDT. The correct implementation of the method and its robustness with respect to the skewness and the optical thickness of the triangle has been verified. The method of manufactured solutions has been employed to obtain a numerical estimate of the spatial convergence order of the method. The same version of the MoSC has then been implemented in MINARET, another solver available in APOLLO3(R). Finally, the modified IDT applied to an unstructured mesh for the C5G7 benchmark has been successfully benchmarked against MC calculations, and the modified MINARET has been applied to a neutron transport calculation for the RJH research reactor

The parareal in time algorithm applied to the kinetic neutron diffusion equation

International audienceIn the framework of nuclear core calculations, the development of efficient tools to run neutron kinetic computations is a field of current active research. While such calculations are crucial for security assessment and the study of new reactor concepts, they present several mathematical and computational issues that still need to be overcome. The exact model (kinetic transport equation) is indeed far too expensive to be simulated for these purposes and different simplifications (multi group diffusion approximation) have led to more tractable numerical simulations. Nevertheless, on real geometries and despite the use of domain decomposition enabling accelerations of the simulations thanks to parallel architectures, there is still need for improvements for applications on regular basis. In this context, the purpose of this work is to investigate the implementation of the parareal in time algorithm within an industrial solver called MINOS developed at C.E.A

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. High Performance Computing for Computational Science — VECPAR 2002, 377-391. doi:10.1007/3-540-36569-9_25Stewart, G. W. (2002). A Krylov--Schur Algorithm for Large Eigenproblems. SIAM Journal on Matrix Analysis and Applications, 23(3), 601-614. doi:10.1137/s0895479800371529Chao, Y. A., & Shatilla, Y. A. (1995). Conformal Mapping and Hexagonal Nodal Methods —II: Implementation in the ANC-H Code. Nuclear Science and Engineering, 121(2), 210-225. doi:10.13182/nse95-a2855

Prognostic and predictive value of Immunoscore in stage III colorectal cancer: pooled analysis of 2,608 cases from the SCOT and IDEA-HORG studies

Purpose Immunoscore (IS) is prognostic in stage III colorectal cancer (CRC) and may predict benefit of duration (6 v 3 months) of adjuvant infusional fluorouracil, leucovorin, and oxaliplatin (FOLFOX) chemotherapy. We sought to determine IS prognostic and predictive value in stage-III CRC treated with adjuvant FOLFOX or oral capecitabine and infusional oxaliplatin (CAPOX) in the SCOT and IDEA-HORG trials. Methods Three thousand sixty-one cases had tumor samples, of which 2,643 (1,792 CAPOX) were eligible for IS testing. Predefined cutoffs (IS-Low and IS-High) were used to classify cases into two groups for analysis of disease-free survival (3-year DFS) and multivariable-adjusted hazard ratios (mvHRs) by Cox regression. Results IS was determined in 2,608 (99.5%) eligible cases, with 877 (33.7%) samples classified as IS-Low. IS-Low tumors were more commonly high-risk (T4 and/or N2; 52.9% IS-Low v 42.2% IS-High; P < .001) and in younger patients (P = .024). Patients with IS-Low tumors had significantly shorter DFS in the CAPOX, FOLFOX, and combined cohorts (mvHR, 1.52 [95% CI, 1.28 to 1.82]; mvHR, 1.58 [95% CI, 1.22 to 2.04]; and mvHR, 1.55 [95% CI, 1.34 to 1.79], respectively; P < .001 all comparisons), regardless of sex, BMI, clinical risk group, tumor location, treatment duration, or chemotherapy regimen. IS prognostic value was greater in younger (≤65 years) than older (>65 years) patients in the CAPOX cohort (mvHR, 1.92 [95% CI, 1.50 to 2.46] v 1.28 [95% CI, 1.01 to 1.63], PINTERACTION = .026), and in DNA mismatch repair proficient than deficient mismatch repair disease (mvHR, 1.68 [95% CI, 1.41 to 2.00] v 0.67 [95% CI, 0.30 to 1.49], PINTERACTION = .03), although these exploratory analyses were uncorrected for multiple testing. Adding IS to a model containing all clinical variables significantly improved prediction of DFS (likelihood ratio test, P < .001) regardless of MMR status. Conclusion IS is prognostic in stage III CRC treated with FOLFOX or CAPOX, including within clinically relevant tumor subgroups. Possible variation in IS prognostic value by age and MMR status, and prediction of benefit from extended adjuvant therapy merit validation

Aubert Claude, Cabestan Jean-Pierre et Lemoine Françoise (dir.), « La Chine après Deng », Revue Tiers-Monde, tome XXXVII, n° 147, juillet-septembre 1996, p. 469-742

Lautard Stéphanie. Aubert Claude, Cabestan Jean-Pierre et Lemoine Françoise (dir.), « La Chine après Deng », Revue Tiers-Monde, tome XXXVII, n° 147, juillet-septembre 1996, p. 469-742. In: Droit et société, n°39, 1998. Une sociologie non culturaliste de la norme en contexte arabe. pp. 446-449

Aubert Claude, Cabestan Jean-Pierre et Lemoine Françoise (dir.), « La Chine après Deng », Revue Tiers-Monde, tome XXXVII, n° 147, juillet-septembre 1996, p. 469-742

Lautard Stéphanie. Aubert Claude, Cabestan Jean-Pierre et Lemoine Françoise (dir.), « La Chine après Deng », Revue Tiers-Monde, tome XXXVII, n° 147, juillet-septembre 1996, p. 469-742. In: Droit et société, n°39, 1998. Une sociologie non culturaliste de la norme en contexte arabe. pp. 446-449