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At least 145 records · Page 8

Self-Consistent Simulation of the Brownian Stage of Dust Growth

It is a widely accepted view that in proto-planetary accretion disks the collision and following sticking of dust particles embedded in the gas eventually leads to the formation of planetesimals (coagulation). For the smallest dust grains, Brownian motion is assumed to be the dominant source of their relative velocities leading to collisions between these dust grains. As the dust grains grow they eventually couple to the turbulent motion of the gas which then drives the coagulation much more efficiently. Many numerical coagulation simulations have been carried out to calculate the fractal dimension of the aggregates, which determines the duration of the ineffective Brownian stage of growth. Predominantly on-lattice and off-lattice methods were used. However, both methods require simplification of the astrophysical conditions. The aggregates found by those methods had a fractal dimension of approximately 2 which is equivalent to a constant, mass-independent friction time. If this value were valid for the conditions in an accretion disk, this would mean that the coagulation process would finally 'freeze out' and the growth of a planetesimal would be impossible within the lifetime of an accretion disk. In order to investigate whether this fractal dimension is model independent, we simulate self-consistently the Brownian stage of the coagulation by an N-particle code. This method has the advantage that no further assumptions about homogeneity of the dust have to be made. In our model, the dust grains are considered as aggregates built up of spheres. The equation of motion of the dust grains is based on the probability density for the diffusive transport within the gas atmosphere. Because of the very low number density of the dust grains, only 2-body-collisions have to be considered. As the Brownian stage of growth is very inefficient, the system is to be simulated over long periods of time. In order to find close particle pairs of the system which are most likely to undergo a collision, we use a particle-in-cell (PIC) method for the early stages of the simulation where the system is still very homogeneous and a tree method later when the particles are more clustered.

Kempf, S.↗

A Threshold Theory for Phase-Locked Loops

A model of a phase-locked loop has been developed which is valid for all signal-to-noise ratios. The model is in the form of a nonlinear feedback system with randomly time-varying parameters. The analysis considers two operating regions. In low signal-to-noise ratio regions, the important consideration is stability. We want to study the asymptotic stability in the mean of a nonlinear system. It follows directly that a necessary condition for asymptotic stability of any nonlinear system is that a linearized model about some equilibrium point be asymptotically stable. By considering all possible equilibrium points, we can find an upper bound on the value of noise density which makes the system unstable. This upper bound represents a threshold value for system operation. In high signal-to-noise ratio regions, our results provide an exact statistical. description of system behavior. Therefore, knowledge of the spectrum of the signal and noise may be used to optimize the system configuration.

Van Trees, H. L.↗

Correlation between aircraft MSS and lidar remotely sensed data on a forested wetland

Inland wetland in a portion of the Savannah River swamp forest were mapped with an overall accuracy of 88.5 percent on April 26,l985 using high resolution aircraft Daedalus AADS-1268 MSS data. In addition, data were acquired using a NASA sensor system flown along two flight lines over the Steel Creek Delta. The data were significantly correlated with in situ tree height measurements. The data were registered to the wetland classification map and correlated. Statistical analyses demonstrated that the laser derived canopy height information was significantly associated with the Steel Creek Delta wetland classes encountered along the transect (an F-value of 58.46 at the 0.0001 level of confidence). The relationship between vegetation height and vegetation type was then used to produce a three-dimensional model of the landscape which can be of value when computing biomass or canopy density in this forested wetland environment.

Jensen, John R.↗

Modeling the Swift BAT Trigger Algorithm with Machine Learning

To draw inferences about gamma-ray burst (GRB) source populations based on Swift observations, it is essential to understand the detection efficiency of the Swift burst alert telescope (BAT). This study considers the problem of modeling the Swift BAT triggering algorithm for long GRBs, a computationally expensive procedure, and models it using machine learning algorithms. A large sample of simulated GRBs from Lien et al. (2014) is used to train various models: random forests, boosted decision trees (with AdaBoost), support vector machines, and artificial neural networks. The best models have accuracies of approximately greater than 97% (approximately less than 3% error), which is a significant improvement on a cut in GRB flux which has an accuracy of 89:6% (10:4% error). These models are then used to measure the detection efficiency of Swift as a function of redshift z, which is used to perform Bayesian parameter estimation on the GRB rate distribution. We find a local GRB rate density of eta(sub 0) approximately 0.48(+0.41/-0.23) Gpc(exp -3) yr(exp -1) with power-law indices of eta(sub 1) approximately 1.7(+0.6/-0.5) and eta(sub 2) approximately -5.9(+5.7/-0.1) for GRBs above and below a break point of z(sub 1) approximately 6.8(+2.8/-3.2). This methodology is able to improve upon earlier studies by more accurately modeling Swift detection and using this for fully Bayesian model fitting. The code used in this is analysis is publicly available online.

gamma rays: general↗

Modeling the Swift Bat Trigger Algorithm with Machine Learning

To draw inferences about gamma-ray burst (GRB) source populations based on Swift observations, it is essential to understand the detection efficiency of the Swift burst alert telescope (BAT). This study considers the problem of modeling the Swift / BAT triggering algorithm for long GRBs, a computationally expensive procedure, and models it using machine learning algorithms. A large sample of simulated GRBs from Lien et al. is used to train various models: random forests, boosted decision trees (with AdaBoost), support vector machines, and artificial neural networks. The best models have accuracies of greater than or equal to 97 percent (less than or equal to 3 percent error), which is a significant improvement on a cut in GRB flux, which has an accuracy of 89.6 percent (10.4 percent error). These models are then used to measure the detection efficiency of Swift as a function of redshift z, which is used to perform Bayesian parameter estimation on the GRB rate distribution. We find a local GRB rate density of n (sub 0) approaching 0.48 (sup plus 0.41) (sub minus 0.23) per cubic gigaparsecs per year with power-law indices of n (sub 1) approaching 1.7 (sup plus 0.6) (sub minus 0.5) and n (sub 2) approaching minus 5.9 (sup plus 5.7) (sub minus 0.1) for GRBs above and below a break point of z (redshift) (sub 1) approaching 6.8 (sup plus 2.8) (sub minus 3.2). This methodology is able to improve upon earlier studies by more accurately modeling Swift detection and using this for fully Bayesian model fitting.

gamma-ray burst: general – gamma-rays: general â↗

Bayes classification of terrain cover using normalized polarimetric data

The normalized polarimetric classifier (NPC) which uses only the relative magnitudes and phases of the polarimetric data is proposed for discrimination of terrain elements. The probability density functions (PDFs) of polarimetric data are assumed to have a complex Gaussian distribution, and the marginal PDF of the normalized polarimetric data is derived by adopting the Euclidean norm as the normalization function. The general form of the distance measure for the NPC is also obtained. It is demonstrated that for polarimetric data with an arbitrary PDF, the distance measure of NPC will be independent of the normalization function selected even when the classifier is mistrained. A complex Gaussian distribution is assumed for the polarimetric data consisting of grass and tree regions. The probability of error for the NPC is compared with those of several other single-feature classifiers. The classification error of NPCs is shown to be independent of the normalization function.

Yueh, H. A.↗

Recognition and characterization of hierarchical interstellar structure. II - Structure tree statistics

A new method of image analysis is described, in which images partitioned into 'clouds' are represented by simplified skeleton images, called structure trees, that preserve the spatial relations of the component clouds while disregarding information concerning their sizes and shapes. The method can be used to discriminate between images of projected hierarchical (multiply nested) and random three-dimensional simulated collections of clouds constructed on the basis of observed interstellar properties, and even intermediate systems formed by combining random and hierarchical simulations. For a given structure type, the method can distinguish between different subclasses of models with different parameters and reliably estimate their hierarchical parameters: average number of children per parent, scale reduction factor per level of hierarchy, density contrast, and number of resolved levels. An application to a column density image of the Taurus complex constructed from IRAS data is given. Moderately strong evidence for a hierarchical structural component is found, and parameters of the hierarchy, as well as the average volume filling factor and mass efficiency of fragmentation per level of hierarchy, are estimated. The existence of nested structure contradicts models in which large molecular clouds are supposed to fragment, in a single stage, into roughly stellar-mass cores.

Houlahan, Padraig↗

Vegetation Change Detection in Southern California Solar Energy Developments

Change detection from satellite sensor vegetation indices (VIs) presents an opportunity to monitor trends and disturbances at the regional scale for southern California's Mojave and Lower Colorado Deserts. Renewable energy sites are being constructed in this region on public lands under the Bureau of Land Management (BLM). We have developed a framework for VI change detection over the past two decades, with initial focus on three sites, Joshua Tree National Park, Mojave National Preserve, and a proximal group of Development Focus Areas (DFAs), for comparison between protected and development-targeted lands. Three Terra MODIS VIs (normalized difference [NDVI], enhanced [EVI], soil-adjusted [SAVI]) were evaluated in the Breaks for Additive Season and Trend (BFAST) setting for the regional MODIS 250-m resolution grid to estimate significant time series shifts (breakpoints) from February 2000 to May 2018. All three VIs tended to detect the maximum number of breakpoints at a grid location, but cross-correlations with precipitation and comparison with timing of wildfire burns near the study sites for breakpoint density (proportion of area with a breakpoint) showed that NDVI had the strongest response to these major disturbances, supporting its use for subsequent analysis. Time series of NDVI breakpoint change densities for individual solar energy sites did not have a consistent vegetation response following construction. Bootstrapping showed that the DFAs had significantly larger kurtosis and variance in the positive NDVI breakpoint distribution than did the protected sites, but there was no significant difference in the negative distribution for all three sites. The inconsistent post-construction NDVI signal and the large number of breakpoints overall suggested that the largest changes in vegetation cover density were tied to seasonal precipitation amounts. The distributional results indicated that existing site-specific conditions were the main control on VI responses, given the history of human disturbances in the DFAs. Although the results do not support persistent VI disturbances resulting from recent solar energy development, continued monitoring and examination of other ecological variables and surface temperatures will be vital to the long-term protection of this desert environment.

Potter, Christopher S.↗

Advanced Intensity-Modulation Continuous-Wave Lidar Techniques for ASCENDS O2 Column Measurements

Global atmospheric carbon dioxide (CO2) measurements for the NASA Active Sensing of CO2 Emissions over Nights, Days, and Seasons (ASCENDS) space mission are critical for improving our understanding of global CO2 sources and sinks. Advanced Intensity- Modulated Continuous-Wave (IM-CW) lidar techniques are investigated as a means of facilitating CO2 measurements from space to meet the ASCENDS measurement requirements. In recent numerical, laboratory and flight experiments we have successfully used the Binary Phase Shift Keying (BPSK) modulation technique to uniquely discriminate surface lidar returns from intermediate aerosol and cloud contamination. We demonstrate the utility of BPSK to eliminate sidelobes in the range profile as a means of making Integrated Path Differential Absorption (IPDA) column CO2 measurements in the presence of optically thin clouds, thereby eliminating the need to correct for sidelobe bias errors caused by the clouds. Furthermore, high accuracy and precision ranging to the surface as well as to the top of intermediate cloud layers, which is a requirement for the inversion of column CO2 number density measurements to column CO2 mixing ratios, has been demonstrated using new hyperfine interpolation techniques that takes advantage of the periodicity of the modulation waveforms. This approach works well for both BPSK and linear swept-frequency modulation techniques. The BPSK technique under investigation has excellent auto-correlation properties while possessing a finite bandwidth. A comparison of BPSK and linear swept-frequency is also discussed in this paper. These results are extended to include Richardson-Lucy deconvolution techniques to extend the resolution of the lidar beyond that implied by limit of the bandwidth of the modulation, where it is shown useful for making tree canopy measurements.

Campbell, Joel F.↗

Characterization of vegetation by microwave and optical remote sensing

Two series of carefully controlled experiments were conducted. First, plots of important crops (corn, soybeans, and sorghum), prairie grasses (big bluestem, switchgrass, tal fescue, orchardgrass, bromegrass), and forage legumes (alfalfa, red clover, and crown vetch) were manipulated to produce wide ranges of phytomass, leaf area index, and canopy architecture. Second, coniferous forest canopies were simulated using small balsam fir trees grown in large pots of soil and arranged systematically on a large (5 m) platform. Rotating the platform produced many new canopies for frequency and spatial averaging of the backscatter signal. In both series of experiments, backscatter of 5.0 GHz (C-Band) was measured as a function of view angle and polarization. Biophysical measurements included leaf area index, fresh and dry phytomass, water content of canopy elements, canopy height, and soil roughness and moisture content. For a subset of the above plots, additional measurements were acquired to exercise microwave backscatter models. These measurements included size and shape of leaves, stems, and fruit and the probability density function of leaf and stem angles. The relationships of the backscattering coefficients and the biophysical properties of the canopies were evaluated using statistical correlations, analysis of variance, and regression analysis. Results from the corn density and balsam fir experiments are discussed and analyses of data from the other experiments are summarized.

Daughtry, C. S. T.↗

Extended Magnetohydrodynamics with Embedded Particle-in-Cell Simulation of Ganymede's Magnetosphere

We have recently developed a new modeling capability to embed the implicit particle-in-cell (PIC) model iPIC3D into the Block-Adaptive-Tree-Solarwind-Roe-Upwind-Scheme magnetohydrodynamic (MHD) model. The MHD with embedded PIC domains (MHO-EPIC) algorithm Is a two-way coupled kinetic-fluid model. As one of the very first applications of the MHD-EPIC algorithm, we simulate the Interaction between Jupiter's magnetospherlc plasma and Ganymede's magnetosphere. We compare the MHO-EPIC simulations with pure Hall MHD simulations and compare both model results with Galileo observations to assess the Importance of kinetic effects In controlling the configuration and dynamics of Ganymede's magnetosphere. We find that the Hall MHD and MHO-EPIC solutions are qualitatively similar, but there are significant quantitative differences. In particular. the density and pressure inside the magnetosphere show different distributions. For our baseline grid resolution the PIC solution is more dynamic than the Hall MHD simulation and it compares significantly better with the Galileo magnetic measurements than the Hall MHD solution. The power spectra of the observed and simulated magnetic field fluctuations agree extremely well for the MHD-EPIC model. The MHO-EPIC simulation also produced a few flux transfer events (FTEs) that have magnetic signatures very similar to an observed event. The simulation shows that the FTEs often exhibit complex 3-0 structures with their orientations changing substantially between the equatorial plane and the Galileo trajectory, which explains the magnetic signatures observed during the magnetopause crossings. The computational cost of the MHO-EPIC simulation was only about 4 times more than that of the Hall MHD simulation.

Toth, Gabor↗

Landscape characterization of peridomestic risk for Lyme disease using satellite imagery

Remotely sensed characterizations of landscape composition were evaluated for Lyme disease exposure risk on 337 residential properties in two communities of suburban Westchester County, New York. Properties were categorized as no, low, or high risk based on seasonally adjusted densities of Ixodes scapularis nymphs, determined by drag sampling during June and July 1990. Spectral indices based on Landsat Thematic Mapper data provided relative measures of vegetation structure and moisture (wetness), as well as vegetation abundance (greenness). A geographic information system (GIS) was used to spatially quantify and relate the remotely sensed landscape variables to risk category. A comparison of the two communities showed that Chappaqua, which had more high-risk properties (P < 0.001), was significantly greener and wetter than Armonk (P < 0.001). Furthermore, within Chappaqua, high-risk properties were significantly greener and wetter than lower-risk properties in this community (P < 0.01). The high-risk properties appeared to contain a greater proportion of broadleaf trees, while lower-risk properties were interpreted as having a greater proportion of nonvegetative cover and/or open lawn. The ability to distinguish these fine scale differences among communities and individual properties illustrates the efficiency of a remote sensing/GIS-based approach for identifying peridomestic risk of Lyme disease over large geographic areas.

Topography, Medical↗

How Did I Get Here?

What country was responsible for much of the early work in laser altimetry, who was the first scientist to look at a vegetation profile generated by a laser, who first related laser ranges to forest structure? The purpose of this paper is to look back 3+ decades ago when forestry lidar was in its formative years and to give credit to those who first thought to employ a laser to measure the Earth's surface. As with much scientific research, advances were often made independently and concurrently in a number of countries. Functioning lasers were first demonstrated in 1960 in the USA and in 1961 in the USSR, but research into the use of lasers as forest measurement tools did not begin for another IS years. Initially, with respect to Earth resources, lasers were employed to measure sea ice surface roughness, to make near-shore bathymetric measurements, to penetrate forests to make detailed topographic measurements, and to fluoresce oceanic phytoplankton for surface current studies. Some of these early studies noted that forest profiles were evident but in fact added noise to topographic retrievals. Trees became the signal rather than noise in 1976 when researchers in the Canadian Forest Service went to an IUFRO conference in Oslo and reported on efforts to better estimate timber volume in tropical forests. They employed large-scale airphotos (1:500 up to 1:4000) to measure the top of the tropical canopy, an avionic radar to measure the location of the ground beneath the canopy, and a barometric sensor to record aircraft/radar height above a datum (e.g., sea level). Their radar did not work well in dense vegetation and mentioned in passing that a laser altimeter had worked well in Canadian forests. But in a report 2 years later they reported that, on a study area in Costa Rica, the radar ground line was much improved and no mention is made of a lidar altimeter. In the USSR in 1977, Russian researchers felled a birch and a spruce, aimed a helium-neon, 0.63 micron laser with a spot size of approx 25mm, at the horizontal trees, produced a profilograph, compared it to tape measurements, and concluded that, with increased power, such a laser could be mounted on an aircraft to remotely measure forest canopies. In 1979, they mounted their He-Ne laser on an AN-2 biplane and acquired their fIrSt airborne profiles. Scientists with TRANARG, a mapping/surveying company in Caracas, Venezuela, reported on 1976 flights employing a helium-neon lidar to collect over 11,000 km of lidar profiles spaced 1.5 km apart in order to construct a topographic map to help site a new reservoir. They noted 35-40 m median canopy heights with emergents up to 55 m in their profiles. These studies and others that utilize these height and canopy density metrics for forest mensuration are reviewed in this glance backwards at the history of forestry lidar.

Nelson, Ross↗

Space communications scheduler: A rule-based approach to adaptive deadline scheduling

Job scheduling is a deceptively complex subfield of computer science. The highly combinatorial nature of the problem, which is NP-complete in nearly all cases, requires a scheduling program to intelligently transverse an immense search tree to create the best possible schedule in a minimal amount of time. In addition, the program must continually make adjustments to the initial schedule when faced with last-minute user requests, cancellations, unexpected device failures, quests, cancellations, unexpected device failures, etc. A good scheduler must be quick, flexible, and efficient, even at the expense of generating slightly less-than-optimal schedules. The Space Communication Scheduler (SCS) is an intelligent rule-based scheduling system. SCS is an adaptive deadline scheduler which allocates modular communications resources to meet an ordered set of user-specified job requests on board the NASA Space Station. SCS uses pattern matching techniques to detect potential conflicts through algorithmic and heuristic means. As a result, the system generates and maintains high density schedules without relying heavily on backtracking or blind search techniques. SCS is suitable for many common real-world applications.

Straguzzi, Nicholas↗

NASA Tech Briefs, September 2005

Topivs include: Diamond-Coated Carbon Nanotubes for Efficient Field Emission; Improved Anode Coatings for Direct Methanol Fuel Cells; Advanced Ablative Insulators and Methods of Making Them; PETIs as High-Temperature Resin-Transfer-Molding Materials; Stable Polyimides for Terrestrial and Space Uses; Low-Density, Aerogel-Filled Thermal-Insulation Tiles; High-Performance Polymers Having Low Melt Viscosities; Nonflammable, Hydrophobic Aerogel Composites for Insulation; Front-Side Microstrip Line Feeding a Raised Antenna Patch; Medium-Frequency Pseudonoise Georadar; Facilitating Navigation Through Large Archives; Program for Weibull Analysis of Fatigue Data; Comprehensive Micromechanics-Analysis Code - Version 4.0; Component-Based Visualization System; Software for Engineering Simulations of a Spacecraft; LabVIEW Interface for PCI-SpaceWire Interface Card; Path Following with Slip Compensation for a Mars Rover; International Space Station Electric Power System Performance Code-SPACE; Software for Automation of Real-Time Agents, Version 2; Software for Optimizing Plans Involving Interdependent Goals; Computing Gravitational Fields of Finite-Sized Bodies; Custom Sky-Image Mosaics from NASA's Information Power Grid; ANTLR Tree Grammar Generator and Extensions; Generic Kalman Filter Software; Alignment Stage for a Cryogenic Dilatometer; Rugged Iris Mechanism; Treatments To Produce Stabilized Aluminum Mirrors for Cryogenic Uses; Making AlNx Tunnel Barriers Using a Low-Energy Nitrogen-Ion Beam; Making Wide-IF SIS Mixers with Suspended Metal-Beam Leads; Sol-Gel Glass Holographic Light-Shaping Diffusers; Automated Counting of Particles To Quantify Cleanliness; Phase Correction for GPS Antenna with Nonunique Phase Center; Compact Infrasonic Windscreen; Broadband External-Cavity Diode Laser; High-Efficiency Solar Cells Using Photonic-Bandgap Materials; Generating Solid Models from Topographical Data; Computationally Lightweight Air-Traffic-Control Simulation; Spool Valve for Switching Air Flows Between Two Beds; Partial Model of Insulator/ Insulator Contact Charging; Asymmetric Electrostatic Radiation Shielding for Spacecraft; and Reusable Hybrid Propellant Modules for Outer-Space Transport.

Source record↗

Assessing Woody Vegetation Trends in Sahelian Drylands Using MODIS Based Seasonal Metrics

Woody plants play a major role for the resilience of drylands and in peoples' livelihoods. However, due to their scattered distribution, quantifying and monitoring woody cover over space and time is challenging. We develop a phenology driven model and train/validate MODIS (MCD43A4, 500m) derived metrics with 178 ground observations from Niger, Senegal and Mali to estimate woody cover trends from 2000 to 2014 over the entire Sahel. The annual woody cover estimation at 500 m scale is fairly accurate with an RMSE of 4.3 (woody cover %) and r(exp 2) = 0.74. Over the 15 year period we observed an average increase of 1.7 (+/- 5.0) woody cover (%) with large spatial differences: No clear change can be observed in densely populated areas (0.2 +/- 4.2), whereas a positive change is seen in sparsely populated areas (2.1 +/- 5.2). Woody cover is generally stable in cropland areas (0.9 +/- 4.6), reflecting the protective management of parkland trees by the farmers. Positive changes are observed in savannas (2.5 +/- 5.4) and woodland areas (3.9 +/- 7.3). The major pattern of woody cover change reveals strong increases in the sparsely populated Sahel zones of eastern Senegal, western Mali and central Chad, but a decreasing trend is observed in the densely populated western parts of Senegal, northern Nigeria, Sudan and southwestern Niger. This decrease is often local and limited to woodlands, being an indication of ongoing expansion of cultivated areas and selective logging.We show that an overall positive trend is found in areas of low anthropogenic pressure demonstrating the potential of these ecosystems to provide services such as carbon storage, if not over-utilized. Taken together, our results provide an unprecedented synthesis of woody cover dynamics in theSahel, and point to land use and human population density as important drivers, however only partially and locally offsetting a general post-drought increase.

Brandt, Martin↗

Multiband radar characterization of forest biomes

The utility of airborne and orbital SAR in classification, assessment, and monitoring of forest biomes is investigated through analysis of orbital synthetic aperature radar (SAR) and multifrequency and multipolarized airborne SAR imagery relying on image tone and texture. Preliminary airborne SAR experiments and truck-mounted scatterometer observations demonstrated that the three dimensional structural complexity of a forest, and the various scales of temporal dynamics in the microwave dielectric properties of both trees and the underlying substrate would severely limit empirical or semi-empirical approaches. As a consequence, it became necessary to develop a more profound understanding of the electromagnetic properties of a forest scene and their temporal dynamics through controlled experimentation coupled with theoretical development and verification. The concatenation of various models into a physically-based composite model treating the entire forest scene became the major objective of the study as this is the key to development of a series of robust retrieval algorithms for forest biophysical properties. In order to verify the performance of the component elements of the composite model, a series of controlled laboratory and field experiments were undertaken to: (1) develop techniques to measure the microwave dielectric properties of vegetation; (2) relate the microwave dielectric properties of vegetation to more readily measured characteristics such as density and moisture content; (3) calculate the radar cross-section of leaves, and cylinders; (4) improve backscatter models for rough surfaces; and (5) relate attenuation and phase delays during propagation through canopies to canopy properties. These modeling efforts, as validated by the measurements, were incorporated within a larger model known as the Michigan Microwave Canopy Scattering (MIMICS) Model.

Dobson, M. Craig↗

Time-dependent radio fine structure of the quasar 3C 345

Results are reported for VLBI observations of 3C 345 at a wavelength of 3.8 cm with left circular polarization. Sixteen sets of correlated flux densities and three sets of closure phases were obtained from observations made over a three-year period with six independent interferometers formed from up to four antennas. The mathematical models employed to represent the radio brightness distribution of the source are described, and the data are analyzed on the basis of a two-component model. The results show that the compact source in 3C 345 consists of two components whose separation increased by about 0.3 milliarcsec over the observational period, that the smaller and weaker component is to the east and south of the larger and stronger one, and that the apparent expansion velocity would be about 2.5c for a redshift of 0.6, a Hubble constant of 60 km/sec per Mpc, and a deceleration parameter of unity. It is concluded that these findings are difficult to reconcile with the 'Christmas tree' model for the apparent change of separation with time over any given series of observations.

Wittels, J. J.↗