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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 1,171 records · Page 65
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

CXSFIT Code Application to Process Charge-Exchange Recombination Spectroscopy Data at the T-10 Tokamak

The applicability of the CXSFIT code to process experimental data from Charge-eXchange Recombination Spectroscopy (CXRS) diagnostics at the T-10 tokamak is studied with a view to its further use for processing experimental data at the ITER facility. The design and operating principle of the CXRS diagnostics are described. The main methods for processing the CXRS spectra of the 5291-Å line of C{sup 5+} ions at the T-10 tokamak (with and without subtraction of parasitic emission from the edge plasma) are analyzed. The method of averaging the CXRS spectra over several shots, which is used at the T-10 tokamak to increase the signal-to-noise ratio, is described. The approximation of the spectrum by a set of Gaussian components is used to identify the active CXRS line in the measured spectrum. Using the CXSFIT code, the ion temperature in ohmic discharges and discharges with auxiliary electron cyclotron resonance heating (ECRH) at the T-10 tokamak is calculated from the CXRS spectra of the 5291-Å line. The time behavior of the ion temperature profile in different ohmic heating modes is studied. The temperature profile dependence on the ECRH power is measured, and the dynamics of ECR removal of carbon nuclei from the T-10 plasma is described. Experimental data from the CXRS diagnostics at T-10 substantially contribute to the implementation of physical programs of studies on heat and particle transport in tokamak plasmas and investigation of geodesic acoustic mode properties.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Development of uncertainty-aware equation-of-state models: Application to copper

Sophisticated hydrodynamic codes are commonly used to understand and predict events relevant to natural and applied sciences. The degree to which these simulations reflect reality, however, is dependent on how well we understand the materials and underlying physics involved. These research communities need material models that communicate the uncertainty in the physical properties, which at their basest form comes from the uncertainty in the underlying experimental measurements. Additionally, we have constructed a new framework for using both experimental measurements and the associated experimental uncertainties to build equation-of-state models that reflect not only current best measurements but also the accuracy of those measurements. This method had been used to construct an ensemble of equation-of-state models for copper that communicates the experimental uncertainties in the data through the equation-of-state model, which is available for application in any simulation metric of interest.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

A universal implementation of radiative effects in neutrino event generators

Due to the similarities between electron-nucleus (eA) and neutrino-nucleus scattering (νA), eA data can contribute key information to improve cross-section modeling in eA and hence in νA event generators. However, to compare data and generated events, either the data must be radiatively corrected or radiative effects need to be included in the event generators. We implemented a universal radiative corrections program that can be used with all reaction mechanisms and any eA event generator. Our program includes real photon radiation by the incident and scattered electrons, and virtual photon exchange and photon vacuum polarization diagrams. It uses the “extended peaking” approximation for electron radiation and neglects charged hadron radiation. This method, validated with GENIE, can also be extended to simulate νA radiative effects. This work facilitates data-event-generator comparisons used to improve νA event generators for the next-generation of neutrino experiments. Program Title: emMCRadCorr CPC Library link to program files:https://doi.org/10.17632/hmsxg82vnf.1 Developer's repository link:https://github.com/e4nu/emMCRadCorr Licensing provisions: AGPLv3 Programming language:C++ Nature of problem: Radiative effects can significantly modify the event kinematics and the resulting cross-sections. Such effects must be accounted for when comparing event generators to eA data. Existing radiative correction codes are tailored to specific processes and topologies, and are limited to a restricted phase space defined by the spectrometer acceptance. Therefore, a more general approach is required to apply radiative corrections to semi-inclusive and exclusive eA measurements. Solution method: Our program incorporates real photon radiation from both the incident and scattered electrons, as well as virtual photon exchange and photon vacuum polarization effects. It employs the “extended peaking” approximation for electron radiation while neglecting contributions from charged hadron radiation. The code is fully decoupled from event generator codes and can be used for all event generators in the market.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

MHD flow in liquid metal blankets: Major design issues, MHD guidelines and numerical analysis

The design of breeding blankets represents the major challenge for fusion reactor engineering because of performance requirements and severe operating conditions in terms of heat load and neutron flux. Liquid metal alloys such as lead-lithium, due to their lithium content, can be used to breed tritium, one of the plasma fuel components, and owing to their high thermal conductivity, they may serve as coolants. On the other hand, there are technical issues related to the fact that the liquid metals are electrically conducting and interact with the plasma-confining magnetic field. Induced electric currents and generated electromagnetic forces affect velocity and pressure distribution in the blankets. Magnetohydrodynamic (MHD) flows for fusion applications have been often investigated in simplified geometries, such as pipes, ducts, bends, with focus on their fundamental features. These analyses are essential, since results remain valid as background for the development of blanket designs, even when a concept is dismissed. However, the conceptual study of fusion blankets requires to take into account the global multiple effects, that arise when the full system is considered. Progress made in fusion-related MHD research results from combined numerical and experimental activities. In this paper we review and summarize features of 2D and 3D MHD flows that are typical in liquid metal blankets, together with available correlations for MHD pressure losses. This knowledge can provide simple design MHD guidelines that support a preliminary estimate of MHD effects in a blanket concept, in terms of pressure drop and flow distribution.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

SPECTRON, a neutron noise measurement system in frequency domain

This paper is dedicated to the presentation and validation of SPECTRON, a novel neutron noise measurement system developed at CEA Cadarache. The device is designed for the measurement of the β{sub eff} parameter (effective fraction of delayed neutrons) of experimental nuclear reactors using the Cohn-α method. An integrated electronic system is used to record the current from fission chambers. Spectra computed from measurement data are processed by a dedicated software in order to estimate the reactor transfer function and then the effective fraction of delayed neutrons as well as the prompt neutron generation time. After a review of the pile noise measurement method in current mode, the SPECTRON architecture is presented. Then, the validation procedure is described and experimental results are shown, supporting the proper functioning of this new measurement system. It is shown that every technical requirement needed for correct measurement of neutron noise is fulfilled. Measurements performed at MINERVE and EOLE, two experimental nuclear reactors at CEA Cadarache, in real conditions allowed us to validate SPECTRON.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2016

Design and validation of an MR-conditional robot for transcranial focused ultrasound surgery in infants

Purpose: Current treatment of intraventricular hemorrhage (IVH) involves cerebral shunt placement or an invasive brain surgery. Magnetic resonance-guided focused ultrasound (MRgFUS) applied to the brains of pediatric patients presents an opportunity to treat IVH in a noninvasive manner, termed “incision-less surgery.” Current clinical and research focused ultrasound systems lack the capability to perform neonatal transcranial surgeries due to either range of motion or dexterity requirements. A novel robotic system is proposed to position a focused ultrasound transducer accurately above the head of a neonatal patient inside an MRI machine to deliver the therapy. Methods: A clinical Philips Sonalleve MRgFUS system was expanded to perform transcranial treatment. A five degree-of-freedom MR-conditional robot was designed and manufactured using MR compatible materials. The robot electronics and control were integrated into existing Philips electronics and software interfaces. The user commands the position of the robot with a graphical user interface, and is presented with real-time MR imaging of the patient throughout the surgery. The robot is validated through a series of experiments that characterize accuracy, signal-to-noise ratio degeneration of an MR image as a result of the robot, MR imaging artifacts generated by the robot, and the robot’s ability to operate in a representative surgical environment inside an MR machine. Results: Experimental results show the robot responds reliably within an MR environment, has achieved 0.59 ± 0.25 mm accuracy, does not produce severe MR-imaging artifacts, has a workspace providing sufficient coverage of a neonatal brain, and can manipulate a 5 kg payload. A full system demonstration shows these characteristics apply in an application environment. Conclusions: This paper presents a comprehensive look at the process of designing and validating a new robot from concept to implementation for use in an MR environment. An MR conditional robot has been designed and manufactured to design specifications. The system has demonstrated its feasibility as a platform for MRgFUS interventions for neonatal patients. The success of the system in experimental trials suggests that it is ready to be used for validation of the transcranial intervention in animal studies.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

SU-F-T-308: Mobius FX Evaluation and Comparison Against a Commercial 4D Detector Array for VMAT Plan QA

Purpose: To evaluate the use of MobiusFX as a pre-treatment verification IMRT QA tool and compare it with a commercial 4D detector array for VMAT plan QA. Methods: 15 VMAT plan QA of different treatment sites were delivered and measured by traditional means with the 4D detector array ArcCheck (Sun Nuclear corporation) and at the same time measurement in linac treatment logs (Varian Dynalogs files) were analyzed from the same delivery with MobiusFX software (Mobius Medical Systems). VMAT plan QAs created in Eclipse treatment planning system (Varian) in a TrueBeam linac machine (Varian) were delivered and analyzed with the gamma analysis routine from SNPA software (Sun Nuclear corporation). Results: Comparable results in terms of the gamma analysis with 99.06% average gamma passing with 3%,3mm passing rate is observed in the comparison among MobiusFX, ArcCheck measurements, and the Treatment Planning System dose calculated. When going to a stricter criterion (1%,1mm) larger discrepancies are observed in different regions of the measurements with an average gamma of 66.24% between MobiusFX and ArcCheck. Conclusion: This work indicates the potential for using MobiusFX as a routine pre-treatment patient specific IMRT method for quality assurance purposes and its advantages as a phantom-less method which reduce the time for IMRT QA measurement. MobiusFX is capable of produce similar results of those by traditional methods used for patient specific pre-treatment verification VMAT QA. Even the gamma results comparing to the TPS are similar the analysis of both methods show that the errors being identified by each method are found in different regions. Traditional methods like ArcCheck are sensitive to setup errors and dose difference errors coming from the linac output. On the other hand linac log files analysis record different errors in the VMAT QA associated with the MLCs and gantry motion that by traditional methods cannot be detected.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

SU-F-T-351: Establishing a Workflow for IMRT Pre-Treatment Reviews for NRG-GY006 Clinical Trial

Purpose: To establish a workflow for NRG-GY006 IMRT pre-treatment reviews, incorporating advanced radiotherapy technologies being evaluated as part of the clinical trial. Methods: Pre-Treatment reviews are required for every IMRT case as part of NRG-GY006 (a randomized phase II trial of radiation therapy and cisplatin alone or in combination with intravenous triapine in women with newly diagnosed bulky stage I B2, stage II, IIIB, or IVA cancer of the uterine cervix or stage II-IVA vaginal cancer. The pretreatment review process includes structures review and generating an active bone marrow(ABM)- to be used as an avoidance structure during IMRT optimization- and evaluating initial IMRT plan quality using knowledgeengineering based planning (KBP). Institutions will initially submit their simulation CT scan, structures file and PET/CT to IROC QA center for generating ABM. The ABM will be returned to the institution for use in planning. Institutions will then submit an initial IMRT plan for review and will receive information back following implementation of a KBP algorithm, for use in re-optimization, before submitting the final IMRT used for treatment. Results: ABM structure is generated using MIM vista software (Version 6.5, MIM corporation, Inc.). Here, the planning CT and the diagnostic PET/CT are fused and a sub threshold structure is auto segmented above the mean value of the SUV of the bone marrow. The generated ABM were compared with those generated with other software system (e.g. Velocity, Varian) and Dice coefficient (reflects the overlap of structures) ranged between 80 – 90% was achieved. A KBP model was built in Varian Eclipse TPS using the RapidPlan KBP software to perform plan quality assurance. Conclusion: The workflow for IMRT pretreatment reviews has been established. It represents a major improvement of NRG Oncology clinical trial quality assurance and incorporates the latest radiotherapy technologies as part of NCI clinical trials. This project was supported by grants U24CA180803 (IROC), UG1CA189867 (NCORP), U10CA180868 (NRG Oncology Operations), U10CA180822 (NRG Oncology SDMC) from the National Cancer Institute (NCI) and PA CURE grant.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

SU-F-T-443: Quantification of Dosimetric Effects of Dental Metallic Implant On VMAT Plans

Purpose: To evaluate the dosimetric impact of metallic implant that correlates with the size of targets and metallic implants and distance in between on volumetric-modulated arc therapy (VMAT) plans for head and neck (H&N) cancer patients with dental metallic implant. Methods: CT images of H&N cancer patients with dental metallic implant were used. Target volumes with different sizes and locations were contoured. Metal artifact regions excluding surrounding critical organs were outlined and assigned with CT numbers close to water (0HU). VMAT plans with half-arc, one-full-arc and two-full-arcs were constructed and same plans were applied to structure sets with and without CT number assignment of metal artifact regions and compared. D95% was utilized to investigate PTV dose coverage and SNC Patient− Software was used for the analysis of dose distribution difference slice by slice. Results: For different targets sizes, variation of PTV dose coverage (Delta-D95%) with and without CT number replacement reduced with larger target volume for all half-arc, one-arc and two-arc VMAT plans even though there were no clinically significant differences. Additionally, there were no significant variations of the maximum percent difference (max.%diff) of dose distribution. With regard to the target location, Delta-D95% and max. %diff dropped with increasing distance between target and metallic implant. Furthermore, half-arc plans showed greater impact than one-arc plans, and two-arc plans had smallest influence for PTV dose coverage and dose distribution. Conclusion: The target size has less correlation of doseimetric impact than the target location relative to metallic implants. Plans with more arcs alleviate the dosimetric effect of metal artifact because of less contribution to the target dose from beams going through the regions with metallic artifacts. Incorrect CT number causes inaccurate dose distribution, therefore appropriately overwriting metallic artifact regions with reasonable CT numbers is recommended. More patient data are collected and under further analysis.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

Approaches to reducing photon dose calculation errors near metal implants

Purpose: Dose calculation errors near metal implants are caused by limitations of the dose calculation algorithm in modeling tissue/metal interface effects as well as density assignment errors caused by imaging artifacts. The purpose of this study was to investigate two strategies for reducing dose calculation errors near metal implants: implementation of metal-based energy deposition kernels in the convolution/superposition (C/S) dose calculation method and use of metal artifact reduction methods for computed tomography (CT) imaging. Methods: Both error reduction strategies were investigated using a simple geometric slab phantom with a rectangular metal insert (composed of titanium or Cerrobend), as well as two anthropomorphic phantoms (one with spinal hardware and one with dental fillings), designed to mimic relevant clinical scenarios. To assess the dosimetric impact of metal kernels, the authors implemented titanium and silver kernels in a commercial collapsed cone C/S algorithm. To assess the impact of CT metal artifact reduction methods, the authors performed dose calculations using baseline imaging techniques (uncorrected 120 kVp imaging) and three commercial metal artifact reduction methods: Philips Healthcare’s O-MAR, GE Healthcare’s monochromatic gemstone spectral imaging (GSI) using dual-energy CT, and GSI with metal artifact reduction software (MARS) applied. For the simple geometric phantom, radiochromic film was used to measure dose upstream and downstream of metal inserts. For the anthropomorphic phantoms, ion chambers and radiochromic film were used to quantify the benefit of the error reduction strategies. Results: Metal kernels did not universally improve accuracy but rather resulted in better accuracy upstream of metal implants and decreased accuracy directly downstream. For the clinical cases (spinal hardware and dental fillings), metal kernels had very little impact on the dose calculation accuracy (<1.0%). Of the commercial CT artifact reduction methods investigated, the authors found that O-MAR was the most consistent method, resulting in either improved dose calculation accuracy (dental case) or little impact on calculation accuracy (spine case). GSI was unsuccessful at reducing the severe artifacts caused by dental fillings and had very little impact on calculation accuracy. GSI with MARS on the other hand gave mixed results, sometimes introducing metal distortion and increasing calculation errors (titanium rectangular implant and titanium spinal hardware) but other times very successfully reducing artifacts (Cerrobend rectangular implant and dental fillings). Conclusions: Though successful at improving dose calculation accuracy upstream of metal implants, metal kernels were not found to substantially improve accuracy for clinical cases. Of the commercial artifact reduction methods investigated, O-MAR was found to be the most consistent candidate for all-purpose CT simulation imaging. The MARS algorithm for GSI should be used with caution for titanium implants, larger implants, and implants located near heterogeneities as it can distort the size and shape of implants and increase calculation errors.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Data for Responsiveness of Miscanthus and Switchgrass Yields to Stand Age and Nitrogen Fertilization: A Meta-regression Analysis

The compiled datasets include plot level observations of energy crops (miscanthus and switchgrass) from recent experimental field trials in the US including dry biomass yield, location, state, region, harvest year, growing season degree days (GDD), winter season heating degree days (HDD), growing season cumulative precipitation, annual nitrogen application rate, age of the pant when harvested, National Commodity Crop Productivity Index (NCCPI) values, and cultivar type (switchgrass) from various published and unpublished sources. The stata codes include estimation procedures for four different specifications, i.e., Model A includes deterministic effect without interaction terms; Model B includes deterministic effect with interaction terms (N2, age2, N × age, GDD2, precip2, N × NCCPI); Model C includes deterministic effect with interaction terms, study, and location random effect; Model D includes deterministic effect with interaction terms, harvest year augmented study, and location random effect.

Age↗
DOE OSTI2023

Synthesis and Crystal Structure of the Zintl Phases NaSrSb, NaBaSb and NaEuSb

This work details the synthesis and the crystal structures of the ternary compounds NaSrSb, NaBaSb and NaEuSb. They are isostructural and adopt the hexagonal ZrNiAl-type structure (space group P6¯2m; Pearson code hP9). The structure determination in all three cases was performed using single-crystal X-ray diffraction methods. The structure features isolated Sb3– anions arranged in layers stacked along the crystallographic c-axis. In the interstices, alkali and alkaline-earth metal cations are found in tetrahedral and square pyramidal coordination environments, respectively. The formal partitioning of the valence electrons adheres to the valence rules, i.e., Na+Sr2+Sb3–, Na+Ba2+Sb3– and Na+Eu2+Sb3– can be considered as Zintl phases with intrinsic semiconductor behavior. Electronic band structure calculations conducted for NaBaSb are consistent with this notion and show a direct gap of approx. 0.9 eV. Additionally, the calculations hint at possible inverted Dirac cones, a feature that is reminiscent of topological quantum materials.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Competing Use Analysis for Offshore Renewables and Subsea Cables

Demand for abundant and diverse resources in the oceans is growing, necessitating marine spatial planning. To inform development of Marine Hydrokinetic (MHK) and Offshore Wind (OSW) resources, the Department of Energy (DOE) has asked NREL to identify the competing uses areas between promising MHK/OSW sites and submarine power and telecommunications cables. The first step in this work is to identify and quantify the overlap between the MHK/OSW resource availability and existing cable routes. The analysis is done in terms of resource area because the task of quantifying actual impacts on available resource is a non-trivial undertaking that involves subjective decisions of identifying resource opportunities. Quantifying overlap in-terms of resource area?on the other hand?is significantly more straight forward, and useful to marine spatial planners. This dataset of polygons describes recommended setback areas from submarine cables for marine renewable energy Development. Two archive files are provided: 1. NREL Cables Setback-Polygons.zip contains the following GeoJSON files: 1.a. cables_100ft.geojson: The Code of Federal Regulations (CFR 585.301) specifies that the legal right of way for submarine cables is 100 ft (~30 meters) to either side of the cable (i.e., 200 ft wide). 1.b. cables_2z.geojson: The International Cable Protection Committee (ICPC) of the North American Submarine Cable Association (NASCA) recommends setback distances for new facilities as the maximum of 500 m or twice the bottom depth (2z), per ICPC Recommendation 13 No. 2 (Communications Security, Reliability and Interoperability Council IV 2014). For depths 250 m, 2 * depth is to be used. 1.c. cables_3z.geojson: The ICPC of NASCA recommends setback distances for new cables as the maximum of 500 m or three times the bottom depth (3z), per ICPC Recommendation 2 No. 10 (Communications Security, Reliability and Interoperability Council IV 2014). So for depths 167 m, 3 * depth is to be used. 2. NREL Submarine Cable Analysis Code Data Presentations.zip contains all files (code, data, README, etc) from release 0.1 of this Github repository for possibly regenerating the product as submarine cable configurations change: https://github.com/ecoquants/nrel-cables. For more details, please see the link to the full report for which this data product is a supplemental output: Submarine Cable Analysis for U.S. Marine Renewable Energy Development by Ben Best and Levi Kilcher National Renewable Energy Laboratory

16 TIDAL AND WAVE POWER↗
DOE OSTI2016

Lecture Notes on Criticality Safety Validation Using MCNP & Whisper

Training classes for nuclear criticality safety, MCNP documentation. The need for, and problems surrounding, validation of computer codes and data area considered first. Then some background for MCNP & Whisper is given--best practices for Monte Carlo criticality calculations, neutron spectra, S(α,β) thermal neutron scattering data, nuclear data sensitivities, covariance data, and correlation coefficients. Whisper is computational software designed to assist the nuclear criticality safety analyst with validation studies with the Monte Carlo radiation transport package MCNP. Whisper's methodology (benchmark selection – C k 's, weights; extreme value theory – bias, bias uncertainty; MOS for nuclear data uncertainty – GLLS) and usage are discussed.

42 ENGINEERING↗
DOE OSTI2023

HopBox: An image analysis pipeline to characterize hop cone morphology

Abstract Hop cone morphology can influence picking and drying ability, and color can impact consumer preference and may be indicative of quality. However, these characteristics are not generally evaluated in hop breeding programs due to the tedious nature of trait quantification and the extensive variation among cones within a genotype. We developed the HopBox, which is a simply constructed light box with a camera mount, and a publicly available image processing pipeline that identifies hop cones within color‐corrected images, reads a QR code within the image, and outputs data on hop cone length, width, area, perimeter, openness, weight, color, and density. The trained model was applied to images of 500 cones each from 15 replicated advanced hop genotypes from the USDA‐ARS breeding program in Prosser, Washington. Analysis of variance revealed significant ( p < 0.001) differences between genotypes for all traits measured, enabling breeders to discriminate between genotypes for selection purposes. Broad sense heritability for all traits ranged from 0.23 to 0.59. A random sampling of hop cones from the complete dataset revealed that imaging only 5–10 cones adequately captured genotypic variation and provided acceptable rank correlations ( r s > 0.75); however, increasing the sample size to 30 provided optimal precision. Instructions for constructing a HopBox and the code for the analysis pipeline are publicly available online and have wide applicability for hop breeding and research.

Altendorf, Kayla R.↗
DOE OSTI2024

Feasibility and performance of the staged Z-pinch: A one-dimensional study with FLASH and MACH2

Z-pinch platforms constitute a promising pathway to fusion energy research. Here, we present a one-dimensional numerical study of the staged Z-pinch (SZP) concept using the FLASH and MACH2 codes. We discuss the verification of the codes using two analytical benchmarks that include Z-pinch-relevant physics, building confidence on the codes' ability to model such experiments. Then, FLASH is used to simulate two different SZP configurations: a xenon gas-puff liner (SZP1*) and a silver solid liner (SZP2). The SZP2 results are compared against previously published MACH2 results, and a new code-to-code comparison on SZP1* is presented. Using an ideal equation of state and analytical transport coefficients, FLASH yields a fuel convergence ratio (CR) of approximately 39 and a mass-averaged fuel ion temperature slightly below 1 keV for the SZP2 scheme, significantly lower than the full-physics MACH2 prediction. For the new SZP1* configuration, full-physics FLASH simulations furnish large and inherently unstable CRs (>300) but achieve fuel ion temperatures of many kilo-electron volts. While MACH2 also predicts high temperatures, the fuel stagnates at a smaller CR. The integrated code-to-code comparison reveals how magnetic insulation, heat conduction, and radiation transport affect platform performance and the feasibility of the SZP concept.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

A Tutorial on Bayesian analysis of linear shock compression data

Gas gun and other shock compression experiments often produce shock wave velocity measurements that are linearly associated with particle velocity. Traditionally, this empirical relationship is quantified with a single Hugoniot curve that is estimated using least squares regression. However, for downstream modeling and simulation tasks, it is often more useful to have multiple Hugoniot curves in the pressure–volume plane that are consistent with the data. We employ Bayesian uncertainty quantification methods as a framework for propagating measurement uncertainty through to model parameters and predictions. Specifically, this Tutorial shows how to sample multiple Hugoniot curves in the pressure–volume plane that are consistent with the shock wave-particle velocity measurements in a two-step Bayesian approach. First, we obtain an analytical expression for the posterior distribution of the linear model parameters using Bayesian linear regression. Second, we propagate samples from the posterior distribution through the Rankine–Hugoniot equations to yield Hugoniot curves in the pressure–volume plane. The procedure is demonstrated with publicly available data on argon, copper, and nickel, and compared against bootstrapping and linear regression. The Bayesian procedure is shown to be interpretable, computationally inexpensive, and less sensitive than an alternative bootstrapping approach to the removal of the point in the copper dataset that has the largest particle velocity. As a Tutorial on Bayesian methodology for the shock compression community, we provide several derivations and explanations that make this paper self-contained, and make all code and data available at github.com/llnl/BALSCD.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗