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Journal Articles

Weierstrass function methodology for uncertainty analysis of random media criticality with spectrum range control

Ueki, Taro

Progress in Nuclear Energy, 144, p.104099_1 - 104099_7, 2022/02

 Times Cited Count:0 Percentile:0.01(Nuclear Science & Technology)

Randomized Weierstrass function (RWF) has been under development for evaluating the uncertainty of random media criticality due to the material mixture under disorder. In this work, the modelling capability of RWF is refined so that the spectrum range can be controlled by specifying its lower and upper ends of the frequency domain variable. As a result, it becomes possible to make fair criticality comparison among replicas of random media under inverse power law power spectra. Technically, the infinite sum of trigonometric terms in RWF is extended to cover the arbitrarily low frequency domain and then truncated to finite terms for the sole purpose of spectrum range control. This means that the refinement is free of the convergence issue towards a fractal characteristic of Weierstrass function and thus termed Incomplete Randomized Weierstrass function (IRWF). As a demonstration, a three-dimensional version of IRWF is applied to the mixture of three fuels with different burnups in a water-moderated environment. Monte Carlo criticality calculations are carried out to evaluate the uncertainty of neutron effective multiplication factor due to the indeterminacy of the fuel mixture formation.

Journal Articles

Monte Carlo criticality calculation of random media formed by multimaterials mixture under extreme disorder

Ueki, Taro

Nuclear Science and Engineering, 195(2), p.214 - 226, 2021/02

 Times Cited Count:5 Percentile:54.54(Nuclear Science & Technology)

A dynamical system under extreme physical disorder has the tendency of evolving toward the equilibrium state characterized by an inverse power law power spectrum. In this paper, a practically implementable three-dimensional model is proposed for the random media formed by multi-materials mixture under such a power spectrum using a randomized form of Weierstrass function, its extension covering the white noise, and partial volumes pairings of constituent materials. The proposed model is implemented in the SOLOMON Monte Carlo solver with delta tracking. Two sets of numerical results are shown using the JENDL-4 nuclear data libraries.

Journal Articles

Judgment on convergence-in-distribution of Monte Carlo tallies under autocorrelation

Ueki, Taro

Nuclear Science and Engineering, 194(6), p.422 - 432, 2020/06

 Times Cited Count:0 Percentile:0.01(Nuclear Science & Technology)

In Monte Carlo criticality calculation, the convergence-in-distribution check of the sample mean of tallies can be approached in terms of the influence range of autocorrelation. In this context, it is necessary to evaluate the attenuation of autocorrelation coefficients over lags. However, in just one replica of calculation, it is difficult to accurately estimate small ACCs at large lags because of the comparability with statistical uncertainty. This paper proposes a method to overcome such an issue. Its essential component is the transformation of a standardized time series of tallies so that the resulting series asymptotically converges in distribution to Brownian motion. The convergence-in-distribution check is constructed based on the independent increment property of Brownian motion. The judgment criterion is set by way of the spectral analysis of fractional Brownian motion. Numerical results are demonstrated for extreme and standard types of criticality calculation.

Journal Articles

Universal methodology for statistical error and convergence of correlated Monte Carlo tallies

Ueki, Taro

Nuclear Science and Engineering, 193(7), p.776 - 789, 2019/07

 Times Cited Count:5 Percentile:49.54(Nuclear Science & Technology)

It is known that the convergence of standardized time series (STS) to Brownian bridge yields standard deviation estimators of the sample mean of correlated Monte Carlo tallies. In this work, a difference scheme based on a stochastic differential equation is applied to STS in order to obtain a new functional statistic (NFS) that converges to Brownian motion (BM). As a result, statistical error estimation improves twofold. First, the application of orthonormal weighting to NFS yields a new set of asymptotically unbiased standard deviation estimators of sample mean. It is not necessary to store tallies once the updating of estimator computation is finished at each generation. Second, it becomes possible to assess the convergence of sample mean in an assumption-free manner by way of the comparison of power spectra of NFS and BM. The methodology is demonstrated for three different types of problems encountered in Monte Carlo criticality calculation.

Journal Articles

Continuous energy Monte Carlo criticality calculation of random media under power law spectrum

Ueki, Taro

Proceedings of International Conference on Mathematics and Computational Methods applied to Nuclear Science and Engineering (M&C 2019) (CD-ROM), p.151 - 160, 2019/00

A dynamical system under extreme physical disorder has the tendency of evolving toward the equilibrium state characterized by an inverse power law spectrum. In this paper, the author proposes a practically implementable modeling of random media under such a spectrum using a randomized form of the Weierstrass function. The proposed modeling is demonstrated by the continuous energy Monte Carlo particle transport with delta tracking for the criticality calculation of a randomized version of the Topsy spherical core in International Criticality Safety Benchmark Evaluation Project.

Journal Articles

Monte Carlo criticality analysis of random media under bounded fluctuation driven by normal noise

Ueki, Taro

Journal of Nuclear Science and Technology, 55(10), p.1180 - 1192, 2018/10

AA2018-0157.pdf:1.15MB

 Times Cited Count:4 Percentile:39.03(Nuclear Science & Technology)

In Monte Carlo criticality analysis under material distribution uncertainty, it is necessary to evaluate the response of neutron effective multiplication factor ($$K_{rm eff}$$) to the space-dependent random fluctuation of volume fractions within a prescribed bounded range. Normal random variables, however, cannot be used in a straightforward manner since the normal distribution has infinite tails. To overcome this issue, a methodology has been developed via forward-backward-superposed reflection Brownian motion (FBSRBM). Here, the forward-backward superposition makes the variance of fluctuation spatially constant and the reflection Brownian motion confines the fluctuation driven by normal noise in a bounded range. FBSRBM was implemented using Karhunen-Loeve expansion and applied to the fluctuation of volume fractions in a model of UO$$_{2}$$-concrete media with stainless steel.

Oral presentation

Statistical error estimation and bias correction in Monte Carlo criticality calculation

Ueki, Taro

no journal, , 

It is essential to examine performance limit in the development of statistical analysis methodology. In this work, we report the performance evaluation of statistical error estimation and bias correction in the Monte Carlo criticality calculation of an extreme version of the k-effective-of-the world problem.

Oral presentation

Development of a Monte Carlo Solver Solomon for criticality safety analysis, 2; Implementation of the probability table method for unresolved resonance cross sections

Nagaya, Yasunobu; Hagura, Hiroyuki*

no journal, , 

In order to build the criticality safety database for fuel debris, a Monte Carlo Solver Solomon has been under development. The probability table method has been implemented into Solomon to treat the self-shielding effect in the unresolved resonance region correctly. The implementation has been verified with the calculation of effective multiplication factors for simple geometry systems.

Oral presentation

Model extension of probabilistically disordered media and its implementation in solomon code

Ueki, Taro

no journal, , 

The randomized Weierstrass function (RWF) is a useful tool for the uncertainty evaluation of the criticality of disordered media. This excerpt reports the extension of RWF methodology covering a wide range of power law spectra in order to simulate various disordered mixtures of materials. The extended RWF is then demonstrated using the Monte Carlo Solver Solomon.

Oral presentation

Development of multi-species material randomization using Monte Carlo solver Solomon

Ueki, Taro

no journal, , 

Randomized Weierstrass function (RWF) is a model specifically designed for the criticality of two material systems under uncertain distribution. It is reported in this excerpt that the RWF has been extended to systems of any number of multi-species materials based on the divisions of volume fractions and the combinatorial couplings of different materials. The extended RWF model is implemented in Monte Carlo solver Solomon.

Oral presentation

Development of a Monte Carlo Solver Solomon for criticality safety analysis, 3; Implementation of thermal neutron scattering models

Nagaya, Yasunobu

no journal, , 

In order to build a criticality characteristics database for fuel debris, a Monte Carlo Solver Solomon has been under development. Thermal neutron scattering models have been implemented into Solomon to extend the applicability area to thermal reactor systems. The implementation has been verified with the inter-code comparison of effective multiplication factors for simple geometries.

Oral presentation

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