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NASA NTRS1978

Infrared excesses in early-type stars - Gamma Cassiopeiae

Spectrophotometry of the classical Be star Gamma Cas (1-4 microns, with about 2% spectral resolution) is presented. These data, together with existing broad-band observations, are accurately described by simple isothermal LTE models for the IR excess which differ from most previously published work in three ways: (1) hydrogenic bound-free emission is included; (2) the attenuation of the star by the shell is included; and (3) no assumption is made that the shell contribution is negligible in some bandpass. It is demonstrated that the bulk of the IR excess consists of hydrogenic bound-free and free-free emission from a shell of hot ionized hydrogen gas, although a small thermal component cannot be ruled out. The bound-free emission is strong, and the Balmer, Paschen, and Brackett discontinuities are correctly represented by the shell model with physical parameters as follows: a shell temperature of approximately 18,000 K, an optical depth (at 1 micron) of about 0.5, an electron density of approximately 1 trillion per cu cm, and a size of about 2 trillion cm. Phantom shells (i.e., ones which do not alter the observed spectrum of the underlying star) are discussed.

Scargle, J. D.↗

NASA NTRS1986

Computation of nozzle flow fields using the PARC2D Navier-Stokes code

Supersonic nozzles which operate at low Reynolds numbers and have large expansion ratios have very thick boundary layers at their exit. This leads to a very strong viscous/inviscid interaction upon the flow within the nozzle and the traditional nozzle design techniques which correct the inviscid core with a boundary layer displacement do not accurately predict the nozzle exit conditions. A full Navier-Stokes code (PARC2D) was used to compute the nozzle flow field. Grids were generated using the interactive grid generator code TBGG. All computations were made on the NASA MSFC CRAY X-MP computer. Comparison was made between the computations and in-house wall pressure measurements for CO2 flow through a conical nozzle having an area ratio of 40. Satisfactory agreement existed between the computations and measurements for a stagnation pressure of 29.4 psia and stagnation temperature of 1060 R. However, agreement did not exist at a stagnation pressure of 7.4 psia. Several reasons for the lack of agreement are possible. The computational code assumed a constant gas gamma whereas gamma for CO2 varied from 1.22 in the plenum chamber to 1.38 at the nozzle exit. Finally, it is possible that condensation occurred during the expansion at the lower stagnation pressure.

Collins, Frank G.↗

NASA NTRS1992

GRO/EGRET data analysis software: An integrated system of custom and commercial software using standard interfaces

The Energetic Gamma Ray Telescope Experiment (EGRET) on the Compton Gamma Ray Observatory has been in orbit for more than a year and is being used to map the full sky for gamma rays in a wide energy range from 30 to 20,000 MeV. Already these measurements have resulted in a wide range of exciting new information on quasars, pulsars, galactic sources, and diffuse gamma ray emission. The central part of the analysis is done with sky maps that typically cover an 80 x 80 degree section of the sky for an exposure time of several days. Specific software developed for this program generates the counts, exposure, and intensity maps. The analysis is done on a network of UNIX based workstations and takes full advantage of a custom-built user interface called X-dialog. The maps that are generated are stored in the FITS format for a collection of energies. These, along with similar diffuse emission background maps generated from a model calculation, serve as input to a maximum likelihood program that produces maps of likelihood with optional contours that are used to evaluate regions for sources. Likelihood also evaluates the background corrected intensity at each location for each energy interval from which spectra can be generated. Being in a standard FITS format permits all of the maps to be easily accessed by the full complement of tools available in several commercial astronomical analysis systems. In the EGRET case, IDL is used to produce graphics plots in two and three dimensions and to quickly implement any special evaluation that might be desired. Other custom-built software, such as the spectral and pulsar analyses, take advantage of the XView toolkit for display and Postscript output for the color hard copy. This poster paper outlines the data flow and provides examples of the user interfaces and output products. It stresses the advantages that are derived from the integration of the specific instrument-unique software and powerful commercial tools for graphics and statistical evaluation. This approach has several proven advantages including flexibility, a minimum of development effort, ease of use, and portability.

Laubenthal, N. A.↗

NASA NTRS1989

Detection and avoidance of errors in computer software

The acceptance test errors of a computer software project to determine if the errors could be detected or avoided in earlier phases of development. GROAGSS (Gamma Ray Observatory Attitude Ground Support System) was selected as the software project to be examined. The development of the software followed the standard Flight Dynamics Software Development methods. GROAGSS was developed between August 1985 and April 1989. The project is approximately 250,000 lines of code of which approximately 43,000 lines are reused from previous projects. GROAGSS had a total of 1715 Change Report Forms (CRFs) submitted during the entire development and testing. These changes contained 936 errors. Of these 936 errors, 374 were found during the acceptance testing. These acceptance test errors were first categorized into methods of avoidance including: more clearly written requirements; detail review; code reading; structural unit testing; and functional system integration testing. The errors were later broken down in terms of effort to detect and correct, class of error, and probability that the prescribed detection method would be successful. These determinations were based on Software Engineering Laboratory (SEL) documents and interviews with the project programmers. A summary of the results of the categorizations is presented. The number of programming errors at the beginning of acceptance testing can be significantly reduced. The results of the existing development methodology are examined for ways of improvements. A basis is provided for the definition is a new development/testing paradigm. Monitoring of the new scheme will objectively determine its effectiveness on avoiding and detecting errors.

Kinsler, Les↗

NASA NTRS2003

Analysis Methods and Results for Weak Gamma-Ray Bursts in the BATSE Data

We report initial results on the statistical properties of the dimmest gamma-ray bursts (GRBs) observed with the Burst and Transient Source Experiment (BATSE), using new ground-based methods to obtain a sample of GRBs from 502 days of BATSE data. Using the most sensitive ground-based detection of GRBs, the sample extends to GRBs much fainter than those detected by the on-board trigger, but because of the temporal resolution of the data, the sample is limited to GRBs of duration of at least 2(approx.)s. For each detected event, Bayesian probabilities are calculated for the event to belong to each of seven classes of differing physical origins. The sample of GRB candidates is defined by the requirement that the Bayesian probability for belonging to the GRB class is higher than 0.5. The intensity distribution of the GRB sample is corrected using a Monte Carlo simulation of the post-flight detection efficiency. The dimmest BATSE bursts of the sample continue the hardness-intensity trend seen in brighter GREs and are consistent with isotropy.

Mitrofanov, I. G.↗

NASA NTRS1986

Can comet clouds around neutron stars explain gamma-ray bursts?

The proposal of Harwit and Salpeter (1973) that gamma-ray bursts are due to impacts of comets onto neutron stars is examined further. It is assumed that most stars are formed with comet clouds similar to the Oort comet cloud which surrounds the sun, and it is suggested that there are at least four mechanisms by wich neutron stars may be formed while retaining their comet clouds: a spherically symmetric supernova explosion in an isolated star, accretion-induced collapse of a white dwarf in a cataclysmic variable with a very low mass secondary, accretion-induced collapse of a white dwarf in a wide binary with a low-mass giant companion, and coalescence of a close binary composed of two white dwarfs. Estimates are given of the cometary impact rates for such systems. It is suggested that if the wide binary scenario is correct, optical bursts may arise from the impact of comets onto the white dwarf remnant of the giant companion.

Tremaine, S.↗

NASA NTRS1985

An internally consistent gamma ray burst time history phenomenology

A phenomenology for gamma ray burst time histories is outlined. Order of their generally chaotic appearance is attempted, based on the speculation that any one burst event can be represented above 150 keV as a superposition of similarly shaped increases of varying intensity. The increases can generally overlap, however, confusing the picture, but a given event must at least exhibit its own limiting characteristic rise and decay times if the measurements are made with instruments having adequate temporal resolution. Most catalogued observations may be of doubtful or marginal utility to test this hypothesis, but some time histories from Helios-2, Pioneer Venus Orbiter and other instruments having one-to several-millisecond capabilities appear to provide consistency. Also, recent studies of temporally resolved Solar Maximum Mission burst energy spectra are entirely compatible with this picture. The phenomenology suggested here, if correct, may assist as an analytic tool for modelling of burst processes and possibly in the definition of burst source populations.

Cline, T. L.↗

NASA NTRS2023

New Insights on the 7[superscript]Be Cycle in the Ocean

The cosmogenic radionuclide 7[superscript]Be has been applied as a tracer of dynamical processes in the upper ocean and of atmospheric deposition of trace elements at the sea surface. These applications usually assume that 7[superscript]Be is entirely in the dissolved form, and that scavenging and downward export of 7[superscript]Be by settling particles can be neglected. In this work, we explore these assumptions and more generally assess the significance of the 7[superscript]Be activity in the particulate fraction, through the generation of vertical profiles of particulate 7[superscript]Be in the open ocean. From detailed measurements obtained from low-background gamma spectrometers placed in underground facilities, we report vertical profiles of 7[superscript]Be activity in suspended particles (7[superscript]Bep[subscript]) collected in various oceanic regions: the Mediterranean Sea (DYFAMED station), the Indian Sector of the Southern Ocean (station A3-2 from the KEOPS2 cruise), the Sargasso Sea (OFP station), and the subpolar North Atlantic Ocean (GEOVIDE cruise). We find that, in each oceanic region, 7[superscript]Bep[subscript] activities are generally higher in the mixed layer than in the thermocline. They vary in the mixed layer from 3.0 dpm/m3 at DYFAMED to 33.1dpm/m3 at GEOVIDE cross-over station 51/60, i.e., within a range consistent with previous 7[superscript]Bep[subscript] measurements for the open ocean. For the GEOVIDE cruise, the 7[superscript]Bep[subscript] activities measured on different filter types at different depths are corrected for filter offsets derived from multiple 7[superscript]Bep[subscript] measurements at a near-coastal station in the western Mediterranean Sea. We then combine measurements of total 7[superscript]Be activity (Shelley et al., 2017) with our measurements of 7[superscript]Bep[subscript] activity to estimate the solid/solution partitioning of 7[superscript]Be. On average, the particulate fraction would represent 6% of total 7[superscript]Be activity at 5-m water depth (n = 6), 22% at 20 m (n = 2) and 9% at 70 m (n = 3). At GEOVIDE stations, 7[superscript]Bep[subscript] inventories range from 5% to 19% of the total 7[superscript]Be inventories. In the Labrador Sea, the measured 7[superscript]Bep[subscript] inventories are lower than the dry 7[superscript]Be deposition fluxes estimated from aerosol samples collected during GEOVIDE, suggesting that a significant portion of 7[superscript]Bep[subscript] may be removed by sinking particles. The distribution coefficient Kd for 7Be increases with depth, with log10Kd averaging 5.2 ± 0.1 at 5 m to 6.1 ± 0.1 between 70 and 150 m, suggesting that scavenging of dissolved 7[superscript]Be by particles is more pronounced in the thermocline than in the mixed layer when differences in particle concentrations are taken into account. Overall, our study suggests that, at least in some oceanic regions, the removal of 7[superscript]Be by marine particles may be significant and that it may need to be considered in applications of 7[superscript]Be as a tracer of oceanic processes and atmospheric deposition.

Beryllium-7↗

NASA NTRS1984

Fabrication development for ODS-superalloy, air-cooled turbine blades

MA-600 is a gamma prime and oxide dispersion strengthened superalloy made by mechanical alloying. At the initiation of this program, MA-6000 was available as an experimental alloy only and did not go into production until late in the program. The objective of this program was to develop a thermal-mechanical-processing approach which would yield the necessary elongated grain structure and desirable mechanical properties after conventional press forging. Forging evaluations were performed to select optimum thermal-mechanical-processing conditions. These forging evaluations indicated that MA-6000 was extremely sensitive to die chilling. In order to conventionally hot forge the alloy, an adherent cladding, either the original extrusion can or a thick plating, was required to prevent cracking of the workpiece. Die design must reflect the requirement of cladding. MA-6000 was found to be sensitive to the forging temperature. The correct temperature required to obtain the proper grain structure after recrystallization was found to be between 1010-1065 C (1850-1950 F). The deformation level did not affect subsequent crystallization; however, sharp transition areas in tooling designs should be avoided in forming a blade shape because of the potential for grain structure discontinuities. Starting material to be used for forging should be processed so that it is capable of being zone annealed to a coarse elongated grain structure as bar stock. This conclusion means that standard processed bar materials can be used.

Moracz, D. J.↗

NASA NTRS1996

The Intensity Distribution for Gamma-Ray Bursts Observed with BATSE

The intensity distributions of gamma-ray bursts observed by BATSE from 19 April 1991 to 19 September 1994 are presented. For this data set, (V/V(sub max)) is 0.329 +/- 0.011, which is 15.5 sigma away from the value of 0.5 expected for a homogeneous distribution. Standard cosmological model parameters are obtained by fitting the differentially binned peak flux distribution expressed in units of photons cm(exp -2) s(exp -1) in the energy range 50-300 keV. The value of z calculated for a peak flux of 1 photon cm(exp -2) s(exp -1) is 0.8 +/- 0.33. The procedures used to produce the peak flux data and C(sub p)/C(sub lim) data are presented. The differences between the two representations of burst intensity are emphasized so that researchers can determine which type of data is most appropriate for their studies. The sky sensitivity correction as a function of intensity for the peak flux data is also described.

Pendleton, Geoffrey N.↗

NASA NTRS2011

BL Lacertae Objects Beyond Redshift 1.3 - UV-to-NIR Photometry and Photometric Redshift for Fermi/LAT Blazars

Context. Observations of the gamma-ray sky with Fermi led to significant advances towards understanding blazars, the most extreme class of Active Galactic Nuclei. A large fraction of the population detected by Fermi is formed by BL Lacertae (BL Lac) objects, whose sample has always suffered from a severe redshift incompleteness due to the quasi-featureless optical spectra. Aims. Our goal is to provide a significant increase of the number of confirmed high-redshift BL Lac objects contained in the 2 LAC Fermi/LAT catalog. Methods. For 103 Fermi/LAT blazars, photometric redshifts using spectral energy distribution fitting have been obtained. The photometry includes 13 broad-band filters from the far ultraviolet to the near-IR observed with Swift/UVOT and the multi-channel imager GROND at the MPG/ESO 2.2m telescope. Data have been taken quasi-simultaneously and the remaining source-intrinsic variability has been corrected for. Results. We release the UV-to-near-IR 13-band photometry for all 103 sources and provide redshift constraints for 75 sources without previously known redshift. Out of those, eight have reliable photometric redshifts at z > or approx. 1.3, while for the other 67 sources we provide upper limits. Six of the former eight are BL Lac objects, which quadruples the sample of confirmed high-redshift BL Lac. This includes three sources with redshifts higher than the previous record for BL Lac, including CRATES J0402-2615, with the best-fit solution at z approx. = 1.9.

Rau, A.↗

NASA NTRS2007

SWIFT Discovery of Gamma-ray Bursts without Jet Break Feature in their X-ray Afterglows

We analyze Swift gamma-ray bursts (GRBs) and X-ray afterglows for three GRBs with spectroscopic redshift determinations - GRB 050401, XRF 050416a, and GRB 050525a. We find that the relation between spectral peak energy and isotropic energy of prompt emissions (the Amati relation) is consistent with that for the bursts observed in pre-Swift era. However, we find that the X-ray afterglow lightcurves, which extend up to 10 - 70 days, show no sign of the jet break that is expected in the standard framework of collimated outflows. We do so by showing that none of the X-ray afterglow lightcurves in our sample satisfies the relation between the spectral and temporal indices that is predicted for the phase after jet break. The jet break time can be predicted by inverting the tight empirical relation between the peak energy of the spectrum and the collimation-corrected energy of the prompt emission (the Ghirlanda relation). We find that there are no temporal breaks within the predicted time intervals in X-ray band. This requires either that the Ghirlanda relation has a larger scatter than previously thought, that the temporal break in X-rays is masked by some additional source of X-ray emission, or that it does not happen because of some unknown reason.

Sato, G.↗

NASA NTRS2004

Observations of X-ray Afterglows

Discussion of X-ray studies of the environs of Gamma Ray Burst (GRB) associated Supernovae using the Chandra and XMM X-Ray Observatories, in particular the long term evolution of their X-ray afterglow lightcurves. For SN 1998bw, we have combined all available observations and derived a smooth X-ray light curve spanning -1300 days, assuming that GRB 980425 and SN 1998bw were coincident at 35.6 Mpc. Perform comparison of this X-ray light curve with those of the X-ray afterglows of ordinary GRBs, X-ray Flashes, and ordinary supernovae, and discuss the emerging evidence for at least two classes of lightcurves, perhaps bounding a continuum. By three to ten years, all these phenomena seem to converge on a common X-ray luminosity, possibly indicative of the supernova underlying them all. One possible explanation for the two classes is a (nearly) standard GRB observed at different angles. If this interpretation is correct, X-ray afterglows with intermediate luminosities should eventually be discovered; GRB 03 1203 maybe just such a case.

Kouveliotou, Chryssa↗

NASA NTRS2000

Quantitative Measurements of Nitric Oxide Concentration in High-Pressure, Swirl-Stabilized Spray Flames

Lean direct-injection (LDI) spray flames offer the possibility of reducing NO(sub x) emissions from gas turbines by rapid mixing of the liquid fuel and air so as to drive the flame structure toward partially-premixed conditions. We consider the technical approaches required to utilize laser-induced fluorescence methods for quantitatively measuring NO concentrations in high-pressure LDI spray flames. In the progression from atmospheric to high-pressure measurements, the LIF method requires a shift from the saturated to the linear regime of fluorescence measurements. As such, we discuss quantitative, spatially resolved laser-saturated fluorescence (LSF), linear laser-induced fluorescence (LIF), and planar laser-induced fluorescence (PLIF) measurements of NO concentration in LDI spray flames. Spatially-resolved LIF measurements of NO concentration (ppm) are reported for preheated, LDI spray flames at pressures of two to five atmospheres. The spray is produced by a hollow-cone, pressure-atomized nozzle supplied with liquid heptane. NO is excited via the Q(sub 2)(26.5) transition of the gamma(0,0) band. Detection is performed in a two nanometer region centered on the gamma(0,1) band. A complete scheme is developed by which quantitative NO concentrations in high-pressure LDI spray flames can be measured by applying linear LIF. NO is doped into the reactants and convected through the flame with no apparent destruction, thus allowing a NO fluorescence calibration to be taken inside the flame environment. The in-situ calibration scheme is validated by comparisons to a reference flame. Quantitative NO profiles are presented and analyzed so as to better understand the operation of lean-direct injectors for gas turbine combustors. Moreover, parametric studies are provided for variations in pressure, air-preheat temperature, and equivalence ratio. Similar parametric studies are performed for lean, premixed-prevaporized flames to permit comparisons to those for LDI flames. Finally, PLIF is expanded to high pressure in an effort to quantify the detected fluorescence image for LDI flames. Success is achieved by correcting the PLIF calibration via a single-point LIF measurement. This procedure removes the influence of any preferential background that occurs in the PLIF detection window. In general, both the LIF and PLIF measurements verify that the LDI strategy could be used to reduce NO(sub x) emissions in future gas turbine combustors.

Cooper, Clayton S.↗

NASA NTRSDate not supplied

Evaluating SAR Radiometric Terrain Correction products: Optimal products for applied users

Operational applications for Synthetic Aperture Radar (SAR) are under development around the world, driven by the free-and-open access of SAR C-band observations that Sentinel-1 of Copernicus has been providing since 2014. Groups like SERVIR, a joint initiative between NASA and USAID, are at the forefront of remote sensing applied uses, and have made many significant contributions to lower the barrier to access, process, and apply SAR for ecosystem services. A takeaway from the SERVIR experience in using SAR is the need to use the appropriate SAR polarimetric product. Radiometric Terrain Correction (RTC) is a key entry-level product for multiple applications that range from ecosystems to hazards. Many software packages exist to create RTC products from SLC or GRD-type Level-1 SAR data, some of which were released only recently, e.g. Interferometric SAR Computing Environment (ISCE) added an RTC module in April 2020. In addition, new versions of open source softwares are expected to address known issues from previous versions, such as Sentinel-1 Toolbox from the European Space Agency (SNAP-7). Despite the growing availability of RTC software solutions, little work has been done to identify differences between RTC products from different softwares. And to address the question, which open-source software produces the most accurate RTC product? This work evaluates Sentinel-1 RTC products created with three different softwares and approaches, including SNAP-7, ISCE-2, and a pseudo RTC product derived from GEE. The GAMMA-derived RTC product, a known optimal RTC and implemented by Alaska Satellite Facility (ASF), is used as a reference. Time series stacks over ten different sites representing varied terrain and ecosystems are evaluated. Products are evaluated for geolocation quality, absolute radiometric calibration, and for the fidelity of the radiometric terrain flattening. The results provide direct guidance and recommendations about the quality of the RTC products obtained from open source methods. This understanding is key to develop operational applications that rely on SAR Sentinel-1 data that need affordable and scalable solutions.

Africa Flores-Anderson↗

NASA NTRS2007

A Spectacular Radio Flare from XRF 050416a at 40 Days and Implications for the Nature of X-Ray Flashes

We present detailed optical, near-infrared, and radio observations of the X-ray flash 050416a obtained with Palomar and Siding Springs Observatories as well as HST and the VLA, placing this event among the best-studied X-ray flashes to date. In addition, we present an optical spectrum from Keck LRIS from which we measure the redshift of the burst, Z=0.6528. At this redshift the isotropic-equivalent prompt energy release was about 10(exp 51) erg, and using a standard afterglow synchrotron model we find that the blastwave kinetic energy is a factor of 10 larger, E-K,iso approximately equals 10 (exp 52) erg. The lack of an observed jet break to t - 20 days indicates that the opening angle is larger than 7 deg and the total beaming-corrected relativistic energy is larger than 10 exp (50) erg. We further show that the burst produced a strong radio flare at t is similar to 40 days accompanied by an observed flattening in the X-ray band which we attribute to an abrupt circumburst density jump or an episode of energy injection (either from a refreshed shock or off-axis ejecta). Late-time observations with HST show evidence for an associated supernova with peak optical luminosity roughly comparable to that of SN 1998bw. Next, we show that the host galaxy of XRF 050416a is actively forming stars at a rate of at least 2 M-solar per year with a luminosity of L-B is similar to 0.5L* and metallicity of Z is similar to 0.2-0.8 Z-solar. Finally, we discuss the nature of XRF 050416a in the context of short-hard gamma-ray bursts and under the framework of off-axis and dirty fireball models for X-ray flashes.

Soderberg, A. M.↗

NASA NTRSDate not supplied

Design and Performance of the CdZnTe VFG Imaging Calorimeter Prototype for Gamma-ray Astronomy

We present the design and first results of the CdZnTe Imaging calorimeter prototype. The CdZnTe Imaging calorimeter has been designed for use in large astrophysical gamma-ray space instruments, and we report here on a small prototype built to validate the approach. The calorimeter is based on virtual Frisch-grid drift-bar CdZnTe detectors. The design is modular, such that multiple crates of 16 bars, each served by a single ASIC, can be arranged in to different configurations depending on the specific requirements for an instrument. The modules are plugged into the readout motherboard in the designed configuration for a given instrument. The detectors are capable of measuring the interaction point of an incident photon in three dimensions and the energy deposited. In this work, we have designed and built a prototype consisting of 4 by 4 module array and have tested it with various radioactive sources to measure its position and energy resolution. The preliminary results demonstrate ~1% FWHM energy resolution and 1-2 mm position resolution for 662 keV photons (Cs137), subject to the further improvement by applying various corrections. We tested the module with a “conventional” analog ASIC readout as well as a wave-front sampling ASIC to compare the results, which is critical for the optimization of the future instrument.

A. A. Moiseev↗

NASA NTRS2000

Inertial Effects in Suspension Dynamics

The present work analyses the dynamics of a suspension of heavy particles in shear flow. The magnitude of the particle inertia is given by the Stokes number St = m(gamma/6(pi)a, which is the ratio of the viscous relaxation time of a particle tau(sub p) = m=6pi(eta)a to the flow time gamma(sup -1). Here, m is the mass of the particle, a is its size, eta is the viscosity of the suspending fluid and gamma is the shear rate. The ratio of the Stokes number to the Reynolds number, Re = (rho)f(gamma)a(exp 2)/eta, is the density ratio rho(sub p)/rho(sub f). Of interest is to understand the separate roles of particle (St) and fluid (Re) inertia in the dynamics of suspensions. In this study we focus on heavy particles, rho(sub p)/rho(sub f) much greater than 1, for which the Stokes number is finite, but the Reynolds number is sufficiently small for inertial forces in the fluid to be neglected; thus, the fluid motion is governed by the Stokes equations. On the other hand, the probability density governing the statistics of the suspended particles satisfies a Fokker-Planck equation that accounts for both configuration and momentum coordinates, the latter being essential for finite St. The solution of the Fokker-Planck equation is obtained to O(St) via a Chapman-Enskog type-procedure, and the conditional velocity distribution so obtained is used to derive a configuration-space Smoluchowski equation with inertial corrections. The inertial effects are responsible for asymmetry in the relative trajectories of two spheres in shear flow, in contrast to the well known symmetric structure in the absence of inertia. Finite St open trajectories in the plane of shear suffer a downward lateral displacement resulting from the inability of a particle of finite mass to follow the curvature of the zero-Stokes-number pathlines. In addition to the induced asymmetry, the O(St) inertial perturbation dramatically alters the nature of the near-field trajectories. The stable closed orbits (for St = 0) in the plane of shear now spiral in, approaching particle-particle contact in the limit. All trajectories starting from an initial offset of O(St(sup 1/2) or less (which remain open for St = 0) also spiral in. The asymmetry of the trajectories leads to a non-Newtonian rheology and diffusive behavior. The latter because a given particle (moving along a finite St open trajectory) suffers a net displacement in the transverse direction after a single interaction. A sequence of such uncorrelated displacements leads to the particle executing a random walk. The inertial diffusivity tensor is anisotropic on account of differing strengths of interaction in the gradient and vorticity directions. Since the entire region (constituting an in finite area) of closed orbits in the plane of shear spirals onto contact for #finite St, the latter represents a singular surface for the pair-distribution function. The exact form of the pair-distribution function at contact is still, however, indeterminate in the absence of non-hydrodynamic effects. It should also be noted that finite St non-rectilinear flows do not support a spatially uniform number density owing to the cross-streamline inertial migration of particles.

J. F. Brady↗