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At least 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Netostat: analyzing dynamic flow patterns in high-speed networks

Understanding flow traffic patterns in networks, such as the Internet or service provider networks, is crucial to improving their design and building them robustly. However, as networks grow and become more complex, it is increasingly cumbersome and challenging to study how the many flow patterns, sizes and the continually changing source-destination pairs in the network evolve with time. Here, we present Netostat, a visualization-based network analysis tool that uses visual representation and a mathematics framework to study and capture flow patterns, using graph theoretical methods such as clustering, similarity and difference measures. Netostat generates an interactive graph of all traffic patterns in the network, to isolate key elements that can provide insights for traffic engineering. We present results for U.S. and European research networks, ESnet and GEANT, demonstrating network state changes, to identify major flow trends, potential points of failure, and bottlenecks.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1979

The monopropellant hydrazine propulsion subsystem for the Pioneer Venus spacecraft

The Pioneer Venus Orbiter and the Multiprobe spacecraft propulsion subsystems and their performance are presented. Monopropellant hydrazine subsystems on each spacecraft provided the capability to spin up the spacecraft after separation and perform all spin rate, velocity, and attitude changes required by the control subsystem to satisfy mission objectives. The propulsion subsystem provides thrust on demand by supplying anhydrous hydrazine from the propellant tanks through manifolds, filters and valves to the thrust chamber assemblies where the hydrazine is catalytically decomposed and expanded in a conical nozzle. The subsystems consist of seven 1 lbf thrusters for the Orbiter and six 1 lbf thrusters for the multiprobe which are isolated by two latch valves from the two propellant tanks so that two redundant thruster clusters are provided to ensure mission completion in the event of a single point failure. The propellant feed system is of all-welded construction to minimize weight and leakage and titanium is used as the primary material of construction. The multiprobe burned up on entering the Venus atmosphere with enough propellant left for the mission and the Orbiter was inserted into Venus orbit with enough propellant remaining for more than 2 earth years of orbital operations.

Barker, F. C.↗
DOE OSTI2023

Lewis Acid Supported Nickel Nitrenoids

Metalation of the polynucleating ligand F,tbs LH 6 (1,3,5-C 6 H 9 (NC 6 H 3 −4-F−2-NSiMe 2 t Bu) 3 ) with two equivalents of Zn(N(SiMe 3 ) 2 ) 2 affords the dinuclear product ( F,tbs LH 2 )Zn 2 (1), which can be further deprotonated to yield ( F,tbs L)Zn 2 Li 2 (OEt 2 ) 4 (2). Transmetalation of 2 with NiCl 2 (py) 2 yields the heterometallic, trinuclear cluster ( F,tbs L)Zn 2 Ni(py) (3). Reduction of 3 with KC 8 affords [KC 222 ][( F,tbs L)Zn 2 Ni] (4) which features a monovalent Ni centre. Addition of 1-adamantyl azide to 4 generates the bridging μ 3 -nitrenoid adduct [K(THF) 3 ][( F,tbs L)Zn 2 Ni(μ 3 -NAd)] (5). EPR spectroscopy reveals that the anionic cluster possesses a doublet ground state (S = 1/2). Cyclic voltammetry of 5 reveals two fully reversible redox events. The dianionic nitrenoid [K 2 (THF) 9 ][( F,tbs L)Zn 2 Ni(μ 3 -NAd)] (6) was isolated and characterized while the neutral redox isomer was observed to undergo both intra- and intermolecular H-atom abstraction processes. Here, Ni K-edge XAS studies suggest a divalent oxidation state for the Ni centres in both the monoanionic and dianionic [Zn 2 Ni] nitrenoid complexes. However, DFT analysis suggests Ni-borne oxidation for 5.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Dual aging pathways of Cu-SSZ-13 SCR catalysts: Hydrothermal vs. sulfur-induced deactivation

Hydrothermal aging (HTA) and chemical poisoning are two primary factors contributing to the real-world degradation of Cu-SSZ-13 SCR catalysts. Investigating field-returned samples offers valuable insights into performance degradation caused by these mechanisms. However, the simultaneous presence of both deactivation pathways complicates the isolation of their individual effects in post-mortem analyses. In this study, we separately prepared model Cu-SSZ-13 SCR catalysts subjected to hydrothermal-aging and sulfur-induced chemical poisoning. Using various characterization techniques, we elucidated the specific role of each aging process in catalyst deactivation and compared the results to real-world field-aged catalysts. Our findings show that hydrothermal aging at 650 °C for 100 h caused dealumination of the zeolite framework but no significant CuO x cluster formation. In contrast, sulfur aging (via sulfur exposure, calcination at 550 °C, and desulfation up to 750 °C) led to CuO x formation without any observable dealumination. On model catalysts, sulfur poisoning was found to reduce Cu mobility and the amount of active Cu sites, thus degrading catalyst activity. Although some activity was recovered upon desulfation, a portion of the initial catalyst activity remained irreversibly lost due to CuO x formation. We demonstrate that this occurs because sulfated species impede the ability of multi-nuclear Cu species (e.g., Cu dimers) to split back into their isolated form, leading to CuSO 4 -clusters that oxidatively desulfate to CuO x species. This degradation pathway explains the significant reduction in activity of field-aged samples, where substantial CuSO 4 -cluster accumulation leads to reduced active Cu and subsequent conversion to CuO x . Furthermore, the conclusions from model catalysts were extended directly to field-aged commercial samples, elucidating the decline in activity and chemical properties during field deployment.

Catalyst Deactivation↗
DOE OSTI2021

Healing of nanocracks by collision cascades in nickel

We use molecular dynamics simulations to investigate the interaction between collision cascades and pre-existing nano-cracks in nickel (Ni). We find that collision cascades cause the cracks to heal whenever a cascade initiates a thermal spike whose core overlaps with the crack. Moreover, crack healing affects the distribution of radiation-induced defects generated during a collision cascade: defect clusters, such as dislocations and stacking fault tetrahedra, dominate in the presence of crack healing, while isolated point defects dominate in its absence. Furthermore, this work indicates that irradiation may reduce the number of pre-existing crack-like flaws in metallic components, potentially improving their mechanical resilience.

36 MATERIALS SCIENCE↗
DOE OSTI2020

A Computational Assessment of Actinide Dioxide Cations AnO 2 2+ for An = U to Lr: The Limited Stability Range of the Hexavalent Actinyl Moiety, [O=An=O] 2+

The isolated gas-phase actinide dioxide dications, AnO 2 2+ , were evaluated by DFT and coupled cluster CCSD(T) calculations for 12 actinides, An = U–Lr. CASSCF calculations were used to define the orbitals for the CCSD(T) calculations. The characteristic linear [O$=$An$=$O] 2+ hexavalent actinyl(VI) was found to be the lowest energy structure for An = U, Np, and Pu, which also form stable actinyl(VI) species in solution and possibly for Am when spin–orbit effects are included. For Am, there is a divalent [An II (O 2 )] 2+ structure where the dioxygen is an end-on physisorbed η 1 - 3 O 2 2 kcal/mol above the actinyl when spin–orbit effects are included which lower the energy of the actinyl structure. For An = Cm, Bk, and Lr, the lowest energy structure is trivalent [An III (O 2 – )] 2+ where the dioxygen is a side-on superoxide, η 2 -O 2 – . For Cm, the actinyl is close in energy to the ground state when spin–orbit effects are included. For An = Cf, Es, Fm, Md, and No, the lowest energy structure is divalent [An II (O 2 )] 2+ where the dioxygen is an end-on physisorbed η 1 - 3 O 2 . The relative energies suggest that curyl(VI) and berkelyl(VI), like well-known americyl(VI), might be stabilized by coordinating ligands in condensed phases. The results further indicate that for californyl and beyond, the actinyl(VI) moieties will probably be elusive even using strong donor ligands. The prevalence of low oxidation states (OSs) An(II) and An(III) for transplutonium actinides reflects stabilization of the 5f orbitals and validates established trends, including the remarkably high stability of divalent No. Finally, bond distances and other parameters suggest maximum bond covalency around plutonyl(VI), with a particularly substantial decrease in bond strength between americyl(VI) and curyl(VI).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Electronic Structure of Atomically Dispersed Supported Iridium Catalyst Controls Iridium Aggregation

Supported iridium complexes, Ir(C 2 H 4 ) 2 /support, were characterized by X-ray absorption spectroscopy during a temperature ramp to 120 °C in flowing H 2 . Iridium in complexes bonded to weak and moderate electron-donor supports, SiO 2 and γ-Al 2 O 3 , underwent aggregation, forming nanoparticles and clusters, respectively. When the support was a strong electron-donor (MgO), iridium remained site-isolated. Density functional theory calculations confirm the dependence of iridium–support bond strength on the support’s electron-donor character. Coating the SiO 2 -supported complexes with 1-n-ethyl-3-methyl-imidazolium acetate enhanced electron density on the iridium, hindering its aggregation. Finally, these results demonstrate opportunities for stabilizing atomically dispersed supported noble metals under reducing conditions by choice of support/ionic liquid sheath combinations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2003

The Petrography of Meteoritic Nano-Diamonds

At least some meteoritic nanodiamonds are likely of presolar origin because of their association with anomalous Xe-HL and Te isotopic components indicative of a supernova (SN) origin. But the abundance of Xe is such that only approx. 1 in 10(exp 6) nano-diamonds contains a Xe atom, and the bulk C-13/C-12 composition of nano-diamond acid residues is chondritic (solar). Therefore, it is possible that a significant fraction of meteoritic nano-diamonds formed within the solar nebula. Nano-diamonds have recently been detected for the first time within the accretion discs of young stars by the Infrared Space Observatory (ISO). No comparable evidence of nanodiamonds in the interstellar medium has yet been found. We have identified nano-diamonds in acid etched thin-sections of meteorites, polar micrometeorites, and interplanetary dust particles (IDPs) with the goal of determining their distribution as a function of heliocentric distance. (It is assumed the meteorites and the polar micrometeorites are from asteroids at 2-4 AU and at least some of the IDPs are from comets at >50AU). We found that nano-diamonds are heterogeneously distributed throughout carbon-rich meteoritic materials (we identified them in some IDPs and not in others), and that their abundance may actually decrease with heliocentric distance, consistent with the hypothesis that some of them formed within the inner solar system and not in a presolar (SN) environment. In order to gain further insight about the origins of meteoritic nano-diamonds we are currently investigating their distribution in unetched thin-sections. We have examined a chondritic cluster IDP (U220GCA), fragments of the Tagish Lake (CM1) meteorite, and a SN graphite spherule (KE3d8) isolated from the Murchison (CM) meteorite. We selected U220GCA because its nano-diamond abundance (in acid etched thin-sections) appears to be as much as approx. 10X higher than in Murchison matrix, Tagish Lake because it has a higher reported nano-diamond abundance than other carbonaceous chondrites (approx. 3650-4330 ppm), and KE3d8 because it is a carbon spherule with an isotopic composition suggesting that it is a bone fide presolar SN grain.

Dai, Z. R.↗
NASA NTRSDate not supplied

Automated Tracking of Shallow Cu Growth Rates on Geostationary Imagery and Linkages to Cloud Organization

Shallow moist convection is ubiquitous throughout the tropics and represents a key player in boundary layer processes. Common tropical cloud features, such as convective rolls and cold pool fronts, form and persist for different periods within environments that support such development. Determining differences in lifecycle amongst these features in varying environments requires viewing their evolution from initiation to decay. Geostationary satellites provide a means to follow the clouds with enhanced spatiotemporal sampling from space. We apply a cloud-tracking tool to study lifecycle properties of shallow cumulus sampled during the NASA Cloud, Aerosol, and Monsoon Processes Philippines Experiment (CAMP2Ex) field campaign of 2019. The mission conducted airborne and shipborne operations over the West Pacific Ocean, in tandem with Rapid Scan imagery from the Advanced Himawari Imager (AHI) on the Japan Meteorological Agency’s (JMA) Himawari-8 satellite. Shallow cumulus was segmented on AHI 0.5-km visible reflectance and tracked during the daylit hours of several research flights that exhibited ideal atmospheric conditions for tracking. The resulting cloud tracks were collected according to regions containing airborne sampling of individual clouds at various stages of their lifecycles, yielding ensembles of tracks in separate environments. We present an analysis on lifecycle properties extracted from the cloud-track ensembles and their potential connections to cloud organizations observed throughout CAMP2Ex. Each ensemble is evaluated by calculating cloud-layer growth rates and comparing to spatial parameters, including track-achieved area and cloud-top height. The apparent clustering of growth rates for specific ensembles is then compared against overall cloud organizations, such as isolated congestus and cold pool fronts, that are observed with the airborne data. Finally, we consider how such differences in cloud growth appear in the airborne radar observations of intercepted cloud tracks.

Cloud Tracking↗
DOE OSTI2023

Tandem Mass-Selective Cryogenic Digital Ion Traps for Enhanced Cluster Formation

We present the implementation of tandem mass-selective cryogenic ion traps, designed to enhance the range of ion processing capabilities that can be performed prior to spectroscopic interrogation. We show that both the formation of ion clusters and mass filtering steps can be combined in a single cryogenic linear quadrupole ion trap driven by RF square waves. Mass filtering and mass isolation can be achieved by manipulation of the RF frequency and duty cycle. Very importantly, this scheme circumvents the need for high-amplitude RF voltages that can be incompatible with typical cryogenic ion processing conditions. In addition, proper adjustment of the stability boundaries during the clustering process allows for the preferential formation of a specific cluster size rather than a broad distribution of sizes. Lastly, we show that a specific cluster size can be formed, mass-selected, and then transferred to another ion trap for a second completely separate ion processing step. Furthermore, the instrumentation and modular design developed here expand the scope of ionic species and clusters that can be accessed by processing electrosprayed ions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Multifactorial genetic control and magnesium levels govern the production of a Streptomyces antibiotic with unusual cell density dependence

Streptomyces bacteria are renowned both for their antibiotic production capabilities and for their cryptic metabolic potential. Their metabolic repertoire is subject to stringent genetic control, with many of the associated biosynthetic gene clusters being repressed by the conserved nucleoid-associated protein Lsr2. In an effort to stimulate new antibiotic production in wild Streptomyces isolates, we leveraged the activity of an Lsr2 knockdown construct and successfully enhanced antibiotic production in the wild Streptomyces isolate WAC07094. We determined that this new activity stemmed from increased levels of the angucycline-like family member saquayamycin. Saquayamycin has both antibiotic and anti-cancer activities, and intriguingly, beyond Lsr2-mediated repression, we found saquayamycin production was also suppressed at high density on solid or in liquid growth media; its levels were greatest in low-density cultures. This density-dependent control was exerted at the level of the cluster-situated regulatory gene sqnR and was mediated in part through the activity of the PhoRP two-component regulatory system, where deleting phoRP led to both constitutive antibiotic production and sqnR expression. This suggests that PhoP functions to repress the expression of sqnR at high cell density. We further discovered that magnesium supplementation could alleviate this density dependence, although its action was independent of PhoP. Finally, we revealed that the nitrogen-responsive regulators GlnR and AfsQ1 could relieve the repression exerted by Lsr2 and PhoP. Intriguingly, we found that this low density-dependent production of saquayamycin was not unique to WAC07094; saquayamycin production by another wild isolate also exhibited low-density activation, suggesting that this spatial control may serve an important ecological function in their native environments.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1994

Internal velocity and mass distributions in simulated clusters of galaxies for a variety of cosmogonic models

The mass and velocity distributions in the outskirts (0.5-3.0/h Mpc) of simulated clusters of galaxies are examined for a suite of cosmogonic models (two Omega(sub 0) = 1 and two Omega(sub 0) = 0.2 models) utilizing large-scale particle-mesh (PM) simulations. Through a series of model computations, designed to isolate the different effects, we find that both Omega(sub 0) and P(sub k) (lambda less than or = 16/h Mpc) are important to the mass distributions in clusters of galaxies. There is a correlation between power, P(sub k), and density profiles of massive clusters; more power tends to point to the direction of a stronger correlation between alpha and M(r less than 1.5/h Mpc); i.e., massive clusters being relatively extended and small mass clusters being relatively concentrated. A lower Omega(sub 0) universe tends to produce relatively concentrated massive clusters and relatively extended small mass clusters compared to their counterparts in a higher Omega(sub 0) model with the same power. Models with little (initial) small-scale power, such as the hot dark matter (HDM) model, produce more extended mass distributions than the isothermal distribution for most of the mass clusters. But the cold dark matter (CDM) models show mass distributions of most of the clusters more concentrated than the isothermal distribution. X-ray and gravitational lensing observations are beginning providing useful information on the mass distribution in and around clusters; some interesting constraints on Omega(sub 0) and/or the (initial) power of the density fluctuations on scales lambda less than or = 16/h Mpc (where linear extrapolation is invalid) can be obtained when larger observational data sets, such as the Sloan Digital Sky Survey, become available.

Cen, Renyue↗
DOE OSTI2025

First-principles elucidation of defect-mediated Li transport in hexagonal boron nitride

Hexagonal boron nitride (hBN) is a promising candidate as a protective membrane or separator in Li-ion and Li–S batteries, given its excellent chemical stability, mechanical robustness, and high thermal conductivity. In addition, hBN can be functionalized by introducing defects and dopants, or be directly integrated into other active components of batteries, which further augments its appeal to the field. Here, we use first-principles simulations to evaluate the role of atomic defects in hBN in regulating the Li-ion diffusion mechanism and associated kinetics. Specifically, the following four distinct types of vacancy defects are considered: isolated single B and N vacancies, a B–N vacancy pair, and a B 3 N vacancy cluster. It is found that these defect sites generally favor Li intercalation and out-of-plane diffusion but slow down in-plane Li-ion diffusion due to a strong Li trapping effect at the defect sites. Such a trapping effect is, however, highly local such that it does not necessarily affect the overall Li-ion conductivity in defected hBN layers. The present systematic evaluation of the impact of atomic defects on Li ion migration and accompanied charge analysis of hBN lattice in response to Li-ion diffusion provide a mechanistic understanding of Li-ion transport behavior in defected hBN and highlight the potential of defect engineering to achieve optimal material performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1996

Adaptive grid methods for RLV environment assessment and nozzle analysis

Rapid access to highly accurate data about complex configurations is needed for multi-disciplinary optimization and design. In order to efficiently meet these requirements a closer coupling between the analysis algorithms and the discretization process is needed. In some cases, such as free surface, temporally varying geometries, and fluid structure interaction, the need is unavoidable. In other cases the need is to rapidly generate and modify high quality grids. Techniques such as unstructured and/or solution-adaptive methods can be used to speed the grid generation process and to automatically cluster mesh points in regions of interest. Global features of the flow can be significantly affected by isolated regions of inadequately resolved flow. These regions may not exhibit high gradients and can be difficult to detect. Thus excessive resolution in certain regions does not necessarily increase the accuracy of the overall solution. Several approaches have been employed for both structured and unstructured grid adaption. The most widely used involve grid point redistribution, local grid point enrichment/derefinement or local modification of the actual flow solver. However, the success of any one of these methods ultimately depends on the feature detection algorithm used to determine solution domain regions which require a fine mesh for their accurate representation. Typically, weight functions are constructed to mimic the local truncation error and may require substantial user input. Most problems of engineering interest involve multi-block grids and widely disparate length scales. Hence, it is desirable that the adaptive grid feature detection algorithm be developed to recognize flow structures of different type as well as differing intensity, and adequately address scaling and normalization across blocks. These weight functions can then be used to construct blending functions for algebraic redistribution, interpolation functions for unstructured grid generation, forcing functions to attract/repel points in an elliptic system, or to trigger local refinement, based upon application of an equidistribution principle. The popularity of solution-adaptive techniques is growing in tandem with unstructured methods. The difficultly of precisely controlling mesh densities and orientations with current unstructured grid generation systems has driven the use of solution-adaptive meshing. Use of derivatives of density or pressure are widely used for construction of such weight functions, and have been proven very successful for inviscid flows with shocks. However, less success has been realized for flowfields with viscous layers, vortices or shocks of disparate strength. It is difficult to maintain the appropriate mesh point spacing in the various regions which require a fine spacing for adequate resolution. Mesh points often migrate from important regions due to refinement of dominant features. An example of this is the well know tendency of adaptive methods to increase the resolution of shocks in the flowfield around airfoils, but in the incorrect location due to inadequate resolution of the stagnation region. This problem has been the motivation for this research.

Thornburg, Hugh J.↗
DOE OSTI2020

Copper Clusters Containing Hydrides in Trigonal Pyramidal Geometry

Structurally precise copper hydrides [Cu 11 H 2 {S 2 P(O i Pr) 2 } 6 (C≡CR) 3 ], R = Ph (1), C 6 H 4 F (2), and C 6 H 4 OMe (3), were first synthesized from the polyhydrido copper cluster [Cu 20 H 11 {S 2 P(O i Pr) 2 } 9 ] with nine equivalents of terminal alkynes. Later, their isolated yields were significantly improved by direct synthesis from [Cu(CH 3 CN) 4 ](PF 6 ), [NH 4 ][S 2 P(O i Pr) 2 ], NaBH 4 , and alkynes along with NEt 3 in THF. 1, 2, and 3 were fully characterized by single-crystal X-ray diffraction, ESI-MS, and multinuclear NMR spectroscopy. All three clustershave 11 copper atoms, adopting 3,3,4,4,4-pentacapped trigonal prismatic geometry, with two hydrides inside the Cu 11 cage, the position of which was ascertained by a single-crystal neutron diffraction structure of cluster 1 co-crystallized with a [Cu 7 (H){S 2 P(O i Pr) 2 } 6 ] (4) cluster. Six dithiophosphate and three alkynyl ligands stabilize the Cu 11 H 2 core in which the two hydrides adopt a trigonal pyramidal coordination mode. This coordination mode is so far unprecedented for hydride. The 1 H NMR resonance frequency of the two hydrides appears at 4.8 ppm, a value further confirmed by 2 H NMR spectroscopy for their deuteride derivatives [Cu 11 (D) 2 {S 2 P(O i Pr) 2 } 6 (C≡CR) 3 ]. A DFT investigation allows understanding the bonding within this new type of copper(I) hydrides.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2008

Formation of Clustered DNA Damage after High-LET Irradiation: A Review

Radiation can cause as well as cure cancer. The risk of developing radiation-induced cancer has traditionally been estimated from cancer incidence among survivors of the atomic bombs in Hiroshima and Nagasaki. These data provide the best estimate of human cancer risk over the dose range for low linear energy transfer (LET) radiations, such as X- or gamma-rays. The situation of estimating the real biological effects becomes even more difficult in the case of high LET particles encountered in space or as the result of domestic exposure to particles from radon gas emitters or other radioactive emitters like uranium-238. Complex DNA damage, i.e., the signature of high-LET radiations comprises by closely spaced DNA lesions forming a cluster of DNA damage. The two basic groups of complex DNA damage are double strand breaks (DSBs) and non-DSB oxidative clustered DNA lesions (OCDL). Theoretical analysis and experimental evidence suggest there is increased complexity and severity of complex DNA damage with increasing LET (linear energy transfer) and a high mutagenic or carcinogenic potential. Data available on the formation of clustered DNA damage (DSBs and OCDL) by high-LET radiations are often controversial suggesting a variable response to dose and type of radiation. The chemical nature and cellular repair mechanisms of complex DNA damage have been much less characterized than those of isolated DNA lesions like an oxidized base or a single strand break especially in the case of high-LET radiation. This review will focus on the induction of clustered DNA damage by high-LET radiations presenting the earlier and recent relative data.

Hada, Megumi↗
NASA NTRS1991

The small-scale clustering properties of dwarf galaxies

Two results on the small-scale clustering properties of dwarf galaxies are reported, which were identified in the vicinity of early-type Shapley-Ames galaxies on high-resolution photographic plates. The first result indicates that dwarf galaxies display the same trend of stronger clustering toward earlier morphological type on small scales as their giant counterparts on larger scales. It is suggested that early-type dwarfs can be used as dynamical probes of dark halos around early-type giant galaxies and as tracers of the dynamical evolution of such halos in dense environments. The second result pertains to the trend of increasing early-type dwarf frequency per early-type giant with environment richness previously established for rich groups. It is found that a minimum value of isolated early-type galaxies is approximately 0.25, as compared to a maximum of approximately 8 in rich environments like the Virgo Cluster.

Vader, J. P.↗