Faculty Profiles - ENDO Tomohiro

Papers - ENDO Tomohiro

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Bias factor method using random sampling technique Reviewed International journal

Tomohiro Endo, Akio Yamamoto, Tomoaki Watanabe

Journal of Nuclear Science and Technology Vol. 53 ( 10 ) page： 1494 - 1501 2016.10

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

Toward the practical use of the bias factor method for actual light water reactor core analyses, the bias factor method using the random sampling technique is newly proposed. The bias factor method is one of the correction methods using information of E/C values in existing measurable systems, to reduce biases and uncertainties of predicted core characteristics parameters. By the aid of the random sampling technique, our proposed bias factor method can be carried out using only forward calculations without any adjoint calculations, and can easily take into account burnup and thermal-hydraulic feedback effects, which are difficult points in the practical application to actual core analyses. Although the statistical error due to the random sampling technique is inevitable in the proposed method, the statistical error can be simply quantified by the resampling technique such as the bootstrap method. As one of the feasibility studies, effectiveness of the proposed method is verified through a numerical experiment which virtually simulates a typical equilibrium pressurized water reactor core. In this verification problem, it is clarified that E/C values of control rod worth at the beginning of cycle under the hot zero power condition are useful information to reduce biases and uncertainties of predicted assembly-wise power distributions during operation of hot full power.

DOI： 10.1080/00223131.2015.1126541

Scopus

Other Link： https://doi.org/10.1080/00223131.2015.1126541

Data Assimilation Using Subcritical Measurement of Prompt Neutron Decay Constant Invited Reviewed International journal Open Access

Tomohiro Endo, Akio Yamamoto

Nuclear Science and Engineering Vol. 194 ( 11 ) page： 1089 - 1104 2020.11

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

The prompt neutron decay constant α in a steady-state subcritical system can be directly measured using a reactor noise analysis method such as the Feynman-α method. To reduce the nuclear data-induced uncertainty of keff for a target system, this study investigates the applicability of data assimilation techniques, i.e., the bias factor method and the cross-section adjustment method, based on a subcritical measurement of α conducted at Kyoto University Critical Assembly (KUCA). The sensitivity coefficients of keff and α with respect to the nuclear data were efficiently estimated using a deterministic SN transport code with first-order perturbation theory. As a result, the a priori relative uncertainty of keff due to the 56-group SCALE covariance data can be reduced if there is strong correlation between the measured α and the target keff. The experimental value of α contributes to improving the nuclear data of total fission spectrum χ and total fission neutron number ν via strong correlations between χ and prompt χp and between ν and prompt νp , by utilizing the sensitivity coefficients of α with respect to prompt χp and νp.

DOI： 10.1080/00295639.2020.1720499

Open Access

Web of Science

Other Link： https://doi.org/10.1080/00295639.2020.1720499

Theoretical Derivation of a Unique Combination Number Hidden in the Higher-Order Neutron Correlation Factors Using the Pál-Bell Equation Invited Reviewed International journal

Tomohiro Endo, Fuga Nishioka, Akio Yamamoto, Kenichi Watanabe, Cheol Ho Pyeon

Nuclear Science and Engineering Vol. 197 ( 2 ) page： 176 - 188 2023.2

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

The Pál-Bell equation is a backward-type master equation that describes the probability generating function (PGF) of neutron counts in a neutron multiplication system. Thanks to the Pál-Bell equation with the two-forked and the fundamental mode approximations, an analytical solution of PGF of neutron counts in a source-driven subcritical system can be theoretically derived. This theoretical derivation clarifies that the unique combination number of double factorial (2n−3)!! does exist in the ratio of the higher-order neutron correlation factors measured in a critical state even for any kind of fissile and moderator materials. Additionally, the unique combination numbers are experimentally validated for the order 3 ≤ n ≤ 6 through reactor noise measurements in actual subcritical systems. This knowledge can be used to judge whether a target system is in a deep subcritical state or to roughly estimate the magnitude of subcriticality, based on the factorial moments of the measured reactor noise in a zero-power state.

DOI： 10.1080/00295639.2022.2049992

Sensitivity Analysis of Prompt Neutron Decay Constant using Perturbation Theory Reviewed International journal Open Access

Tomohiro Endo, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 55 ( 11 ) page： 1245 - 1254 2018.11

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

Experimental results of prompt neutron decay constant α is useful information to validate numerical results of ω-eigenvalue for spatial and energetic fundamental mode. In order to accomplish the data assimilation technique using α, it is desirable to establish an efficient numerical calculation method for sensitivity coefficient analysis of α. For this purpose, the numerical calculation method using the first-order perturbation theory is investigated. A specific theoretical formula is derived to evaluate the sensitivity coefficient of α to nuclear data. The derived rigorous formula utilizes forward and adjoint eigenfunctions which consist of neutron flux and delayed neutron precursor densities. Using the prompt approximation, the derived formula can be simplified without the term involving the delayed neutron precursor densities. By calculating α using the multi-energy-group neutron transport code for an ICSBEP benchmark problem, the derived formula for sensitivity analysis using the perturbation theory is verified by comparing with the reference results using the direct method. Consequently, the efficient numerical procedures for uncertainty quantification of α can be established by the aid of the sensitivity coefficients based on the perturbation theory.

DOI： 10.1080/00223131.2018.1491902

Open Access

Comparison of theoretical formulae and bootstrap method for statistical error estimation of Feynman-α method Reviewed International journal Open Access

Tomohiro Endo, Akio Yamamoto

Annals of Nuclear Energy Vol. 124 page： 606 - 615 2019.2

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Elsevier B.V.

This paper discusses the statistical error of the variance-to-mean ratio, or the Y value in the Feynman-α method, from a single measurement of reactor noise. As a theoretical approach, two practical theoretical formulae are derived to estimate the statistical error of Y: one is based on the propagation of uncertainty with unbiased estimators for the third-and fourth-order central moments; the other is a simplified formula that reuses the Y value under the fundamental mode approximation, where the subcriticality is approximately less than 10,000 pcm. As a numerical approach, the bootstrap method is improved to efficiently estimate the correlations of Y between different counting gate widths, or covariance matrix Σ_Y , due to the bunching method. Through an actual reactor noise experiment at the Kyoto University Criticality Assembly, the statistical errors of Y using the theoretical formulae and the bootstrap method are validated by comparing the reference statistical errors that are estimated from the multiple experiments of reactor noise. Furthermore, the impact of Σ_Y on the statistical error of the prompt neutron decay constant α is numerically investigated. Consequently, in the case of this experimental analysis, it was confirmed that the bootstrap method with the correlations of Y seems to be slightly better from the viewpoint of the coverage probability of the estimated confidence intervals of α, although the fitting error method without the correlation of Y could be useful for the order estimation of the statistical error of α.

DOI： 10.1016/j.anucene.2018.10.032

Open Access

Web of Science

Other Link： https://doi.org/10.1016/j.anucene.2018.10.032

Application of dynamic mode decomposition to Rossi-α method in a critical state using file-by-file moving block bootstrap method Reviewed International journal Open Access

Tomohiro Endo, Fuga Nishioka, Akio Yamamoto, Kenichi Watanabe, Cheol Ho Pyeon

Journal of Nuclear Science and Technology Vol. 59 ( 9 ) page： 1117 - 1126 2022.9

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis

Prompt neutron decay constant α in a critical state is useful information to validate the numerically predicted ratio of the point kinetics parameters βeff/ℓ, where βeff and ℓ are the effective delayed neutron fraction and prompt neutron lifetime, respectively. To directly measure α in a target critical system, this study proposes the application of the dynamic mode decomposition (DMD) to the reactor noise analysis based on the Rossi-α method. The DMD-based Rossi-α method enables us to robustly estimate the fundamental mode component of α from the Rossi-α histograms measured using multiple neutron detectors. Furthermore, the file-by-file moving block bootstrap method is newly proposed for the statistical uncertainty quantification of α to prevent huge memory usage when the neutron count rate is high and/or the total measurement time is long. A critical experiment has been conducted at Kyoto University Critical Assembly to demonstrate the proposed method. As a result, the proposed method can uniquely determine the α value of which the statistical uncertainty is smallest. By utilizing this experimental result of α, numerical results of βeff/ℓ ratio using the continuous energy Monte Carlo code MCNP6.2 with recent nuclear data libraries, which are processed by the nuclear data processing code FRENDY, are validated.

DOI： 10.1080/00223131.2022.2030260

Open Access

Deterministic sampling method using simplex ensemble and scaling method for efficient and robust uncertainty quantification Reviewed International journal

Tomohiro Endo, Shuhei Maruyama, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 61 ( 3 ) page： 363 - 374 2024.3

Authorship：Lead author Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis

Uncertainty quantification (UQ) of the neutron multiplication factor is important to investigate the appropriate safety margin for a target system. Although the random sampling method is a practical and useful UQ method, a large computational cost is required to reduce the statistical error of the estimated uncertainty. Furthermore, if an input variable follows a normal distribution with a large standard deviation, the perturbed input variable by the random sampling method may become a physically inappropriate or negative value. To address these issues for the efficient and robust UQ, a modified deterministic sampling method using the simplex ensemble and the scaling method is proposed. The features of the proposed method are summarized as follows: The sample size is (r+2), where r corresponds to the effective rank of the covariance matrix between the input variables; depending on a situation of target UQ, the amounts of perturbations for the input parameters can be arbitrarily given by the scaling factor method; the scaling factor can be updated to avoid physically inappropriate in the perturbed input variables. The effectiveness of the proposed method is demonstrated through the UQ of the neutron multiplication factor due to fuel manufacturing uncertainties for a typical PWR pin-cell burnup calculation.

DOI： 10.1080/00223131.2023.2231931

Experimental validation of unique combination numbers for third- and fourth-order neutron correlation factors of zero-power reactor noise Reviewed International journal

Tomohiro Endo, Akio Yamamoto, Masao Yamanaka, Cheol Ho Pyeon

Journal of Nuclear Science and Technology Vol. 56 ( 4 ) page： 322 - 336 2019.4

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

Zero-power reactor noise is useful for subcriticality measurements. Based on the nuclear reactor physics and the theory of neutron detection, this paper theoretically clarifies that the third- and fourth-order neutron correlation factors Y_3 and Y_4 can be expressed as functions of the second-order neutron correlation factor Y. In particular, if the neutron-counting gate width is sufficiently large, the saturation values Y_3⁄Y^2 and Y_4⁄Y^3 are almost equal to the unique combination numbers, ‘3’ and ‘15,’ for a source-driven subcritical system, where the subcriticality is less than 10000 pcm. These unique combination numbers, ‘3’ and ‘15,’ for Y_3⁄Y^2 and Y_4⁄Y^3 were validated using actual zero-power reactor noise measurements carried out at the Kyoto University Criticality Assembly. In this study, the estimation of statistical errors and correlations between different gate widths owing to the bunching method was achieved by the moving block bootstrap method. For a sufficiently long measured reactor noise in a steady and unperturbed state, a statistical test for the evaluation of the critical state and the absolute measurement of subcriticality can be carried out by statistically quantifying the difference between the measurement value of Y_3⁄Y^2 and the unique combination number.

DOI： 10.1080/00223131.2019.1580625

Web of Science

Other Link： https://doi.org/10.1080/00223131.2019.1580625

Confidence interval estimation by bootstrap method for uncertainty quantification using random sampling method Invited Reviewed International journal

Tomohiro Endo, Tomoaki Watanabe, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 52 ( 7-8 ) page： 993 - 999 2015.8

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

Confidence interval estimation by the bootstrap method is investigated for the uncertainty quantification of neutronics calculation using the random sampling method. The random sampling method is a simple and practical technique to quantify an uncertainty (standard deviation) of the target parameter calculated by a core analysis code. It is noted that a statistical error is inevitably included in the estimated uncertainty because of the probabilistic method using random numbers. In order to estimate the statistical error of uncertainty, we focus on the bootstrap method. The bootstrap method is one of the resampling techniques to evaluate variance and confidence interval of a sample estimate (e.g. variance) without the assumption of normality. Through a lattice burnup calculation for a simplified boiling water reactor (BWR) fuel assembly, it is verified that the bootstrap method can reasonably estimate the confidence interval of uncertainty of infinite neutron multiplication factor (k(inf)) due to covariance data of JENDL-4.0. In the case of this problem, the distribution of k(inf) is well approximated by a normal distribution; thus, the confidence interval of uncertainty can be also estimated by the aid of chi-squared distribution. The merit using the bootstrap method is to simply estimate the confidence interval of uncertainty without the assumption of normality.

DOI： 10.1080/00223131.2015.1034216

Web of Science

Detected-neutron multiplication factor measured by neutron source multiplication method Reviewed International journal

Tomohiro Endo, Akio Yamamoto, Yoshihiro Yamane

Annals of Nuclear Energy Vol. 38 ( 11 ) page： 2417 - 2427 2011.11

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Elsevier B.V.

An alternative definition of neutron multiplication factor measured by the neutron source multiplication (NSM) method is newly proposed. This newly defined neutron multiplication factor, kdet, is derived on the basis of neutron detection process in a subcritical system with an external neutron source. The definition of kdet is expressed as a ratio of total number of detected fission-neutrons to total number of detected all neutrons. In this paper, a heuristic derivation of kdet is presented, and another interpretation of kdet is explained by using the detector importance function. Based on the idea of kdet, the measurement principle of NSM method is reinterpreted, and the correction factors in the NSM method are clarified. In order to verify our proposed NSM method, numerical analysis of the NSM method is carried out. The numerical results suggest that target neutron multiplication factors of the NSM method can be well estimated even without any corrections by putting a neutron detector where the effective neutron multiplication factor keff is well approximated by kdet.

DOI： 10.1016/j.anucene.2011.01.007

Scopus

Development of new solid angle quadrature sets to satisfy even- and odd-moment conditions Reviewed International journal

Tomohiro Endo, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 44 ( 10 ) page： 1249 - 1258 2007.10

Authorship：Lead author,　Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis, Ltd.

In this paper, we propose new solid angle quadrature sets named EON for the SN method. The EON quadrature sets are developed for the 3-D xyz geometry, and satisfy not only even-moment conditions but also odd-moment conditions for direction cosines over an octant of the sphere. We can accurately calculate the numerical integration of the polynomial of direction cosines using EON. We verify the effectiveness of EON through the 2-D bulk shield problem and the 3-D neutron transport benchmark problems. The verification results indicate that the angular discretization error of EON is much smaller than that of the conventional level symmetric quadrature set.

DOI： 10.1080/18811248.2007.9711368

Scopus

Fundamental properties and characteristics of flux distribution tallies using proper orthogonal decomposition Reviewed International journal

Ryoichi Kondo, Akio Yamamoto, Tomohiro Endo

EPJ Nuclear Sciences & Technologies Vol. 11 page： 21 2025.6

Authorship：Last author Language：English Publishing type：Research paper (scientific journal) Publisher：EDP Sciences

The flux distribution tallies using the proper orthogonal decomposition (POD) called “the POD tallies” have been developed in our previous study. The POD tallies can achieve dimensionality and statistical uncertainty reduction for a finely discretized flux distribution. Some characteristics of the POD tallies, which are left by our previous work, are revealed in the present study. Firstly, the POD tallies with the track length estimator are newly implemented. Since the statistical uncertainty of the POD tallies is reduced compared with the cell tallies, the POD tallies with the track length estimator can obtain the most precise result among the present implantations. Secondly, the basis vectors obtained by the deterministic and the stochastic methods are compared. The statistical uncertainty of the snapshot data invokes the degradation of the extracted basis vectors. This result indicates that the deterministic method might be more efficient for the snapshot calculation. Finally, the impact of the covariances of expansion coefficients on the statistical uncertainty of expanded flux distribution is investigated. The reconstructed statistical uncertainty considering only the variances of the expansion coefficients differs from the reference. This result reveals that the covariances of the expansion coefficients are important to estimate the statistical uncertainty of the local flux in the flux distribution.

DOI： 10.1051/epjn/2025019

Reduction of γ-ray-induced Noise of Diamond Detector Elements and Estimation of Neutron Detection Efficiency for the Development of a Criticality Proximity Monitoring System for the Decommissioning of the Fukushima Daiichi Nuclear Power Plant Reviewed International journal

Kengo Oda, Junichi H. Kaneko, Yusuke Kobayakawa, Kenichi Watanabe, Youichi Fujita, Eitaro Hamada, Tetsuichi Kishishita, Masaya Miyahara, Masayoshi Shoji, Hironori Uchinoyae, Sho Nishino, Yoshihiko Tanimura, Akiyoshi Chayahara, Takehiro Shimaoka, Hideaki Yamada, Tomohiro Endo, Yuto Akashi, Manobu M. Tanaka

Sensors and Materials Vol. 37 ( 5 ) page： 1977 - 1991 2025.5

Language：English Publishing type：Research paper (scientific journal) Publisher：MYU K.K.

In this paper, we discuss the development of a diamond detector element for a criticality proximity monitoring system, which is essential for the decommissioning of the Fukushima Daiichi Nuclear Power Plant. The system must withstand γ-rays at a dose rate of 1 kGy/h with minimal shielding due to payload constraints. We evaluated the effects of γ-rays on prototype diamond detectors and confirmed that removing the lift-off separation surface of diamond membrane by ion beam etching and adding a p+ diamond layer effectively reduced the effect of γ-rays. A prototype detector combined a 180-µm-thick 6LiF sintered neutron-to-charged-particle converter with a diamond detector having a 2.53 mm² sensitive area. With a threshold energy set at 1 MeV, a neutron detection efficiency of 3.0 × 10−4 cps/nv was obtained for a 252Cf source. The combination of a radiation-resistant front-end integrated circuit and a diamond detector resulted in an estimated γ-ray noise level of 0.001 cps at 0.915 MeV, based on the measurements with γ-rays at a dose rate of up to 600 Gy/h using a 60Co source. Furthermore, at a dose rate of 1 kGy/h, the γ-ray noise was 0.0004 cps, satisfying the S/N ratio of ≥1 required by the Feynman-α method. We suggest that by using 1024 diamonds in the future, the criticality proximity monitoring system could achieve a neutron detection efficiency of 1.9 cps/nv.

DOI： 10.18494/sam5597

A deterministic transport calculation method of α-eigenvalue for non-multiplying system using framework of k-eigenvalue calculation Reviewed International journal

Akio Yamamoto, Kosuke Tsujita, Tomohiro Endo

Journal of Nuclear Science and Technology Vol. xxx ( xx ) page： xxx - xxx 2025.5

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis

A new α-eigenvalue calculation method for a non-multiplying system using the framework of conventional k-eigenvalue calculation of a deterministic transport code is proposed. The time-derivative or the time-absorption term in α-eigenvalue calculation is moved to the right-hand side of the transport equation and is considered as a virtual fission source. The present method is applied to a simple three-dimensional problem with the one-group cross section and a small water tank system with the 252-group cross section. The calculation results indicate that the present method provides accurate α-eigenvalue with rapid convergence and no numerical instability.

DOI： 10.1080/00223131.2025.2507866

Hybrid data assimilation methods for nuclear-data-induced uncertainties Reviewed International journal

Shuhei Maruyama, Akio Yamamoto, Tomohiro Endo

Journal of Nuclear Science and Technology Vol. xx ( xx ) page： xx - xx 2025.5

Authorship：Last author Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis

This study proposes new hybrid data assimilation (DA) methods to effectively use experimental data represented in two different ways in the DA process for reducing nuclear-data-induced uncertainties. Conventional DA methods often assume a linear model, where data in a DA database are represented by their differential coefficients, i.e. nuclear data sensitivity coefficients. In contrast, more rigorous and versatile DA methods based on sampling techniques have been proposed recently. These sampling-based DA methods describe data for DA using results derived from direct transport calculations performed with perturbed nuclear data samples. The proposed hybrid DA methods simultaneously use both types of data described by sensitivity coefficients and sampling results and thus are called ‘hybrid.’ Two hybrid DA methods are proposed herein: the simple hybrid DA and efficient hybrid DA methods. Among these, the simple method is based on a straightforward concept that uses a random sampling technique. In contrast, the efficient method employs a more technical method that effectively combines a new deterministic sampling technique with sensitivity coefficients to reduce statistical uncertainties associated with the simple method. The efficient method is expected to be a candidate to achieve high precision and rigorous DA with a realistic sample size.

DOI： 10.1080/00223131.2025.2500579

Treatment of corner crossing ray-traces in CMFD acceleration of MOC Reviewed International journal Open Access

Akio Yamamoto, Tomohiro Endo

Journal of Nuclear Science and Technology Vol. xxx ( xx ) page： xx - xx 2025.4

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis

Treatment of corner crossing ray traces in the coarse-mesh finite-difference (CMFD) acceleration of a method of characteristics (MOC) transport calculation is discussed. The contribution of the corner crossing ray trace at a CMFD mesh is independently tallied as partial current at the corner of the CMFD mesh to reduce computational burden during transport sweeps in MOC. The tallied partial current at the corner is distributed to the partial currents at the sides of CMFD meshes. Some details of implementations in rectangular and triangular CMFD meshes are explained. The present method is implemented to the GENESIS neutron transport code, and its validity is confirmed through the 3×3 square cells and the hexagonal cell geometries. The calculation results indicate that the present method resolves the issue of corner crossing ray trace in the CMFD acceleration of MOC.

DOI： 10.1080/00223131.2025.2490832

Open Access

Impact of nuclear data updates from JENDL-4.0 to JENDL-5 on burnup calculations of light-water reactor fuels Reviewed International journal

Tomoaki Watanabe, Kenichi Tada, Tomohiro Endo, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. xx ( xx ) page： xxx - xxx 2025.4

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis

This study investigated the impact of nuclear data updates from JENDL-4.0 (J4) to JENDL-5 (J5) on the light-water reactor fuel burnup calculations. Burnup calculations were conducted with J4 and J5 for pressurized water reactor pin-cell and boiling water reactor (BWR) fuel assembly geometries. The calculation results revealed significant burnup-dependent differences in the neutron multiplication factor (kinf). Across the burnup range of 0–50 GWd/t, kinf values of J5 were consistently smaller than those of J4 and the difference gradually increased as burnup progressed. Direct sensitivity calculations, in which each nuclide data was replaced from J4 to J5, indicated that updates to the cross-sections of U-235, U-238, and Pu-239 and the thermal scattering law data of H in H2O notably impacted the kinf differences. For the BWR assembly geometry containing Gd fuels, large kinf differences were observed in the burnup range of 10–15 GWd/t. This difference was primarily attributed to updates in the cross-sections of U-235, Gd-155, Gd-157, and thermal scattering law data of H in H2O. Furthermore, we investigated how the nuclear data updates affected the kinf differences by examining nuclide number densities, the energy-dependent sensitivities, and the neutron spectra.

DOI： 10.1080/00223131.2025.2486798

Development of Multigroup Monte Carlo Neutron Transport Method with Regionwise Even-Parity Discontinuity Factor Reviewed International journal

Yoshiki Oshima, Tomohiro Endo, Akio Yamamoto

Nuclear Science and Engineering Vol. 199 ( 4 ) page： 586 - 598 2025.4

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis

The multigroup Monte Carlo (MC) neutron transport method with a regionwise even-parity discontinuity factor (REPDF), i.e. the discontinuity factor (DF)–MC method, is developed with the aim to provide a reference solution for deterministic transport calculations with DF. Applying the analogy with optics, neutrons are transmitted or reflected at a region surface during random walks. The probability of transmission or reflection is determined by REPDFs in adjacent regions. The DF is traditionally used in deterministic neutron transport methods to reduce the discretization error due to spatial homogenization and energy condensation. The DF-MC method can treat DF in the framework of the multigroup MC method.
In this paper, the weight cancellation technique based on the closest pair of points using the divide-and-conquer algorithm is used because negative weights appear due to the neutron reflection. The REPDF is calculated by the method of characteristics (MOC). The verification calculations are carried out in the pin-by-pin homogenized and assembly homogenized KAIST-2A core geometry. The DF-MC calculation can reproduce the results of the MOC with the REPDF. These results demonstrate the principle of the DF-MC method and extend the application of the DF to the probabilistic neutron transport method.

DOI： 10.1080/00295639.2024.2383102

Reduced order SP3 core calculation based on Local/Global iterations using proper orthogonal decomposition Reviewed International journal

Masato Ito, Tomohiro Endo, Akio Yamamoto, Taichi Takeishi, Yasuhiro Kodama, Hideaki Hyoudou

Journal of Nuclear Science and Technology Vol. 62 ( 4 ) page： 366 - 378 2025.4

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis

For an efficient heterogeneous neutron transport calculation, this study newly proposes a reduced order core calculation method by applying proper orthogonal decomposition (POD) to the simplified P3 (SP3) calculation with the local/global iterations. The fine mesh SP3 calculation (local calculation) for each single assembly can be efficiently solved using POD, thanks to the matrix form-based SP3 equation and the relatively small system of linear equations. By reconstructing the fine mesh distribution of neutron flux and partial neutron currents from the POD bases and the expansion coefficients estimated by the local calculation, the partial current-based coarse mesh finite difference (p-CMFD) calculation is applied to the coarse mesh calculation (global calculation). Using the global calculation results, each local boundary condition can be updated. These local and global calculations are iterated until convergence. Through a two-dimensional UO2-MOX whole core calculation with different fuel loading patterns, the proposed method is verified in comparison with the reference result by the conventional fine mesh SP3 calculation. The calculation results show that the proposed method accurately reconstructs the fine mesh distribution of neutron flux.

DOI： 10.1080/00223131.2024.2436958

Flux distribution tallies using proper orthogonal decomposition in Monte Carlo calculations Reviewed International journal

Ryoichi Kondo, Tomohiro Endo, Akio Yamamoto

Journal of Nuclear Science and Technology Vol. 61 ( 12 ) page： 1536 - 1545 2024.12

Language：English Publishing type：Research paper (scientific journal) Publisher：Taylor & Francis

In this paper, a new tallying method for a neutron flux distribution using the proper orthogonal decomposition is proposed for dimensionality reduction. The target spatial flux distribution is expanded by orthogonal basis vectors. Expansion coefficients are tallied during the random walk of the Monte Carlo calculation. The orthogonal basis vectors are extracted from the pre-calculated snapshots by the singular value decomposition. The proposed method is verified in the multi-group Monte Carlo calculation with the one-dimensional heterogeneous whole core geometry as a feasibility study. The flux distribution for each of the assemblies and energy groups is expanded by the basis vectors. The fewer basis vectors obtained from snapshots can reconstruct the target distribution well compared with the conventional Legendre polynomials used in the functional expansion tallies. The dimension of the solution in the proposed method is reduced by a factor of twenty compared with the conventional cell tally. In addition, the statistical error is reduced through dimensionality reduction thanks to the methodological feature of the proposed method. The results indicate that the proposed method has the capability of dimensionality reduction to tally the finely discretized flux distribution.

DOI： 10.1080/00223131.2024.2365445

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Papers - ENDO Tomohiro