Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “conditional probability”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,423 records · Page 79

Population Viability Analysis (PVA) as a Platform for Predicting Outcomes of Management Options for the Florida Scrub-Jay in Brevard County

The Florida scrub-jay (FSJ) is a species in decline because of extinction debt caused by habitat fragmentation and degradation. Understanding and managing the species and its habitats is challenging due to the complex interactions among the social system, a dynamic mosaic of scrub habitat, and active management. To provide insights into the possible fates of the FSJ populations of mainland, cape, and island sections of Brevard County, we modeled the population dynamics using the Vortex population viability analysis (PVA) software. Vortex is an individual-based simulation that allowed us to include such factors as demographic rates dependent on habitat state, impact of helpers on breeding success, and helper to breeder transition probabilities responding to availability of nearby vacant optimal habitat and vacancies due to the death of breeders. Detailed modeling of the FSJ was possible only because a lot of data about the species and its habitats have been gathered over decades of intensive research. We followed a phased approach to constructing population models that incorporated the best available science and data to address a variety of conservation actions. The first phase focused on constructing a model that incorporates sociobiology and source-sink habitat dynamics. This model allowed us to address some of the most important questions about population size and habitat quality. Once the model framework was in place, we considered the real landscapes and actual local populations, rather than just generic representations of typical FSJ dynamics. After examining the viability of the metapopulations under current conditions, we explored the likely consequences of various management actions that might slow or reverse population declines.

Population Viability Analysis↗

Probabilistic Structural Analysis Program

NASA/NESSUS 6.2c is a general-purpose, probabilistic analysis program that computes probability of failure and probabilistic sensitivity measures of engineered systems. Because NASA/NESSUS uses highly computationally efficient and accurate analysis techniques, probabilistic solutions can be obtained even for extremely large and complex models. Once the probabilistic response is quantified, the results can be used to support risk-informed decisions regarding reliability for safety-critical and one-of-a-kind systems, as well as for maintaining a level of quality while reducing manufacturing costs for larger-quantity products. NASA/NESSUS has been successfully applied to a diverse range of problems in aerospace, gas turbine engines, biomechanics, pipelines, defense, weaponry, and infrastructure. This program combines state-of-the-art probabilistic algorithms with general-purpose structural analysis and lifting methods to compute the probabilistic response and reliability of engineered structures. Uncertainties in load, material properties, geometry, boundary conditions, and initial conditions can be simulated. The structural analysis methods include non-linear finite-element methods, heat-transfer analysis, polymer/ceramic matrix composite analysis, monolithic (conventional metallic) materials life-prediction methodologies, boundary element methods, and user-written subroutines. Several probabilistic algorithms are available such as the advanced mean value method and the adaptive importance sampling method. NASA/NESSUS 6.2c is structured in a modular format with 15 elements.

Pai, Shantaram S.↗

Real Options Analysis for Valuation of Climate Adaptation Pathways With Application to Transit Infrastructure

Climate change and sea level rise (SLR) are expected to increase the frequency and intensity of coastal flood events, posing risks to coastal communities and infrastructure. While regional climate adaptation investments can provide substantive flood protection, existing plans often neglect uncertainty in future climate conditions and adaptation performance, consequently neglecting the option value of flexibly implementing proposed projects. Addressing this gap, we develop and employ a generalizable real options analysis (ROA) valuation framework that considers how uncertainty in adaptation project costs, SLR, flood severity, and flood losses inform the full range of adaptation performance outcomes. We further propose and apply a novel, computationally efficient flood loss sampling algorithm to estimate the consequences of randomly arriving coastal flood events. We apply this ROA framework to assess the option value of flexibly timing adaptation investments over time, investigating an adaptation pathway proposed by the City of Boston from the perspective of the regional transit system manager. Our results suggest that flexible implementation can provide significant option value in the near-to mid-term(>30 years), with highest option values under low-probability, high consequence scenarios. Our results also suggest adaptation pathway performance in the latter half of the 21stcenturyis most sensitive to uncertainty in sea level rise, flood loss estimates, and flood frequency, underscoring the importance of uncertainty quantification in the long-term valuation of adaptation investments.

Michael V. Martello↗

Further Discussion: Parametric Study of Wind Generated Supermicron Particle Effects in Large Fires

In their reply (Porch et al., 1987) to our comments (Turco et al., 1987) on their smoke-scavenging-by-dust paper, Porch et al. attempt to justify a number of parameter assumptions in their original article, again revealing the extreme nature of those assumptions, particularly in the situation where all are taken simultaneously. In critiquing Porch et al.'s calculations, have not applied "opinion", but rather physical reality and common sense expressed through basic experimental results and logical physical bounds. A few examples of the unrealistic conditions required by the Porch et al. scavenging scheme, as described in their paper and comments, should suffice here. ) Porch et al. have fabricated a "fetch" region for dust particles in large fire plumes that logically must extend over an area up to 50 times greater than the fire area itself. Alternatively, they have invoked significant "necking down' of the fire plume, so that its cross-sectional area is at most a few percent of the fire area. Such severe constriction is seen only in very small fires with strong, organized vorticity, and then only over a limited plume rise region. No "fetch" has ever been noted in any large-scale fires we have observed, or for which accounts are available. Indeed, as we deduced in our original comments, complete dust scavenging even within the fire zone would probably occur less than 10% of the time for large urban fires.

Toon, O. B.↗

Plant Response to Microwaves at 2.45 GHz

One method of beaming to Earth energy captured by Space Solar Power (SSP) satellites is by using microwaves. Since microwaves are non-ioniz ing and of low energy they probably will have little or no direct eff ect (either long- or short-term) on terrestrial biota. This contentio n must to be proved however, before the public will accept a continuo us beam of microwaves being sent to the ground near populated areas or onto agricultural lands. To begin to address this question, an exper iment has been done that exposed an important agronomic plant speaes (alfalfa, Medicago sativa L.) to a continuous microwave beam at 2.45 GHz and from between 0.5 to 1.2 milli-watts per square centimeter. Th e hypothesis was that plants exposed to microwaves will be no differe nt from those control plants that were not exposed to microwaves. The microwaves were broadcast over a tray of mature, growing plants in the laboratory. The control plants were subjected to the same environme ntal conditions (light, temperature, soil and nutrients) minus the mi crowave exposure. Both populations of plants were watered as needed. As may be seen, the experiment was designed so that the only variable to which the test plants were subjected was microwave exposure. Prec ise, non-destructive measurements were taken of leaf chlorophyll concentration over the period of the experiment. Also measured were gross plant variables such as stem length, internodal distance, and, at the end of the experiment, above-ground biomass, both fresh and dry weig hts. Soil temperatures on bare soil and under the plant canopy were a lso measured. After seven weeks of exposure to microwaves there was n o sigruficant difference between control and test plant populations. A number of other plant/ microwave exposure studies will be discussed in this presentation. However, this experiment is one of the few publ ished examples of organisms being exposed to continuos microwave illu mination at one of the proposed SSP microwave frequencies and intensi ties.

Skiles, J. W.↗

Global Positioning System (GPS) Precipitable Water in Forecasting Lightning at Spaceport Canaveral

Using meteorology data, focusing on precipitable water (PW), obtained during the 2000-2003 thunderstorm seasons in Central Florida, this paper will, one, assess the skill and accuracy measurements of the current Mazany forecasting tool and, two, provide additional forecasting tools that can be used in predicting lightning. Kennedy Space Center (KSC) and Cape Canaveral Air Force Station (CCAFS) are located in east Central Florida. KSC and CCAFS process and launch manned (NASA Space Shuttle) and unmanned (NASA and Air Force Expendable Launch Vehicles) space vehicles. One of the biggest cost impacts is unplanned launch scrubs due to inclement weather conditions such as thunderstorms. Each launch delay/scrub costs over a quarter million dollars, and the need to land the Shuttle at another landing site and return to KSC costs approximately $ 1M. Given the amount of time lost and costs incurred, the ability to accurately forecast (predict) when lightning will occur can result in significant cost and time savings. All lightning prediction models were developed using binary logistic regression. Lightning is the dependent variable and is binary. The independent variables are the Precipitable Water (PW) value for a given time of the day, the change in PW up to 12 hours, the electric field mill value, and the K-index value. In comparing the Mazany model results for the 1999 period B against actual observations for the 2000-2003 thunderstorm seasons, differences were found in the False Alarm Rate (FAR), Probability of Detection (POD) and Hit Rate (H). On average, the False Alarm Rate (FAR) increased by 58%, the Probability of Detection (POD) decreased by 31% and the Hit Rate decreased by 20%. In comparing the performance of the 6 hour forecast period to the performance of the 1.5 hour forecast period for the Mazany model, the FAR was lower by 15% and the Hit Rate was higher by 7%. However, the POD for the 6 hour forecast period was lower by 16% as compared to the POD of the 1.5 hour forecast period. Neither forecast period performed at the accuracy measures expected. A 2-Hr Forecasting Tool was developed to support a Phase I Lightning Advisory, which requires a 30-minute lead time for predicting lightning.

Kehrer, Kristen↗

Markov Decision Process based Trajectory Planning for UAVs under Uncertain Wind Conditions

In this paper we propose a Markov Decision Process (MDP) algorithm for path-planning of Unmanned Aviation Vehicles (UAVs) under varying wind conditions. Solutions to path-planning for UAVs are becoming increasingly necessary as autonomous UAVs continue to enter commercial and government spaces. Path-planning is inherently challenging, as UAVs needs to account for dynamically changing flying conditions such as weather, obstacle or no-fly zones, degraded vehicle health and off-nominal battery power consumption. Machine learning methods such as Markov Decision Process (MDPs) have the potential to revolutionize how vehicles navigate in such uncertain environments. Previous papers have demonstrated the use of MDPs to optimize UAV path-planning for energy consumption under time-varying wind distribution. In this study, UAV trajectories from a pre-determined waypoint to target cell, will be computed on a 7X7 grid environment by optimizing parameters for mission assurance and safety limits in addition to the energy consumption, and operation time. The UAV navigates the grid by taking actions to move in either of the eight cardinal and intercardinal directions, under constant thrust profile. The next state of the UAV is calculated by considering its action, transition probability, obstacle cells and the wind speed magnitude and direction. Both constant and stochastic wind will be considered in this paper, the parameters being extracted from real wind measurements in proximity to an experimental UAV flight. One of the studies to be demonstrated in this paper is that as the unmanned airspace gets more complex with multiple vehicles and environmental uncertainties, trade-offs between energy consumption, operation time, risk tolerance, and mission assurance needs to be made. Further, MDPs are capable of fast computation of UAV trajectories under varying wind, hence making them suitable for in-flight path planners.

decision-making↗

Effects of aerosols and surface shadowing on bidirectional reflectance measurements of deserts

Desert surfaces are probably one of the most stable of the Earth's natural targets for remote sensing. The bidirectional reflectance properties of the Saudi Arabian desert was investigated during the Summer Monsoon Experiment (Summer Monex). A comparison of high-altitude with near-surface measurements of the White Sands desert showed significant differences. These discrepancies have been attributed to forward scattering of the dust-laden atmosphere prevalent during Summer Monex. This paper is concerned in general with modeling the effects of atmospheric aerosols and surface shadowing on the remote sensing of bidirectional reflectance factors of desert targets, and in particular with comparing the results of these models with flight results. Although it is possible to approximate the latter, it is felt that a surface reflectance model with a smaller specular component would have permitted using a more realistic set of atmospheric conditions in the simulations.

Bowker, David E.↗

Eutectic superalloys by edge-defined, film-fed growth

The feasibility of producing directionally solidified eutectic alloy composites by edge-defined, film-fed growth (EFG) was carried out. The three eutectic alloys which were investigated were gamma + delta, gamma/gamma prime + delta, and a Co-base TaC alloy containing Cr and Ni. Investigations into the compatibility and wettability of these metals with various carbides, borides, nitrides, and oxides disclosed that compounds with the largest (negative) heats of formation were most stable but poorest wetting. Nitrides and carbides had suitable stability and low contact angles but capillary rise was observed only with carbides. Oxides would not give capillary rise but would probably fulfill the other wetting requirements of EFG. Tantalum carbide was selected for most of the experimental portion of the program based on its exhibiting spontaneous capillary rise and satisfactory slow rate of degradation in the liquid metals. Samples of all three alloys were grown by EFG with the major experimental effort restricted to gamma + delta and gamma/gamma prime + delta alloys. In the standard, uncooled EFG apparatus, the thermal gradient was inferred from the growth speed and was 150 to 200 C/cm. This value may be compared to typical gradients of less than 100 C/cm normally achieved in a standard Bridgman-type apparatus. When a stream of helium was directed against the side of the bar during growth, the gradient was found to improve to about 250 C/cm. In comparison, a theoretical gradient of 700 C/cm should be possible under ideal conditions, without the use of chills. Methods for optimizing the gradient in EFG are discussed, and should allow attainment of close to the theoretical for a particular configuration.

Hurley, G. F.↗

NASCAP modelling computations on large optics spacecraft in geosynchronous substorm environments

Satellites in geosynchronous orbits have been found to be charged to significant negative voltages during encounters with geomagnetic substorms. When satellite surfaces are charged, there is a probability of enhanced contamination from charged particles attracted back to the satellite by electrostatic forces. This could be particularly disturbing to large satellites using sensitive optical systems. In this study the NASA Charging Analyzer Program (NASCAP) is used to evaluate qualitatively the possibility of such enhanced contamination on a conceptual version of a large satellite. The evaluation is made by computing surface voltages on the satellite due to encounters with substorm environments and then computing charged-particle trajectories in the electric fields around the satellite. Particular attention is paid to the possibility of contaminants reaching a mirror surface inside a dielectric tube because this mirror represents a shielded optical surface in the satellite model used. Deposition of low energy charged particles from other parts of the spacecraft onto the mirror was found to be possible in the assumed moderate substorm environment condition. In the assumed severe substorm environment condition, however, voltage build up on the inside and edges of the dielectric tube in which the mirror is located prevents contaminants from reaching the mirror surface.

Stevens, N. J.↗

Investigation of superlattice device structures

This report describes the investigation of growth properties, and the structure of epitaxial multilayer Si(Si(1x)Ge(x)) films grown on bulk Silicon Substrates. It also describes the fabrication and characterization of MOSFET and MESFET devices made on these epitaxial films. Films were grown in a CVD reactor using hydrides of Si and Ge with H2 and He as carrier gases. Growth temperatures were between 900 C and 1050 C with most films grown at 1000 C. Layer thickness was between 300A and 2000A and total film thickness was between 0.25 micro m and 7 micro m. The Ge content (X) in the alloy layers was between .05 and 0.2. N-type multilayer films grown on (100) p-type Si showed Hall mobility in the range 1000 to 1500 sq cm/v for an average carrier concentration of approx. 10 to the 16th power/cu cm. This is up to 50% higher than the Hall mobility observed in epitaxial Si films grown under the same conditions and with the same average carrier concentration. The mobility enhancement occurred in films with average carrier concentration (n) from 0.7 x 10 to the 16th power to 2 x 10 to the 17th power/cu cm, and total film thickness greater than 1.0 micro m. No mobility enhancement was seen in n-type multilayer films grown on (111) Si or in p-type multilayer films. The structure of the films was investigated was using SEM, TEM, AES, SIMS, and X-ray double crystal diffraction techniques. The film composition profile (AES, SIMS) showed that the transition region between layers is of the order of about 100A. The TEM examination revealed a well defined layered structure with fairly sharp interfaces and good crystalline quality. It also showed that the first few layers of the film (closest to the substrate) are uneven, most probably due to the initial growth pattern of the epitaxial film where growth occurs first in isolated islands that eventually growth and coalesce. The X-ray diffraction measurement determined the elastic strain and strain relief in the alloy layers of the film and the elastic strain in the intervening Si layers.

Gergis, I. S.↗

Results of November 1981 and May 1982 ATMAP Campaigns at Adelaide (35 Deg S, 138 Deg E)

The mean zonal circulation for both the November and May campaigns are representative of early summer and winter conditions. The mean meridional flow in November was stable and typical of summer conditions at Adelaide. The conditions in May were, however, more variable and appeared to be changing significantly during the campaign. It is possible that there was a strong influence from a large scale wave which could account for the large meridional wind values observed. Overall, the mean tidal structures observed during the core periods were not significantly different from those observed in two-week intervals centered on the cores. In May both components show evidence for propagating components with 30 to 40 km vertical wavelengths. For the semidiurnal components, the phase structures show evidence for vertical propagation with apparent vertical wavelengths of the order of 50 km. The mean amplitudes for the semidiurnal components in May are close to the noise level. Typical errors from the harmonic analysis are + or - 1 to 2 ms(-1) in amplitude and + or - 0.5 hr in phase, but these are probably underestimates.

Vincent, R. A.↗

Measuring Gap Fraction, Element Clumping Index and LAI in Sierra Forest Stands Using a Full-Waveform Ground-Based Lidar

The Echidna Validation Instrument (EVI), a ground-based, near-infrared (1064 nm) scanning lidar, provides gap fraction measurements, element clumping index measurements, effective leaf area index (LAIe) and leaf area index (LAI) measurements that are statistically similar to those from hemispherical photos. In this research, a new method integrating the range dimension is presented for retrieving element clumping index using a unique series of images of gap probability (Pgap) with range from EVI. From these images, we identified connected gap components and found the approximate physical, rather than angular, size of connected gap component. We conducted trials at 30 plots within six conifer stands of varying height and stocking densities in the Sierra National Forest, CA, in August 2008. The element clumping index measurements retrieved from EVI Pgap image series for the hinge angle region are highly consistent (R2=0.866) with those of hemispherical photos. Furthermore, the information contained in connected gap component size profiles does account for the difference between our method and gap-size distribution theory based method, suggesting a new perspective to measure element clumping index with EVI Pgap image series and also a potential advantage of three dimensional Lidar data for element clumping index retrieval. Therefore further exploration is required for better characterization of clumped condition from EVI Pgap image series.

Zhao, Feng↗

Assessing Risk Due to Small Sample Size in Probability of Detection Analysis Using Tolerance Intervals

Small sample size (e.g.6-30) poses risk in results of probability of detection (POD) analysis using tolerance intervals. This method is also called as the limited sample or LS POD. The analysis is performed either during NDE procedure qualification or for assessment of reliability of an NDE procedure. The risk is primarily due to sampling error. Smaller samples are not likely to be random to the population or representative of the population. The small samples are likely to be biased. Biased samples have smaller standard deviation compared to the population. POD analysis with small biased sample can lead to overestimation of POD. Many sampling schemes are available in statistics to mitigate sampling risk. Primary objective of POD analysis is to determine a decision threshold from signal response measurements of a sample such that it is less than or equal to population decision threshold for 90% POD. Sampling error implies that this NDE reliability condition is violated. One of sampling types is called a representative sample. Representative samples reduce variance in POD estimates but also reduce magnitude of the error. Sampling sensitivity analysis for some sampling types is performed here using repetitive random sampling or Monte Carlo method. Six sampling types are considered for comparison. Some of the sampling types are similar to drawing a representative sample. LS POD model assumes random sampling. Therefore, random sampling is used as a basis for comparison with each sampling type. The sampling types used in the analysis are, A. Nominal and worst-case sampling, B. Worst-case sampling, C. Nominal case sampling, D. Random sampling, E. Random target, and sub-target sampling. F. Nominal target and sub-target sampling. Results of Monte Carlo simulation indicate that type F sampling can mitigate sampling risk and is also more practical to implement. Type A sampling may also mitigate the sampling risk, but it may be less practical to implement.

Ajay M Koshti↗

An ultrasonic technique to measure the depth of burn wounds in humans

Whenever ultrasound encounters discontinuity in its medium of propagation, some energy is reflected from the interface. Such reflections or echoes occur when incident energy encounters the front skin, viable/necrotic, and dermis/fat skin tissue interfaces. It was shown that the most probable cause of the viable/necrotic interface is the uncoiling of collagen in the necrotic tissue, which can cause a reflection at the viable/necrotic interface of approximately 10 percent of the wave amplitude, and is approximately the same as that from the other two interfaces noted. The instrument, still in the prototype stage, was designed to detect the various reflections from within the skin layer. It is shown that, by studying the timing between the various echoes, one can use ultrasound as an aid in diagnosing the depth of burned skin tissue in humans. The instrument is a 60-MHz A-scan unit, modified to more easily identify the echoes occurring within the short time interval during which the reflections are received from the skin layers. A high frequency unit was selected so that various transducers could be utilized to optimize the system. Signal conditioning circuits were modified and added to provide an adequate display of the principle reflections expected. The unit was successful in studying burned tissue in pigs and was recently used to study burn wounds in humans. Measurement techniques and preliminary results are presented.

Yost, William T.↗

Possible Effects of Climate Warming on Selected Populations of Polar Bears (Ursus maritimus) in the Canadian Arctic

Polar bears are dependent on sea ice for survival. Climate warming in the Arctic has caused significant declines in coverage and thickness of sea ice in the polar basin and progressively earlier breakup in some areas. In four populations of polar bears in the eastern Canadian Arctic (including Western Hudson Bay), Inuit hunters report more bears near settlements during the open water period in recent years. These observations have been interpreted as evidence of increasing population size, resulting in increases in hunting quotas. However, long-term data on the population size and condition of polar bears in Western Hudson Bay, and population and harvest data from Baffin Bay, make it clear that those two populations at least are declining, not increasing. While the details vary in different arctic regions, analysis of passive-microwave satellite imagery, beginning in the late 1970s, indicates that the sea ice is breaking up at progressively earlier dates, so that bears must fast for longer periods during the open water season. Thus, at least part of the explanation for the appearance of more bears in coastal communities is likely that they are searching for alternative food sources because their stored body fat depots are being exhausted. We hypothesize that, if the climate continues to warm as projected by the IPCC, then polar bears in all five populations discussed in this paper will be stressed and are likely to decline in numbers, probably significantly so. As these populations decline, there will likely also be continuing, possibly increasing, numbers of problem interactions between bears and humans as the bears seek alternate food sources. Taken together, the data reported in this paper suggest that a precautionary approach be taken to the harvesting of polar bears and that the potential effects of climate warming be incorporated into planning for the management and conservation of this species throughout the Arctic.

Parkinson, Claire L.↗

Use of CCSDS and OSI Protocols on the Advanced Communications Technology Satellite

Although ACTS (Advanced Communications Technology Satellite) provides an almost error-free channel during much of the day and under most conditions, there are times when it is not suitable for reliably error-free data communications when operating in the uncoded mode. Because coded operation is not always available to every earth station, measures must be taken in the end system to maintain adequate throughput when transferring data under adverse conditions. The most effective approach that we tested to improve performance was the addition of an 'outer' Reed-Solomon code through use of CCSDS (Consultative Committee for Space Data Systems) GOS 2 (a forward error correcting code). This addition can benefit all users of an ACTS channel including those applications that do not require totally reliable transport, but it is somewhat expensive because additional hardware is needed. Although we could not characterize the link noise statistically (it appeared to resemble uncorrelated white noise, the type that block codes are least effective in correcting), we did find that CCSDS GOS 2 gave an essentially error-free link at BER's (bit error rate) as high as 6x10(exp -4). For users that demand reliable transport, an ARQ (Automatic Repeat Queuing) protocol such as TCP (Transmission Control Protocol) or TP4 (Transport Protocol, Class 4) will probably be used. In this category, it comes as no surprise that the best choice of the protocol suites tested over ACTS was TP4 using CCSDS GOS 2. TP4 behaves very well over an error-free link which GOS 2 provides up to a point. Without forward error correction, however, TP4 service begins to degrade in the 10(exp -7)-10(exp -6) range and by 4x10(exp -6), it barely gives any throughput at all. If Congestion Avoidance is used in TP4, the degradation is even more pronounced. Fortunately, as demonstrated here, this effect can be more than compensated for by choosing the Selective Acknowledgment option. In fact, this option can enable TP4 to deliver some throughput at error rates as high as 10(exp -5).

Chirieleison, Don↗

A homogeneous sample of binary galaxies: Basic observational properties

A survey of optical characteristics for 585 binary systems, satisfying a condition of apparent isolation on the sky, is presented. Influences of various selection effects distorting the average parameters of the sample are noted. The pair components display mutual similarity over all the global properties: luminosity, diameter, morphological type, mass-to-luminosity ratio, angular momentum etc., which is not due only to selection effects. The observed correlations must be caused by common origin of pair members. Some features (nuclear activity, color index) could acquire similarity during synchronous evolution of double galaxies. Despite the observed isolation, the sample of double systems is seriously contaminated by accidental pairs, and also by members of groups and clusters. After removing false pairs estimates of orbital mass-to-luminosity ratio range from 0 to 30 f(solar), with the mean value (7.8 plus or minus 0.7) f(solar). Binary galaxies possess nearly circular orbits with a typical eccentrity e = 0.25, probably resulting from evolutionary selection driven by component mergers under dynamical friction. The double-galaxy population with space abundance 0.12 plus or minus 0.02 and characteristic merger timescale 0.2 H(exp -1) may significantly influence the rate of dynamical evolution of galaxies.

Karachentsev, I. D.↗