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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 253 records · Page 14

Technique for rapid determination of relative ages of lunar areas from orbital photography.

Development of a technique for determining relative ages of regions of the lunar surface from orbital photography using a model of small-impact erosion. The erosion model relates the shape of a crater to the integrated flux of debris that has impacted the surface since that crater was fresh. The shape of the most modified crater of a particular diameter is thereby related to the relative age of the surface. Application of this analysis to orbital photography reveals that the major mare units vary in the accumulation of impacts by more than a factor of 3. Comparison of these data with crystallization ages determined from samples collected during the Apollo 11 and 12 missions indicates that the impact fluxes were decreasing during the stages of mare formation. An exponentially decaying flux for the last 3.5 b.y. with a half-life of 0.6 to 1.4 b.y. is compatible with the data.

Soderblom, L. A.↗

Electroweak three-body decays in the presence of two- and three-body bound states

Recently, formalism has been derived for studying electroweak transition amplitudes for three-body systems both in infinite and finite volumes. The formalism provides exact relations that the infinite-volume amplitudes must satisfy, as well as a relationship between physical amplitudes and finite-volume matrix elements, which can be constrained from lattice QCD calculations. This formalism poses additional challenges when compared with the analogous well-studied two-body equivalent one, including the necessary step of solving integral equations of singular functions. In this work, we provide some non-trivial analytical and numerical tests on the aforementioned formalism. In particular, we consider a case where the three-particle system can have three-body bound states as well as bound states in the two-body subsystem. For kinematics below the three-body threshold, we demonstrate that the scattering amplitudes satisfy unitarity. We also check that for these kinematics the finite-volume matrix elements are accurately described by the formalism for two-body systems up to exponentially suppressed corrections. Finally, we verify that in the case of the three-body bound state, the finite-volume matrix element is equal to the infinite-volume coupling of the bound state, up to exponentially suppressed errors.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Finite-volume formalism for physical processes with an electroweak loop integral

This study investigates finite-volume effects in physical processes that involve the combination of long-range hadronic matrix elements with electroweak loop integrals. We adopt the approach of implementing the electroweak part as the infinite-volume version, which is denoted as the EW ∞ method in this work. A general approach is established for correcting finite-volume effects in cases where the hadronic intermediate states are dominated by either a single particle or two particles. For the single-particle case, this work derives the infinite volume reconstruction method from a new perspective. For the two-particle case, we provide the correction formulas for power-law finite-volume effects and unphysical terms with exponentially divergent time dependence. The finite-volume formalism developed in this study has broad applications, including the QED corrections in various processes and the two-photon exchange contribution in 𝐾 𝐿 → 𝜇 + ⁢𝜇 − or 𝜂 → 𝜇 + ⁢𝜇 − decays.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Development of OPTIMOD - The new Space Shuttle Orbiter/Payload Thermal Integration Model

The development of the Orbiter/Payload Thermal Integration Model (OPTIMOD), a simplified Space Shuttle Orbiter thermal math model to be used for payload thermal integration analysis, is described. The Orbiter lower fuselage math model has been reduced to the minimum level of detail consistent with accuracy requirements. Instead, an 'environment radiation sensor', a simple closed-end cylinder oriented in a fixed position with respect to the Orbiter, is introduced. Equations are presented which relate the cylinder surface heating rates to external fuselage steady-state temperatures. These equations were derived from a regression correlation analysis of steady-state Orbiter thermal solutions for 2372 points on orbit, representing a complete range of vehicle-earth-sun orientations. An exponential equation is developed to relate the steady-state data to time-variant temperatures for the particular transient attitude timeline being simulated. The accuracy of OPTIMOD is shown to be excellent in the payload bay and to compare favorably with previous models in Orbiter elements outside the bay.

Russell, David J.↗

Growth-associated polyhydroxybutyrate accumulation in Azospira suillum PS during aerobic and perchlorate respiration

Polyhydroxyalkanoates (PHAs) are widespread microbial storage polymers increasingly recognized for roles beyond carbon and energy storage, including redox homeostasis and stress physiology. While PHA accumulation is classically associated with stationary-phase metabolism under severe nutrient imbalance, comparatively little is known about growth-associated PHA synthesis in facultative anaerobes with unusual respiratory strategies. Here, we investigated polyhydroxybutyrate (PHB) metabolism in Azospira suillum PS, a genetically tractable perchlorate-reducing bacterium capable of both aerobic and anaerobic respiration. Using physiological growth experiments, targeted gene deletions, PHB extractions, and intracellular redox measurements, we examined PHB accumulation under varying respiratory and nutrient conditions. We demonstrate that PHB accumulates during exponential growth under moderately nitrogen-limited conditions, both aerobically and during perchlorate respiration, representing a rare example of growth-associated PHB synthesis under anaerobic conditions. Genomic analysis revealed four phaC homologs, one of which could not be deleted under the experimental conditions tested and co-localized with phaB and phaR. Redox profiling further revealed a strong positive correlation between PHB accumulation and intracellular NADPH/NADP+ ratios. Together, these findings expand the physiological contexts in which PHB synthesis is known to occur and highlight perchlorate-respiring bacteria as underexplored model systems for studying growth-integrated carbon and redox storage strategies.

Meier, David A O↗

Prediction of Turbulence-Generated Noise in Unheated Jets: JeNo Technical Manual (Version 1.0) - Part 1

The model-based approach, used by the JeNo code to predict jet noise spectral directivity, is described. A linearized form of Lilley's equation governs the non-causal Green s function of interest, with the non-linear terms on the right hand side identified as the source. A Reynolds-averaged Navier-Stokes (RANS) solution yields the required mean flow for the solution of the propagation Green s function in a locally parallel flow. The RANS solution also produces time- and length-scales needed to model the non-compact source, the turbulent velocity correlation tensor, with exponential temporal and spatial functions. It is shown that while an exact non-causal Green s function accurately predicts the observed shift in the location of the spectrum peak with angle as well as the angularity of sound at low to moderate Mach numbers, the polar directivity of radiated sound is not entirely captured by this Green s function at high subsonic and supersonic acoustic Mach numbers. Results presented for unheated jets in the Mach number range of 0.51 to 1.8 suggest that near the peak radiation angle of high-speed jets, a different source/Green s function convolution integral may be required in order to capture the peak observed directivity of jet noise. A sample Mach 0.90 heated jet is also discussed that highlights the requirements for a comprehensive jet noise prediction model.

Khavaran, Abbas↗

Integrative mapping reveals molecular features underlying the mechanism of nucleocytoplasmic transport

Nuclear pore complexes (NPCs) enable rapid, selective, and robust nucleocytoplasmic transport. To explain how transport emerges from the system components and their interactions, we used experimental data and theoretical information to construct an integrative Brownian dynamics model of transport through an NPC, coupled to a kinetic model of transport in the cell. The model recapitulates key aspects of transport for a wide range of molecular cargoes, including preribosomes and viral capsids. Our model quantifies how flexible phenylalanine-glycine (FG) repeat proteins create an entropic barrier to passive diffusion and how this barrier is selectively lowered in facilitated diffusion by the many transient interactions of nuclear transport receptors with the FG repeats. Selective transport is enhanced by “fuzzy” multivalent interactions, redundant FG repeat mass, coupling to the energy-dependent RanGTP concentration gradient, and exponential dependence of transport kinetics on the transport barrier. Our model will facilitate rational modulation of the NPC and its artificial mimics.

Raveh, Barak [School of Computer Science and Engin↗

A Methodology for Quantifying Certain Design Requirements During the Design Phase

A methodology for developing and balancing quantitative design requirements for safety, reliability, and maintainability has been proposed. Conceived as the basis of a more rational approach to the design of spacecraft, the methodology would also be applicable to the design of automobiles, washing machines, television receivers, or almost any other commercial product. Heretofore, it has been common practice to start by determining the requirements for reliability of elements of a spacecraft or other system to ensure a given design life for the system. Next, safety requirements are determined by assessing the total reliability of the system and adding redundant components and subsystems necessary to attain safety goals. As thus described, common practice leaves the maintainability burden to fall to chance; therefore, there is no control of recurring costs or of the responsiveness of the system. The means that have been used in assessing maintainability have been oriented toward determining the logistical sparing of components so that the components are available when needed. The process established for developing and balancing quantitative requirements for safety (S), reliability (R), and maintainability (M) derives and integrates NASA s top-level safety requirements and the controls needed to obtain program key objectives for safety and recurring cost (see figure). Being quantitative, the process conveniently uses common mathematical models. Even though the process is shown as being worked from the top down, it can also be worked from the bottom up. This process uses three math models: (1) the binomial distribution (greaterthan- or-equal-to case), (2) reliability for a series system, and (3) the Poisson distribution (less-than-or-equal-to case). The zero-fail case for the binomial distribution approximates the commonly known exponential distribution or "constant failure rate" distribution. Either model can be used. The binomial distribution was selected for modeling flexibility because it conveniently addresses both the zero-fail and failure cases. The failure case is typically used for unmanned spacecraft as with missiles.

Adams, Timothy↗

The Cooling Loop A Anomaly of 2013: A Case Study in Human-Systems Resilience

Throughout the history of human spaceflight, NASA has employed an operational paradigm of 24/7 dependence on experts in Mission Control Center (MCC). In addition to nominal flight control and mission operations, these 85+ experts per shift manage anomaly detection, diagnosis, and response, and support the crew in real-time in performing maintenance and repair, procedure execution, and other complex mission operations. Future long-duration exploration missions (LDEMs) beyond low-Earth orbit (LEO) will not operate successfully using this same Human-Systems Integration Architecture (HSIA) where crew rely on ground controllers, have ready access to resupply, and have a fallback plan of evacuation. As distance from Earth increases and the communication delay grows, crews will need to respond independently and adequately to time-critical vehicle malfunctions. It will not always be sufficient or even possible to ‘safe the system’ and then wait upon ground intervention. A new and radically different HSIA is needed to accommodate the paradigm shift of deep-space travel. Historical International Space Station (ISS) data show that for a 30-day mission, the likelihood of a high-consequence vehicle anomaly of uncertain origin that requires rapid response is greater than 10%. The likelihood of such an event is 50% by the fourth month of the mission, and it grows exponentially with time. Our team has conducted in-depth investigations into these events and their corresponding anomaly resolution activities. Using MCC and Mission Evaluation Room (MER) anomaly resolution artifacts (including meeting summaries, caution and warning data, and ISS daily summaries), we created timelines detailing ground actions and in-orbit events for two significant anomalies. We then mapped these timelines onto Mars transit conditions, introducing a ground-crew communications time delay and shifting immediate response, time-critical task execution, and vehicle commanding to the crew. In detailing successful anomaly resolution in transit to Mars, the timelines highlight where effective resolution requires drastically evolved onboard capabilities. Though this research has yielded a rich data set based on ground response in past missions, there is still insufficient knowledge to assess the potential impact of inflight anomalies on a small autonomous crew on future LDEMs beyond LEO. To begin building an evidence base that will inform future HSIA standards and requirements, we are developing an approach to systematically capture crew anomaly response and procedure execution during early Artemis missions. Being the first human spaceflight beyond LEO since Apollo, early Artemis missions provide a rare and unique opportunity to serve as a testbed for Mars missions. Our work aims to capitalize on planned data collection to derive crew operational responses to anomalous events in real-time. Our team is also researching the level of simulation fidelity required for empirically validating proposed HSIA standards and evaluating HSIA implementations for LDEMs beyond LEO. This work will produce a trade space study of HSIA simulation objectives and fidelity requirements. Ultimately, these research efforts will assist in developing the standards and technologies needed to build a next-generation HSIA for LDEMs beyond LEO.

human-systems integration architecture↗

Data-Informed Evaluation Framework for Integrated Energy Systems: Insights from Power, Process Heat, and Hydrogen Production Applications

The multi-criteria decision analysis (MCDA) framework provides a systematic evaluation of the diverse preferences and performance metrics associated with alternative solutions. This approach is advantageous over a single-criterion methodology, which are only valid under conditions that assume ceteris paribus or an "apples-to-apples" comparison. However, selecting suitable technologies for integrated energy systems (IES) can be likened to an "apples-to-oranges" comparison, given the heterogeneous factors at stake. These factors include economics and performance parameters, geological compatibility, and environmental impacts. Consequently, past research has often employed a mixture of qualitative and quantitative criteria tailored to the specific interests of each study. While the method proves effective in handling the intricate interplay of criteria, the resulting rankings and scores can vary from study to study. This inconsistency is introduced from the use of subjectively defined thresholds and weights. As a result, decision-makers frequently find it challenging to establish clear connections between specific criteria and the resulting scores, as the transformation of criteria into ordinal scores results in a substantial loss of information. To address this challenge, we introduce a data-informed IES evaluation framework that offers comprehensive, interpretable, and traceable evaluations backed by quantifiable rationale. First, we identified key IES evaluation criteria from a decade of literature, focusing on relevant IES applications in power, process heat, and hydrogen production. We leveraged state-of-the-art cost estimates from the Idaho National Laboratory (INL) and technical data from 78 reactor designs from the International Atomic Energy Agency (IAEA) and the Organization for Economic Co-operation and Development - Nuclear Energy Agency (OECD-NEA). Lastly, we established thresholds by analyzing the mean, variance, root mean square, and slope of values across alternatives, categorizing the preferences of decision-makers into distinct utility functions, such as linear, saturating, exponential, and stepwise. Our approach yielded two main outcomes: (1) it provided consistent assessments across different stakeholder groups and (2) it visualized uncertainties in the decision-making context via comprehensive sensitivity analysis. To demonstrate the impact of our framework, we conducted case studies on 6 reactor designs (AP1000, NuScale, BWRX-300, Xe-100, eVinci, iMSR) for the three applications. Our data-driven framework proved to be highly effective in addressing heterogenous uncertainties faced by varied decision-makers? preferences and IES applications, as well as cost and technical estimates of advanced reactors.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Data-Informed Evaluation Framework for Integrated Energy Systems: Insights from Power, Process Heat, and Hydrogen Production Applications

The multi-criteria decision analysis (MCDA) framework provides a systematic evaluation of the diverse preferences and performance metrics associated with alternative solutions. This approach is advantageous over a single-criterion methodology, which are only valid under conditions that assume ceteris paribus or an "apples-to-apples" comparison. However, selecting suitable technologies for integrated energy systems (IES) can be likened to an "apples-to-oranges" comparison, given the heterogeneous factors at stake. These factors include economics and performance parameters, geological compatibility, and environmental impacts. Consequently, past research has often employed a mixture of qualitative and quantitative criteria tailored to the specific interests of each study. While the method proves effective in handling the intricate interplay of criteria, the resulting rankings and scores can vary from study to study. This inconsistency is introduced from the use of subjectively defined thresholds and weights. As a result, decision-makers frequently find it challenging to establish clear connections between specific criteria and the resulting scores, as the transformation of criteria into ordinal scores results in a substantial loss of information. To address this challenge, we introduce a data-informed IES evaluation framework that offers comprehensive, interpretable, and traceable evaluations backed by quantifiable rationale. First, we identified key IES evaluation criteria from a decade of literature, focusing on relevant IES applications in power, process heat, and hydrogen production. We leveraged state-of-the-art cost estimates from the Idaho National Laboratory (INL) and technical data from 78 reactor designs from the International Atomic Energy Agency (IAEA) and the Organization for Economic Co-operation and Development - Nuclear Energy Agency (OECD-NEA). Lastly, we established thresholds by analyzing the mean, variance, root mean square, and slope of values across alternatives, categorizing the preferences of decision-makers into distinct utility functions, such as linear, saturating, exponential, and stepwise. Our approach yielded two main outcomes: (1) it provided consistent assessments across different stakeholder groups and (2) it visualized uncertainties in the decision-making context via comprehensive sensitivity analysis. To demonstrate the impact of our framework, we conducted case studies on 6 reactor designs (AP1000, NuScale, BWRX-300, Xe-100, eVinci, iMSR) for the three applications. Our data-driven framework proved to be highly effective in addressing heterogenous uncertainties faced by varied decision-makers? preferences and IES applications, as well as cost and technical estimates of advanced reactors.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Renewable Energy Potential Model: Hawaii Geothermal Supply Curves

This dataset extends the development of the Renewable Energy Potential (reV) model to include geothermal energy, with a specific focus on Hawaii. Provided here are the results of two scenarios that were modeled for geothermal energy in Hawaii: binary enhanced geothermal systems (EGS) at a depth of 2.5 km and hydrothermal binary systems at a depth of 1.5 km. The resource data for both scenarios were derived from Lautze and Haskins (2024) using an exponential method. The PFA probability of heat map was used as a look up table for which temperature gradient to use (Lautze and Haskins, 2024). The dataset provides geospatial and techno-economic details for evaluating geothermal energy potential. It includes spatial coordinates, estimated capacity factors, developable area, resource potential, and annual energy production metrics. Economic details such as levelized cost of electricity (LCOE), site development costs, transmission costs, and fixed-charge rates are also included. The reV model, originally developed for wind and solar energy, incorporates these variables to evaluate deployment constraints related to land use, environmental and cultural factors, and grid integration.

15 GEOTHERMAL ENERGY↗

Review of MLI Behavior at Low Temperatures and Application to L'Ralph Thermal Modeling

In this presentation, the theory and application of multi-layer insulation (MLI) behavior, with a specific focus on lower temperature applications (<180K), is discussed. Many parameters can affect the performance of MLI (i.e. construction method, size, materials, grounding, penetrations, etc.) and these factors can make the prediction of MLI performance a challenge. Often, MLI performance is measured in terms of estar, and analysts commonly apply bias between a high and a low estar value. However, this approach can be dangerous when a mission goes through a wide range of temperatures during its lifetime (such as our mission, L'Ralph) due to temperature dependence of estar, with estar values increasing exponential as temperatures get colder. Many research papers and correlations have been published about MLI behavior, showing how estar values can rapidly rise at low temperatures. These correlations also show how the different parameters of MLI can affect and amplify this growth. Various correlations are presented as well as how L'Ralph is approaching the MLI problem. L'Ralph thermal model is built with Thermal Desktop (TD), and a discussion of how to apply the temperature dependent MLI behavior within TD is included. The presentation also includes reviews of different methods of mitigating heat leaks through MLI, touching briefly on topics such as integrated-MLI (IMLI), Dacron vs silk netting, and using multi-layered meshes to improve estar performance.

MLI↗

Modeling of Turbulence Generated Noise in Jets

A numerically calculated Green's function is used to predict jet noise spectrum and its far-field directivity. A linearized form of Lilley's equation governs the non-causal Green s function of interest, with the non-linear terms on the right hand side identified as the source. In this paper, contributions from the so-called self- and shear-noise source terms will be discussed. A Reynolds-averaged Navier-Stokes solution yields the required mean flow as well as time- and length scales of a noise-generating turbulent eddy. A non-compact source, with exponential temporal and spatial functions, is used to describe the turbulence velocity correlation tensors. It is shown that while an exact non-causal Green's function accurately predicts the observed shift in the location of the spectrum peak with angle as well as the angularity of sound at moderate Mach numbers, at high subsonic and supersonic acoustic Mach numbers the polar directivity of radiated sound is not entirely captured by this Green's function. Results presented for Mach 0.5 and 0.9 isothermal jets, as well as a Mach 0.8 hot jet conclude that near the peak radiation angle a different source/Green's function convolution integral may be required in order to capture the peak observed directivity of jet noise.

Khavaran, Abbas↗

Altered morphology and diffusivity of water confined in MXenes: Machine learning–accelerated computations combined with experiments

Nanoconfined water exhibits unique properties compared to bulk water due to limited quantities, frustrated hydrogen bonding, and surface interactions, which are fundamental for energy storage and transport applications. We integrate machine learning–accelerated ab initio molecular dynamics with x-ray diffraction (XRD) and inelastic neutron scattering (INS) to systematically analyze the thermodynamic and dynamic behavior of water confined between functionalized (-F, -O, and -OH) two-dimensional (2D) Ti 3 C 2 T x MXene layers. As water intercalates between layers, the interlayer spacing exhibits layer-dependent staging characteristics. The water polarization can be flipped by the count and morphology of intercalated molecules interacting with MXene surface groups, resulting in varying electrostatic potential profiles. On the basis of interfacial electrostatic potential, hydrogen bond lifetime, and molecular orientation, we establish a linear combination of exponential model describing water diffusivity. These computational insights align well with experimental x-ray and neutron measurements, suggesting strategies for tuning water morphology and transport by tailoring MXene surface chemistry and water content for electrochemical energy storage and nanofluidic applications.

Tang, Jiawei [Southeast Univ., Nanjing (China)] (O↗

Force Density Function Relationships in 2-D Granular Media

An integral transform relationship is developed to convert between two important probability density functions (distributions) used in the study of contact forces in granular physics. Developing this transform has now made it possible to compare and relate various theoretical approaches with one another and with the experimental data despite the fact that one may predict the Cartesian probability density and another the force magnitude probability density. Also, the transforms identify which functional forms are relevant to describe the probability density observed in nature, and so the modified Bessel function of the second kind has been identified as the relevant form for the Cartesian probability density corresponding to exponential forms in the force magnitude distribution. Furthermore, it is shown that this transform pair supplies a sufficient mathematical framework to describe the evolution of the force magnitude distribution under shearing. Apart from the choice of several coefficients, whose evolution of values must be explained in the physics, this framework successfully reproduces the features of the distribution that are taken to be an indicator of jamming and unjamming in a granular packing. Key words. Granular Physics, Probability Density Functions, Fourier Transforms

Youngquist, Robert C.↗

Stellar Population Properties in the Stellar Streams around SPRC047

Abstract We have investigated the properties (e.g., age, metallicity) of the stellar populations of a ringlike tidal stellar stream (or streams) around the edge-on galaxy SPRC047 (z= 0.031) using spectral energy distribution (SED) fits to integrated broadband aperture flux densities. We used visual images in six different bands and Spitzer/IRAC 3.6μm data. We have attempted to derive best-fit stellar population parameters (metallicity, age) in three noncontiguous segments of the stream. Due to the very low surface brightness of the stream, we have performed a deconvolution with a Richardson–Lucy–type algorithm of the low spatial resolution 3.6μm IRAC image, thereby reducing the effect of the point-spread function aliasedemissionfrom the bright edge-on central galaxy at the locations of our three stream segments. Our SED fits that used several different star formation (SF) history priors, from an exponentially decaying SF burst to continuous SF, indicate that the age–metallicity–dust degeneracy is not resolved, most likely because of inadequate wavelength coverage and low signal-to-noise ratios of the low surface brightness features. We also discuss how future deep visual–near-infrared observations, combined with absolute flux calibration uncertainties at or below the 1% level, complemented by equally well absolute flux-calibrated observations in ultraviolet and mid-infrared bands, would improve the accuracy of broadband SED fitting results for low surface brightness targets, such as stellar streams around nearby galaxies that are not resolved into stars.

Astronomy & Astrophysics↗

Shuttle Risk Progression: Use of the Shuttle Probabilistic Risk Assessment (PRA) to Show Reliability Growth

It is important to the Space Shuttle Program (SSP), as well as future manned spaceflight programs, to understand the early mission risk and progression of risk as the program gains insights into the integrated vehicle through flight. The risk progression is important to the SSP as part of the documentation of lessons learned. The risk progression is important to future programs to understand reliability growth and the first flight risk. This analysis uses the knowledge gained from 30 years of operational flights and the current Shuttle PRA to calculate the risk of Loss of Crew and Vehicle (LOCV) at significant milestones beginning with the first flight. Key flights were evaluated based upon historical events and significant re-designs. The results indicated that the Shuttle risk tends to follow a step function as opposed to following a traditional reliability growth pattern where risk exponentially improves with each flight. In addition, it shows that risk can increase due to trading safety margin for increased performance or due to external events. Due to the risk drivers not being addressed, the risk did not improve appreciably during the first 25 flights. It was only after significant events occurred such as Challenger and Columbia, where the risk drivers were apparent, that risk was significantly improved. In addition, this paper will show that the SSP has reduced the risk of LOCV by almost an order of magnitude. It is easy to look back afte r 30 years and point to risks that are now obvious, however; the key is to use this knowledge to benefit other programs which are in their infancy stages. One lesson learned from the SSP is understanding risk drivers are essential in order to considerably reduce risk. This will enable the new program to focus time and resources on identifying and reducing the significant risks. A comprehensive PRA, similar to that of the Shuttle PRA, is an effective tool quantifying risk drivers if support from all of the stakeholders is given.

Hamlin, Teri L.↗