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Non-LTE effects on the strength of the Lyman edge in quasar accretion disks

We have calculated UV/EUV (300 A which is less than or equal to lambda which is less than or equal to 1500 A) continuous energy distributions of accretion disks in the centers of active galactic nuclei (AGNs) for disk luminosities in the range 0.1 L(sub Edd) less than or equal to L(sub acc) less than 1.0 L(sub Edd) and central masses ranging from 10(exp 8) solar mass to 10(exp 9) solar mass. The vertical gas pressure structure of the disk and the disk height are obtained analytically; the temperature stratification and the resulting continuum radiation fields are calculated numerically. We have included non-Local Thermodynamic Equilibrium (LTE) effects of both the ionization equilibrium and the level populations of hydrogen and helium. We show that these non-LTE effects reduce the strength of the Lyman edge when comapred to the LTE case. In non-LTE we find that the edge can be weakly in emission or absorption for disks seen face-on, depending on the disk parameters.

Stoerzer, H.↗

The location of planetary bow shocks: A critical overview of theory and observations

A bow shock (BS has been observed in the collisionless solar wind upstream of every planet except Pluto, which has yet to be visited by a spacecraft. They are all of similar character, but their size relative to the planet varies widely, e.g., the planeto-centric distance to the BS nose ranges from about 1.4 R(sub V) for Venus to 88 R(sub J) or more for Jupiter. Comparisons are reviewed that show its location may be represented satisfactorily by a gasdynamic (GD) model, provided the properties of the solar wind and planetary magnetic field and ionosphere are known and used as input in the application. Factors that determine the location are discussed, and examples are presented to illustrate effects of their variation, including which part of a BS is influenced by a local variation of the magneto/ionopause (MIP) shape. The interplanetary magnetic field (IMF) has no influence on the BS location in the GD model, but is shown to have a small effect in corresponding solutions of the basic MHD model from which the GD model is derived as the limit for weak IMF. Nearly all GD and MHD solutions are for steady flow, but a solution for unsteady flow associated with the passage of an interplanetary shock is also presented. It shows that the BS moves rapidly from its initial to final location, e.g., in about minute for the earth. Since many changes in the solar wind occur over longer intervals, these results help explain the success of quasi-stationary solutions in modeling the BS in time-varying solar wind flows.

Spreiter, J. R.↗

Plasma Sheet Source and Loss Processes

Data from the TIMAS ion mass spectrometer on the Polar satellite, covering 15 ev/e to 33 keV/e in energy and essentially 4(pi) in view angles, are used to investigate the properties of earthward (sunward) field-aligned flows of ions, especially protons, in the plasma sheet-lobe transition region near local midnight. A total of 142 crossings of this region are analyzed at 12-sec time resolution, all in the northern hemisphere, at R(SM) approx. 4 - 7 R(sub E), and most (106) in the poleward (sunward) direction. Earthward proton flows are prominent in this transition region (greater than 50% of the time), typically appearing as sudden "blasts" with the most energetic protons (approx. 33 keV) arriving first with weak flux, followed by protons of decreasing energy and increasing flux until either: (1) a new "blast" appears, (2) the flux ends at a sharp boundary, or (3) the flux fades away within a few minutes as the mean energy drops to a few keV. Frequent step-like changes (less than 12 sec) of the flux suggest that perpendicular gradients on the scale of proton gyroradii are common. Peak flux is similar to central plasma sheet proton flux (10(exp 5) - 10(exp 6)/[cq cm sr sec keV/e] and usually occurs at E approx. 4 - 12 keV. Only the initial phase of each "blast" (approx. 1 min) displays pronounced field-alignment of the proton velocity distribution, consistent with the time-of-flight separation of a more or less isotropic source distribution with df/d(nu) less than 0. The dispersive signatures are often consistent with a source at R(SM) less than or equal to 30 R(sub E). No systematic latitudinal velocity dispersion is found, implying that the equatorial plasma source is itself convecting. In short, the proton "blasts" appear as sudden local expansions of central plasma sheet particles along reconfigured ("dipolarized") magnetic field lines.

Lennartsson, O. W.↗

Measuring coal deposits by radar

Front-surface, local-oscillator radar directly compares frequency of signals reflected from front and back surfaces of coal deposits. Thickness is measured directly as frequency difference. Transmitter is frequency modulated, so thickness is computed directly from frequency difference. Because front and back reflections are detected in combination rather than separately, masking of comparatively weak back signal is less problem. Also system is not sensitive to extraneous reflections from targets between transmitting antenna and coal surface.

Barr, T. A.↗

Nonadiabatic transport features in the outer cusp region

The dayside to nightside circulation of plasma along the magnetopause inside the magnetosphere is examined by means of three-dimensional single-particle codes. It is demonstrated that particles incident upon the outer cusp region experience transient non-adiabatic motions, owing to a localized minimum in the field magnitude. Here, possibly large magnetic moment changes yield injection into the loss cone of fractions of the incoming population or, alternatively, enhanced bouncing motions at high altitudes. It is shown that particles gaining access to the magnetotail over the polar cap are progressively extracted from the weak field region by the large-scale convection electric field. In this latter case, the trajectory simulations suggest an implicit 'entry boundary' into the nightside magnetosphere, which corresponds to the sunward edge of field lines featuring monotonic decrease of the field magnitude along their length.

Delcourt, D. C.↗

TMI Rain Rate Estimation Over Land and Ocean Utilizing Convective and Stratiform Discrimination

Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) radiometer brightness temperature data in the 85 GHz channel (T85) reveal distinct local minima in a regional map containing a Mesoscale Convective System (MCS). This is because of relatively small footprint size (approximately 5.5 km) and strong extinction properties in this channel of the TMI. A map of rain rate for that region, deduced from simultaneous measurements made by the Precipitation Radar (PR) on board the TRMM satellite, reveals that these T85 minima, produced by scattering, correspond to local PR rain maxima. Utilizing the PR rain rate map as a guide, we infer from TMI data the presence of three different kinds of thunderstorms or Cbs. They are young, mature, and decaying Cbs that have a scale of about 20 km on the average. Two parameters enable us to infer these three kinds of Cbs objectively: a) the magnitude of scattering depression deduced from local T85 minima and b) the mean horizontal gradient of T85 around such minima. Knowing the category of a given Cb, we can estimate the rain rate associated with it. Such estimation is done with the help of relationships linking T85 minimum to rain rate in each Cb type. Similarly, a weak background rain rate in all the areas where T85 is less than 260 K is deduced with another relationship linking T85 to rain rate. In our rain retrieval model, this background rain constitutes the stratiform rain where the Cbs are absent. Initially, these relationships are optimized or tuned utilizing the PR and TMI data of a few MCS events. After such tuning, the model is applied to independent MCS cases. The areal distribution of light (1-10 mm/hr), moderate (10-20 mm/hr), and intense (> 20 mm/hr) rain rates are retrieved satisfactorally. Accuracy in the estimates of the light, moderate and intense rain areas and the mean rain rates associated with such areas in these independent MCS cases is on the average about 15%. Taking advantage of this ability of our retrieval method, one could derive the latent heat input into the atmosphere over the 760 km wide swath of the TMI radiometer in the tropics.

Prabhakara, C.↗

A TRMM Microwave Radiometer Rain Rate Estimation Method with Convective and Stratiform Discrimination

Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) radiometer brightness temperature data in the 85 GHz channel (T85) reveal distinct local minima (T85min) in a regional map containing a Mesoscale Convective System (MCS). This is because of relatively small footprint size (approximately 5.5 km) and strong extinction properties in this channel of the TMI. A map of surface rain rate for that region, deduced from simultaneous measurements made by the Precipitation Radar (PR) on board the TRMM satellite, reveals that these T85(sub min), produced by scattering, correspond to local PR rain maxima. Utilizing the PR rain rate map as a guide, we infer empirically from TMI data the presence of three different kinds of thunderstorms or Cbs. These Cbs are classified as young, mature, and decaying types, and are assumed to have a scale of about 20 km on the average. Two parameters are used to classify these three kinds of Cbs based on the T85 data: a) the magnitude of scattering depression deduced from local T85(sub min) and b) the mean horizontal gradient of T85 around such minima. Knowing the category of a given Cb, we can estimate the rain rate associated with it. Such estimation is done with the help of relationships linking T85min to rain rate in each Cb type. Similarly, a weak background rain rate in all the areas where T85 is less than 260 K is deduced with another relationship linking T85 to rain rate. In our rain retrieval model, this background rain constitutes stratiform rain where the Cbs are absent. Initially, these relationships are optimized or tuned utilizing the PR and TMI data of a few MCS events. After such tuning, the model is applied to independent MCS cases. The areal distribution of light (1-10 mm/hr), moderate (10-20 mm/hr), and intense (>= 20 mm/hr) rain rates are retrieved satisfactorily. Accuracy in the estimates of the light, moderate, and intense rain areas and the mean rain rates associated with such areas in these independent MCS cases is on the average about 15 %. Taking advantage of this ability of our retrieval method, one could derive the latent heat input into the atmosphere over the 760 km wide swath of the TMI radiometer in the tropics.

Prabhakara, C.↗

Winds at the Mars 2020 Landing Site: 1. Near-Surface Wind Patterns at Jezero Crater

This is the first part of a two-part paper. NASA's Mars 2020 Perseverance rover measured winds on the Jezero crater floor close to the delta of an ancient river. A mostly repeatable diurnal cycle was observed and presented two regimes: (a) a convective regime, from dawn to sunset, with average easterly to southeasterly winds, during which maximum wind speeds were measured, and (b) a nighttime regime with westerly-northwesterly winds followed by a relatively calm period with highly variable wind directions as a function of sol and time of night. The timing and magnitude of the observed regimes are consistent with primary control by regional and local slope flows. Data suggest that the surface circulation at Jezero region in northern spring and summer is highly unaffected by large-scale circulation except during particular periods in the diurnal cycle or generally during dust storms, which is supported by MarsWRF model simulations. Consequently, the observed seasonal variability was weak. However, sol-to-sol and seasonal variability were measured, most of it during certain nighttime periods. Traveling waves consistent with baroclinic instability were clearly observed in surface winds at L_s ∼ 75°. The early MY36/2022A regional dust storm at L_s ∼ 153° disturbed the wind patterns with changes suggesting enhanced tidal flows. After sunset, the dust storm also produced detectable gravity wave activity, increasing the mixing in the nighttime planetary boundary layer during storm conditions. Inferred wind directions from dust devil movies strongly suggest that prevailing winds continued to be slope-driven during the late summer, fall and early winter seasons.

D. Viúdez-Moreiras↗

Quantitative Measurements of Electronically Excited CH Concentration in Normal Gravity and Microgravity Coflow Laminar Diffusion Flames

With the conclusion of the SLICE campaign aboard the ISS in 2012, a large amount of data was made available for the analysis of the effect of microgravity on laminar coflow diffusion flames. Previous work focused on the study of sooty flames in microgravity as well as the ability of numerical models to predict its formation in a simplified buoyancy-free environment. The current work shifts the investigation to soot-free flames, putting an emphasis on the chemiluminescence emission from electronically excited CH (CH*). This radical species is of significant interest in combustion studies: it has been shown that the electronically excited CH spatial distribution is indicative of the flame front position and, given the relatively simple diagnostic involved with its measurement, several works have been done trying to understand the ability of electronically excited CH chemiluminescence to predict the total and local flame heat release rate. In this work, a subset of the SLICE nitrogen-diluted methane flames has been considered, and the effect of fuel and coflow velocity on electronically excited CH concentration is discussed and compared with both normal gravity results and numerical simulations. Experimentally, the spectral characterization of the DSLR color camera used to acquire the flame images allowed the signal collected by the blue channel to be considered representative of the electronically excited CH emission centered around 431 nm. Due to the axisymmetric flame structure, an Abel deconvolution of the line-of-sight chemiluminescence was used to obtain the radial intensity profile and, thanks to an absolute light intensity calibration, a quantification of the electronically excited CH concentration was possible. Results show that, in microgravity, the maximum flame electronically excited CH concentration increases with the coflow velocity, but it is weakly dependent on the fuel velocity; normal gravity flames, if not lifted, tend to follow the same trend, albeit with different peak concentrations. Comparisons with numerical simulations display reasonably good agreement between measured and computed flame lengths and radii, and it is shown that the integrated electronically excited CH emission scales proportionally to the computed total heat release rate; the two-dimensional electronically excited CH spatial distribution, however, does not appear to be a good marker for the local heat release rate.

chemiluminescence↗

Space Transformation -- Localizing the Remote and Connecting the Isolated

In motivating the Space Transformation theme for this year’s 4S symposium, the organizers provided the following context, “Transformation of economies are driven by a change in values and accelerated by new technologies.” These words rang particularly true when I read them at the beginning of the holiday season. Like so many others, I was in the early phases of my Christmas shopping procrastination campaign, and I’d just been reflecting on how Amazon Prime was the transformational tool I’d been waiting for. Basic limiting principles of time and space, supply and demand, were all but erased by the Amazon Prime phenomenon. Coupled with emerging 3D printing and other adaptive manufacturing technologies, a transformation from deliberate planning to “think it … have it” had occurred, empowering me to procrastinate longer than I’d ever dreamed possible. The organizers went on to ponder, “Will space transformation also affect society?”, just as our team at the Air Force Research Lab’s (AFRL) Center for Rapid Innovation (CRI) were working alongside partners within our larger Integrated Capabilities Directorate, NASA’s Flight Opportunities and Small Spacecraft Technology programs, and DARPA’s Luna-10 program to develop technologies and execute demonstration missions that leverage the space domain to genuinely connect even the most remote and austere domains on the timeline of need. Picking apart the miracle that is Amazon prime, where does the model fail, and why? More relevantly to the theme of this year’s symposium, how can the space domain be used to overcome its limitations and minimize its weaknesses? Perhaps it is best assessed in the context of Use Cases. What are the Amazon delivery cost, schedule, and cargo limiters to the Amundsen-Scott South Pole Research Station, or the Lunar South Pole Research Station? This paper will explore enabling infrastructure that allows Amazon prime to thrive and assess the transformational enabling technologies that would be necessary to extend that miracle to the truly remote or the truly austere. Localizing the Remote • First, it will evaluate the ability of the on-going AFRL Rocket Cargo and Space Initiatives Ringside Seats systems, coupled with Astrobotic’s Xodiak and Xogdor capabilities, developed to support the NASA Flight Opportunities Program (FOP), to supply orbital/suborbital delivery to both improved and austere sites on the Earth and Moon. • Then, it will add the surface terminal distribution leg, with an examination of Lunar Outpost’s Mobile Autonomous Prospecting Platform (MAPP), equipped with Mobile Autonomous Robotic Swarm (MARS) software, and Intuitive Machine’s Hopper, developed with support of AFRL and NASA’s Commercial Lunar Payload Services (CLPS) program. Connecting the Isolated From there, it will focus on the destination, asking what implied destination services are required to support highly assured autonomous delivery. • Specifically, it will highlight Astrobotic’s Skymage mesh-networked publish and subscribe communication and navigation service, as well as AFRL’s on-going developments of radioisotope and reactor nuclear-sourced thermoelectric power generation and distribution systems under development under the Joint Emergent Technology Supplying On-orbit Nuclear Power (JETSON) program by Lockheed Martin, Westinghouse, Intuitive Machines, and Zeno Power, to provide the power service to locations well off the grid. • Finally, the paper will connect to the “human machine”. What connects the remote or in-situ human consumer to the remote domain? What connects the diverse international government and commercial services to each other? The former will focus on AFRL’s OraCloud feeding their Space Defense Control and Characterization System (SDCCS) and Lunar Station’s MoonHacker systems, while the latter will focus on the BlueHalo/Tensor LunX Technology Platform for the Cislunar Commodity Marketplace. In 1984, Krafft Ehricke famously remarked that, “If God wanted man to become a spacefaring species, He would have given man a Moon.” This paper is not about the Moon, but is about humans as a spacefaring species, shedding the pesky land/air limitations of the Amazon Prime model … so that we can all live a procrastinator’s “think it … have it” existence.

Charles Finley↗

Windowed and Wavelet Analysis of Marine Stratocumulus Cloud Inhomogeneity

To improve radiative transfer calculations for inhomogeneous clouds, a consistent means of modeling inhomogeneity is needed. One current method of modeling cloud inhomogeneity is through the use of fractal parameters. This method is based on the supposition that cloud inhomogeneity over a large range of scales is related. An analysis technique named wavelet analysis provides a means of studying the multiscale nature of cloud inhomogeneity. In this paper, the authors discuss the analysis and modeling of cloud inhomogeneity through the use of wavelet analysis. Wavelet analysis as well as other windowed analysis techniques are used to study liquid water path (LWP) measurements obtained during the marine stratocumulus phase of the First ISCCP (International Satellite Cloud Climatology Project) Regional Experiment. Statistics obtained using analysis windows, which are translated to span the LWP dataset, are used to study the local (small scale) properties of the cloud field as well as their time dependence. The LWP data are transformed onto an orthogonal wavelet basis that represents the data as a number of times series. Each of these time series lies within a frequency band and has a mean frequency that is half the frequency of the previous band. Wavelet analysis combined with translated analysis windows reveals that the local standard deviation of each frequency band is correlated with the local standard deviation of the other frequency bands. The ratio between the standard deviation of adjacent frequency bands is 0.9 and remains constant with respect to time. This ratio defined as the variance coupling parameter is applicable to all of the frequency bands studied and appears to be related to the slope of the data's power spectrum. Similar analyses are performed on two cloud inhomogeneity models, which use fractal-based concepts to introduce inhomogeneity into a uniform cloud field. The bounded cascade model does this by iteratively redistributing LWP at each scale using the value of the local mean. This model is reformulated into a wavelet multiresolution framework, thereby presenting a number of variants of the bounded cascade model. One variant introduced in this paper is the 'variance coupled model,' which redistributes LWP using the local standard deviation and the variance coupling parameter. While the bounded cascade model provides an elegant two- parameter model for generating cloud inhomogeneity, the multiresolution framework provides more flexibility at the expense of model complexity. Comparisons are made with the results from the LWP data analysis to demonstrate both the strengths and weaknesses of these models.

Gollmer, Steven M.↗

Degree of Weathering of H-Chondrites from Frontier Mountain, Antarctica

One of the factors that determines the survival time of meteorites on the Earth's surface is the rate of weathering. For meteorites from hot deserts, a clear correlation is found between the degree of weathering and the terrestrial age, but for Antarctic meteorites this correlation is weak or even lacking. The lack of a clear correlation can partly be attributed to the two-stage history of many Antarctic meteorites, which spend part of their terrestrial residence time in the ice before they are exposed on the ice. Recently, it was found that for Lewis Cliff (LEW) meteorites local conditions on the ice play an important role in the weathering process. This work focuses on weathering effects in ordinary chondrites from Frontier Mountain (FRO), North Victoria Land. Although most FRO meteorites were classified as weathering category A or B, many are contaminated with terrestrial uranium, deposited from meltwater. This suggests that weathering plays a more significant role than the qualitative A-B-C weathering index indicates. We therefore determined the degree of weathering more quantitatively, by deriving the amount of oxidized metal from the concentrations of Fe and Ni in the nonmagnetic fraction of 23 H-chondrites and 1 L-chondrite. The results will be compared with those of LEW meteorites and will be discussed in terms of terrestrial age and location of find on the ice.

Welten, K. C.↗

Degree of Weathering of H-Chondrites From Frontier Mountain, Antarctica

One of the factors that determines the survival time of meteorites on the Earth's surface is the rate of weathering. For meteorites from hot deserts, a clear correlation is found between the degree of weathering, and the terrestrial age, but for Antarctic meteorites this correlation is weak or even lacking. The lack of a clear correlation can partly be attributed to the two-stage history of many Antarctic meteorites, which spend part of their terrestrial residence time in the ice before they are exposed on the ice. Recently, it was found that for Lewis Cliff (LEW) meteorites local conditions on the ice play an important role in the weathering process. This work focuses on weathering effects in ordinary chondrites from Frontier Mountain (FRO), North Victoria Land. Although most FRO meteorites were classified as weathering category A or B, many are contaminated with terrestrial uranium, deposited from meltwater. This suggests that weathering plays a more significant role than the qualitative A-B-C weathering index indicates. We therefore determined the degree of weathering more quantitatively, by deriving the amount of oxidized metal from the concentrations of Fe and Ni in the nonmagnetic fraction of 23 H-chondrites and 1 L-chondrite The results will be compared with those of LEW meteorites and will be discussed in terms of terrestrial age and location of find on the ice.

Welten, K. C.↗

Diagnosing Warm Frontal Cloud Formation in a GCM: A Novel Approach Using Conditional Subsetting

This study analyzes characteristics of clouds and vertical motion across extratropical cyclone warm fronts in the NASA Goddard Institute for Space Studies general circulation model. The validity of the modeled clouds is assessed using a combination of satellite observations from CloudSat, Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO), Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E), and the NASA Modern-Era Retrospective Analysis for Research and Applications (MERRA) reanalysis. The analysis focuses on developing cyclones, to test the model's ability to generate their initial structure. To begin, the extratropical cyclones and their warm fronts are objectively identified and cyclone-local fields are mapped into a vertical transect centered on the surface warm front. To further isolate specific physics, the cyclones are separated using conditional subsetting based on additional cyclone-local variables, and the differences between the subset means are analyzed. Conditional subsets are created based on 1) the transect clouds and 2) vertical motion; 3) the strength of the temperature gradient along the warm front, as well as the storm-local 4) wind speed and 5) precipitable water (PW). The analysis shows that the model does not generate enough frontal cloud, especially at low altitude. The subsetting results reveal that, compared to the observations, the model exhibits a decoupling between cloud formation at high and low altitudes across warm fronts and a weak sensitivity to moisture. These issues are caused in part by the parameterized convection and assumptions in the stratiform cloud scheme that are valid in the subtropics. On the other hand, the model generates proper covariability of low-altitude vertical motion and cloud at the warm front and a joint dependence of cloudiness on wind and PW.

cyclones↗

Metal-Poor, Strongly Star-Forming Galaxies in the DEEP2 Survey: The Relationship Between Stellar Mass, Temperature-Based Metallicity, and Star Formation Rate

We report on the discovery of 28 redshift (z) approximately equal to 0.8 metal-poor galaxies in DEEP2. These galaxies were selected for their detection of the weak [O (sub III)] lambda 4363 emission line, which provides a "direct" measure of the gas-phase metallicity. A primary goal for identifying these rare galaxies is to examine whether the fundamental metallicity relation (FMR) between stellar mass, gas metallicity, and star formation rate (SFR) holds for low stellar mass and high SFR galaxies. The FMR suggests that higher SFR galaxies have lower metallicity (at fixed stellar mass). To test this trend, we combine spectroscopic measurements of metallicity and dust-corrected SFR with stellar mass estimates from modeling the optical photometry. We find that these galaxies are 1.05 plus or minus 0.61 dex above the redshift (z) approximately 1 stellar mass-SFR relation and 0.23 plus or minus 0.23 dex below the local mass-metallicity relation. Relative to the FMR, the latter offset is reduced to 0.01 dex, but significant dispersion remains dex with 0.16 dex due to measurement uncertainties). This dispersion suggests that gas accretion, star formation, and chemical enrichment have not reached equilibrium in these galaxies. This is evident by their short stellar mass doubling timescale of approximately equal to 100 (sup plus 310) (sub minus 75) million years which suggests stochastic star formation. Combining our sample with other redshift (z) of approximately 1 metal-poor galaxies, we find a weak positive SFR-metallicity dependence (at fixed stellar mass) that is significant at 94.4 percent confidence. We interpret this positive correlation as recent star formation that has enriched the gas but has not had time to drive the metal-enriched gas out with feedback mechanisms.

Metal-Poor↗

Extent and character of early tertiary penetrative deformation, Sonora, Northwest Mexico

Reconnaissance field work has led to the recognition of extensive Early Tertiary gneiss and schist which are distinguished by weakly developed to highly conspicous northeast to east-trending stretching lineation commonly accompanied by low-dipping foliation. This structural fabric has been imposed on Precambrian to Paleogene rocks. Regionally, minimum ages of deformation are based upon interpreted U-Pb isotopic ages from suites of cogenetic zircon from the Paleogene orthogneiss. Locally, the interpreted ages indicate that ductile deformation continued as late as Oligocene (Anderson and others, 1980; Silver and Anderson, 1984). The consistency of the deformational style is such that, although considerable variation in intensity exists, the fabric can be recognized and correlated in rocks away from the Paleogene orthogneiss.

Anderson, T. H.↗

A planar oblique wave model for the Euler equations

A numerical method in which any transition between neighboring states in a multidimensional flowfield is reconstructed by a pattern of oblique waves. The wave pattern is obtained from a superposition of model waves which arise in a local linearization based on Rankine-Hugoniot averaging. The strengths and orientations of these waves are derived from a minimum path length rule applied in state space. Two test cases with comparisons to other methods in planar flow problems are presented to demonstrate the strengths of the method, and to point out its weaknesses.

Parpia, Ijaz H.↗

Microjansky source counts and spectral indices at 8.44 GHz

Deep images were made with 10 arcsec resolution at 8.44 GHz with microjansky sensitivity of two regions previously imaged at several lower frequencies. The differential microjansky source count fits a power-law distribution with slope 2.3 +/- 0.2. This slope is roughly constant between 1.41 and 8.44 GHz and between S(v) = about 4 and X(v) = 1000 microJy. Unless the majority of radio sources at microJy levels are local, their average luminosity and/or space density probably has evolved with cosmic epoch in order to sustain the steep and nearly Euclidean value of the slope over such a large range in flux density. The 8.44 GHz counts probably converge at less than the 1 microjansky level if the evolutionary properties of these weak sources are similar to those of luminous gE radio galaxies and quasars. The median angular size of sources detected at 8.44 GHz at microjansky levels is 2.6 +/- 1.4 arcsec, and 40 percent of the source are larger than 5 arcsec.

Windhorst, Rogier A.↗