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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Prediction of liver remnant regeneration after living donor liver transplantation using preoperative CT texture analysis

Purpose: To predict the rate of liver regeneration after living donor liver transplantation (LDLT) using pre-operative computed tomography (CT) texture analysis. Materials and methods: 112 living donors who performed right hepatectomy for LDLT were included retrospectively. We measured the volume of future remnant liver (FLR) on pre-operative CT and the volume of remnant liver (LR) on follow-up CT, taken at a median of 123 days after transplantation. The regeneration index (RI) was calculated using the following equation: [(V{sub LR}−V{sub FLR})/V{sub FLR}] × 100. Computerized texture analysis of the semi-automatically segmented FLR was performed. We used a stepwise, multivariable linear regression to assess associations of clinical features and texture parameters in relation to RI and to make the best-fit predictive model. Results: The mean RI was 110.7 ± 37.8%, highly variable ranging from 22.4% to 247.0%. Among texture parameters, volume of FLR, standard deviation, variance, and gray level co-occurrence matrices (GLCM) contrast were found to have significant correlations between RI. In multivariable analysis, smaller volume of FLR (ß − 0.17, 95% CI − 0.22 to − 0.13) and lower GLCM contrast (ß − 1.87, 95% CI − 3.64 to − 0.10) were associated with higher RI. The regression equation predicting RI was following: RI = 203.82 + 10.42 × pre-operative serum total bilirubin (mg/dL) − 0.17 × V{sub FLR} (cm{sup 3}) − 1.87 × GLCM contrast (× 100). Conclusion: Volume of FLR and GLCM contrast were independent predictors of RI, showing significant negative correlations. Pre-operative CT with texture analysis can be useful for predicting the rate of liver regeneration in living donor of liver transplantation.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2022

The DESI N -body Simulation Project – II. Suppressing sample variance with fast simulations

ABSTRACT Dark Energy Spectroscopic Instrument (DESI) will construct a large and precise three-dimensional map of our Universe. The survey effective volume reaches $\sim 20\, h^{-3}\, \mathrm{Gpc}^{3}$. It is a great challenge to prepare high-resolution simulations with a much larger volume for validating the DESI analysis pipelines. AbacusSummit is a suite of high-resolution dark-matter-only simulations designed for this purpose, with $200\, h^{-3}\, \mathrm{Gpc}^{3}$ (10 times DESI volume) for the base cosmology. However, further efforts need to be done to provide a more precise analysis of the data and to cover also other cosmologies. Recently, the CARPool method was proposed to use paired accurate and approximate simulations to achieve high statistical precision with a limited number of high-resolution simulations. Relying on this technique, we propose to use fast quasi-N-body solvers combined with accurate simulations to produce accurate summary statistics. This enables us to obtain 100 times smaller variance than the expected DESI statistical variance at the scales we are interested in, e.g. $k \lt 0.3\, h\, \mathrm{Mpc}^{-1}$ for the halo power spectrum. In addition, it can significantly suppress the sample variance of the halo bispectrum. We further generalize the method for other cosmologies with only one realization in AbacusSummit suite to extend the effective volume ∼20 times. In summary, our proposed strategy of combining high-fidelity simulations with fast approximate gravity solvers and a series of variance suppression techniques sets the path for a robust cosmological analysis of galaxy survey data.

cosmology: theory↗
DOE OSTI2025

TOFHunter—unlocking rapid untargeted screening of inductively coupled plasma–time-of-flight–mass spectrometry data

This study provides an overview of a newly developed open source program written in Python, TOFHunter, which permits the rapid and untargeted screening of inductively coupled plasma (ICP)-time-of-flight (TOF)-mass spectrometry (MS) datasets. ICP-TOF-MS is an analytical tool capable of providing quasi simultaneous detection of all nuclides from Li to Pu. This capability has triggered an increase in studies investigating single-particle analysis in which the TOF-MS provides correlated elemental/isotopic signatures on a particle basis in time. Similarly, laser ablation mapping has seen rapid growth owing to ICP-TOF-MS's capacity to handle fast washout times (<10 ms) while providing a broad nuclide coverage. The caveat to this broad mass coverage and high time resolution comes in the form of large, overwhelming datasets. With datasets typically on the scale of gigabytes, it is easy for a user to only focus on very targeted analytes; however, this focus diminishes the opportunity offered by the TOF-MS detector. TOFHunter applies chemometric methods, principal component analysis (PCA), and interesting features finder (IFF) on ICP-TOF-MS data, allowing for investigation of correlations, major and minor variance sources, and sample screening. The unique spectra identified by the (IFF) are used to generate a list of mass peaks, which are then matched with both nuclides and potential interferences before being exported for the user to investigate. Several case studies are discussed herein, demonstrating TOFHunter's ability to screen aqueous injections, single-particle/single-cell analysis, and probe laser ablation mapping files for unique regions of interest.

47 OTHER INSTRUMENTATION↗
DOE OSTI2018

Second-Order Sensitivity Analysis of Uncollided Particle Contributions to Radiation Detector Responses

This work presents an application of Cacuci’s Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) to the simplified Boltzmann equation that models the transport of uncollided particles through a medium to compute efficiently and exactly all of the first- and second-order derivatives (sensitivities) of a detector’s response with respect to the system’s isotopic number densities, microscopic cross sections, source emission rates, and detector response function. The off-the-shelf PARTISN multigroup discrete ordinates code is employed to solve the equations underlying the 2nd-ASAM. The accuracy of the results produced using PARTISN is verified by using the results of three test configurations: (1) a homogeneous sphere, for which the response is the exactly known total uncollided leakage, (2) a multiregion two-dimensional (r-z) cylinder, and (3) a two-region sphere for which the response is a reaction rate. For the homogeneous sphere, results for the total leakage as well as for the respective first- and second-order sensitivities are in excellent agreement with the exact benchmark values. For the nonanalytic problems, the results obtained by applying the 2nd-ASAM to compute sensitivities are in excellent agreement with central-difference estimates. The efficiency of the 2nd-ASAM is underscored by the fact that, for the cylinder, only 12 adjoint PARTISN computations were required by the 2nd-ASAM to compute all of the benchmark’s 18 first-order sensitivities and 224 second-order sensitivities, in contrast to the 877 PARTISN calculations needed to compute the respective sensitivities using central finite differences, and this number does not include the additional calculations that were required to find appropriate values of the perturbations to use for the central differences.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

A Regularized Variance-Reduced Modified Extragradient Method for Stochastic Hierarchical Games

We consider an N -player hierarchical game in which the i th player’s objective comprises of an expectation-valued term, parametrized by rival decisions, and a hierarchical term. Such a framework allows for capturing a broad range of stochastic hierarchical optimization problems, Stackelberg equilibrium problems, and leader-follower games. We develop an iteratively regularized and smoothed variance-reduced modified extragradient framework for iteratively approaching hierarchical equilibria in a stochastic setting. We equip our analysis with rate statements, complexity guarantees, and almost-sure convergence results. We then extend these statements to settings where the lower-level problem is solved inexactly and provide the corresponding rate and complexity statements. Our model framework encompasses many game theoretic equilibrium problems studied in the context of power markets. We present a realistic application to the study of virtual power plants, emphasizing the role of hierarchical decision making and regularization. Preliminary numerics suggest that empirical behavior compares well with theoretical guarantees.

Tikhonov regularization↗
DOE OSTI2014

SOARCA Peach Bottom Atomic Power Station Long-Term Station Blackout Uncertainty Analysis: Knowledge Advancement.

This paper describes the knowledge advancements from the uncertainty analysis for the State-of- the-Art Reactor Consequence Analyses (SOARCA) unmitigated long-term station blackout accident scenario at the Peach Bottom Atomic Power Station. This work assessed key MELCOR and MELCOR Accident Consequence Code System, Version 2 (MACCS2) modeling uncertainties in an integrated fashion to quantify the relative importance of each uncertain input on potential accident progression, radiological releases, and off-site consequences. This quantitative uncertainty analysis provides measures of the effects on consequences, of each of the selected uncertain parameters both individually and in interaction with other parameters. The results measure the model response (e.g., variance in the output) to uncertainty in the selected input. Investigation into the important uncertain parameters in turn yields insights into important phenomena for accident progression and off-site consequences. This uncertainty analysis confirmed the known importance of some parameters, such as failure rate of the Safety Relief Valve in accident progression modeling and the dry deposition velocity in off-site consequence modeling. The analysis also revealed some new insights, such as dependent effect of cesium chemical form for different accident progressions. (auth)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2016

Modelling safety of multistate systems with ageing components

An innovative approach to safety analysis of multistate ageing systems is presented. Basic notions of the ageing multistate systems safety analysis are introduced. The system components and the system multistate safety functions are defined. The mean values and variances of the multistate systems lifetimes in the safety state subsets and the mean values of their lifetimes in the particular safety states are defined. The multi-state system risk function and the moment of exceeding by the system the critical safety state are introduced. Applications of the proposed multistate system safety models to the evaluation and prediction of the safty characteristics of the consecutive “m out of n: F” is presented as well.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Future projections and uncertainty assessment of precipitation extremes in the Korean peninsula from the CMIP5 ensemble

Abstract Projections of changes in extreme climate are sometimes predicted by multimodel ensemble methods that combine forecasts from individual simulation models using weighted averaging. One method to assign weight to each model is the Bayesian model averaging (BMA) in which posterior probability is used. For the cases of extreme climate, the generalized extreme value distribution (GEVD) is typically used. We applied the approach of GEV‐embedded BMA to a series of 35 years of the annual maximum daily precipitation data (both historical data and data gathered from simulation experiments for future periods) over the Korean peninsula as simulated by the models in the Coupled Model Intercomparison Project Phase 5 (CMIP5). Simulation data under two Representative Concentration Pathway (RCP) scenarios, namely RCP4.5 and RCP8.5, were used. Observed data and 17 CMIP5 models for 12 gird cells in Korea have been examined to predict future changes in precipitation extremes. A simple regional frequency analysis of pooling observations from three stations in each cell was employed to reduce the estimation variance and local fluctuations. A bias correction technique using the regression‐type transfer function was applied to these simulation data. Return levels spanning over 20 and 50 years, as well as the return periods relative to the reference years (1971–2005), were estimated for two future periods, namely Period 1 (2021–2050) and Period 2 (2066–2095). From these analyses, relative increase observed in the spatially averaged 20‐year (50‐year) return level was approximately 23% (16%) and 45% (36%) in the RCP4.5 and RCP8.5 experiments, respectively, by the end of the 21st century. We concluded that extreme rainfalls will likely occur two times and four times more frequently in the RCP4.5 and RCP8.5 scenarios, respectively, as compared to in the reference years by the end of the 21st century.

Lee, Youngsaeng↗
DOE OSTI2019

Reducing Interanalyst Variability in Photovoltaic Degradation Rate Assessments

The economic return on investment of a commercial photovoltaic system depends greatly on its performance over the long term and, hence, its degradation rate. Many methods have been proposed for assessing system degradation rates from outdoor performance data. However, comparing reported values from one analyst and research group to another requires a common baseline of performance; consistency between methods and analysts can be a challenge. An interlaboratory study was conducted involving different volunteer analysts reporting on the same photovoltaic performance data using different methodologies. Initial variability of the reported degradation rates was so high that analysts could not come to a consensus whether a system degraded or not. More consistent values are received when written guidance is provided to each analyst. Further improvements in analyst variance was accomplished by using the free open-source software RdTools, allowing a reduction in variance between analysts by more than two orders of magnitude over the first round, where multiple analysis methods are allowed. This article highlights many pitfalls in conducting 'routine' degradation analysis, and it addresses some of the factors that must be considered when comparing degradation results reported by different analysts or methods.

14 SOLAR ENERGY↗
DOE OSTI2022

Real-Time Distribution System State Estimation with Asynchronous Measurements

We report state estimation is a fundamental task in power systems. Although distribution systems are increasingly equipped with sensing devices and smart meters, measurements are typically reported at different rates and asynchronously; these aspects pose severe strains on workhorse state estimation algorithms, which are designed to process batches of data collected in a synchronous manner from all the measurement units. In this paper, we develop a novel state estimation algorithm to continuously update the estimate of the state based on measurements received in an asynchronous manner from measurement units. The synthesis of the algorithm hinges on a proximal-point type method, implemented in an online fashion, and capable of processing measurements received sequentially from sensors. A performance analysis is presented by providing bounds on the estimation error in terms of the mean and variance that hold at each iteration and asymptotically. The scheme is also compared with a more traditional Weighted Least Squares estimator that compensates for the lack of measurement data by using, as pseudo measurements, the measurement retrieved during a certain time window. Numerical simulations on the IEEE 37-bus feeder corroborate the analytical findings.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Did You Win the GPU Cloud Lottery? Benchmarking from TFLOPS to Tokens/$

Cloud GPUs are commonly assumed to deliver consistent performance for a given GPU model. This assumption does not always hold: cloud providers employ diverse system configurations and virtualization mechanisms, and GPUs themselves exhibit non-negligible manufacturing variability (the silicon lottery). In this work, we present a large-scale measurement study of GPU performance variability across 11 cloud providers, covering over 3,500 physical GPUs and 6,800 benchmark runs. Our hierarchical analysis shows that while execution-level variation stays below 9%, performance varies by up to 38% across devices and providers for the same GPU model. Regression analysis indicates that driver- and OS-related software factors contribute less than 1% of the variance; instead, silicon lottery effects dominate observed performance variation, and cloud providers further amplify them through persistent, systematic second-order effects.

Slynko, Platon [Silicon Data, New York, USA] (ORCI↗
DOE OSTI2016

Convergence Study in Global Sensitivity Analysis

Monte Carlo (MC) sampling is a common method used to randomly sample a range of scenarios. The associated error follows a predictable rate of convergence of $1/\sqrt{N}$, such that quadrupling the sample size halves the error. This method is often employed in performing global sensitivity analysis which computes sensitivity indices, measuring fractional contributions of uncertain model inputs to the total output variance. In this study, several models are used to observe the rate of decay in the MC error in the estimation of the conditional variance, the total variance in the output, and the global sensitivity indices. The purpose is to examine the rate of convergence of the error in existing specialized, albeit MC-based, sampling methods for estimation of the sensitivity indices. It was found that the conditional variances and sensitivity indices all follow the $1/\sqrt{N}$ convergence rate. Future work will test the convergence of observables from more complex models such as ignition time in combustion.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

An analysis of various solution strategies and perturbations on inputs of the reactor shielding problem - 25584

Previous work focused on the use of automated variance reduction parameters for use in a fixed source reactor shielding problem to solve for ex-core particle transport results. The current work assesses that strategy in light of a fully-coupled Monte Carlo problem run as a critical system with parallel processing and the use of moderate variance reduction parameters set manually. The results from the two strategies compare well. Also, results are compared between the MCNP, Virtual Environment for Reactor Applications (VERA) and Shift computer codes. Shift and VERA deliver similar results and compare well to MCNP. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

DEEPEN Global Standardized Categorical Exploration Datasets for Magmatic Plays

DEEPEN stands for DE-risking Exploration of geothermal Plays in magmatic ENvironments. As part of the development of the DEEPEN 3D play fairway analysis (PFA) methodology for magmatic plays (conventional hydrothermal, superhot EGS, and supercritical), weights needed to be developed for use in the weighted sum of the different favorability index models produced from geoscientific exploration datasets. This was done using two different approaches: one based on expert opinions, and one based on statistical learning. This GDR submission includes the datasets used to produce the statistical learning-based weights. While expert opinions allow us to include more nuanced information in the weights, expert opinions are subject to human bias. Data-centric or statistical approaches help to overcome these potential human biases by focusing on and drawing conclusions from the data alone. The drawback is that, to apply these types of approaches, a dataset is needed. Therefore, we attempted to build comprehensive standardized datasets mapping anomalies in each exploration dataset to each component of each play. This data was gathered through a literature review focused on magmatic hydrothermal plays along with well-characterized areas where superhot or supercritical conditions are thought to exist. Datasets were assembled for all three play types, but the hydrothermal dataset is the least complete due to its relatively low priority. For each known or assumed resource, the dataset states what anomaly in each exploration dataset is associated with each component of the system. The data is only a semi-quantitative, where values are either high, medium, or low, relative to background levels. In addition, the dataset has significant gaps, as not every possible exploration dataset has been collected and analyzed at every known or suspected geothermal resource area, in the context of all possible play types. The following training sites were used to assemble this dataset: - Conventional magmatic hydrothermal: Akutan (from AK PFA), Oregon Cascades PFA, Glass Buttes OR, Mauna Kea (from HI PFA), Lanai (from HI PFA), Mt St Helens Shear Zone (from WA PFA), Wind River Valley (From WA PFA), Mount Baker (from WA PFA). - Superhot EGS: Newberry (EGS demonstration project), Coso (EGS demonstration project), Geysers (EGS demonstration project), Eastern Snake River Plain (EGS demonstration project), Utah FORGE, Larderello, Kakkonda, Taupo Volcanic Zone, Acoculco, Krafla. - Supercritical: Coso, Geysers, Salton Sea, Larderello, Los Humeros, Taupo Volcanic Zone, Krafla, Reyjanes, Hengill. **Disclaimer: Treat the supercritical fluid anomalies with skepticism. They are based on assumptions due to the general lack of confirmed supercritical fluid encounters and samples at the sites included in this dataset, at the time of assembling the dataset. The main assumption was that the supercritical fluid in a given geothermal system has shared properties with the hydrothermal fluid, which may not be the case in reality. Once the datasets were assembled, principal component analysis (PCA) was applied to each. PCA is an unsupervised statistical learning technique, meaning that labels are not required on the data, that summarized the directions of variance in the data. This approach was chosen because our labels are not certain, i.e., we do not know with 100% confidence that superhot resources exist at all the assumed positive areas. We also do not have data for any known non-geothermal areas, meaning that it would be challenging to apply a supervised learning technique. In order to generate weights from the PCA, an analysis of the PCA loading values was conducted. PCA loading values represent how much a feature is contributing to each principal component, and therefore the overall variance in the data.

15 GEOTHERMAL ENERGY↗
DOE OSTI2015

Principal component analysis of computed emission lines from protostellar jets

A very important issue concerning protostellar jets is the mechanism behind their formation. Obtaining information on the region at the base of a jet can shed light on the subject, and some years ago this was done through a search for a rotational signature in the jet line spectrum. The existence of such signatures, however, remains controversial. In order to contribute to the clarification of this issue, in this paper we show that principal component analysis (PCA) can potentially help to distinguish between rotation and precession effects in protostellar jet images. This method reduces the dimensions of the data, facilitating the efficient extraction of information from large data sets such as those arising from integral field spectroscopy. PCA transforms the system of correlated coordinates into a system of uncorrelated coordinates, the eigenvectors, ordered by principal components of decreasing variance. The projection of the data on these coordinates produces images called tomograms, while eigenvectors can be displayed as eigenspectra. The combined analysis of both can allow the identification of patterns correlated to a particular physical property that would otherwise remain hidden, and can help to separate the effects of physically uncorrelated phenomena in the data. These are, for example, rotation and precession in the kinematics of a stellar jet. In order to show the potential of PCA analysis, we apply it to synthetic spectro-imaging datacubes generated as an output of numerical simulations of protostellar jets. In this way we generate a benchmark with which a PCA diagnostics of real observations can be confronted. Using the computed emission line profiles for [O i]λ6300 and [S ii]λ6716, we recover and analyze the effects of rotation and precession in tomograms generated by PCA. We show that different combinations of the eigenvectors can be used to enhance and to identify the rotation features present in the data. Our results indicate that PCA can be useful for disentangling rotation from precession in jets with an inclination of the jet with respect to the plane of the sky as high as 45&deg;. We have been able to recover the initially imposed rotation jet profile for models at a moderate inclination angle (&straightphi;&NestedLessLess;15&deg;) and without precession.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Automatic Analyte-Ion Recognition and Background Removal for Ambient Mass-Spectrometric Data Based on Cross-Correlation

Ambient mass spectrometry is a powerful approach for rapid, high-throughput, and direct sample analysis. Due to the open-air desorption and ionization processes, random fluctuations of ambient conditions can lead to large variances in mass-spectral signals over time. The mass-spectral data also can be further complicated due to multiple analytes present in the sample, background-ion signals stemming from the desorption/ionization source itself, and other laboratory-specific conditions (e.g., ambient laboratory air, nearby hardware). Thus, background removal and analyte-ion recognition can be quite difficult, particularly in non-targeted analyses. Here, we demonstrate the use of a cross-correlation-based approach to exploit chemical information encoded in the time domain to group/categorize mass-spectral peaks from a single analysis dataset. Ions that originate from ambient (or other) background species were readily flagged and removed from spectra; the result was a decrease in mass-spectral complexity by over 70% due to the removal of these background ions. Meanwhile, analyte ions were differentiated and categorized based on their time-domain profiles. With sufficient mass resolving-power and mass-spectral acquisition rate, isolated mass spectra containing ions from the same species in a sample could be extracted, leading to a reduction in mass-spectral complexity by more than 98% in some cases. The cross-correlation approach was tested with different ionization sources as well as reproducible and irreproducible sample introduction. Software built in-house enabled fully automated data processing, which can be performed within a few seconds. Ultimately, this approach provides an additional dimension of analyte separation in ambient mass-spectrometric analyses with information that is already recorded throughout the analysis. .

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2016

A mixed model approach for evaluating yield improvements in interspecific hybrids of shrub willow, a dedicated bioenergy crop

Lignocellulosic bioenergy crops such as shrub willow (Salix spp.) are expected to have a significant role in climate mitigation strategies. Yield is perhaps the most important trait for genetic selection and development of biomass feedstocks, but the selection process is complicated by the strong influence that environmental factors has on cultivar performance. Understanding the genotype-by-environment interactions using regional yield trials of shrub willow will inform future breeding efforts and improve the ability to make regionally-specific cultivar recommendations. Here we analyzed two yield trial datasets containing genotypes from successive rounds of breeding using a series of mixed models. Stability variance parameters were used together with overall yields to identify genotypes with stable yields or specific adaptation. Analysis of the first dataset revealed a group of triploid interspecific hybrid cultivars with exceptional performance and specific adaptation to either poor or good quality environments. The best performing cultivar showed a 14% yield improvement over the mean of the check cultivars. In the second dataset, new selections were assessed along with the top performing cultivars from dataset 1. New triploid hybrids had yields 19 to 27% greater than the check cultivar and exhibited similar patterns of specific adaptation as some of the selections from the first dataset. Partial least squares regression analysis indicated that top-yielding genotypes were favored in environments with higher temperatures and greater growing degree days. This analysis demonstrates incremental improvements in yield with successive rounds of breeding through the development of interspecific triploid hybrids.

09 BIOMASS FUELS↗
DOE OSTI2017

Evaluation of the Pool Critical Assembly Benchmark with Explicitly-Modeled Geometry using MCNP6

Despite being one of the most widely used benchmarks for qualifying light water reactor (LWR) radiation transport methods and data, no benchmark calculation of the Oak Ridge National Laboratory (ORNL) Pool Critical Assembly (PCA) pressure vessel wall benchmark facility (PVWBF) using MCNP6 with explicitly modeled core geometry exists. As such, this paper provides results for such an analysis. First, a criticality calculation is used to construct the fixed source term. Next, ADVANTG-generated variance reduction parameters are used within the final MCNP6 fixed source calculations. These calculations provide unadjusted dosimetry results using three sets of dosimetry reaction cross sections of varying ages (those packaged with MCNP6, from the IRDF-2002 multi-group library, and from the ACE-formatted IRDFF v1.05 library). These results are then compared to two different sets of measured reaction rates. The comparison agrees in an overall sense within 2% and on a specific reaction- and dosimetry location-basis within 5%. Except for the neptunium dosimetry, the individual foil raw calculation-to-experiment comparisons usually agree within 10% but is typically greater than unity. Finally, in the course of developing these calculations, geometry that has previously not been completely specified is provided herein for the convenience of future analysts.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗