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DOE OSTI2016

LATE POP III STAR FORMATION DURING THE EPOCH OF REIONIZATION: RESULTS FROM THE RENAISSANCE SIMULATIONS

We present results on the formation of Population III (Pop III) stars at redshift 7.6 from the Renaissance Simulations, a suite of extremely high-resolution and physics-rich radiation transport hydrodynamics cosmological adaptive-mesh refinement simulations of high-redshift galaxy formation performed on the Blue Waters supercomputer. In a survey volume of about 220 comoving Mpc{sup 3}, we found 14 Pop III galaxies with recent star formation. The surprisingly late formation of Pop III stars is possible due to two factors: (i) the metal enrichment process is local and slow, leaving plenty of pristine gas to exist in the vast volume; and (ii) strong Lyman–Werner radiation from vigorous metal-enriched star formation in early galaxies suppresses Pop III formation in (“not so”) small primordial halos with mass less than ∼3 × 10{sup 7} M {sub ⊙}. We quantify the properties of these Pop III galaxies and their Pop III star formation environments. We look for analogs to the recently discovered luminous Ly α emitter CR7, which has been interpreted as a Pop III star cluster within or near a metal-enriched star-forming galaxy. We find and discuss a system similar to this in some respects, however, the Pop III star cluster is far less massive and luminous than CR7 is inferred to be.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

MASS TRANSPORT AND TURBULENCE IN GRAVITATIONALLY UNSTABLE DISK GALAXIES. II. THE EFFECTS OF STAR FORMATION FEEDBACK

Self-gravity and stellar feedback are capable of driving turbulence and transporting mass and angular momentum in disk galaxies, but the balance between them is not well understood. In the previous paper in this series, we showed that gravity alone can drive turbulence in galactic disks, regulate their Toomre Q parameters to ∼1, and transport mass inwards at a rate sufficient to fuel star formation in the centers of present-day galaxies. In this paper we extend our models to include the effects of star formation feedback. We show that feedback suppresses galaxies’ star formation rates by a factor of ∼5 and leads to the formation of a multi-phase atomic and molecular interstellar medium. Both the star formation rate and the phase balance produced in our simulations agree well with observations of nearby spirals. After our galaxies reach steady state, we find that the inclusion of feedback actually lowers the gas velocity dispersion slightly compared to the case of pure self-gravity, and also slightly reduces the rate of inward mass transport. Nevertheless, we find that, even with feedback included, our galactic disks self-regulate to Q ∼ 1, and transport mass inwards at a rate sufficient to supply a substantial fraction of the inner disk star formation. We argue that gravitational instability is therefore likely to be the dominant source of turbulence and transport in galactic disks, and that it is responsible for fueling star formation in the inner parts of galactic disks over cosmological times.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

The relative rate of LGRB formation as a function of metallicity

There is now strong evidence that long-duration gamma-ray bursts (LGRBs) are preferentially formed in low-metallicity environments. However, the magnitude of this effect and its functional dependence on metallicity have not been well characterized. In our previous paper, we compared the metallicity distribution of LGRB host galaxies to that of star-forming galaxies in the local universe. Here we build upon this work by in effect dividing one distribution by the other, and thus directly determine the relative rate of LGRB formation as a function of metallicity in the low-redshift universe. We find a dramatic cutoff in LGRB formation above a metallicity of log(O/H)+12≈8.3 in the KK04 scale, with LGRBs forming between 10 and 50 times more frequently per unit star formation below this cutoff than above. Furthermore, our data suggest that the rate of LGRB formation per unit star formation continues to fall above this break. We estimate that the LGRB formation rate per unit star formation may drop by as much as a factor of 100 between one-third solar and solar metallicity.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Star Formation Quenching Timescale of Central Galaxies in a Hierarchical Universe

Central galaxies make up the majority of the galaxy population, including the majority of the quiescent population at M{sub ∗}>10{sup 10}M{sub ⊙}. Thus, the mechanism(s) responsible for quenching central galaxies play a crucial role in galaxy evolution as whole. We combine a high-resolution cosmological N-body simulation with observed evolutionary trends of the “star formation main sequence,” quiescent fraction, and stellar mass function at z<1 to construct a model that statistically tracks the star formation histories and quenching of central galaxies. Comparing this model to the distribution of central galaxy star formation rates in a group catalog of the SDSS Data Release 7, we constrain the timescales over which physical processes cease star formation in central galaxies. Over the stellar mass range 10{sup 9.5}--10{sup 11}M{sub ⊙} we infer quenching e-folding times that span 1.5–0.5 Gyr with more massive central galaxies quenching faster. For M{sub ∗}=10{sup 10.5}M{sub ⊙}, this implies a total migration time of ∼4 Gyr from the star formation main sequence to quiescence. Compared to satellites, central galaxies take ∼2 Gyr longer to quench their star formation, suggesting that different mechanisms are responsible for quenching centrals versus satellites. Finally, the central galaxy quenching timescale we infer provides key constraints for proposed star formation quenching mechanisms. Our timescale is generally consistent with gas depletion timescales predicted by quenching through strangulation. However, the exact physical mechanism(s) responsible for this remain unclear.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Active Galactic Nuclei Feedback in SDSS-IV MaNGA: AGNs Have Suppressed Central Star Formation Rates

Despite the importance of feedback from active galactic nuclei (AGNs) in models of galaxy evolution, observational constraints on the influence of AGN feedback on star formation remain weak. To this end, we have compared the star formation trends of 279 low-redshift AGN galaxies with 558 inactive control galaxies using integral field unit spectroscopy from the Sloan Digital Sky Survey-IV Mapping Nearby Galaxies at Apache Point Observatory survey. With a Gaussian-process-based methodology, we reconstruct nonparametric star formation histories in spatially resolved spaxels covering the face of each galaxy. Based on the galaxy-wide star formation rates (SFRs) alone, we find no obvious signatures of AGN feedback. However, the AGN galaxies have significantly suppressed central (kiloparsec-scale) SFRs, lying up to a factor of 2 below those of the control galaxies, providing direct observational evidence of AGN feedback suppressing star formation. The suppression of central SFRs in the AGN galaxies began in the central regions ~6 Gyr ago (redshift z ~ 0.7), taking place over a few gigayears. A small subset of the AGN galaxies were rapidly driven to quiescence shortly before being observed (in the last 500 Myr), potentially indicating instances of AGN-driven feedback. More frequently, however, star formation continues in the AGN galaxies, with suppression primarily in the central regions. This is suggestive of a picture in which integrated (gigayear-timescale) AGN feedback can significantly affect central star formation, but may be inefficient in driving galaxy-wide quenching in low-redshift galaxies, instead leaving them in the green valley.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

The Origin of Star Formation in Early-type Galaxies Inferred from Spatially Resolved Spectroscopy

Abstract We investigate the origin of star formation activity in early-type galaxies with current star formation using spatially resolved spectroscopic data from the Mapping Nearby Galaxies at Apache Point Observatory in the Sloan Digital Sky Survey (SDSS). We first identify star-forming early-type galaxies from the SDSS sample, which are morphologically early-type but show current star formation activity in their optical spectra. We then construct comparison samples with different combinations of star formation activity and morphology, which include star-forming late-type galaxies, quiescent early-type galaxies, and quiescent late-type galaxies. Our analysis of the optical spectra reveals that the star-forming early-type galaxies have two distinctive episodes of star formation, which is similar to late-type galaxies but different from quiescent early-type galaxies with a single star formation episode. Star-forming early-type galaxies have properties in common with star-forming late-type galaxies, which include stellar population, gas and dust content, mass, and environment. However, the physical properties of star-forming early-type galaxies derived from spatially resolved spectroscopy differ from those of star-forming late-type galaxies in the sense that the gas in star-forming early-type galaxies is more concentrated than their stars, and is often kinematically misaligned with stars. The age gradient of star-forming early-type galaxies also differs from those of star-forming late-type galaxies. Our findings suggest that the current star formation in star-forming early-type galaxies has an external origin including galaxy mergers or accretion gas from the cosmic web.

Astronomy & Astrophysics↗
DOE OSTI2016

Real-time measurements of secondary organic aerosol formation and aging from ambient air in an oxidation flow reactor in the Los Angeles area

Field studies in polluted areas over the last decade have observed large formation of secondary organic aerosol (SOA) that is often poorly captured by models. The study of SOA formation using ambient data is often confounded by the effects of advection, vertical mixing, emissions, and variable degrees of photochemical aging. An oxidation flow reactor (OFR) was deployed to study SOA formation in real-time during the California Research at the Nexus of Air Quality and Climate Change (CalNex) campaign in Pasadena, CA, in 2010. A high-resolution aerosol mass spectrometer (AMS) and a scanning mobility particle sizer (SMPS) alternated sampling ambient and reactor-aged air. The reactor produced OH concentrations up to 4 orders of magnitude higher than in ambient air. OH radical concentration was continuously stepped, achieving equivalent atmospheric aging of 0.8 days–6.4 weeks in 3 min of processing every 2 h. Enhancement of organic aerosol (OA) from aging showed a maximum net SOA production between 0.8–6 days of aging with net OA mass loss beyond 2 weeks. Reactor SOA mass peaked at night, in the absence of ambient photochemistry and correlated with trimethylbenzene concentrations. Reactor SOA formation was inversely correlated with ambient SOA and O x , which along with the short-lived volatile organic compound correlation, indicates the importance of very reactive ( τ OH ~ 0.3 day) SOA precursors (most likely semivolatile and intermediate volatility species, S/IVOCs) in the Greater Los Angeles Area. Evolution of the elemental composition in the reactor was similar to trends observed in the atmosphere (O : C vs. H : C slope ~ –0.65). Oxidation state of carbon (OSc) in reactor SOA increased steeply with age and remained elevated (OS C ~ 2) at the highest photochemical ages probed. The ratio of OA in the reactor output to excess CO (ΔCO, ambient CO above regional background) vs. photochemical age is similar to previous studies at low to moderate ages and also extends to higher ages where OA loss dominates. The mass added at low-to-intermediate ages is due primarily to condensation of oxidized species, not heterogeneous oxidation. The OA decrease at high photochemical ages is dominated by heterogeneous oxidation followed by fragmentation/evaporation. A comparison of urban SOA formation in this study with a similar study of vehicle SOA in a tunnel suggests the importance of vehicle emissions for urban SOA. Pre-2007 SOA models underpredict SOA formation by an order of magnitude, while a more recent model performs better but overpredicts at higher ages. Furthermore, these results demonstrate the value of the reactor as a tool for in situ evaluation of the SOA formation potential and OA evolution from ambient air.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2017

Secondary organic aerosol formation from in situ OH, O 3 , and NO 3 oxidation of ambient forest air in an oxidation flow reactor

Ambient pine forest air was oxidized by OH, O 3 , or NO 3 radicals using an oxidation flow reactor (OFR) during the BEACHON-RoMBAS (Bio–hydro–atmosphere interactions of Energy, Aerosols, Carbon, H 2 O, Organics and Nitrogen – Rocky Mountain Biogenic Aerosol Study) campaign to study biogenic secondary organic aerosol (SOA) formation and organic aerosol (OA) aging. A wide range of equivalent atmospheric photochemical ages was sampled, from hours up to days (for O 3 and NO 3 ) or weeks (for OH). Ambient air processed by the OFR was typically sampled every 20–30 min, in order to determine how the availability of SOA precursor gases in ambient air changed with diurnal and synoptic conditions, for each of the three oxidants. More SOA was formed during nighttime than daytime for all three oxidants, indicating that SOA precursor concentrations were higher at night. At all times of day, OH oxidation led to approximately 4 times more SOA formation than either O 3 or NO 3 oxidation. This is likely because O 3 and NO 3 will only react with gases containing C = C bonds (e.g., terpenes) to form SOA but will not react appreciably with many of their oxidation products or any species in the gas phase that lacks a C = C bond (e.g., pinonic acid, alkanes). In contrast, OH can continue to react with compounds that lack C = C bonds to produce SOA. Closure was achieved between the amount of SOA formed from O 3 and NO 3 oxidation in the OFR and the SOA predicted to form from measured concentrations of ambient monoterpenes and sesquiterpenes using published chamber yields. This is in contrast to previous work at this site (Palm et al., 2016), which has shown that a source of SOA from semi- and intermediate-volatility organic compounds (S/IVOCs) 3.4 times larger than the source from measured VOCs is needed to explain the measured SOA formation from OH oxidation. This work suggests that those S/IVOCs typically do not contain C = C bonds. O 3 and NO 3 oxidation produced SOA with elemental O : C and H : C similar to the least-oxidized OA observed in local ambient air, and neither oxidant led to net mass loss at the highest exposures, in contrast to OH oxidation. An OH exposure in the OFR equivalent to several hours of atmospheric aging also produced SOA with O : C and H : C values similar to ambient OA, while higher aging (days–weeks) led to formation of SOA with progressively higher O : C and lower H : C (and net mass loss at the highest exposures). NO 3 oxidation led to the production of particulate organic nitrates (pRONO 2 ), while OH and O 3 oxidation (under low NO) did not, as expected. These measurements of SOA formation provide the first direct comparison of SOA formation potential and chemical evolution from OH, O 3 , and NO 3 oxidation in the real atmosphere and help to clarify the oxidation processes that lead to SOA formation from biogenic hydrocarbons.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Processes contributing to cloud dissipation and formation events on the North Slope of Alaska

Abstract. Clear-sky periods across the high latitudes have profound impacts on the surface energy budget and lower atmospheric stratification; however an understanding of the atmospheric processes leading to low-level cloud dissipation and formation events is limited. A method to identify clear periods at Utqiaġvik (formerly Barrow), Alaska, during a 5-year period (2014–2018) is developed. A suite of remote sensing and in situ measurements from the high-latitude observatory are analyzed; we focus on comparing and contrasting atmospheric properties during low-level (below 2 km) cloud dissipation and formation events to understand the processes controlling clear-sky periods. Vertical profiles of lidar backscatter suggest that aerosol presence across the lower atmosphere is relatively invariant during the periods bookending clear conditions, which suggests that a sparsity of aerosol is not frequently a cause for cloud dissipation on the North Slope of Alaska. Further, meteorological analysis indicates two active processes ongoing that appear to support the formation of low clouds after a clear-sky period: namely, horizontal advection, which was dominant in winter and early spring, and quiescent air mass modification, which was dominant in the summer. During summer, the dominant mode of cloud formation is a low cloud or fog layer developing near the surface. This low cloud formation is driven largely by air mass modification under relatively quiescent synoptic conditions. Near-surface aerosol particles concentrations changed by a factor of 2 around summer formation events. Thermodynamic adjustment and increased aerosol presence under quiescent atmospheric conditions are hypothesized as important mechanisms for fog formation.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1982

LANDSAT-D data format control book. Volume 2: Telemetry

The formats used for the transmission of LANDSAT-D and LANDSAT-D Prime spacecraft telemetry data through either the TDRS/GSTDN via the NASCOM Network to the CSF are described as well as the telemetry flow from the command and data handling subsystem, a telemetry list and telemetry matrix assignment for the mission and engineering formats. The on-board computer (OBC) controlled format and the dwell format are also discussed. The OBCs contribution to telemetry, and the format of the reports, are covered. The high rate data channel includes the payload correction data format, the narrowband tape recorder and the OBC dump formats.

Talipsky, R.↗
NASA NTRS1983

Shock tube study of the fuel structure effects on the chemical kinetic mechanisms responsible for soot formation

Soot formation in toluene-, benzene-, and acetylene-oxygen-argon mixtures was investigated to study soot formation in a combustion environment. High concentrations of oxygen completely suppress soot formation. The addition of oxygen at relatively low concentrations uniformly suppresses soot formation at high pressures, while at relatively lower pressures it suppresses soot formation at higher temperatures while promoting soot production at lower temperatures. The observed behavior indicates that oxidation reactions compete with ring fragmentation. The main conclusion to be drawn from the results is that the soot formation mechanism is probably the same for the pyrolysis and oxidation of hydrocarbons. That is, the addition of oxygen does not alter the soot route but rather promotes or inhibits this route by means of competitive reactions. An approach to empirical modeling of soot formation during pyrolysis of aromatic hydrocarbons is also presented.

Frenklach, M.↗
NASA NTRS1985

The effects of prostaglandin E2 in growing rats - Increased metaphyseal hard tissue and cortico-endosteal bone formation

The role of in vivo prostaglandin E2 (PGE2) in bone formation is investigated. Twenty-five male Sprague-Dawley rats weighing between 223-267 g were injected subcutaneously with 0.3, 1.0, 3.0, and 6.0 mg of PGE2-kg daily for 21 days. The processing of the tibiae for observation is described. Radiographs and histomorphometric analyses are also utilized to study bone formation. Body weight, weights of soft tissues and bones morphometry are evaluated. It is observed that PGE2 depressed longitudinal bone growth, increased growth cartilage thickness, decreased degenerative cartilage cell size and cartilage cell production, and significantly increased proximal tibial metaphyseal hard tissue mass. The data reveal that periosteal bone formation is slowed down at higher doses of PGE2 and endosteal bone formation is slightly depressed less than 10 days post injection; however, here is a late increase (10 days after post injection) in endosteal bone formation and in the formation of trabecular bone in the marrow cavity of the tibial shaft. It is noted that the effects of PGE2 on bone formation are similar to the responses of weaning rats to PGE2.

Jee, W. S. S.↗
NASA NTRS1987

High mass star formation in the galaxy

The Galactic distributions of HI, H2, and HII regions are reviewed in order to elucidate the high mass star formation occurring in galactic spiral arms and in active galactic nuclei. Comparison of the large scale distributions of H2 gas and radio HII regions reveals that the rate of formation of OB stars depends on (n sub H2) sup 1.9 where (n sub H2) is the local mean density of H2 averaged over 300 pc scale lengths. In addition the efficiency of high mass star formation is a decreasing function of cloud mass in the range 200,000 to 3,000,000 solar mass. These results suggest that high mass star formation in the galactic disk is initiated by cloud-cloud collisions which are more frequent in the spiral arms due to orbit crowding. Cloud-cloud collisions may also be responsible for high rates of OB star formation in interacting galaxies and galactic nuclei. Based on analysis of the Infrared Astronomy Satellite (IRAS) and CO data for selected GMCs in the Galaxy, the ratio L sub IR/M sub H2 can be as high as 30 solar luminosity/solar mass for GMCs associated with HII regions. The L sub IR/M sub H2 ratios and dust temperature obtained in many of the high luminosity IRAS galaxies are similar to those encountered in galactic GMCs with OB star formation. High mass star formation is therefore a viable explanation for the high infrared luminosity of these galaxies.

Scoville, N. Z.↗
NASA NTRS1988

An evaluation of flight path formats head-up and head-down

Flight path primary flight display formats were incorporated on head-up and head-down electronic displays and integrated into an Advanced Concepts Flight Simulator. Objective and subjective data were collected while ten airline pilots evaluated the formats by flying an approach and landing task under various ceiling, visibility and wind conditions. Deviations from referenced/commanded airspeed, horizontal track, vertical track and touchdown point were smaller using the head-up display (HUD) format than the head-down display (HDD) format, but not significantly smaller. Subjectively, the pilots overwhelmingly preferred (1) flight path formats over attitude formats used in current aircraft, and (2) the head-up presentation over the head-down, primarily because it eliminated the head-down to head-up transition during low visibility landing approaches. This report describes the simulator, the flight displays, the format evaluation, and the results of the objective and subjective data.

Sexton, George A.↗
NASA NTRS1990

Innovative design of composite structures: The use of curvilinear fiber format in structural design of composites

The influence is investigated of a curvilinear fiber format on load carrying capacity of a layered fiber reinforced plate with a centrally located hole. A curvilinear fiber format is descriptive of layers in a laminate having fibers which are aligned with the principal stress directions in those layers. Laminates of five curvilinear fiber format designs and four straightline fiber format designs are considered. A quasi-isotropic laminate having a straightline fiber format is used to define a baseline design for comparison with the other laminate designs. Four different plate geometries are considered and differentiated by two values of hole diameter/plate width equal to 1/6 and 1/3, and two values of plate length/plate width equal to 2 and 1. With the plates under uniaxial tensile loading on two opposing edges, alignment of fibers in the curvilinear layers with the principal stress directions is determined analytically by an iteration procedure. In-plane tensile load capacity is computed for all of the laminate designs using a finite element analysis method. A maximum strain failure criterion and the Tsai-Wu failure criterion are applied to determine failure loads and failure modes. Resistance to buckling of the laminate designs to uniaxial compressive loading is analyzed using the commercial code Engineering Analysis Language. Results indicate that the curvilinear fiber format laminates have higher in-plane tensile load capacity and comparable buckling resistance relative to the straightline fiber format laminates.

Charette, R. F.↗
NASA NTRS1989

Photoionization-regulated star formation and the structure of molecular clouds

A model for the rate of low-mass star formation in Galactic molecular clouds and for the influence of this star formation on the structure and evolution of the clouds is presented. The rate of energy injection by newly formed stars is estimated, and the effect of this energy injection on the size of the cloud is determined. It is shown that the observed rate of star formation appears adequate to support the observed clouds against gravitational collapse. The rate of photoionization-regulated star formation is estimated and it is shown to be in agreement with estimates of the observed rate of star formation if the observed molecular cloud parameters are used. The mean cloud extinction and the Galactic star formation rate per unit mass of molecular gas are predicted theoretically from the condition that photionization-regulated star formation be in equilibrium. A simple model for the evolution of isolated molecular clouds is developed.

Mckee, Christopher F.↗
NASA NTRS1993

Was Martian mantle wet? A possible consequence of rapid core formation

Degassing of H2O in the planetary interior possibly plays an important role in the evolution of surface environment as well as geologic activity on the terrestrial planets. Mars may be such a planet that well preserves the materials and the geologic features directly related to early evolution of H2O. H2O content in the interior of proto-Mars during accretion and also core formation were investigated. Geodetic data shows that Mars has a dense core. The existence of iron-rich core on Mars may be also supported by the depletion of siderophile elements in SNC meteorites assuming that these samples came from Mars. Isotope systematics of these meteorites indicate that the core formation occurred very early, probably concurrently with Mars formation. Considering the kinetics of metal segregation from silicate, the melting of silicate is likely to precede the core formation. Once the core formation occurs, substantial amount of gravitational energy is released and thus the planetary interior is heated. This energy may be large enough to keep the silicate material in partially molten state along with the accretional heating. Under such circumstances, the silicate melt probably migrates to the surface. Early crustal formation, therefore, is also likely to be associated with the core formation.

Kuramoto, Kiyoshi↗
NASA NTRS1995

Grain formation around carbon stars. 1: Stationary outflow models

Asymptotic giant branch (AGB) stars are known to be sites of dust formation and undergo significant mass loss. The outflow is believed to be driven by radiation pressure on grains and momentum coupling between the grains and gas. While the physics of shell dynamics and grain formation are closely coupled, most previous models of circumstellar shells have treated the problem separately. Studies of shell dynamics typically assume the existence of grains needed to drive the outflow, while most grain formation models assume a constant veolcity wind in which grains form. Furthermore, models of grain formation have relied primarily on classical nucleation theory instead of using a more realistic approach based on chemical kinetics. To model grain formation in carbon-rich AGB stars, we have coupled the kinetic equations governing small cluster growth to moment equations which determine the growth of large particles. Phenomenological models assuming stationary outflow are presented to demonstrate the differences between the classical nucleation approach and the kinetic equation method. It is found that classical nucleation theory predicts nucleation at a lower supersaturation ratio than is predicted by the kinetic equations, resulting in significant differences in grain properties. Coagulation of clusters larger than monomers is unimportant for grain formation in high mass-loss models but becomes more important to grain growth in low mass-loss situations. The properties of the dust grains are altered considerably if differential drift velocities are ignored in modeling grain formation. The effect of stellar temperature, stellar luminosity, and different outflow velocities are investigated. The models indicate that changing the stellar temperature while keeping the stellar luminosity constant has little effect on the physical parameters of the dust shell formed. Increasing the stellar luminosity while keeping the stellar temperature constant results in large differences in grain properties. For small outflow velocities, grains form at lower supersaturation ratios and close to the stellar photosphere, resulting in larger but fewer grains. The reverse is true when grains form under high outflow velocities, i.e., they form at higher supersaturation ratios, farther from the star, and are much smaller but at larger quantities.

Egan, Michael P.↗