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At least 1,315 records · Page 73

PyTUQ: Python Toolkit for Uncertainty Quantification

SAND2025-03661O PyTUQ is a user-friendly software toolkit designed to help researchers and professionals understand and manage uncertainty in several scientific fields. By providing tools for analyzing how uncertainties affect outcomes, PyTUQ can be applied in areas such as energy production, and biology. Its unique approach allows users to make more informed decisions by assessing risks and improving predictions. Whether you're studying combustion processes or exploring complex biological systems, PyTUQ empowers you to gain deeper insights and enhance the reliability of your results. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

SciDAC↗

Understanding Uncertainties in Tropical Cyclone Rainfall Hazard Modeling Using Synthetic Storms

Tropical cyclone (TC) rainfall hazard assessment is subject to the bias in TC climatology estimation from climate simulations or synthetic downscaling. In this study, we investigate the uncertainty in TC rainfall hazard assessment induced by this bias using both rain gauge and radar observations and synthetic-storm-model-coupled TC rainfall simulations. We identify the storm’s maximum intensity, impact duration, and minimal distance to the site to be the three most important storm parameters for TC rainfall hazard, and the relationship between the important storm parameters and TC rainfall can be well captured by a physics-based TC rainfall model. The uncertainty in the synthetic rainfall hazard induced by the bias in TC climatology can be largely explained by the bias in the important storm parameters simulated by the synthetic storm model. Correcting the distribution of the most biased parameter may significantly improve rainfall hazard estimation. Bias correction based on the joint distribution of the important parameters may render more accurate rainfall hazard estimations; however, the general technical difficulties in resampling from high-dimensional joint probability distributions prevent more accurate estimations in some cases. The results of the study also support future investigation of the impact of climate change on TC rainfall hazards through the lens of future changes in the identified important storm parameters.

54 ENVIRONMENTAL SCIENCES↗

Early arrival waveform inversion using data uncertainties and matching filters with application to near-surface seismic refraction data

We develop an early arrival waveform inversion (EAWI) technique for high-resolution near-surface velocity estimation by iteratively updating the P-wave velocity model to minimize the difference between the observed and calculated seismic refraction data. Traditional EAWI uses a least-squares penalty function and an acoustic forward-modeling engine. Conventional least-squares error is sensitive to data with low signal-to-noise ratio (S/N) and iterations of EAWI stop at a local-minimum data misfit or at the preassigned maximum number of iterations. These stopping criteria can result in overfitting the data. In addition, fitting the elastic field data with an acoustic modeling engine can introduce artifacts in velocity estimation, especially in land data with significant elastic effects. To overcome these challenges, we develop a robust EAWI (REAWI) method by (1) incorporating the data uncertainties into the penalty function and (2) mitigating the elastic effects using a matching filter workflow. The data uncertainties are estimated from waveform reciprocal errors. When full-waveform reciprocity is not available, trace interpolation is applied. The proposed method prevents closely fitting data with low S/N, avoids overall overfitting by stopping the iterations when a normalized chi-square ([Formula: see text]) waveform misfit of one is achieved, and is less affected by elastic effects. Numerical examples and application to near-surface refraction data at a groundwater contamination site suggest that the final REAWI models are more accurate than the corresponding EAWI models, at the same level of misfit. This is the first known application of a matching filter workflow to real land data. The final REAWI models satisfy an appropriate misfit between the real data and predicted elastic P-wave data, making this approach in this respect equivalent to elastic waveform inversion. We also develop a method to analyze model constraint by examining the energy of the wavefield Fréchet derivative thereby avoiding the influence of the data residuals in traditional Fréchet kernels.

Geochemistry & Geophysics↗

Dynamic Transmission Line Switching Amid Wildfire-Prone Weather Under Decision-Dependent Uncertainty

During dry and windy seasons, environmental conditions significantly increase the risk of wildfires, exposing power grids to disruptions caused by transmission line failures. Wildfire propagation exacerbates grid vulnerability, potentially leading to prolonged power outages. To address this challenge, we propose a multistage optimization model that dynamically adjusts transmission grid topology in response to wildfire propagation, aiming to develop an optimal response policy. By accounting for decision-dependent uncertainty, where line survival probabilities depend on usage, we employ distributionally robust optimization to model uncertainty in line survival distributions. We adapt the stochastic nested decomposition algorithm and derive a deterministic upper bound for its finite convergence. To enhance computational efficiency, we exploit the Lagrangian dual problem structure for a faster generation of Lagrangian cuts. Using realistic data from the California transmission grid, we demonstrate the superior performance of dynamic response policies against two-stage alternatives through a comprehensive case study. In addition, after solving the multistage formulation, we construct easy-to-implement policies that significantly reduce computational burden while maintaining good performance in real-time deployment. History: Accepted by Russell Bent, Area Editor for Network Optimization: Algorithms and Applications. Funding: This work was supported by the U.S. Department of Energy, Office of Electricity [Grant DE-AC02-05CH11231]. The work of R. Jiang was supported in part by the U.S. National Science Foundation, Division of Electrical, Communications and Cyber Systems [Grant ECCS-1845980] and the U.S. Air Force Office of Scientific Research [Grant FA9550-23-1-0323]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2025.1210 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2025.1210 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Estrada-Garcia, Juan-Alberto↗

Knowledge-Informed Uncertainty-Aware Machine Learning for Time Series Forecasting of Dynamical Engineered Systems

The high complexity and multiscale nature of many engineered systems—such as those in nuclear power plants—make representing and forecasting their dynamic behavior challenging. Physics-based models can be overly complex and computationally intractable, whereas machine learning (ML) tools are often data-hungry and prone to unphysical solutions. This study proposes a knowledge-informed ML-aided hybrid residual modeling approach that offers accurate and efficient time series forecasting for the operation of dynamical engineered systems. Hybrid residual modeling entails a baseline solution from domain knowledge and known physics expressions about the system dynamics integrated with an ML model to capture undiscovered information from the mismatch (i.e., residuals) between true states from measurements and baseline-predicted outputs. This study further quantifies the ML model uncertainty to provide trustworthy solutions. Real-time operational data from thermal-hydraulic flow loops of the cryogenic moderator system in Oak Ridge National Laboratory’s Spallation Neutron Source facility were used to demonstrate the potential of knowledge-informed uncertainty-aware ML in real-world applications. The state variables of the cryogenic helium loop were modeled with (1) first principles–based system identification (sysID), (2) long short-term memory (LSTM) neural network, and (3) hybrid sysID (baseline) + LSTM (residual). The superior predictive capability of the sysID+LSTM model versus stand-alone sysID and LSTM is confirmed by average performance metrics and individual data points across different prediction horizons. By creating a robust representation of the underlying physical system, the widely applicable hybrid residual modeling approach will enable the future development of digital twins for performance prediction, prognostics, and operation control.

Zhao, Xingang↗

Uncertainty analysis for VERA problem 2 using the cell-code Condor v2.8.05

Condor is a cell-level neutronic calculation code that applies multi-group collision probabilities with heterogeneous response coupling method within generic geometry configurations. Under the Condor's code continuous development, the incorporation of up-to-date methodologies and state-of-the-art practices in reactor analysis represents a driving force. In this work, the capabilities of Condor v2.8.05 to develop an uncertainty analysis for realistic PWR-kind fuel assemblies are studied. The Total Monte Carlo approach is applied to quantify the impact of fabrication tolerances in the code's results for reactivity and power distributions, by means of randomly sampled input values using the VERA problem 2 as basis. The VERA problem 2 proposes a series of Westinghouse 2D 17 x 17-type fuel lattices, to be calculated reflected at beginning-of-life without Xe. The configurations correspond to a modern PWR. Selected neutronic parameters from Condor runs are thus analyzed in terms of the observed spread as well as the obtained distributions for the randomly perturbed cases, showing the capability of the code to handle the required input data, as well as its ability to provide valuable insights regarding uncertainty quantification.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Sensitivity and uncertainty analysis of PWR spent fuel observables to operational and model parameters

Sensitivity and uncertainty analyses of spent nuclear fuel (SNF) observables - decay heat, neutron and γ-ray emission rate - to operational and model parameters have been performed. A 2D model representing a typical PWR 17x17 UO{sub 2} fuel assembly has been taken as reference. The Serpent code and ENDF/B-VII.1 evaluated nuclear data library have been used for the analyses. Relative uncertainty of decay heat, neutron and γ-ray emission rates due to Monte Carlo counting statistics, as well as the number of fuel pin radial regions required for an accurate characterization of SNF neutron emission, have been estimated. A parametric study has been carried out to investigate the impact of the homogenization to an average value of the fuel and moderator temperature, boron concentration power and burnup on the prediction of the selected observables. In addition, linear sensitivity coefficients have been calculated. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Rossi-alpha Uncertainty Quantification by Analytic, Bootstrap, and Sample Methods to Inform Fitting Best Practices

The prompt neutron period (the negative reciprocal of the prompt neutron decay constant) can be estimated using the Rossi-alpha technique that is predicated on fitting Rossi alpha histograms and of interest in nuclear criticality safety and nonproliferation. The histograms are traditionally fit with a one-exponential model; however, recent work has proposed a two-exponential model to account for reflector induced phenomenon. Until recently, the uncertainty quantification for either model was inadequate (inaccurate and demanded large measurement times). Measurement uncertainty quantification by sample and analytic methods was developed and validated in Ref. The purpose of this transaction is to (i) validate a new bootstrap method by comparing bin-by-bin error bar estimates and (ii) demonstrate how to choose bin widths and reset times to optimize precision and accuracy.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NEON AOP foliar trait maps, maps of model uncertainty estimates, and conifer map, East River, CO 2018

This data package contains mapped trait estimates and their uncertainties, and conifer map, for the National Ecological Observatory Network's Airborne Observation Platform survey data acquired over the Upper East River, Colorado in 2018. For full details, please see associated reference. in brief, trait models were developed independently for needle and non-needle leaf species using partial least squares regression (PLSR) using ground data from additional datasets: doi:10.15485/1618130, doi:10.15485/1618132, and doi:10.15485/1631278, merged with extracted spectral data from doi:10.15485/1618131. We separated vegetated pixels into needle and non-needle classes in order to generate a classification map based on the spectral differences between these leaf types (conifer.tif). We trained a deep learning model with custom architecture, detailed in Chadwick et al. In Press. The model performed with 0.998 true positive rate and 0.982 true negative rate, with ‘positives’ being non-needle identification. We then utilized PLSR to generate models of foliar traits for each leaf type. So that we could also map uncertainty in these predictions, we generated ten different models for needle and non-needle leaf species using different testing holdout sets of discrete sites. Each of these models was developed with a 100-fold cross validation procedure that utilized a 70% training set and 30% validation set with each fold, and then assessed based on the 10% of testing sites that were not included in that model’s development. The mean predicted value across the 10 models is used for the trait estimate in each pixel across the study area. The models are applied according to the leaf type designation in the conifer.tif map. The errors are the standard deviation across the 10 different models developed, with high error suggesting instability in model prediction and areas where values may not be reliable for ecological inference. These maps are only applied to areas with a NDVI > 0.5 to exclude non-vegetated areas. Shade masks could be applied to these data (doi:10.15485/1618131), but have not been for this data package. These data are also available on Google Earth Engine: https://code.earthengine.google.com/?asset=users/kdc/ER_NEON

54 ENVIRONMENTAL SCIENCES↗

Maps of plant functional type (PFT), PFT fractional cover, and uncertainty derived from AVIRIS-NG data, 2019, Seward Peninsula

Remote sensing maps of plant functional type (PFT), PFT fractional cover (fCover), and fCover uncertainty maps derived from NASA’s Airborne Visible / Infrared Imaging Spectrometer – Next Generation (AVIRIS-NG). The AVIRIS-NG imaging spectroscopy data (380 ~ 2510 nm) was collected as a part of the collaboration between NASA’s Arctic-Boreal Vulnerability Experiment (ABoVE; Miller et al., 2019) and DOE’s Next Generation Ecosystem Experiment in the Arctic (NGEE-Arctic). This package includes maps for flights over Teller, Kougarok, and Council watersheds created using eight AVIRIS-NG imagery collected in July, 2019. The map data and metadata are provided as image (ENVI, *.png) and text (*.txt, *hdr) formats. Additional supporting map quicklooks are provided as GIS *.kml files. Detailed description of the methods for each map are provided in Yang et al., (2023). These datasets are provided in support of Yang et al., (In revision) “Topography and Functional Traits Control the Distribution of Key Shrub Plant Functional Types in Low-Arctic Tundra”.The Next-Generation Ecosystem Experiments: Arctic (NGEE Arctic), was a research effort to reduce uncertainty in Earth System Models by developing a predictive understanding of carbon-rich Arctic ecosystems and feedbacks to climate. NGEE Arctic was supported by the Department of Energy's Office of Biological and Environmental Research.The NGEE Arctic project had two field research sites: 1) located within the Arctic polygonal tundra coastal region on the Barrow Environmental Observatory (BEO) and the North Slope near Utqiagvik (Barrow), Alaska and 2) multiple areas on the discontinuous permafrost region of the Seward Peninsula north of Nome, Alaska.Through observations, experiments, and synthesis with existing datasets, NGEE Arctic provided an enhanced knowledge base for multi-scale modeling and contributed to improved process representation at global pan-Arctic scales within the Department of Energy's Earth system Model (the Energy Exascale Earth System Model, or E3SM), and specifically within the E3SM Land Model component (ELM).

54 ENVIRONMENTAL SCIENCES↗

Exploring Uncertainty in Moment Estimation for Small Earthquakes in Southern Nevada Using the Coda Envelope Method

Compiling source parameter estimates for small earthquakes is important both for our understanding of earthquake physics and for accurately assessing earthquake hazard. Reliable source parameter estimates are difficult to achieve for small earthquakes, in part due to our inability to accurately model the relevant physical processes at high frequencies. The coda envelope methodology developed by Mayeda and Walter (1996) and Mayeda et al. (2003) can mitigate this concern and estimate the moment of small earthquakes by determining the parameters that control the shape of the S-wave coda envelope while eliminating path effects by minimizing the scatter between seismic stations. Here, we use an open-source implementation of this technique called the Coda Calibration Tool (CCT; Barno, 2017) to calculate CCT-based moment magnitude estimates of small earthquakes (M L 0–3) in the Rock Valley, Nevada, region within the Nevada National Security Site. The Rock Valley data set is of particular interest because it allows us to explore the changes in uncertainties of the coda calibration method with earthquake size and depth. We found that a consistent linear relationship exists between the local magnitude M L and our coda-derived M w estimates for earthquakes as small as M L 0–3, but that current CCT workflows do not accurately characterize very shallow events. We also demonstrate that the epistemic uncertainty in the apparent stress value assumed by the CCT algorithm can influence magnitude estimates of small earthquakes. In conclusion, these results provide valuable insight into the seismicity of this region, and inform future analysis and modeling efforts for nuclear monitoring and seismic hazard.

58 GEOSCIENCES↗

Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization Parameter Estimation Uncertainty Quantification and Sensitivity Analysis: Version 6.12 User's Manual

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a user's manual for the Dakota software and provides capability overviews and procedures for software execution, as well as a variety of example studies.

97 MATHEMATICS AND COMPUTING↗

An Overview of the State-of-the-Art Reactor Consequence Uncertainty Assessment Accident Progression Insights

The U.S. Nuclear Regulatory Commission (NRC) with Sandia National Laboratories (Sandia) have completed three uncertainty analyses (UAs) as part of the State-of-the-Art Reactor Consequence Analyses (SOARCA) program. The SOARCA UAs included an integrated evaluation of uncertainty in accident progression, radiological release, and offsite health consequence projections. The UA for Peach Bottom, a boiling-water reactor (BWR) with a Mark I containment located in the State of Pennsylvania, analyzed the unmitigated long-term station blackout SOARCA scenario. The UA for Sequoyah, a 4-loop Westinghouse pressurized-water reactor (PWR) located in the State of Tennessee, analyzed the unmitigated short-term station blackout SOARCA scenario, with a focus on issues unique to the ice condenser containment and the potential for early containment failure due to hydrogen deflagration. The UA for Surry, a 3-loop Westinghouse PWR with a sub-atmospheric large dry containment located in the State of Virginia, analyzed the unmitigated short-term station blackout SOARCA scenario including the potential for thermally-induced steam-generator tube rupture. These three UAs are currently documented in three NUREG/CR reports. This report provides input to planned NRC documentation on the insights and findings from the SOARCA UA program. The purpose of the summary report is to provide a useful reference for regulatory applications that require the evaluation of offsite consequence risk from beyond design basis event severe accidents. This report focuses on the accident progression and source term insights developed from the MELCOR analyses. MELCOR is the NRC's best-estimate, severe accident computer code used in the SOARCA UAs. In anticipation of the SOARCA UA insights work, NRC and Sandia benchmarked the response of the Peach Bottom model to selected reference calculations from the Peach Bottom SOARCA UA. Peach Bottom was the first SOARCA UA performed and was completed in 2015 using the MELCOR 1.8.6 code. The PWR SOARCA UAs evolved the original methodology and utilized the updated MELCOR 2.2 computer code. The Peach Bottom model has been systematically updated for other NRC research efforts and has been updated to MELCOR 2.2. computer code. The findings from the new reference calculations using the updated model with the MELCOR 2.2 code are also integrated into the report. A second objective is an assessment of the applicability of the results to the other nuclear reactors in the U.S. As the key findings are reviewed, judgments are presented on the applicability of the results to other U.S. nuclear power plants. An important objective of the SOARCA program relied on high- fidelity plant-specific modeling. However, the nature of the insights and conclusions allowed judgements to be made on the applicability of the various insights to the same general classification of plant (i.e., BWR or PWR) or the entire fleet of plants. Finally, the results from the SOARCA UA accident progression calculations contain a wealth of information not previously documented in the NUREG/CRs. This report includes new but related information that can be used to benchmark past or support future regulatory decisions related to severe accidents. The new work includes a benchmark of the NUREG-1465 licensing source term definitions, the variability of key accident progression events and timing to radionuclide release, and an improved understanding of the timing and source terms from consequential steam generator tube ruptures. iii ACKNOWLEDGEMENTS The Sandia authors gratefully acknowledge the significant technical and programmatic contributions from the NRC SOARCA team which are reflected throughout the report. Dr. Tina Ghosh has been involved throughout the SOARCA UAs, providing the primary managerial and technical oversight. The long lists of NRC and Sandia contributors from the SOARCA UAs are cited in the three NUREG/CRs and are also gratefully acknowledged by the small team of authors compiling the results of their efforts. Significant technical contributions, advice, and reviews were provided by Dr. Hossein Esmaili, Dr. Alfred Hathaway, and Dr. Edward Fuller (retired) of the NRC. Dr. Randal Gauntt (retired), Mr. Patrick Mattie, Mr. Joseph Jones (retired), and Dr. Doug Osborn from Sandia are recognized as the SOARCA UA managers guiding the past efforts. There is a comparable list of project managers at the NRC including Ms. Patricia Santiago, Dr. Salman Haq, and Mr. Jon Barr. Sadly, we have lost Mr. Charlie Tinkler and Mr. Robert Prato, who were important contributors to the original SOARCA project. Finally, Mr. Kyle Ross and Mr. Mark Leonard have also retired but were significant technical contributors. Mr. Kyle Ross was the technical lead on all three SOARCA UAs and the original pressurized water reactor SOARCA study. Mr. Leonard was the technical lead on the original boiling water reactor SOARCA study and a key contributor to the first Peach Bottom SOARCA UA. iv

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Automated Segmentation of Porous Thermal Spray Material CT Scans with Geometric Uncertainty Estimation

Thermal sprayed metal coatings are used in many industrial applications, and characterizing the structure and performance of these materials is vital to understanding their behavior in the field. X-ray Computed Tomography (CT) machines enable volumetric, nondestructive imaging of these materials, but precise segmentation of this grayscale image data into discrete material phases is necessary to calculate quantities of interest related to material structure. In this work, we present a methodology to automate the CT segmentation process as well as quantify uncertainty in segmentations via deep learning. Neural networks (NNs) are shown to accurately segment full resolution CT scans of thermal sprayed materials and provide maps of uncertainty that conservatively bound the predicted geometry. These bounds are propagated through calculations of material properties such as porosity that may provide an understanding of anticipated behavior in the field.

36 MATERIALS SCIENCE↗

Learning Hidden Structure in Multi-Fidelity Information Sources for Efficient Uncertainty Quantification (LDRD 218317)

This report summarizes the work done under the Laboratory Directed Research and Development (LDRD) project entitled "Learning Hidden Structure in Multi-Fidelity Information Sources for Efficient Uncertainty Quantification". In this project we investigated multi-fidelity strategies for fusing data from information sources of varying cost and accuracy. Most existing strategies exploit hierarchical relationships between models, for example that occur when different models are generated by refining a numerical discretization parameter. In this work we focused on encoding the relationships between information sources using directed acyclic graphs. The multi-fidelity networks can have general structure and represent a significantly greater variety of modeling relationships than recursive networks used in the current state literature. Numerical results show that a non-hierarchical multi-fidelity Monte Carlo strategy can reduce the cost of estimating uncertainty in predictions of a model of plasma expanding in a vacuum by almost two orders of magnitude.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Revision of Fission Yields Uncertainties in ENDF/B-VIII.0

The spontaneous and neutron-induced fission yield sublibraries in the Evaluated Nuclear Data Files (ENDF/B) contain cumulative and independent fission yield values for dozens of fissioning systems, and hundreds of fission products. In this work, we report on a correction step that was undertaken after observing anomalously large uncertainties for several end-of-chain fission products. A total of 17 cumulative fission yield uncertainties and the value of 2 independent yields were corrected as a result of this revision.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

MELCOR 2.2 Benchmarks of Peach Bottom NUREG/CR 7155 Uncertainty Analysis

The U.S. Nuclear Regulatory Commission (NRC) performed a first-of-a-kind uncertainty analysis (UA) of the accident progression, radiological releases, and offsite consequences for the State-of- the-Art Reactor Consequence Analyses (SOARCA) of an unmitigated long-term station blackout (LTSBO) severe accident scenario at the Peach Bottom Atomic Power Station. The objective of the UA was to evaluate the robustness of the SOARCA deterministic "best estimate results and conclusions documented in NUREG-1935, and to develop insight into the overall sensitivity of the SOARCA results to uncertainty in key modeling inputs. The study was completed in 2015 and documented in NUREG/CR-7155. Since 2015, two other SOARCA UAs were completed for two pressurized water reactor (PWR) plants. The PWR UAs incrementally updated the approach and methodology, including using the latest release of the MELCOR 2.2 computer code. There were also advances made in the state-of-the-art modeling related to NRC efforts using the Peach Bottom model in NUREG-2206, which provided the technical basis for the containment protection and release reduction rulemaking for boiling water reactors with Mark I and Mark II containments. This report documents the input model changes from the NUREG/CR-7155 study and performs a small number of reference calculations to assess the changes of the new computer code and the model input updates. The objective of the work is to verify whether the updated Peach Bottom MELCOR model and updated version of MELCOR support the conclusions formed in the Peach Bottom SOARCA UA by performing these representative calculations.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗