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DOE OSTI2025

Structural Evolution and Stability of Rh/TiO 2 Catalysts under CO 2 Hydrogenation Conditions: Influence of the Initial Rh Structure

Characterizing catalyst stability by identifying the predominant mechanisms, timescales and driving forces of catalyst reconstruction under relevant reaction conditions is necessary for the design and commercialization of new catalysts. Here, in this paper, we study Rh/TiO 2 catalysts under CO 2 hydrogenation conditions (773 K, 75% H 2 , 25% CO 2 ) at high conversion and utilize reactivity studies along with ex-situ and in-situ spectroscopy and microscopy to characterize changes in catalyst activity and structure as a function of time on stream and the initial catalyst structure. This is a prototypical catalyst for CO 2 hydrogenation where Rh structure and Rh-TiO 2 interactions have been proposed to explain reactivity, selectivity (between CO and CH 4 formation) and catalyst stability. The influence of the initial Rh structure (varying from Rh single atoms to Rh nanoparticles), support stability, regeneration and pretreatment(s), and the chemical potential(s) of the reaction environment on reaction selectivity and catalyst stability were explored. The product selectivity between CO and CH 4 was determined to be dependent on the relative fraction of Rh single atoms and Rh nanoparticle-TiO 2 interfacial sites under reaction conditions, each exhibiting distinct stability under prolonged time on stream. Surprisingly, Rh single atoms exhibited stability for the duration of 90 h reactivity measurements, even at high Rh density (≥ 1.8 Rh atoms/nm 2 ) on the support, while Rh nanoparticles sintered under reaction conditions. As a result, all catalysts exhibited increasing selectivity to CO with increasing time on stream (> 10 h). We conclude the distribution of Rh structures evolved over time under reaction conditions through three distinct reconstruction mechanisms (Rh particle fragmentation, Ostwald ripening, and particle migration and coalescence) that occurred on varying timescales. Catalyst stability on the ~90 h time scale was ultimately controlled by the initial Rh structure.

25 ENERGY STORAGE↗

DOE OSTI2023

The impact of the $\text{WHIM}$ on the $\text{IGM}$ thermal state determined from the low- z Lyman $\alpha$ forest

At z ≲ 1, shock heating caused by large-scale velocity flows and possibly violent feedback from galaxy formation, converts a significant fraction of the cool gas (T ~ 10 4 K) in the intergalactic medium (IGM) into warm–hot phase (WHIM) with T > 10 5 K, resulting in a significant deviation from the previously tight power-law IGM temperature–density relationship, T = T 0 (P/$\bar{p}$) γ-1 ⁠. This study explores the impact of the WHIM on measurements of the low-z IGM thermal state, [T 0 , γ], based on the b–NH 1 distribution of the Ly α forest. Exploiting a machine learning-enabled simulation-based inference method trained on Nyx hydrodynamical simulations, we demonstrate that [T 0 , γ] can still be reliably measured from the b–NH 1 distribution at z = 0.1, notwithstanding the substantial WHIM in the IGM. To investigate the effects of different feedback, we apply this inference methodology to mock spectra derived from the IllustrisTNG and Illustris simulations at z = 0.1. The results suggest that the underlying [T 0 , γ] of both simulations can be recovered with biases as low as |Δlog(T 0 /K)| ≲ 0.05 dex, |Δγ| ≲ 0.1, smaller than the precision of a typical measurement. Given the large differences in the volume-weighted WHIM fractions between the three simulations (Illustris 38 percent, IllustrisTNG 10 percent, and Nyx 4 per cent), we conclude that the b–N H1 distribution is not sensitive to the WHIM under realistic conditions. Finally, we investigate the physical properties of the detectable Ly α absorbers, and discover that although their T and Δ distributions remain mostly unaffected by feedback, they are correlated with the photoionization rate used in the simulation.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1973

High latitude ionospheric winds related to solar-interplanetary conditions

Treated jointly, two recent results imply that the distribution of winds in the polar ionosphere should change as a function of the direction of the interplanetary magnetic field. (1) From the motions of chemically released ion and neutral clouds, it is apparent that neutral winds in the high latitude ionosphere are driven principally by ion drag forces. (2) OGO-6 electric field measurements have demonstrated that there are definite relationships between the time-latitude distribution of ionospheric plasma convection and interplanetary magnetic field parameters, and also that the distribution is most sensitive to the azimuthal angle of the interplanetary field. Although direct neutral wind to interplanetary magnetic field comparisons are not available, logic clearly implies a close relationship. The lower altitude, meteorological effects of these externally driven ionospheric winds are not known. However, observations of infrasonic waves following sudden ionization enhancements indicate the existence of momentum transfer.

Heppner, J. P.↗

NASA NTRS1975

High-latitude ionospheric winds related to solar-interplanetary conditions

Treated jointly, two recent results imply that the distribution of winds in the polar ionosphere should change as a function of the direction of the interplanetary magnetic field. From the motions of chemically released ion and neutral clouds, it is apparent that neutral winds in the high-latitude ionosphere are driven principally by ion drag forces. OGO 6 electric field measurements demonstrate that there are definite relationships between the time/latitude distribution of ionospheric plasma convection and interplanetary magnetic field parameters, and also that the distribution is most sensitive to the azimuthal angle of the inter planetary field. Although direct neutral wind to interplanetary magnetic field comparisons are not available, logic clearly implies a close relationship. Observations of infrasonic waves following sudden ionization enhancements indicate the existence of momentum transfer.

Heppner, J. P.↗

NASA NTRS1982

Subkilometer Martian volcanoes - Properties and possible terrestrial analogs

Kilometer to subkilometer cones with large central craters are the most numerous volcanic structures in the northern plains of Mars. Based on examination of more than 12,000 high resolution Viking Orbiter images, most of these very small cones are located in parts of Eastern Acidalia and Utopia-Isidis-Elysium Planitia. Measurements of base and pit diameter for some 2000 well-resolved features show small variations in the histogram of base diameters between and within regions but remarkable similarity in the distribution of crater/cone diameter ratios. This suggests that the small cones had a similar origin with only minor variations in local conditions. The Acidalia cones are generally larger, more widely distributed, and occur on a greater variety of terrains than those in Utopia-Isidis-Elysium. Based on morphology, distribution, and the crater/cone ratio histograms, the smallest Martian cones may be similar to Icelandic pseudocraters. Somewhat larger, steeper cones with smaller crater/cone ratios which also occur in Eastern Acidalia may be analogs of terrestrial cinder cones.

Frey, H.↗

NASA NTRS2008

A Theoretical Solid Oxide Fuel Cell Model for Systems Controls and Stability Design

As the aviation industry moves toward higher efficiency electrical power generation, all electric aircraft, or zero emissions and more quiet aircraft, fuel cells are sought as the technology that can deliver on these high expectations. The hybrid solid oxide fuel cell system combines the fuel cell with a micro-turbine to obtain up to 70% cycle efficiency, and then distributes the electrical power to the loads via a power distribution system. The challenge is to understand the dynamics of this complex multidiscipline system and the design distributed controls that take the system through its operating conditions in a stable and safe manner while maintaining the system performance. This particular system is a power generation and a distribution system, and the fuel cell and micro-turbine model fidelity should be compatible with the dynamics of the power distribution system in order to allow proper stability and distributed controls design. The novelty in this paper is that, first, the case is made why a high fidelity fuel cell mode is needed for systems control and stability designs. Second, a novel modeling approach is proposed for the fuel cell that will allow the fuel cell and the power system to be integrated and designed for stability, distributed controls, and other interface specifications. This investigation shows that for the fuel cell, the voltage characteristic should be modeled but in addition, conservation equation dynamics, ion diffusion, charge transfer kinetics, and the electron flow inherent impedance should also be included.

Kopasakis, George↗

NASA NTRS1984

Measurement results from a balloon experiment simulating land mobile satellite transmissions

A transmitter operating at 869.525 MHz was twice carried by a stratospheric balloon to an altitude of about 40 km. A motor vehicle was driven within the line-of-sight from the transmitter. Measurements of the received signal strength were made every 1/8 wavelength for an overall travelling distance of about seven hundred kilometers. This scenario was to simulate a satellite system providing mobile communications to rural areas. The statistics of the sampled field, consisting of a combination of direct wave, specular reflection and diffuse components, are presented as a function of elevation angle. Parameters such as type of road driven (mostly 2 lane) or type of landscape (rolling to flat) and vegetation (pine and mixed forest) encountered are described where possible. The power distribution function for all the data, at elevation angles from 10 to 35 degrees, is 1 dB below the free space mean at the 50% level, 7 dB below at the 90% level, and 18 dB below at the 99% level. In the elevation angle range of 30 to 35 degrees the corresponding values were found to be .5, 1.2, and 4.5 dB. The conditional fade duration and level crossing rate distribution functions are also presented. The former shows some dependence on the threshold level, the latter almost none.

Vogel, W. J.↗

NASA NTRS2012

Aerodynamic Investigation of Incidence Angle Effects in a Large Scale Transonic Turbine Cascade

Aerodynamic measurements showing the effects of large incidence angle variations on an HPT turbine blade set are presented. Measurements were made in NASA's Transonic Turbine Blade Cascade Facility which has been used in previous studies to acquire detailed aerodynamic and heat transfer measurements for CFD code validation. The current study supports the development of variable-speed power turbine (VSPT) speed-change technology for the NASA Large Civil Tilt Rotor (LCTR) vehicle. In order to maintain acceptable main rotor propulsive efficiency, the VSPT operates over a nearly 50% speed range from takeoff to altitude cruise. This results in 50 degrees or more variations in VSPT blade incidence angles. The cascade facility has the ability to operate over a wide range of Reynolds numbers and Mach numbers, but had to be modified in order to accommodate the negative incidence angle variation required by the LCTR VSPT operation. Using existing blade geometry with previously acquired aerodynamic data, the tunnel was re-baselined and the new incidence angle range was exercised. Midspan exit total pressure and flow angle measurements were obtained at seven inlet flow angles. For each inlet angle, data were obtained at five flow conditions with inlet Reynolds numbers varying from 6.83 × 10(exp 5) to 0.85 ×10(exp 5) and two isentropic exit Mach numbers of 0.74 and 0.34. The midspan flowfield measurements were acquired using a three-hole pneumatic probe located in a survey plane 8.6% axial chord downstream of the blade trailing edge plane and covering three blade passages. Blade and endwall static pressure distributions were also acquired for each flow condition

McVetta, Ashlie B.↗

DOE OSTI2017

Modelling and validation of particle size distributions of supported nanoparticles using the pair distribution function technique

The particle size of supported catalysts is a key characteristic for determining structure–property relationships. It is a challenge to obtain this information accurately and in situ using crystallographic methods owing to the small size of such particles (<5 nm) and the fact that they are supported. In this work, the pair distribution function (PDF) technique was used to obtain the particle size distribution of supported Pt catalysts as they grow under typical synthesis conditions. The PDF of Pt nanoparticles grown on zeolite X was isolated and refined using two models: a monodisperse spherical model (single particle size) and a lognormal size distribution. The results were compared and validated using scanning transmission electron microscopy (STEM) results. Both models describe the same trends in average particle size with temperature, but the results of the number-weighted lognormal size distributions can also accurately describe the mean size and the width of the size distributions obtained from STEM. Since the PDF yields crystallite sizes, these results suggest that the grown Pt nanoparticles are monocrystalline. This work shows that refinement of the PDF of small supported monocrystalline nanoparticles can yield accurate mean particle sizes and distributions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2013

Aerodynamic Investigation of Incidence Angle Effects in a Large Scale Transonic Turbine Cascade

Aerodynamic measurements showing the effects of large incidence angle variations on an HPT turbine blade set are presented. Measurements were made in NASA's Transonic Turbine Blade Cascade Facility which has been used in previous studies to acquire detailed aerodynamic and heat transfer measurements for CFD code validation. The current study supports the development of variable-speed power turbine (VSPT) speed-change technology for the NASA Large Civil Tilt Rotor (LCTR) vehicle. In order to maintain acceptable main rotor propulsive efficiency, the VSPT operates over a nearly 50 percent speed range from takeoff to altitude cruise. This results in 50deg or more variations in VSPT blade incidence angles. The cascade facility has the ability to operate over a wide range of Reynolds numbers and Mach numbers, but had to be modified in order to accommodate the negative incidence angle variation required by the LCTR VSPT operation. Using existing blade geometry with previously acquired aerodynamic data, the tunnel was re-baselined and the new incidence angle range was exercised. Midspan exit total pressure and flow angle measurements were obtained at seven inlet flow angles. For each inlet angle, data were obtained at five flow conditions with inlet Reynolds numbers varying from 6.83×10(exp 5) to 0.85×10(exp 5) and two isentropic exit Mach numbers of 0.74 and 0.34. The midspan flowfield measurements were acquired using a three-hole pneumatic probe located in a survey plane 8.6 percent axial chord downstream of the blade trailing edge plane and covering three blade passages. Blade and endwall static pressure distributions were also acquired for each flow condition.

McVetta, Ashlie B.↗

NASA NTRS2014

Aerodynamic Investigation of Incidence Angle Effects in a Large Scale Transonic Turbine Cascade

Aerodynamic measurements showing the effects of large incidence angle variations on an HPT turbine blade set are presented. Measurements were made in NASA's Transonic Turbine Blade Cascade Facility which has been used in previous studies to acquire detailed aerodynamic and heat transfer measurements for CFD code validation. The current study supports the development of variable-speed power turbine (VSPT) speed-change technology for the NASA Large Civil Tilt Rotor (LCTR) vehicle. In order to maintain acceptable main rotor propulsive efficiency, the VSPT operates over a nearly 50 percent speed range from takeoff to altitude cruise. This results in 50 deg or more variations in VSPT blade incidence angles. The cascade facility has the ability to operate over a wide range of Reynolds numbers and Mach numbers, but had to be modified in order to accommodate the negative incidence angle variation required by the LCTR VSPT operation. Using existing blade geometry with previously acquired aerodynamic data, the tunnel was re-baselined and the new incidence angle range was exercised. Midspan exit total pressure and flow angle measurements were obtained at seven inlet flow angles. For each inlet angle, data were obtained at five flow conditions with inlet Reynolds numbers varying from 6.83×10 (exp 5) to 0.85×10(exp 5) and two isentropic exit Mach numbers of 0.74 and 0.34. The midspan flowfield measurements were acquired using a three-hole pneumatic probe located in a survey plane 8.6 percent axial chord downstream of the blade trailing edge plane and covering three blade passages. Blade and endwall static pressure distributions were also acquired for each flow condition.

McVetta, Ashlie B.↗

NASA NTRS1987

A free-wake rotor analysis including ground effect

The objective of this work is to develop a computer program which analytically estimates the wake geometry, vorticity, and velocity distribution over a rotor and in the neighboring airflow for a variety of conditions in and out of ground effect. The resulting wake is used to provide an assessment of the blade loading distribution for various hover and low speed flight conditions. The computer program is based on a lifting line free wake model and provides stable solutions for a variety of steady state conditions, including ground effect and forward flight. The wake program was validated by comparing the computed wake geometry and experimental test data for two different rotors.

Saberi, H. A.↗

DOE OSTI2024

Distribution of centrality measures on undirected random networks via the cavity method

The Katz centrality of a node in a complex network is a measure of the node’s importance as far as the flow of information across the network is concerned. For ensembles of locally tree-like undirected random graphs, this observable is a random variable. Its full probability distribution is of interest but difficult to handle analytically because of its “global” character and its definition in terms of a matrix inverse. Leveraging a fast Gaussian Belief Propagation-Cavity algorithm to solve linear systems on tree-like structures, we show that i) the Katz centrality of a single instance can be computed recursively in a very fast way, and ii) the probability P ( K ) that a random node in the ensemble of undirected random graphs has centrality K satisfies a set of recursive distributional equations, which can be analytically characterized and efficiently solved using a population dynamics algorithm. We test our solution on ensembles of Erdős-Rényi and Scale Free networks in the locally tree-like regime, with excellent agreement. The analytical distribution of centrality for the configuration model conditioned on the degree of each node can be employed as a benchmark to identify nodes of empirical networks with over- and underexpressed centrality relative to a null baseline. We also provide an approximate formula based on a rank- 1 projection that works well if the network is not too sparse, and we argue that an extension of our method could be efficiently extended to tackle analytical distributions of other centrality measures such as PageRank for directed networks in a transparent and user-friendly way.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

SU-E-I-16: Scan Length Dependency of the Radial Dose Distribution in a Long Polyethylene Cylinder

Purpose: The area-averaged dose in the central plane of a long cylinder following a CT scan depends upon the radial dose distribution and the length of the scan. The ICRU/TG200 phantom, a polyethylene cylinder 30 cm in diameter and 60 cm long, was the subject of this study. The purpose was to develop an analytic function that could determine the dose for a scan length L at any point in the central plane of this phantom. Methods: Monte Carlo calculations were performed on a simulated ICRU/TG200 phantom under conditions of cylindrically symmetric conditions of irradiation. Thus, the radial dose distribution function must be an even function that accounts for two competing effects: The direct beam makes its weakest contribution at the center while the scatter begins abruptly at the outer radius and grows as the center is approached. The scatter contribution also increases with scan length with the increase approaching its limiting value at the periphery faster than along the central axis. An analytic function was developed that fit the data and possessed these features. Results: Symmetry and continuity dictate a local extremum at the center which is a minimum for the ICRU/TG200 phantom. The relative depth of the minimum decreases as the scan length grows and an absolute maximum can occur between the center and outer edge of the cylinders. As the scan length grows, the relative dip in the center decreases so that for very long scan lengths, the dose profile is relatively flat. Conclusion: An analytic function characterizes the radial and scan length dependency of dose for long cylindrical phantoms. The function can be integrated with the results expressed in closed form. One use for this is to help determine average dose distribution over the central cylinder plane for any scan length.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2023

Semi-Annual Report for Horizontal Compact High Temperature Gas Reactor (HC-HTGR) Development during Performance Period April 2023 – September 2023

Horizontal Compact High Temperature Gas Reactor (HC-HTGR) is being designed by a multi-disciplinary team of nuclear, mechanical, and structural engineers under the support of a DOE-NE Advanced Reactor Demonstration Program’s Advanced Reactor Concepts-20 (ARC-20) award. The objective of this ARC-20 project is to deliver a conceptual design for the proposed HC-HTGR in 3 years and support its commercialization as a safe, low-cost HTGR. Argonne National Laboratory (Argonne) is responsible for the design and analysis of the reactor cavity cooling system (RCCS) as a safety system for passive decay heat removal of the reactor concept. Additionally, Argonne is providing analysis of the primary coolant system to ensure temperatures within the core remain below safety margins during steady-state and potential accident scenarios. This fourth semi-annual report summarized the progress made at Argonne on the two tasks during the second half of FY23. As a part of the RCCS design task, recent efforts have been made to complete a conceptual design of the RCCS for the HC-HTGR, including the design update of the water panel and system configuration favorable in point of view of fabrication and system operation. Design calculations were conducted under various heat load conditions to validate the system design. Transient simulations using RELAP5-3D were conducted to investigate system dynamics under transients of interest and to evaluate the system performance in the design condition. The results demonstrated the overall system feasibility that the RCCS design maintains structures temperatures lower than maximum allowable temperature with sufficient system inventory without any active heat sink. In the primary system thermal hydraulics task, the preliminary analysis was performed for a long term pressurized conduction cooldown (PCC) transient. This analysis used a combination of a fully resolved and coarse homogenized mesh to predict the temperature distribution for the steady-state initial condition and the PCC transient. The steady-state initial condition was determined using a fully resolved full core model with 3D solid to 1D fluid coupling. The fully resolved mesh was also used to model the first 20 seconds of the PCC. The temperature difference between fuel pins and the graphite matrix becomes minimal and the dominant heat transfer shifts to a larger scale radially towards the RCCS. After 20 seconds, a homogenized coarse mesh is used, greatly reducing the computational costs of the model. These results demonstrate that the core is designed to passively remove enough decay heat in a protected loss of primary coolant flow to prevent an unsafe rise of core temperatures.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2021

An adaptive Hessian approximated stochastic gradient MCMC method

Bayesian approaches have been successfully integrated into training deep neural networks. One popular family is stochastic gradient Markov chain Monte Carlo methods (SG-MCMC), which have gained increasing interest due to their ability to handle large datasets and the potential to avoid overfitting. Although standard SG-MCMC methods have shown great performance in a variety of problems, they may be inefficient when the random variables in the target posterior densities have scale differences or are highly correlated. Here, we present an adaptive Hessian approximated stochastic gradient MCMC method to incorporate local geometric information while sampling from the posterior. The idea is to apply stochastic approximation (SA) to sequentially update a preconditioning matrix at each iteration. The preconditioner possesses second-order information and can guide the random walk of a sampler efficiently. Instead of computing and saving the full Hessian of the log posterior, we use limited memory of the samples and their stochastic gradients to approximate the inverse Hessian-vector multiplication in the updating formula. Moreover, by smoothly optimizing the preconditioning matrix via SA, our proposed algorithm can asymptotically converge to the target distribution with a controllable bias under mild conditions. To reduce the training and testing computational burden, we adopt a magnitude-based weight pruning method to enforce the sparsity of the network. Our method is user-friendly and demonstrates better learning results compared to standard SG-MCMC updating rules. The approximation of inverse Hessian alleviates storage and computational complexities for large dimensional models. Numerical experiments are performed on several problems, including sampling from 2D correlated distribution, synthetic regression problems, and learning the numerical solutions of heterogeneous elliptic PDE. The numerical results demonstrate great improvement in both the convergence rate and accuracy.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1937

Pressure-Distribution Measurements on O-2H Airplane in Flight

Results are given of pressure-distribution measurements made over two different horizontal tail surfaces and the right wing cellule, including the slipstream area, of an observation-type biplane. Measurements were also taken of air speed, control-surface positions, control-stick forces, angular velocities, and accelerations during various abrupt maneuvers. These maneuvers consisted of push-downs and pull-ups from level flight, dive pull-outs, and aileron rolls with various thrust conditions. The results from the pressure-distribution measurements over the wing cellule are given on charts showing the variation of individual rib coefficients with wing coefficients; the data from the tail-surface pressure-distribution measurements are given mainly as total loads and moments. These data are supplemented by time histories of the measured quantities and isometric views of the rib pressure distributions occurring in abrupt maneuvers.

Pearson, H A↗

NASA NTRS2010

Aero-Heating of Shallow Cavities in Hypersonic Freestream Flow

The purpose of these experiments and analysis was to augment the heating database and tools used for assessment of impact-induced shallow-cavity damage to the thermal protection system of the Space Shuttle Orbiter. The effect of length and depth on the local heating disturbance of rectangular cavities tested at hypersonic freestream conditions has been globally assessed using the two-color phosphor thermography method. These rapid-response experiments were conducted in the Langley 31-Inch Mach 10 Tunnel and were initiated immediately prior to the launch of STS-114, the initial flight in the Space Shuttle Return-To-Flight Program, and continued during the first week of the mission. Previously-designed and numerically-characterized blunted-nose baseline flat plates were used as the test surfaces. Three-dimensional computational predictions of the entire model geometry were used as a check on the design process and the two-dimensional flow assumptions used for the data analysis. The experimental boundary layer state conditions were inferred using the measured heating distributions on a no-cavity test article. Two test plates were developed, each containing 4 equally-spaced spanwise-distributed cavities. The first test plate contained cavities with a constant length-to-depth ratio of 8 with design point depth-to-boundary-layer-thickness ratios of 0.1, 0.2, 0.35, and 0.5. The second test plate contained cavities with a constant design point depth-to-boundary-layer-thickness ratio of 0.35 with length-to-depth ratios of 8, 12, 16, and 20. Cavity design parameters and the test condition matrix were established using the computational predictions. Preliminary results indicate that the floor-averaged Bump Factor (local heating rate nondimensionalized by upstream reference) at the tested conditions is approximately 0.3 with a standard deviation of 0.04 for laminar-in/laminar-out conditions when the cavity length-to-boundary-layer thickness is between 2.5 and 10 and for cavities in the depth-to-boundary-layer-thickness range of 0.3 to 0.8. Over this same range of conditions and parameters, preliminary results also indicate that the maximum Bump Factor on the cavity centerline falls between 2.0 and 2.75, as long as the cavity-exit conditions remain laminar. Cavities with length-to-boundary-layer-thickness ratio less than 2.5 can not be easily classified with this approach and require further analysis.

Everhart, Joel L.↗