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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 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Identification Uncertainty in Inverse Material Model Parameter Determination: A Sensitivity‐Based Decision Process for Load Path Selection

This research proposes a sensitivity-based framework for selecting the optimal prescribed loading path for a biaxial cruciform specimen. Optimality here is determined by the direction and magnitude of the prescribed displacement that minimizes the influence of random noise on the material model parameter identification. Using simulated experimental data based on finite element simulation, in this work, we identify the material model parameters of a Ludwik hardening model and plane stress implementation of the Hill-48 yield criterion using finite element model updating (FEMU). Our analysis reveals that the identification (or estimator) uncertainty of model parameters depends on the displacement boundary conditions (i.e., loading sequence) and the ground-truth value of the individual parameters. Optimal experimental design (OED) criteria based on the Fisher information matrix were investigated to mitigate indecision in the choice of optimal load path when the identification uncertainty of different material model parameters optimized at different load paths. The determinant of the Fisher information matrix was chosen here as the more useful metric due to its ability to capture uncertainty of the most influential material model parameters. The proposed framework demonstrates potential for real-time automated load step selection using scalar criteria derived prior to mechanical loading. The framework can be generalized to other geometries, boundary conditions and material models, allowing this procedure to be utilized for different experimental configurations and materials.

Fayad, Samuel S. [University of Illinois at Urbana↗
NASA NTRSDate not supplied

Probabilistic Modeling of a Three-Stage Human Landing System Architecture

Unmitigated uncertainties are known to have previously led to failed development programs; in order to combat these uncertainties, risks and their impacts must be understood and handled to ensure program success. In this paper, a probabilistic methodology to handle uncertainties is demonstrated on a three-element Human Landing System (HLS) concept, which allows tracking of current best estimates of the vehicle’s performance and assessment of its robustness against uncertainties. This methodology has two key parts: first, the creation of a dynamic architecture model of a three-element HLS concept; and second, its use with surrogate modeling and range estimating techniques to capture and propagate uncertainties. The DYnamic Rocket EQuation Tool (DYREQT), a space systems synthesis and sizing framework used by NASA, was used as to model the HLS architecture. For the probabilistic analysis, uncertainties of interest within the HLS concept were enumerated and represented as parameters within the DYREQT model as inputs for vehicle stages or mission profile events. Range estimating — a probabilistic method that combines Monte Carlo sampling, focus on critical parameters, and heuristics to assess risk and opportunities — is then adapted with operational parameters as well as vehicle parameters in the DYREQT model to capture mission uncertainty alongside vehicle uncertainty. To perform the range estimation portion of this methodology, the DYREQT model was sampled using a Design of Experiments (DoE) to efficiently explore the architecture design space with respect to the set of uncertainty parameters. Then, the results were used to create surrogate models, multivariate regressions that can visualize hypercube trends in the design space, of the architecture with respect to the uncertainty parameters. Using a correlation matrix constructed for the uncertainty parameters, previously independent samples were transformed to perform a Correlated Monte Carlo on the surrogate models. This probabilistic methodology was proved to provide insight into the underlying uncertainties of the three-element HLS architecture.

Stephanie Y Zhu↗
NASA NTRSDate not supplied

Probabilistic Modeling of a Three-Stage Human Landing System Architecture

Unmitigated uncertainties are known to have previously led to failed development programs; in order to combat these uncertainties, risks and their impacts must be understood and handled to ensure program success. In this paper, a probabilistic methodology to handle uncertainties is demonstrated on a three-element Human Landing System (HLS) concept, which allows tracking of current best estimates of the vehicle’s performance and assessment of its robustness against uncertainties. This methodology has two key parts: first, the creation of a dynamic architecture model of a three-element HLS concept; and second, its use with surrogate modeling and range estimating techniques to capture and propagate uncertainties. The DYnamic Rocket EQuation Tool (DYREQT), a space systems synthesis and sizing framework used by NASA, was used as to model the HLS architecture. For the probabilistic analysis, uncertainties of interest within the HLS concept were enumerated and represented as parameters within the DYREQT model as inputs for vehicle stages or mission profile events. Range estimating — a probabilistic method that combines Monte Carlo sampling, focus on critical parameters, and heuristics to assess risk and opportunities — is then adapted with operational parameters as well as vehicle parameters in the DYREQT model to capture mission uncertainty alongside vehicle uncertainty. To perform the range estimation portion of this methodology, the DYREQT model was sampled using a Design of Experiments (DoE) to efficiently explore the architecture design space with respect to the set of uncertainty parameters. Then, the results were used to create surrogate models, multivariate regressions that can visualize hypercube trends in the design space, of the architecture with respect to the uncertainty parameters. Using a correlation matrix constructed for the uncertainty parameters, previously independent samples were transformed to perform a Correlated Monte Carlo on the surrogate models. This probabilistic methodology was proved to provide insight into the underlying uncertainties of the three-element HLS architecture.

Stephanie Y. Zhu↗
DOE OSTI2025

Pervaporative Dehydration of 2,3-Butanediol by Dense Poly(vinylidene fluoride) Hollow Fiber Membranes: Parameter Estimation, Process Design, and Technoeconomic Evaluation under Uncertainty

Pervaporation, combined with other separation processes, can effectively remove water from fermentation product streams, making it highly suitable for purifying alcohols like 2,3-butanediol (BDO). In this study, a dense poly(vinylidene fluoride) (PVDF) hollow fiber membrane module prototype was fabricated for BDO dehydration, achieving >0.2 LMH total flux and >95% BDO rejection. With a Markov chain Monte Carlo (MCMC) approach, Bayesian inference was used to quantify the uncertainty of the permeance parameters. A membrane cascade model was developed to scale up a process that purifies a preconcentrated BDO feed (70 wt %) to high purity (90 wt %). Through propagation of the uncertainty of the parameters and sensitivity analyses of the process variables, a cascade design was recommended. Despite data and model limitations, the framework enabled a reliable system analysis and economic evaluation, validated through tight confidence intervals in key process metrics, establishing the foundation for future applications of Bayesian methods in membrane-based processes.

Animal feed↗
DOE OSTI2025

Uncertainty quantification and optimization of precipitating hydrometeor parameters for winter precipitation in a cloud microphysics scheme

The precipitating hydrometeor parameters used in cloud microphysics schemes carry inherent uncertainties. The quantification of these uncertainties, together with parameter optimization, can significantly improve precipitation forecasts. This study investigates the effects of 13 parameters in the Weather Research and Forecasting (WRF) Double-Moment 6-class (WDM6) microphysics scheme, which define the hydrometeor characteristics such as fall velocity–diameter and mass–diameter relationships, as well as the shape parameter of the drop size distribution for precipitating particles such as rain, snow, and graupel on simulated winter precipitation. A comparison between the model's pre-defined parameters and observations from the International Collaborative Experiments for the PyeongChang 2018 Olympic and Paralympic winter games (ICE-POP 2018) field campaign reveals that the fall velocity–diameter relationship for rain, the mass–diameter relationships for snow and graupel, and the shape parameters for all precipitating particles in the WDM6 scheme deviate from the median values observed by the two-dimensional video disdrometer (2DVD). To quantify parameter sensitivities, a perturbed parameter ensemble (PPE) of 256 simulations was conducted within parameter ranges constrained by 2DVD observations for three winter precipitation cases. Bayesian optimization was then applied to identify parameter sets that minimized the root mean square error (RMSE) for each case, achieving reductions of up to 30.2 %. These results demonstrate that ensemble-based uncertainty quantification and parameter optimization can help identify key parameters and provide a pathway to improving precipitation simulation performance. In addition, measurement sites can be strategically selected based on regions that show high sensitivity to variations in hydrometeor characteristic parameters.

Bayesian optimization↗
NASA NTRS1980

Uncertainty in ring current parameters due to the quiet magnetic field variability at mid-latitudes

At midlatitudes the presence of Sq variation is a problem, as variability of Sq currents may produce magnetic perturbations comparable to the magnetic effects of the partial ring current on comparable time scales. The paper reports the results of an empirical determination of the quiet magnetic field, which includes the Sq variation and secular variation at 27 midlatitude magnetic observatories for the 1967-1968 period. The main concern is with the consequences of the quiet field uncertainty in terms of using midlatitude magnetic data to quantify the size and location of the magnetic disturbances caused by substorms and the ring current. Attention is given to investigating the error associated with the empirical model used. It is shown how the uncertainty can be reduced by examining the changes occurring in some interval of time.

Clauer, C. R.↗
NASA NTRSDate not supplied

Quantifying Uncertainty in Particle Size Distribution Parameters Inferred from SAGE III/ISS Extinction Spectra

Stratospheric aerosols play key roles in the chemistry and radiation balance of the atmosphere and are a key input parameter for global chemistry and climate models. The degree to which aerosols impact chemistry and radiation balance depends primarily on their microphysical properties such as particle size distribution (PSD). The PSD is a mathematical description of the relative abundance of different sized particles within a sampling volume. If the PSD is accurately known then other key modeling parameters (e.g., surface area density) can be derived. Occultation observations from orbital instruments such as SAGE III/ISS have been used to infer these PSD parameters by inverting the extinction coefficient spectra. However, past efforts failed to address two key issues with this methodology: 1. The measurement uncertainty was not accounted for; 2. They assumed the PSDs to be single-mode only, while “real-world” PSDs are predominantly bi-modal. Accounting for both issues in the retrieval will yield an expanded solution space to the inferred PSD parameters; the question is “by how much?” To address this knowledge gap, we propose to carry out a series of simulations and, for every valid SAGE III/ISS data point, determine the range of PSD parameters that yield extinction spectra that are indistinguishable from the SAGE III/ISS data, within the limits of the reported uncertainty. Further, we will expand the solution space, for the first time, to include bimodal distributions. The results of this work will advance Earth system modeling/prediction capability through identifying the uncertainty of PSD parameter estimates using SAGE III/ISS data. The key benefits of this study over previous studies are twofold: 1. we will provide PSD estimates that include bimodal distributions in the solution space, 2. we will provide an uncertainty estimate for these parameters. The results of this study may be used directly in current and future climate and chemistry models.

SAGE III/ISS↗
NASA NTRS1998

A Monte Carlo Uncertainty Analysis of Ozone Trend Predictions in a Two Dimensional Model

We use Monte Carlo analysis to estimate the uncertainty in predictions of total O3 trends between 1979 and 1995 made by the Goddard Space Flight Center (GSFC) two-dimensional (2D) model of stratospheric photochemistry and dynamics. The uncertainty is caused by gas-phase chemical reaction rates, photolysis coefficients, and heterogeneous reaction parameters which are model inputs. The uncertainty represents a lower bound to the total model uncertainty assuming the input parameter uncertainties are characterized correctly. Each of the Monte Carlo runs was initialized in 1970 and integrated for 26 model years through the end of 1995. This was repeated 419 times using input parameter sets generated by Latin Hypercube Sampling. The standard deviation (a) of the Monte Carlo ensemble of total 03 trend predictions is used to quantify the model uncertainty. The 34% difference between the model trend in globally and annually averaged total O3 using nominal inputs and atmospheric trends calculated from Nimbus 7 and Meteor 3 total ozone mapping spectrometer (TOMS) version 7 data is less than the 46% calculated 1 (sigma), model uncertainty, so there is no significant difference between the modeled and observed trends. In the northern hemisphere midlatitude spring the modeled and observed total 03 trends differ by more than 1(sigma) but less than 2(sigma), which we refer to as marginal significance. We perform a multiple linear regression analysis of the runs which suggests that only a few of the model reactions contribute significantly to the variance in the model predictions. The lack of significance in these comparisons suggests that they are of questionable use as guides for continuing model development. Large model/measurement differences which are many multiples of the input parameter uncertainty are seen in the meridional gradients of the trend and the peak-to-peak variations in the trends over an annual cycle. These discrepancies unambiguously indicate model formulation problems and provide a measure of model performance which can be used in attempts to improve such models.

Considine, D. B.↗
DOE OSTI2024

Interlaced Characterization and Calibration (ICC) for Improved Computational Simulation Credibility

Accurate material characterization and model calibration are pivotal for simulations used for high-consequence engineering decisions. Current characterization and calibration methods (1) use simplified test specimen geometries and global data, (2) cannot guarantee that sufficient characterization data is collected for a specific model of interest, (3) provide only mean parameter values with no uncertainty quantification, and (4) are sequential, inflexible, and time-consuming. This work developed a new paradigm—coined Interlaced Characterization and Calibration (ICC)—which drives forward the state-of-the-art in model calibration by bringing together recent advancements into one improved workflow. The ICC paradigm (1) employs tools to efficiently use full-field data to calibrate high-fidelity material models, (2) aligns the data needed with the data collected by adopting an optimal experimental design protocol, (3) provides uncertainty metrics on the calibrated model parameters, and (4) incorporates these advances into a quasi real-time feedback loop. The ICC framework was validated synthetically with both low-fidelity and high-fidelity simulations paired with several different elastoplastic material models, and was also demonstrated experimentally with an aluminum 6061 cruciform exemplar specimen. Results showed that the ICC framework—in which Bayesian optimal experimental design actively guided the experiment— resulted in calibrations with similar or better accuracy than predetermined experiments based on subject matter expertise. Moreover, the ICC framework produced a complete model calibration— with quantified uncertainties on model parameters—in 1 week, a 5 - 10× increase in efficiency over traditional approaches. Thus, the ICC paradigm improves both the calibration process and quality, by (1) improving efficiency, which increases agility of solid mechanics modeling and enables utilization of computational simulation (CompSim) at earlier stages of the design cycle and (2) providing quantified, and in some cases reduced, parameter uncertainties, which increases confidence in model predictions and supports credible decision making.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Emulator-based Bayesian calibration of a subglacial drainage model

Subglacial drainage models, often motivated by the relationship between hydrology and ice flow, sensitively depend on numerous unconstrained parameters. We explore using borehole water-pressure time series to calibrate the uncertain parameters of a popular subglacial drainage model, taking a Bayesian perspective to quantify the uncertainty in parameter estimates and in the calibrated model predictions. To reduce the computation time associated with Markov Chain Monte Carlo sampling, we construct a fast Gaussian process emulator to stand in for the subglacial drainage model. We first carry out a calibration experiment using synthetic observations consisting of model simulations with hidden parameter values as a demonstration of the method. Using real borehole water pressures measured in western Greenland, we find meaningful constraints on four of the eight model parameters and a factor-of-three reduction in uncertainty of the calibrated model predictions. These experiments illustrate Gaussian process-based Bayesian inference as a useful tool for calibration and uncertainty quantification of complex glaciological models using field data. However, significant differences between the calibrated model and the borehole data suggest that structural limitations of the model, rather than poorly constrained parameters or computational cost, remain the most important constraint on subglacial drainage modelling.

58 GEOSCIENCES↗
NASA NTRS2014

Study of Aerothermodynamic Modeling Issues Relevant to High-Speed Sample Return Vehicles

This paper examines the application of state-of-the-art coupled ablation and radiation simulations to highspeed sample return vehicles, such as those returning from Mars or an asteroid. A defining characteristic of these entries is that the surface recession rates and temperatures are driven by nonequilibrium convective and radiative heating through a boundary layer with significant surface blowing and ablation products. Measurements relevant to validating the simulation of these phenomena are reviewed and the Stardust entry is identified as providing the best relevant measurements. A coupled ablation and radiation flowfield analysis is presented that implements a finite-rate surface chemistry model. Comparisons between this finite-rate model and a equilibrium ablation model show that, while good agreement is seen for diffusion-limited oxidation cases, the finite-rate model predicts up to 50% lower char rates than the equilibrium model at sublimation conditions. Both the equilibrium and finite rate models predict significant negative mass flux at the surface due to sublimation of atomic carbon. A sensitivity analysis to flowfield and surface chemistry rates show that, for a sample return capsule at 10, 12, and 14 km/s, the sublimation rates for C and C3 provide the largest changes to the convective flux, radiative flux, and char rate. A parametric uncertainty analysis of the radiative heating due to radiation modeling parameters indicates uncertainties ranging from 27% at 10 km/s to 36% at 14 km/s. Applying the developed coupled analysis to the Stardust entry results in temperatures within 10% of those inferred from observations, and final recession values within 20% of measurements, which improves upon the 60% over-prediction at the stagnation point obtained through an uncoupled analysis. Emission from CN Violet is shown to be over-predicted by nearly and order-of-magnitude, which is consistent with the results of previous independent analyses. Finally, the coupled analysis is applied to a 14 km/s Earth entry representative of a Mars sample return. Although the radiative heating provides a larger fraction of the total heating, the influence of ablation and radiation on the flowfield are shown to be similar to Stardust.

Johnston, Christopher O.↗
DOE OSTI2024

Bayes_Opt-SWMM: A Gaussian process-based Bayesian optimization tool for real-time flood modeling with SWMM

Real-time flood model plays a pivotal role in averting urban flood damage, particularly when there is minimal lead time for preparatory measures. However, urban flood modeling in real-time often contends with inherent uncertainties arising from input data uncertainty and parameter ambiguities. Here this study introduces a real-time calibration (RTC) tool called Bayes_Opt-SWMM, specifically tailored for real-time urban flood modeling and uncertainty optimization. This tool leverages the Gaussian process-based Bayesian optimization algorithm and interfaces seamlessly with the Stormwater Management Model (SWMM). It integrates real-time model forcing data and flood monitoring collected through sensors and gauges which are strategically placed within critical locations of urban drainage systems. Our approach hinges on the Surrogate Model based Uncertainty Optimization (SMUO) concept, providing an avenue for enhancing real-time flood modeling. Bayes_Opt-SWMM runs the optimization process using a surrogate model called Gaussian Process emulator with two inference methods: (1) the Gaussian Process (GP) model and (2) Markov Chain Monte Carlo (MCMC) algorithm in GP model (GP_MCMC). Furthermore, three acquisition functions, namely Expected Improvement (EI), Maximum Probability of Improvement (MPI), and Lower Confidence Bound (LCB), facilitate optimal parameter fitting within the surrogate models. The efficiency of GP-based surrogate models in learning SWMM model parameters, leads to an improved uncertainty quantification and accelerated real-time flood modeling in urban areas. Overall, Bayes_Opt-SWMM emerges as a cost-effective and valuable tool for real-time flood modeling and monitoring, with significant potential for managing intelligent storm water systems in urban environments.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2018

The Effects of Uncertainty in Initial CME Input Parameters on Deflection, Rotation, Bz, and Arrival Time Predictions

Understanding the effects of coronal mass ejections (CMEs) requires knowing if and when they will impact and their properties upon impact. Of particular importance is the strength of a CME's southward magnetic field component (Bz ). Kay et al. (2013, https://doi:10.1088/0004-637X/775/1/5, 2015, https://doi:10.1088/948 0004-637X/805/2/168) have shown that the simplified analytic model Forecasting a CME's Altered Trajectory (ForeCAT) can reproduce the deflection and rotation of CMEs. Kay, Gopalswamy, Reinard, and Opher (2017, https://doi.org/10.3847/1538-4357/835/2/117) introduced ForeCAT In situ Data Observer, which uses ForeCAT results to simulate magnetic field profiles. ForeCAT In situ Data Observer reproduces the in situ observations on roughly hourly time scales, suggesting that these models could be extremely useful for predictions of Bz . However, as with all models, both models are sensitive to their input parameters, which may not be precisely known for predictions. We explore this sensitivity using ensembles having small changes in the initial latitude, longitude, and orientation of the erupting CME. We explore the effects of different background magnetic field models and find that the changes in deflection and rotation resulting from the uncertainty in the initial parameters tend to exceed the changes from dierent magnetic backgrounds. The range in the in situ proles tends to scale with the range in the deflection and rotation. We also consider a simple arrival time model using ForeCAT results and nd an average absolute error of only 3 hr. We show that an uncertainty in the CME position of 8.1 ± 6.9 leads to variations of 6 hr in the arrival time. This measure depends strongly on the location of impact within the CME with the arrival time changing less for impacts near the nose.

Kay, Christina D.↗
DOE OSTI2025

Perspectives on Systematic Cloud Microphysics Scheme Development With Machine Learning

Cloud microphysics—the collection of processes that govern the small‐scale formation, evolution, and interactions of liquid droplets and ice crystals in clouds and precipitation—remains a major source of uncertainty in weather and climate models. Although too small in scale to be explicitly resolved in any large‐eddy simulation, weather, or climate model, the representation of cloud microphysical processes has significant impact at the climate scale. Current microphysical schemes are limited by both parametric uncertainty, linked to uncertainty in physical parameter values, and structural uncertainty, arising from incomplete physical understanding of the processes at play or approximations made for computational efficiency. Recent advances in the application of machine learning (ML) to the physical sciences show significant potential for minimizing these limitations by leveraging high‐fidelity simulations and observations. Here we outline the challenges that must be addressed to apply ML toward cloud microphysics scheme development. This perspectives paper synthesizes recent progress in using data‐driven methods, including ML, to improve cloud microphysics parameterizations and highlights opportunities to address key uncertainties. We discuss the roles of aleatoric (irreducible, or statistical) and epistemic (reducible, or systematic) errors in contributing to microphysics parameterization uncertainty. ML can leverage observations to improve microphysical schemes via bottom‐up and top‐down constraints. Methods such as differentiable programming and ML‐enhanced sampling strategies and the creation of large scale benchmark data sets promise to bridge the gap between observations and models and to improve the consistency of cloud microphysical representation across temporal and spatial scales.

Lamb, Kara D. [Columbia Univ., New York, NY (Unite↗
NASA NTRS1980

Delta V errors due to attitude correction maneuvers of a spinning spacecraft

A statistical error analysis has been performed to evaluate the change in velocity of a spin stabilized spacecraft due to thruster induced attitude correction maneuvers. Analytical expressions were developed to determine the mean and variance of the velocity in terms of the nominal values and uncertainties of key spacecraft parameters. These parameters include thrust, thruster timing, thruster alignment, plume impingement force and estimated spacecraft mass. Typical values of these parameters and their uncertainties for NASA's Galileo spacecraft were used to evaluate these expressions. The results of the analysis allow the effect of attitude correction maneuvers to be evaluated with respect to the functional requirements on nongravitational acceleration. Other results include the identification of major sources of delta V error and studies of the sensitivity of delta V to variations in the error sources.

Zipursky, H. J.↗
NASA NTRS2008

Hybrid Gibbs Sampling and MCMC for CMB Analysis at Small Angular Scales

A) Gibbs Sampling has now been validated as an efficient, statistically exact, and practically useful method for "low-L" (as demonstrated on WMAP temperature polarization data). B) We are extending Gibbs sampling to directly propagate uncertainties in both foreground and instrument models to total uncertainty in cosmological parameters for the entire range of angular scales relevant for Planck. C) Made possible by inclusion of foreground model parameters in Gibbs sampling and hybrid MCMC and Gibbs sampling for the low signal to noise (high-L) regime. D) Future items to be included in the Bayesian framework include: 1) Integration with Hybrid Likelihood (or posterior) code for cosmological parameters; 2) Include other uncertainties in instrumental systematics? (I.e. beam uncertainties, noise estimation, calibration errors, other).

Gibbs sampling↗
NASA NTRS2012

Impact of Calibrated Land Surface Model Parameters on the Accuracy and Uncertainty of Land-Atmosphere Coupling in WRF Simulations

Land-atmosphere (L-A) interactions play a critical role in determining the diurnal evolution of both planetary boundary layer (PBL) and land surface temperature and moisture budgets, as well as controlling feedbacks with clouds and precipitation that lead to the persistence of dry and wet regimes. Recent efforts to quantify the strength of L-A coupling in prediction models have produced diagnostics that integrate across both the land and PBL components of the system. In this study, we examine the impact of improved specification of land surface states, anomalies, and fluxes on coupled WRF forecasts during the summers of extreme dry (2006) and wet (2007) land surface conditions in the U.S. Southern Great Plains. The improved land initialization and surface flux parameterizations are obtained through the use of a new optimization and uncertainty estimation module in NASA's Land Information System (LIS-OPT/UE), whereby parameter sets are calibrated in the Noah land surface model and classified according to a land cover and soil type mapping of the observation sites to the full model domain. The impact of calibrated parameters on the a) spinup of the land surface used as initial conditions, and b) heat and moisture states and fluxes of the coupled WRF simulations are then assessed in terms of ambient weather and land-atmosphere coupling along with measures of uncertainty propagation into the forecasts. In addition, the sensitivity of this approach to the period of calibration (dry, wet, average) is investigated. Finally, tradeoffs of computational tractability and scientific validity, and the potential for combining this approach with satellite remote sensing data are also discussed.

Santanello, Joseph A., Jr.↗