On the stability of the Discrete Generalized Multigroup method

This paper investigates the stability of the recondensation procedure of the Discrete Generalized Multigroup method and proposes alternatives to improve stability of the original formulation. Instabilities are shown to happen when employing a simple Picard fixed point iteration and an ill-informed group mapping scheme. This work presents a mapping procedure that improves stability of the original method for fine group calculations. Additionally, a relaxation scheme, Krasnoselskij iteration, is introduced to the fixed point iteration to further improve the stability characteristics and remove the need for fine group flux updates. Both improvements are applied on heterogeneous problems using the SHEM361 and the NG2042 group structures. The results indicate improved stability from a well-informed group mapping and demonstrate the possibility of eliminating the need for fine group flux updates.United States. Dept. of Energy. Naval Reactors Divisio

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

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

Palmer-Chalker correlations in the XY pyrochlore antiferromagnet Er2Sn2O7

\ersn\, is considered, together with \erti, as a realization of the XY antiferromagnet on the pyrochlore lattice. We present magnetization measurements confirming that \ersn\, does not order down to 100 mK but exhibits a freezing below 200 mK. Our neutron scattering experiments evidence the strong XY character of the \er moment and point out the existence of short range correlations in which the magnetic moments are in peculiar configurations, the Palmer-Chalker states, predicted theoretically for an XY pyrochlore antiferromagnet with dipolar interactions. Our estimation of the \ersn\, parameters confirm the role of the latter interactions on top of relatively weak and isotropic exchange couplings

Motor unit firing pattern, synchrony and coherence in a deafferented patient

International audienceThe firing of spinal motoneurons (MNs) is controlled continuously by inputs from muscle, joint and skin receptors. Besides altering MN synaptic drive, the removal of these inputs is liable to alter the synaptic noise and, thus, the variability of their tonic activity. Sensory afferents, which are a major source of common and/or synchronized inputs shared by several MNs, may also contribute to the coupling in the time and frequency domains (synchrony and coherence, respectively) observed when cross-correlation and coherence analyses are applied to the discharges of MN pairs. Surprisingly, no consistent changes in firing frequency, nor in synchrony and coherence were reported to affect the activity of 3 pairs of motor units (MUs) tested in a case of sensory polyradiculoneuropathy (SPRNP), leading to an irreversible loss of large diameter sensory afferents (Farmer et al., 1993). Such a limited sample, however, precludes a definite conclusion about the actual impact that a chronic loss of muscle and cutaneous afferents may have on the firing properties of human MUs. To address this issue, the firing pattern of 92 MU pairs was analyzed at low contraction force in a case of SPRNP leading similarly to a permanent loss of proprioceptive inputs. Compared with 8 control subjects, MNs in this patient tended to discharge with slightly shorter inter-spike intervals but with greater variability. Synchronous firing tended to occur more frequently with a tighter coupling in the patient. There was no consistent change in coherence in the 15–30 Hz frequency range attributed to the MN corticospinal drive, but a greater coherence was observed below 5 Hz and between 30 and 60 Hz in the patient. The possible origins of the greater irregularity in MN tonic discharges, the tighter coupling of the synchronous firing and the changes in coherence observed in the absence of proprioceptive inputs are discussed

The OpenMC Monte Carlo particle transport code

A new Monte Carlo code called OpenMC is currently under development at the Massachusetts Institute of Technology as a tool for simulation on high-performance computing platforms. Given that many legacy codes do not scale well on existing and future parallel computer architectures, OpenMC has been developed from scratch with a focus on high performance scalable algorithms as well as modern software design practices. The present work describes the methods used in the OpenMC code and demonstrates the performance and accuracy of the code on a variety of problems.United States. Department of Energy (DE-AC05-00OR22725

Opencg: A Combinatorial Geometry Modeling Tool for Data Processing and Code Verification

Combinatorial Geometry (CG) is one formulation for computational geometric models that is commonly used in many neutron transport simulation codes. The use of CG is advantageous since it permits an accurate yet concise representation of complex reactor models with a nominal memory footprint. OpenCG is a software package for combinatorial geometry models being developed at the Massachusetts Institute of Technology. The goal for OpenCG is to provide an easy-to-use, physics agnostic library to build geometry models of nuclear reactor cores. OpenCG is a free, open source library with an easy-to-use Python interface to provide nuclear engineers a single, powerful framework for modeling complex reactor geometries. Compatibility modules for commonly used nuclear reactor physics codes, such as OpenMC, OpenMOC, and Serpent, are being concurrently developed for rapid and easy exportation of an OpenCG model directly into the relevant input file format for each code of interest. The present work describes OpenCG and describes some of the novel and useful algorithms included with the software package.National Science Foundation (U.S.). Graduate Research Fellowship Program (Grant 112237)United States. Department of Energy (Center for Exascale Simulation of Advanced Reactors (CESAR). Contract DE-AC02-06CH11357)

Direct Doppler broadening in Monte Carlo simulations using the multipole representation

A new approach for direct Doppler broadening of nuclear data in Monte Carlo simulations is proposed based on the multipole representation. The multipole representation transforms resonance parameters into a set of poles and residues only some of which exhibit a resonant behavior. A method is introduced to approximate the contribution to the background cross section in an effort to reduce the number of poles needing to be broadened. The multipole representation results in memory savings of 1–2 orders of magnitude over comparable techniques. This approach provides a simple way of computing nuclear data at any temperature which is essential for multi-physics calculations, while having a minimal memory footprint which is essential for scalable high performance computing. The concept is demonstrated on two major isotopes of uranium (U-235 and U-238) and implemented in the OpenMC code. Two LEU critical experiments were solved and showed great accuracy with a small loss of efficiency (10–30%) over a single-temperature pointwise library.United States. Dept. of Energy. Office of Advanced Scientific Computing Research (Contract DE-AC02-06CH11357

A Cumulative migration method for computing rigorous transport cross sections and diffusion coefficients for LWR lattices with Monte Carlo

A new method for computing homogenized assembly neutron transport cross sections and diffusion coefficients that is both rigorous and computationally efficient is proposed in this paper. In the limit of a homogeneous hydrogen slab, the new method is equivalent to the long-used, and only-recently-published CASMO transport method. The rigorous method is used to demonstrate the sources of inaccuracy in the commonly applied “out-scatter” transport correction. It is also demonstrated that the newly developed method is directly applicable to lattice calculations performed by Monte Carlo and is capable of computing rigorous homogenized transport cross sections for arbitrarily heterogeneous lattices. Comparisons of several common transport cross section approximations are presented for a simple problem of infinite medium hydrogen. The new method has also been applied in computing 2-group diffusion data for an actual PWR lattice from BEAVRS benchmark.Idaho National Laboratory (Contract DE-AC07-05ID14517

Predicting Correlation Coefficients for Monte Carlo Eigenvalue Simulations

Monte Carlo methods are most often considered as a reference for neutron transport simulations since very limited approximations are made abount nuclear data and system geometry. To report uncertainty of any tally evaluated as generation averages, the sample variance is divided by the number of active generations, which is based on the assumption that the neutron generations are independent. Correlation effects between neutrons in multiplying systems, particularly when performing power iteration to evaluate eigenvalues have been observed in previous work. Neglecting the correlation effect results in an underestimate of uncertainty reported by Monte Carlo calculations. Previous work has also proposed methods to predict the underestimation ratio. Yamamoto et al expanded the fission source distribution with diffusion equation modes, performed numerical simulation of the AR(autoregressive) process of the expansion coefficients and used the correlation of the AR process to predict that of the Monte Carlo eigenvalue simulation. Sutton applied the discretized phase space (DPS) approach to predict the underestimation ratio but the method cannot predict the ratio when one neutron generates offspring in different phase space regions or generates a random number of offspring. This paper presents a method to predict the correlation effect with the model of multitype branching processes (MBP). The method requires simulations for one generation of neutrons without knowing the source distribution and can predict the underestimation ratio for the cases where the traditional DPS approach does not work. The generation-to-generation correlation determines the convergence rate of active generations, the bias of variance estimator for each generation and the underestimation ratio of variance estimator for tallies averaged over active generations. The generation-to-generation correlation is characterized by the Auto-Correlation Coefficients (ACC) between tallies from different generations.United States. Dept. of Energy (Consortium for Advanced Simulation of Light Water Reactors. Contract DE-AC05-00OR22725

Analysis of correlations and their impact on convergence rates in Monte Carlo eigenvalue simulations

This paper provides an analysis of the generation-to-generation correlations as observed when solving full core eigenvalue problems on PWR systems. Many studies have in the past looked at the impact of these correlations on reported variance and this paper extends the analysis to the observed convergence rate on the tallies, the effect of tally size and the effect of generation size. Since performing meaningful analysis on such a large problem is inherently difficult, a simple homogeneous reflective cube problem with analytical solution was developed that exhibits similar behavior to the full core PWR benchmark. The data in this problem was selected to match the dimensionality of the reactor problem and preserve the migration length travelled by neutrons. Results demonstrate that the variance will deviate significantly from the 1/N (N being the number of simulated particles) convergence rate associated with truly independent generations, but will eventually asymptote to 1/N after 1000's of generations regardless of the numbers of neutrons per generation. This indicates that optimal run strategies should emphasize lower number of active generations with greater number of neutrons per generation to produce the most accurate tally results. This paper also describes and compares three techniques to evaluate suitable confidence intervals in the presence of correlations, one based on using history statistics, one using generation statistics and one batching generations to reduce batch-to-batch correlation. Keywords: Monte Carlo, Tally Convergence, Autocorrelation, Confidence IntervalsUnited States. Department of Energy (Consortium for Advanced Simulation of Light Water Reactors. Contract DE-AC05-00OR22725