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DOE OSTI2022

Laser melting modes in metal powder bed fusion additive manufacturing

In laser powder bed fusion additive manufacturing of metals, extreme thermal conditions create many highly dynamic physical phenomena such as vaporization and recoil, Marangoni convection, and protrusion and keyhole instability. Collectively however, the full set of phenomena is too complicated for practical applications and, in reality, the melting modes are used as a guideline for printing. With increasing local material temperature beyond the boiling point, the mode can change from conduction to keyhole. These mode designations ignore laser-matter interaction details but in many cases are adequate to determine the approximate microstructures and hence the properties of the build. To date, no consistent, common, and coherent definitions have been agreed upon because of historic limitations in melt pool and vapor depression morphology measurements. Here, we distinguish process-based definitions of different melting modes from those based on postmortem evidence. The latter are mainly derived from the transverse cross-sections of the fusion zone, whereas the former come directly from time-resolved x-ray imaging of melt pool and vapor depression morphologies. These process-based definitions are more strict and physically sound, and they offer new guidelines for laser additive manufacturing practices and create new research directions. Further, we highlight the significance of the keyhole, which substantially enhances the laser energy absorption by the melt pool. Recent studies strongly suggest that stable-keyhole laser melting enables efficient, sustainable, and robust additive manufacturing. The realization of this scenario demands the development of multiphysics models, signal translations from morphology to other feasible signals, and in-process metrology across platforms and scales.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1994

Non-local thermodynamic equilibrium limb radiance from O3 and CO2 in the 9-11 micrometer spectral region

Satellite remote sensing of mesospheric and thermospheric O3 abundance in the terrestrial atmosphere often uses 9-11 micrometer thermal emission. In this paper, we apply a line-by-line non-local thermodynamic equilibrium (non-LTE) radiance model to this spectral region and investigate the conditions of LTE breakdown and the effect that this has on the limb radiance measured by an i.r. sounder. Monochromatic and band-integrated radiance calculations have been performed for limb view tangent heights between 55 and 105 km under daytime and nighttime conditions. Non-LTE emission from both O3 and CO2 are shown to be important with the divergence of radiance from LTE values and the diurnal variation being band dependent. We have shown that the contribution of the CO2 bands to the Limb Infrared Monitor of the Stratosphere O3 channel is significant for daytime conditions at tangent heights above about 60 km. A study has been made to choose O3 sounding channel spectral passbands for the High Resolution Dynamics Limb Sounder. High resolution calculations are required to determine those spectral intervals that will filter radiance from selected bands and characterize their non-LTE behavior. This will allow for improved O3 retrievals above 70 km and non-LTE studies.

Edwards, David P.↗

NASA NTRS1979

Soft X-ray structure of the Coma cluster of galaxies

Results are reported for an observation of the Coma cluster with an imaging X-ray telescope system aboard a sounding rocket. A two-dimensional X-ray map of the cluster in the energy range from 0.15 to 2.0 keV is presented. The radial distribution, granularity, and ellipticity of the X-ray surface brightness are investigated, and the spectrum and flux within the field of view are analyzed. These properties are then examined quantitatively by comparing the observations with models through the use of a chi-squared test. It is found that: (1) no single galaxy contributes more than a few percent of the total X-ray flux of the Coma cluster; (2) the X-ray source is diffuse but granular on a scale of several arcmin, particularly in the central region; (3) the centroid of the X-ray source is at a local intensity minimum; and (4) the data are most consistent with an isothermal hydrostatic model.

Gorentstein, P.↗

NASA NTRSDate not supplied

Payload Fairing Acoustic Trade Study: Fill Effect Modeling

A review of acoustic fill effect was conducted using vibroacoustic models of the NASA Space Launch System Block 1B 8.4-meter Payload Fairing. Fill effect is the term used to describe how sound pressure levels (SPLs) inside of a launch vehicle’s payload cavity change when a payload is present, compared to that of an unfilled cavity. Several vibroacoustic models with various payload shapes were developed and the deviation in output from an unfilled cavity model were compared to an analytical fill effect calculation. The analytical expression for the fill effect correction factor, known as the fill factor, is published in NASA-STD-7001B. The development and validation of the NASA fill factor is discussed to provide context for this study and define important variables including the volume fill percentage and the fairing-payload separation gap. The fill factor is reviewed from two perspectives; a global perspective which defines the volume ratio with respect to the entire fairing cavity, and a local perspective which defines the volume ratio with respect to a zone of interest dependent on the payload’s height. The global perspective was considered because it allows a decoupling of the volume ratio and fairing-payload separation gap variables. Both the global and local fill factor methods have difficulty capturing low frequency SPL because of a breakdown in the underlying assumptions of a diffuse acoustic field. Spatial variation in the pressure field at low frequency showed that axially oriented standing waves may be of concern for sensitive payload components; radial variation in SPL was found to be less significant. Further, a novel secondary derivation of the theoretical fill factor is posed for future work in which the absorption characteristics of the payload and fairing surfaces are considered. This work is supported by the NASA Glenn Research Center and the Space Launch System Payload Fairing Working Group.

Spacecraft environments↗

DOE OSTI2021

Testing Surrogate-Based Optimization with the Fortified Branin-Hoo Extended to Four Dimensions

Some popular functions used to test global optimization algorithms have multiple local optima, all with the same value, making them all global optima. It is easy to make them more challenging by fortifying them via adding a localized bump at the location of one of the optima. In previous work the authors illustrated this for the Branin-Hoo function and the popular differential evolution algorithm, showing that the fortified Branin-Hoo required an order of magnitude more function evaluations. This paper examines the effect of fortifying the Branin-Hoo function on surrogate- based optimization, which usually proceeds by adaptive sampling. Two algorithms are considered. The EGO algorithm, which is based on a Gaussian process (GP) and an algorithm based on radial basis functions (RBF). EGO is found to be more frugal in terms of the number of required function evaluations required to identify the correct basin, but it is expensive to run on a desktop, limiting the number of times the runs could be repeated to establish sound statistics on the number of required function evaluations. The RBF algorithm was cheaper to run, providing more sound statistics on performance. A four-dimensional version of the Branin-Hoo function was introduced in order to assess the effect of dimensionality. Furthermore, it was found that the difference between the ordinary function and the fortified one was much more pronounced for the four-dimensional function compared to the two dimensional one.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Emergent hydrodynamic mode on SU(2) plaquette chains and quantum simulation

We search for emergent hydrodynamic modes in real-time Hamiltonian dynamics of 2+1-dimensional SU(2) lattice gauge theory on a quasi-one-dimensional plaquette chain, by numerically computing symmetric correlation functions of energy densities on lattice sizes of about 20 with the local Hilbert space truncated at 𝑗 max = $\frac{1}{2}$. Because of the Umklapp processes, we only find a mode for energy diffusion. The symmetric correlator exhibits transport peak near zero frequency with a width approximately proportional to momentum squared at small momentum, when the system is fully quantum ergodic, as indicated by the eigenenergy level statistics. This transport peak leads to a power-law 𝑡 −$\frac{1}{2}$ decay of the symmetric correlator at late time, also known as the long-time tail, as well as diffusionlike spreading in position space. We also introduce a quantum algorithm for computing the symmetric correlator on a quantum computer and find it gives results consistent with exact diagonalization when tested on the IBM emulator. Finally we discuss the future prospect of searching for the sound modes.

Hamiltonian systems↗

NASA NTRS1997

West-Antarctic Ice Streams: Analog to Ice Flow in Channels on Mars

Sounding of the sea floor in front of the Ross Ice Shelf in Antarctica recently revealed large persistent patterns of longitudinal megaflutes and drumlinoid forms, which are interpreted to have formed at the base of ice streams during the list glacial advance. The flutes bear remarkable resemblance to longitudinal grooves and highly elongated streamlined islands found on the floors of some large martian channels, called outflow channels. ln addition, other similarities exist between Antarctic ice streams and outflow channels. Ice streams are 30 to 80 km wide and hundreds of kilometers long, as are the martian channels. Ice stream beds are below sea level. Floors of many martian outflow channels lie below martian datum, which may have been close to or below past martian sea levels. The Antarctic ice stream bed gradient is flat and locally may go uphill, and surface slopes are exceptionally low. So are gradients of martian channels. The depth to the bed in ice streams is 1 to 1.5 km. At bankful stage, the depth of the fluid in outflow channels would have been 1 to 2 km. These similarities suggest that the martian outflow channels, whose origin is commonly attributed to gigantic catastrophic floods, were locally filled by ice that left a conspicuous morphologic imprint. Unlike the West-Antarctic-ice streams, which discharge ice from an ice sheet, ice in the martian channels came from water erupting from the ground. In the cold martian environment, this water, if of moderate volume, would eventually freeze. Thus it may have formed icings on springs, ice dams and jams on constrictions in the channel path, or frozen pools. Given sufficient thickness and downhill surface gradient, these ice masses would have moved; and given the right conditions, they could have moved like Antarctic ice streams.

Lucchitta, B. K.↗

NASA NTRS1997

Ice in Channels and Ice-Rock Mixtures in Valleys on Mars: Did They Slide on Deformable Rubble Like Antarctic Ice Streams?

Recent studies of ice streams in Antarctica reveal a mechanism of basal motion that may apply to channels and valleys on Mars. The mechanism is sliding of the ice on deformable water-saturated till under high pore pressures. It has been suggested by Lucchitta that ice was present in outflow channels on Mars and gave them their distinctive morphology. This ice may have slid like Antarctic ice streams but on rubbly weathering products rather than till. However, to generate water under high pore pressures, elevated heatflow is needed to melt the base of the ice. Either volcanism or higher heatflow more than 2 b.y. ago could have raised the basal temperature. Regarding valley networks, higher heatflow 3 b.y. ago could have allowed sliding of ice-saturated overburden at a few hundred meters depth. If the original, pristine valleys were somewhat deeper than they are now, they could have formed by the same mechanism. Recent sounding of the seafloor in front of the Ross Ice Shelf in Antarctica reveals large persistent patterns of longitudinal megaflutes and drumlinoid forms, which bear remarkable resemblance to longitudinal grooves and highly elongated streamlined islands found on the floors of martian outflow channels. The flutes are interpreted to have formed at the base of ice streams during the last glacial advance. Additional similarities of Antarctic ice streams with martian outflow channels are apparent. Antarctic ice streams are 30 to 80 km wide and hundreds of kilometers long. Martian outflow channels have similar dimensions. Ice stream beds are below sea level. Carr determined that most common floor elevations of martian outflow channels lie below martian datum, which may have been close to or below past martian sea levels. The Antarctic ice stream bed gradient is flat and locally may go uphill, and surface slopes are exceptionally. Martian channels also have floor gradients that are shallow or go uphill locally and have low surface gradients. The depth to the bed in ice streams is 1 to 1.5 km. At bankful stage, the depth of the fluid in outflow channels was 1 to 2 km, according to the height of bordering scarps. The similarity between Antarctic ice streams and martian outflow channels suggests that ice may have flowed through and shaped the outflow channels, and that perhaps the mechanism of motion of Antarctic ice streams also operated in outflow channels. In addition, sliding on deformable rubble may explain the formation of small valley networks. The large Siple Coast Antarctic ice streams are thought to slide over longitudinally grooved, deforming till, where much of the movement is within the till. The till is saturated with water at high pore pressures that nearly supports all of the weight of the ice. The small differential between overburden pressure and pore pressure at the bed is more important than the volume of water, but water needs to be supplied to the till interface. For pore pressures to remain high, the ice streams have to act as a seal that blocks the flow of water through them, and the rock underneath has to be of low permeability to prevent the water from draining away.

Lucchitta, B. K.↗

NASA NTRS2001

Satellite Retrieval of Atmospheric Water Budget over Gulf of Mexico- Caribbean Basin: Seasonal Variability

This study presents results from a multi-satellite/multi-sensor retrieval system designed to obtain the atmospheric water budget over the open ocean. A combination of hourly-sampled monthly datasets derived from the GOES-8 5 Imager and the DMSP 7-channel passive microwave radiometer (SSM/I) have been acquired for the Gulf of Mexico-Caribbean Sea basin. Whereas the methodology is being tested over this basin, the retrieval system is designed for portability to any open-ocean region. Algorithm modules using the different datasets to retrieve individual geophysical parameters needed in the water budget equation are designed in a manner that takes advantage of the high temporal resolution of the GOES-8 measurements, as well as the physical relationships inherent to the SSM/I passive microwave signals in conjunction with water vapor, cloud liquid water, and rainfall. The methodology consists of retrieving the precipitation, surface evaporation, and vapor-cloud water storage terms in the atmospheric water balance equation from satellite techniques, with the water vapor advection term being obtained as the residue needed for balance. Thus, we have sought to develop a purely satellite-based method for obtaining the full set of terms in the atmospheric water budget equation without requiring in situ sounding information on the wind profile. The algorithm is partly validated by first cross-checking all the algorithm components through multiple-algorithm retrieval intercomparisons. More fundamental validation is obtained by directly comparing water vapor transports into the targeted basin diagnosed from the satellite algorithm to those obtained observationally from a network of land-based upper air stations that nearly uniformly surround the basin. Total columnar atmospheric water budget results will be presented for an extended annual cycle consisting of the months of October-97, January-98, April-98, July-98, October-98, and January-1999. These results are used to emphasize the changing relationship in E-P, as well as in the varying roles of storage and advection in balancing E-P both on daily and monthly time scales and on localized and basin space scales. Results from the algorithm-to-algorithm intercomparisons will also be presented in the context of sensitivity testing to help understand the intrinsic uncertainties in the water budget terms.

Smith, Eric A.↗

NASA NTRS1995

Atmospheric infrared sounder

This report summarizes the activities of two Atmospheric Infrared Sounder (AIRS) team members during the first half of 1995. Changes to the microwave first-guess algorithm have separated processing of Advanced Microwave Sounding Unit A (AMSU-A) from AMSU-B data so that the different spatial resolutions of the two instruments may eventually be considered. Two-layer cloud simulation data was processed with this algorithm. The retrieved water vapor column densities and liquid water are compared. The information content of AIRS data was applied to AMSU temperature profile retrievals in clear and cloudy atmospheres. The significance of this study for AIRS/AMSU processing lies in the improvement attributable to spatial averaging and in the good results obtained with a very simple algorithm when all of the channels are used. Uncertainty about the availability of either a Microwave Humidity Sensor (MHS) or AMSU-B for EOS has motivated consideration of possible low-cost alternative designs for a microwave humidity sensor. One possible configuration would have two local oscillators (compared to three for MHS) at 118.75 and 183.31 GHz. Retrieval performances of the two instruments were compared in a memorandum titled 'Comparative Analysis of Alternative MHS Configurations', which is attached.

Rosenkranz, Philip, W.↗

NASA NTRS2005

SABER Observations of the OH Meinel Airglow Variability Near the Mesopause

The Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) instrument, one of four on board the TIMED satellite, observes the OH Meinel emission at 2.0 m that peaks near the mesopause. The emission results from reactions between members of the oxygen and hydrogen chemical families that can be significantly affected by mesopause dynamics. In this study we compare SABER measurements of OH Meinel emission rates and temperatures with predictions from a 3-dimensional chemical dynamical model. In general, the model is capable of reproducing both the observed diurnal and seasonal OH Meinel emission variability. The results indicate that the diurnal tide has a large effect on the overall magnitude and temporal variation of the emission in low latitudes. This tidal variability is so dominant that the seasonal cycle in the nighttime emission depends very strongly on the local time of the analysis. At higher latitudes, the emission has an annual cycle that is due mainly to transport of oxygen by the seasonally reversing mean circulation.

Marsh, Daniel R.↗

DOE OSTI2024

Electron Heating in the Transrelativistic Perpendicular Shocks of Tilted Accretion Flows

Abstract General relativistic magnetohydrodynamic (GRMHD) simulations of black hole tilted disks—where the angular momentum of the accretion flow at large distances is misaligned with respect to the black hole spin—commonly display standing shocks within a few to tens of gravitational radii from the black hole. In GRMHD simulations of geometrically thick, optically thin accretion flows, applicable to low-luminosity sources like Sgr A* and M87*, the shocks have transrelativistic speed, moderate plasma beta (the ratio of ion thermal pressure to magnetic pressure is β pi1 ∼ 1–8), and low sonic Mach number (the ratio of shock speed to sound speed is M s ∼ 1–6). We study such shocks with 2D particle-in-cell simulations, and we quantify the efficiency and mechanisms of electron heating for the special case of preshock magnetic fields perpendicular to the shock direction of propagation. We find that the postshock electron temperature T e2 exceeds the adiabatic expectation T e2,ad by an amount T e 2 / T e 2 , ad − 1 ≃ 0.0016 M s 3.6 , nearly independent of the plasma beta and of the preshock electron-to-ion temperature ratio T e1 / T i1 , which we vary from 0.1 to unity. We investigate the heating physics for M s ∼ 5–6 and find that electron superadiabatic heating is governed by magnetic pumping at T e1 / T i1 = 1, whereas heating by B -parallel electric fields (i.e., parallel to the local magnetic field) dominates at T e1 / T i1 = 0.1. Our results provide physically motivated subgrid prescriptions for electron heating at the collisionless shocks seen in GRMHD simulations of black hole accretion flows.

Astronomy & Astrophysics↗

NASA NTRS1990

SPEAR-1: An experiment to measure current collection in the ionosphere by high voltage biased conductors

An experiment is described in which a high electrical potential difference, up to 45 kV, was applied between deployed conducting spheres and a sounding rocket in the ionosphere. Measurements were made of the applied voltage and the resulting currents for each of 24 applications of different high potentials. In addition, diagnostic measurements of optical emissions in the vicinity of the spheres, energetic particle flow to the sounding rocket, dc electric field and wave data were made. The ambient plasma and neutral environments were measured by a Langmuir probe and a cold cathode neutral ionization gauge, respectively. The payload is described and examples of the measured current and voltage characteristics are presented. The characteristics of the measured currents are discussed in terms of the diagnostic measurements and the in-situ measurements of the vehicle environment. In general, it was found that the currents observed were at a level typical of magnetically limited currents from the ionospheric plasma for potentials less than 12 kV, and slightly higher for larger potentials. However, due to the failure to expose the plasma contactor, the vehicle sheath modified the sphere sheaths and made comparisons with the analytic models of Langmuir-Blodgett and Parker-Murphy less meaningful. Examples of localized enhancements of ambient gas density resulting from the operation of the attitude control system thrusters (cold nitrogen) were obtained. Current measurements and optical data indicated localized discharges due to enhanced gas density that reduced the vehicle-ionosphere impedance.

Raitt, W. John↗

DOE OSTI2026

Using Machine Learning to Understand Electric and Hybrid Vehicles Ownership in Burdened and Nonburdened Communities

Transitioning to electric and hybrid vehicles (EHVs) for all communities is a pivotal step toward sustainable transportation and environmental conservation. This paper aims to understand the adoption of EHVs, focusing on burdened communities (BCs) in the United States. The EHV ownership-based analysis combines two datasets—behavioral data from the Puget Sound Regional Travel Survey integrated with BCs (Justice40) data covering transportation insecurity, environmental burden, social vulnerability, health vulnerability, and climate and disaster risk burden. After creating this unique database, descriptive analysis and modeling are used to analyze the data and predict EHV ownership in the future. Specifically, we use a new method that combines particle swarm optimization (PSO) with a stacking model named PSO-Stacking, which incorporates heterogeneous base learners of machine learning and deep learning. PSO applies a customized objective function to select the optimal hyperparameters for heterogeneous learners within the stacking model, effectively addressing challenges such as multicollinearity, data imbalance, nonlinearity, and overfitting. The proposed solution covers more accurate results than standard benchmark models for EHV ownership in BCs and non-BCs. In addition, the results of the PSO-Stacking method are explained using the local interpretable model-agnostic explanations technique. Results show a negative correlation between the BCs indicators, that is, higher transportation insecurity associated with lower EHV ownership. Furthermore, BCs have higher future climate risk scores, diesel particulate matter levels, and PM2.5 in the air than non-BCs because of higher conventional vehicle ownership. These communities are at higher risk and can benefit from electrification, EV infrastructure, and EV policies to address environmental challenges.

Aslam, Zeeshan [ORNL]↗

NASA NTRSDate not supplied

A Field-Deployable Wireless Data Acquisition System for Ground-Test Arrays

This paper describes the development, characterization, and deployment of a field-deployable wireless data acquisition system for ground-test arrays, applicable in noise-source localization or beamforming measurements such as those encountered during airframe noise flyover measurement tests. The system design is enabled by commercially available, low-power Internet of Things (IoT) processors and Wi-Fi communication components. Time is synchronized across the array wirelessly by leveraging the Coordinated Universal Time (UTC) time provided by the Global Positioning System (GPS). Initial laboratory characterization of the system demonstrated its ability to meet acoustic bandwidth, dynamic range, time synchronization, environmental, and battery life requirements for typical ground-test array deployments. A successful system deployment at NASA Langley was performed that included measurement of a suspended elevated static noise source, and Uncrewed Aerial System (UAS) vehicle measurements using a quadcopter operated both in hover mode and forward flight. Beamform analysis of the acquired data showed an excellent ability of the array to extract accurate sound pressure levels from the suspended source. Synchronization of the array and vehicle GPS timecodes allowed the ability to extract acoustic signatures from the UAS vehicle during hover and forward flight maneuvers over the array. These results validate that the use of a high channel count wireless array is advantageous in airframe and propulsion noise flyover test campaigns.

wireless↗

NASA NTRS2013

A Preview of the OCO-2 Spatial and Temporal Sampling Strategy

For routine science observations, the OC0-2 spacecraft bus points the instrument bore sight either at the local nadir (85 < 85deg) or at the glint spot (85 < 81 deg) and collects -106 soundings/day over the sunlit hemisphere. center dot Nadir observations: expected to yield more spatially-homogeneous optical paths in partially cloudy regions and over topographically rough land regions center dot Glint observations are expected to yield (much) higher SNR over dark ocean or ice covered surfaces. center dot For both glint and nadir observations, the spacecraft performs a yaw maneuver to orient the long axis of the spectrometer slits perpendicular to the principle plane center dot The nominal plan is to alternate between glint and nadir observations on alternate 16-day ground repeat cycles, but this strategy may be modified to maximize coverage Target observations: For calibration and validation, the spacecraft bus can also point the instrument bore sight at a stationary surface target center dot Collects up to 12,000 soundings at observing zenith angles from +75deg GEO CL-

Orbiting Carbon Observatory-2↗

NASA NTRS2018

Analysis of Simulated and Experimental Noise Sources of Boeing 777 Main Gear Model via CLEAN in 3D

Previously obtained experimental and simulated phased microphone array data for the NASA 26%-scale model of a six-wheel main landing gear, with and without a toboggan-shaped noise reduction fairing, were analyzed using the CLEAN technique in three dimensions. The model is a high-fidelity representation of the Boeing 777-200 aircraft main landing gear. The reprocessing of the acoustic data was undertaken to address the deficiencies encountered in the source localization (beamform) maps and the integrated farfield spectra at mid to high frequencies in our previous study, where conventional array processing techniques were applied to the same data sets. Application of the CLEAN approach resulted in higher quality beamform maps with many of the previously observed side lobes either eliminated or suppressed significantly. As a result, integration of the experimentally and computationally based maps showed substantial improvement in the quality of the high-frequency spectral content relative to the corresponding spectra generated via conventional array processing, thus extending the good agreement achieved between the measured and predicted farfield spectra from 8 kHz to 14 kHz in model-scale frequencies. In addition, an examination of the simulated surface pressure fluctuations, off-surface flow field, and three-dimensionally constructed noise sources was conducted to determine the cause of the subtle discrepancies between measured and predicted sound pressure levels that occur in the 1,800 Hz to 4,000 Hz model-scale frequency range.

Ravetta, Patricio↗

NASA NTRS1991

Simulated optical images of galaxies at z about 1 using ultraviolet images of nearby galaxies

Ultraviolet sounding rocket images of several nearby galaxies are used to simulate the appearance in optical bandpasses of similar systems at redshifts z = 0.5-2.67, as observed by the WFPC on HST and by ground-based instruments. Since the morphology of galaxies is a strong function of the wavelength, the appearance of galaxies at large redshifts is subjected to a large k-correction effect. The strong dependence of monochromatic surface brightness on redshift also implies that observed morphology of distant systems will be crucially dependent on the limiting surface brightness set by the sky background. Although the angle subtended by sources depends only weakly on z, the fraction of a galaxy whose surface brightness is above the detection threshold varies strongly with z. Morphological distinctions of spiral from elliptical, spiral from irregular, and barred from unbarred types become more difficult, as does accurate evaluation of interactions or of the local environment.

Bohlin, Ralph C.↗