SEARCH · Search NASA

Results for “analysis codes”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 595 records · Page 33

All sources NASA NTRS DOE OSTI

DOE OSTI2026

HFIR Steady State Heat Transfer Code (HSSHTC) Statistical Uncertainty Analysis

HSSHTC, the safety basis steady state TH code for HFIR, uses a highly conservative approach in which all input and calculation uncertainties are resolved simultaneously at their most limiting setting. This results in excessive conservatism which does not account for the high unlikelihood of such simultaneous worst-case conditions. The present study explores an alternative approach, BEPU, in which reasonable working assumptions for the probability distribution of each input uncertainty are used to determine a relationship between burnout power margin and core fuel failure probability. This was performed under a philosophy of perturbing uncertainty parameters already defined within the HSSHTC methodology while preserving the HSSHTC calculation approach and solution methodology itself. Based on the assumptions employed in this study, the BEPU approach resulted in a 0.29 increase in burnout power ratio (25 MW increase in burnout power) compared to the latest HSSHTC calculations of C-HFIR-2026-004. The study can be refined in the future by employing fuel fabrication data to provide more realistic input distributions. Future changes to the HSSHTC methodology would potentially allow a more comprehensive treatment of uncertainties which may further increase the burnout power ratio.

Wysocki, Aaron [ORNL] (ORCID:0000000222043779)↗

DOE OSTI2012

Best-estimate plus uncertainty thermal-hydraulic stability analysis of BWRs using TRACG code

Over the last decade, Boiling Water Reactor (BWR) power up-rates have increased plant rated power output significantly. Subsequent projects have expanded flow domains (e.g. MELLLA+) for operation at these higher power levels. This has resulted in an increase in the power to flow ratio in regions susceptible to reactor thermal-hydraulic instabilities. Since BWRs are susceptible to coupled thermal-hydraulic/nuclear oscillations when operating at these conditions, such oscillations must be prevented or reliably detected and suppressed. The Detect and Suppress Solution - Confirmation Density (DSS-CD) is the most sophisticated GEH BWR instability protection system ever employed. DSS-CD implements algorithms that monitor closely-spaced groups of Local Power Range Monitor (LPRM) detectors to detect periodic behavior typical of reactor instability events. This system is able to detect small, localized power variations in the core, distinguish between true instabilities and plant noise, and trip/scram the reactor while maintaining adequate safety margins. The combination of hardware, software, and system setpoints provides protection against violation of the Safety Limit Minimum Critical Power Ratio (SLMCPR) for anticipated oscillations. To support DSS-CD implementation, the TRACG system code is used to simulate events to confirm the capability of the DSS-CD solution for early oscillation detection and suppression. TRACG is a GEH proprietary version of the Transient Reactor Analysis Code (TRAC). TRACG includes a multi-dimensional, two-fluid model for the reactor thermal-hydraulics and a three-dimensional reactor kinetics model. The models are qualified to simulate a large variety of tests and reactor configurations, including thermal-hydraulic stability events. These features allow for detailed, best-estimate simulation of a wide range of BWR phenomena. A set of integrated TRACG event simulations for reasonably limiting anticipated events can be used to calculate the effect on the Minimum Critical Power Ratio (MCPR) performance. The purpose of the DSS-CD TRACG analysis is to confirm the inherent MCPR margin afforded by the solution design. This paper presents the Best Estimate Plus Uncertainty (BEPU) DSS-CD TRACG methodology and its application to BWR Thermal-Hydraulic (T-H) stability analyses. The statistical Code Scaling, Applicability and Uncertainty (CSAU) methodology (defined in NUREG/CR-5249) is used to calculate the MCPR uncertainty. The TRACG simulation includes a full core individual bundle model in which each fuel bundle is modeled as an individual T-H channel. The complete CSAU analysis of full core individual bundle model is an innovative solution represents the state-of-the-art stability analysis of BWRs and is the first ever full statistical analysis for stability safety analyses. The adoption of BEPU methodologies for stability analyses advances the understanding of the associated physical phenomena and maintains the safety of reactor plant operation in expanded operation domain with up-rated power. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2023

Recent progress towards incorporating radiochemical analysis in LANL ASC codes

This document summarizes the recent progress towards incorporating charged-particle radiochemical (RadChem) analysis in different LANL codes within the Advanced Scientific Computing (ASC) Program. The first section is focused on xRAGE and the implementation of the necessary physics packages to build an in-line RadChem capability. The second section provides a summary of the current RadChem postprocessing capabilities.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

DOE OSTI2016

V and V of the HTR Code Package (HCP) as a comprehensive HTR steady state and transient safety analysis framework - 18664

The HTR code package (HCP) allows for the simulation of several safety-related aspects of a High Temperature Reactor core in a highly integrated manner. HCP currently couples the thermo-fluid dynamics and time dependent neutronics code MGT, the spectrum code TRISHA, the burn up code TNT, the fuel management code SHUFLE and the fission product release code STACY. During its development, state-of-the-art programming techniques and standards are applied. The cross sections in HCP are generated by a 0D- or 1D solver featuring an innovative approach to treat the double heterogeneity of pebble fuel. Also major improvements have been made to optimize the nuclear data library based on ENDF/B-VII. Two advanced fuel management models are provided by the code module SHUFLE that go far beyond the capabilities of existing system codes like VSOP. The source term analysis code module STACY is coupled to HCP providing release rate calculations with a high spatial resolution making use of the nuclide densities provided by TNT. An outstanding new feature of HCP is the possibility to simulate long-term operation scenarios based on OTTO or MEDUL fuel shuffling schemes as well as selected transients in one integrated code package. Even alternating steady state/transient/steady state simulations are possible. So with HCP different fuel strategies and their influence on various kinds of accidents can be examined with one consistent reactor model. This paper provides an overview of the development status of the HCP and reports about selected benchmark results. It is demonstrated that the new system code HCP is capable to replace existing stand-alone codes like VSOP, TINTE/MGT, FRESCO or PANAMA while introducing new features, which so far to our knowledge were not available in the field of HTR safety research. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2011

Renewable Energy Requirements for Future Building Codes: Energy Generation and Economic Analysis

As the model energy codes are improved to reach efficiency levels 50 percent greater than current codes, installation of on-site renewable energy generation is likely to become a code requirement. This requirement will be needed because traditional mechanisms for code improvement, including the building envelope, mechanical systems, and lighting, have been maximized at the most cost-effective limit.

energy codes↗

DOE OSTI2024

Efficient continuous Energy-Multigroup hybrid depletion scheme using the Shift Monte Carlo code. Part I: Energy condensation sensitivity analysis

Monte Carlo (MC) codes coupled to depletion solvers are increasingly used to provide high fidelity fuel cycle modeling capabilities. Here, these coupled depletion-MC tools produce accurate results in general but can experience nonphysical spatial oscillations when time steps are large or when a system’s dominance ratio approaches unity. Two substepping techniques have been developed previously to remedy and dampen these spatial oscillations without needing to reduce step sizes. The first approach relied on higher-order techniques to account for spectral changes within steps (extrapolation and interpolation techniques). The second approach used the first order perturbation (FOP) theory to account for the change in the one-group spatial flux distribution within steps. This paper develops a hybrid depletion methodology which, in a way, combines how the flux is handled in both substepping techniques. Specifically, the multigroup (MG) MC Shift code is used to update the flux distribution within steps rather than a one-group FOP solver. A fully reflected pincell is investigated, which is not spatially dependent in the MG representation. Thus, the analysis in this paper is an initial demonstration of hybrid depletion. An upcoming companion paper will focus on how the hybrid depletion dampens spatial oscillations. The hybrid depletion approach is verified to be consistent with previous constant extrapolation depletion (CED) methods. This paper finds that the hybrid CED exhibits some error in the eigenvalue and one group constants within macro steps. To address this discrepancy, a simple interpolation scheme (CELI) is investigated. This work found that CELI sufficiently addresses the discrepancy in spectrum for macro steps up to 100 days. Overall, this work demonstrates that the hybrid depletion method can significantly reduce the number of high fidelity MC executions in a MC-coupled depletion with an acceptable eigenvalue error.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2017

Numerical Uncertainties vs. Model Uncertainties in Two-phase Flow Simulations

In recent years, verification, validation and uncertainty quantification (VVUQ) have become a common practice in thermal-hydraulics analysis. In general, these activities deal with propagations of uncertainties in computer code simulations, e.g., through system analysis codes. However, most existing such activities in thermal-hydraulics analysis have been primarily focused on model uncertainties, while numerical uncertainties were largely overlooked. Numerical uncertainties (or numerical errors) can appear in many different forms, e.g., round-off error, statistical sampling error, and discretization error. As pointed out by Oberkampf and Roy, discretization error is usually the largest however the most difficult type of error to estimate reliably. In thermal-hydraulics analysis, especially two-phase flow simulations commonly encountered in reactor safety analysis, the lack of consideration on discretization error is mainly due to the difficulty in estimating them. Accurate estimations on discretization error require continuous mesh refinement and/or implementation of high-order numerical schemes in system analysis code, both of which are unfortunately difficult to achieve for existing codes. At first, it should be emphasized that mesh refinement (or mesh sensitivity study) is a well-understood concept in the thermal-hydraulics field. However, it is not commonly practiced for many reasons, e.g., lack of understanding on numerical errors by code users, consideration on computational cost, deteriorated numerical stability performance with refined meshes, and etc. Secondly, high-order (e.g., second-order) numerical schemes are simply unavailable in almost any existing system analysis code. Implementation of high-order numerical schemes in these codes is difficult, if not impossible, given the complexity of these codes. On the other hand, people tend to argue that numerical uncertainties (or discretization error as we have emphasized) are not as important as the commonly large uncertainties in two-phase flow models, e.g., closure correlations. As a result, nodalization is sometimes played unintentionally, or maybe intentionally, to match experimental data, which is referred as 'user effects' or 'compensating errors' in thermal-hydraulics community. Such a practice is highly criticized by Levy. In this work, we will at first build a computer code that incorporates both first-order and second-order numerical methods to solve the two-phase flow problems. The first-order method resembles the one used in many existing system analysis codes; and the second-order method works as the reference to estimate numerical errors. Numerical verifications on spatial discretization schemes will be presented in the form of mesh convergence study. It will also be demonstrated that, in practical scenarios, discretization errors can be as large as, or even larger than, model uncertainties via case studies.

42 ENGINEERING↗

DOE OSTI2026

FastrSHWFS Analysis

This code analyzes the reflection geometry of modified Shack-Hartmann Wavefront Sensor (SHWFS) masks, with a focus on the fastrSHWFS designs. It takes a height map of a reflective mask, divides it into sub apertures, removes the global focus term by referencing a central block, and fits local surface planes to each sub aperture. From these fits it computes reflection angles and propagates the corresponding rays downstream to determine spot positions and the overall reflected beam footprint as a function of distance. The implementation is parameterized in sub aperture size, number of sub apertures, focal length, and mask dimensions, so it can be adapted to different mask designs beyond the two current fastrSHWFS masks. The code: Converts mask bitmaps into physical height in microns and reconstructs a focus subtracted mask, divides the mask into a grid of sub apertures and assigns pixel and micron coordinates to each block, excludes user specified unused sub apertures from the analysis, fits a plane to each sub aperture to obtain local surface normals, propagates reflected rays to a range of z positions to compute ray spots and the full reflected beam width, computes the effective mask tilt angle with respect to the incoming beam as a function of propagation distance, and provides helper routines for plotting the grid over the mask and for visualizing the beam geometry. These tools are intended for iterating on fastrSHWFS mask designs and for planning downstream optical layouts, for example choosing lens positions and apertures that capture the reflected beam given known focal plane distances and beam widths.

Gerard, BenjaminL [Lawrence Livermore National Lab↗

DOE OSTI2013

ALFITeX: A code introducing improvements in the analysis of alpha spectra

A new code for the deconvolution of complex alpha-particle spectra, called ALFITeX, has been developed. The procedure is based on the Levenberg-Marquardt algorithm, with the curve fitting being the mathematical function formed by the convolution of a Gaussian with two left-handed exponential curves in the low-energy-tail region. ALFITeX has been checked with its application to the calculation of the alpha-particle emission probabilities of several nuclides.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2018

EFFECT OF DISCRETIZATION ERROR ON THE QUANTIFICATION OF MODEL UNCERTAINTY IN TWO-PHASE FLOW SIMULATIONS

Verification, validation and uncertainty quantification (VVUQ) have become a common practice in thermal-hydraulics analysis. In general, these activities deal with propagations of uncertainties in computer code simulations, e.g., through system analysis codes. However, most existing such activities in thermal-hydraulics analysis have been primarily focused on input and model uncertainties, while numerical errors were largely overlooked. Numerical errors can appear in many different forms, e.g., round-off error, statistical sampling error, and discretization error. In thermal-hydraulics analysis, especially two-phase flow simulations commonly encountered in reactor safety analysis, the lack of consideration of discretization error is mainly due to the difficulty in estimating them. Accurate estimations of discretization error require continuous mesh refinement and/or implementation of high-order numerical schemes in system analysis code, both of which are difficult to achieve in existing codes. In this work, we will build a computer code that incorporates both first-order and second-order numerical methods to solve the two-phase flow problems. The first-order method resembles the one used in many existing system analysis codes; and the second-order method works as the reference to estimate numerical errors. Numerical verification of spatial discretization schemes will be presented in the form of mesh convergence study. It will also be demonstrated via case studies that, in practical scenarios, discretization errors can be as large as, or even larger than, model uncertainties.

42 ENGINEERING↗

DOE OSTI2022

Modeling of a Generic Pebble Bed High-temperature Gas-cooled Reactor (PB-HTGR) with SAM

This report presents the modeling of the core of a generic pebble-bed reactor (PBR) at the system level using the System Analysis Module (SAM) code. This work is an extension of a previous work by the authors (Ooi et al. (2021)) that used the so-called 2-D ring model approach to model the PBMR-400. With the new approach, the pebble bed of the reactor is modeled with multiple PBCoreChannel components with spherical heat structures which allows the code to calculate thermal fluid parameters with built-in closure relations. The new core-channel approach is an improvement to the 2-D ring model approach as it does not introduce geometric distortions to the model and thus reduces the uncertainties of the predictions. In addition to thermal fluid simulations, point kinetics (PKE) are included to the model. Simulations are performed under a steady-state normal operation condition and a load-following transient scenario. This particular transient scenario is chosen as it tests both the thermal fluid and neutronics aspects of the model. The predicted results from both the steady-state and transient scenarios are compared with the results by Stew- art et al. (2021) who performed similar simulations with a Griffin-Pronghorn coupled tool. Despite the differences between the codes, with SAM being a system-analysis code and Pronghorn being a porous-medium code, both sets of results compare favorably. The over- all profiles and trends of the predicted temperatures and reactivities from the SAM and Griffin/Pronghorn simulations are similar, with some differences in their predicted values. The first part of the report covers the significance of a relatively fast-running approach that is capable of modeling the pebble bed reactor at the system-level while simultaneously capturing the radial thermal behavior of the core. Then, the modeling approach used in this work is discussed in details. Lastly, the results and comparisons with the Griffin/Pronghorn simulation are presented.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Antiproton bounds on dark matter annihilation from a combined analysis using the DRAGON2 code

Abstract Early studies of the AMS-02 antiproton ratio identified a possible excess over the expected astrophysical background that could be fit by the annihilation of a weakly interacting massive particle (WIMP). However, recent efforts have shown that uncertainties in cosmic-ray propagation, the antiproton production cross-section, and correlated systematic uncertainties in the AMS-02 data, may combine to decrease or eliminate the significance of this feature. We produce an advanced analysis using the DRAGON2 code which, for the first time, simultaneously fits the antiproton ratio along with multiple secondary cosmic-ray flux measurements to constrain astrophysical and nuclear uncertainties. Compared to previous work, our analysis benefits from a combination of: (1) recently released AMS-02 antiproton data, (2) updated nuclear fragmentation cross-section fits, (3) a rigorous Bayesian parameter space scan that constrains cosmic-ray propagation parameters.We find no statistically significant preference for a dark matter signal and set strong constraints on WIMP annihilation tobb̅, ruling out annihilation at the thermal cross-section for dark matter masses below ∼ 200 GeV. We do find a positive residual that is consistent with previous work, and can be explained by a ∼ 70 GeV WIMP annihilating below the thermal cross-section. However, our default analysis finds this excess to have a local significance of only 2.8σ, which is decreased to 1.8σwhen the look-elsewhere effect is taken into account.

Astronomy & Astrophysics↗

DOE OSTI2012

Inference of Causal Networks from Time-Varying Transcriptome Data via Sparse Coding

Temporal analysis of genome-wide data can provide insights into the underlying mechanism of the biological processes in two ways. First, grouping the temporal data provides a richer, more robust representation of the underlying processes that are co-regulated. The net result is a significant dimensional reduction of the genome-wide array data into a smaller set of vocabularies for bioinformatics analysis. Second, the computed set of time-course vocabularies can be interrogated for a potential causal network that can shed light on the underlying interactions. The method is coupled with an experiment for investigating responses to high doses of ionizing radiation with and without a small priming dose. From a computational perspective, inference of a causal network can rapidly become computationally intractable with the increasing number of variables. Additionally, from a bioinformatics perspective, larger networks always hinder interpretation. Therefore, our method focuses on inferring the simplest network that is computationally tractable and interpretable. The method first reduces the number of temporal variables through consensus clustering to reveal a small set of temporal templates. It then enforces simplicity in the network configuration through the sparsity constraint, which is further regularized by requiring continuity between consecutive time points. We present intermediate results for each computational step, and apply our method to a time-course transcriptome dataset for a cell line receiving a challenge dose of ionizing radiation with and without a prior priming dose. Our analyses indicate that (i) the priming dose increases the diversity of the computed templates (e.g., diversity of transcriptome signatures); thus, increasing the network complexity; (ii) as a result of the priming dose, there are a number of unique templates with delayed and oscillatory profiles; and (iii) radiation-induced stress responses are enriched through pathway and subnetwork studies.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

Implementation of Additional Models into the MACCS Code for Nearfield Consequence Analysis

The NRC’s Non-Light Water Reactor Vision and Strategy report discusses the MACCS code readiness for nearfield analyses. To increase the nearfield capabilities of MACCS, the plume meander model from Ramsdell and Fosmire was integrated into MACCS and the MACCS plume meander model based on U.S. NRC Regulatory Guide 1.145 was updated. Test cases were determined to verify the plume meander model implementation into MACCS 4.1. The results using the implemented MACCS plume meander models match the comparisons with other codes and analytical calculations. This verifies that the additional MACCS plume meander models have been successfully implemented into MACCS 4.1. This report documents the verification of these model implementations into MACCS and a comparison of the results using

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2024

Analysis of the ASME Code Rules for Subsection III-5-HHB (Composite Materials) for Current HTR Design Requirements

This document includes the critical analysis review of the American Society of Mechanical Engineers (ASME) Section III Division 5 Subsection HH Subpart B (HHB), including Mandatory Appendices, that was published in 2023. In the context of this document, reference to “the code” is specific to this subsection unless otherwise specified. A specific composites task group within the ASME Nonmetallic Design and Materials Working Group, with the support of external experts, was established to perform a gap analysis review. The significant findings are summarized here. The committee response with suggested action items are detailed in the body of the report.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Gamma Spectrometry Code Rodeo for Uranium Enrichment—FY 2021 Report

In FY22, the participating Department of Energy (DOE) laboratories continued the work on the project “Gamma Spectrometry Code Rodeo for Uranium Enrichment”. Oak Ridge National Laboratory (ORNL) and Lawrence Livermore National Laboratory (LLNL) continued their efforts to acquire spectra using uranium sources. A collimator (with side and back shields) was custom designed and constructed at ORNL. Spectra were acquired at ORNL using the uranium enrichment standards supplied by New Brunswick Laboratory (NBL) and the collimated M400 detector. Spectra were also acquired using steel absorbers of different thickness placed between the source and the collimated M400 detector. The plan was to ship the collimator to LLNL so that spectra could be acquired using the LLNL detector in collimated geometries. This activity was suspended since problems were noticed with the performance of the LLNL M400 detector. Also, it was brought to light to the project team that some of the aspects of the M400 detector had been updated by the vendor H3D in response to requests by the IAEA. In February 2021, the ORNL and LLNL M400 detectors were returned to the H3D factory in order to resolve the problems with the LLNL detector and to update ORNL and LLNL detectors to the same configuration as the M400 supplied to the IAEA. H3D repaired the LLNL M400 and performed the IAEA updates on both the ORNL and LLNL detectors. ORNL and LLNL received the detectors in April 2021. Data acquisition was continued using the upgraded detectors. ORNL re-collected the spectra using point sources and the NBL standards in uncollimated and collimated geometries. The collimator was shipped from ORNL to LLNL. Spectra were acquired at LLNL through Q4 of FY22. When the ORNL spectra were examined closely, it became apparent that there were spurious artifacts present in some of the spectra. This rendered suspect the ORNL spectra collected in June/July 2021 time frame. ORNL contacted H3D and per H3D’s advice, the M400 detector was returned to H3D for repairs in mid-August 2021. H3D diagnosed the problem and established that the root cause was the extra tight packaging that created a strain on the CZT crystals, causing one of them to break down. The repaired M400 was returned to ORNL in early September 2021. ORNL re-started data acquisition for the third time. Data was continued to be acquired at ORNL and LLNL through September 2021. The ORNL and LLNL data will be shared with the principal investigators from the analyzing laboratories. The GADRAS code and FRAM have been developed to have the capability to analyze the M400 spectra. Good quality spectra from FY21 have been analyzed using modified versions of GADRAS and FRAM. The spectra have also been analyzed using the GEM code. The analysis results from GADRAS, FRAM and GEM codes are presented and discussed in this report. Some preliminary results from FRAM and GEM analysis were presented in February 2021 at the U-Pu Isotopics Workshop sponsored by the IAEA. CZTU code is being modified to analyze M400 spectra. Data collection, code development and analysis will be continued in FY22 as per the FY22 Project Work Plan (PWP).

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2012

Verification and validation of the PLTEMP/ANL code for thermal hydraulic analysis of experimental and test reactors

The document compiles in a single volume several verification and validation works done for the PLTEMP/ANL code during the years of its development and improvement. Some works that are available in the open literature are simply referenced at the outset, and are not included in the document. PLTEMP has been used in conversion safety analysis reports of several US and foreign research reactors that have been licensed and converted. A list of such reactors is given. Each chapter of the document deals with the verification or validation of a specific model. The model verification is usually done by comparing the code with hand calculation, Microsoft spreadsheet calculation, or Mathematica calculation. The model validation is done by comparing the code with experimental data or a more validated code like the RELAP5 code.

Kalimullah, M.↗

DOE OSTI2018

Demonstration of LOTUS multiphysics BEPU analysis framework for LB-LOCA simulations

The LOCA Toolkit for U.S. light water reactors (LOTUS) currently under development at Idaho National Labs (INL) is a plug and play, multiphysics environment to be used in support of system level plant transient analysis. New proposed rule changes in LOCA safety regulations (10 CFR 50.46c) require the inclusion of cladding hydrogen content in the evaluation of equivalent cladding reacted (ECR) and peak cladding temperature (PCT). The potential for a future implementation of said rule change motivates the current development of a unique union of core design, system analysis, and fuel performance codes within a framework allowing for uncertainty quantification (UQ). A demonstration of LOTUS capabilities to address this potential need is performed with an integration of the core design code PHISICS, the fuel performance code FRAPCON, and the system analysis code RELAP5-3D. UQ is performed via Wilks’ method to compute the one sided 95/95 confidence values of the aforementioned safety metrics. Results demonstrate the benefits of the Multiphysics Best Estimate Plus Uncertainty (MP-BEPU) methodology and provide useful visualization of the limiting cases.

10CFR50.46c↗