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NASA NTRS1994

On the minimum of independent geometrically distributed random variables

The expectations E(X(sub 1)), E(Z(sub 1)), and E(Y(sub 1)) of the minimum of n independent geometric, modifies geometric, or exponential random variables with matching expectations differ. We show how this is accounted for by stochastic variability and how E(X(sub 1))/E(Y(sub 1)) equals the expected number of ties at the minimum for the geometric random variables. We then introduce the 'shifted geometric distribution' and show that there is a unique value of the shift for which the individual shifted geometric and exponential random variables match expectations both individually and in the minimums.

Ciardo, Gianfranco↗

NASA NTRS1994

The cosmic-ray oxygen and helium spectra measured at Pioneer 10 over the time of the 1987 modulation minimum, and implications for the He/O source ratio

At the time of the recent sunspot minimum in 1987 when the cosmic-ray intensity within the heliosphere was a maximum, Pioneer 10(P10) was at a radial distance of approximately 42 AU. The solar modulation parameter Phi is estimated to have reached a minimum value of approximately 150 MV at P10 at that time, as compared with a minimum value of approximately 500 MV at the Earth. Thus P10 is in a sense effectively approximately 0.7 of the way to the heliospheric modulation boundary whatever its physical distance in astronomical units. Accordingly, the spectra of the various cosmic-ray species are much nearer to the interstellar spectra than any spectra ever before measured. We have therefore examined the penetrating high energy telescope (HET) data from P10 for a 2.5 yr period around 1987 to obtain a statistically accurate spectrum of oxygen nuclei over the energy range from 90 to 450 MeV/nucleon for comparison with a 'reference' interstellar spectrum. A similar spectrum is derived for helium nuclei. These two spectra and their ratios constitute important 'reference' spectra for all of the heavier cosmic-ray nuclei. The cosmic-ray source ratio required to explain the observed He/O ratio, when a full Galactic propagation calculation is carried out including secondary He-4 and He-3 production, is 15.9. The implications of this very low ratio and a comparison with the He/O ratio measured at high energies are discussed.

Webber, W. R.↗

NASA NTRS2004

Application of Satellite-Derived Land Surface Temperature to Minimum Temperature Forecasting

Satellite-derived land surface temperature (LST) is studied for the purpose of understanding regional skin temperature dependency and variability, and its relationship to corresponding, site-specific air temperature. Skin temperature is highly correlated with surface-air temperature although it differs depending on land surface characteristics, terrain, and atmospheric conditions on a diurnal and seasonal scale. The high temporal resolution of the Geostationary Operational Environmental Satellite (GOES) -12 sounder is used to compare the diurnal cycles of LST and surface-air temperature. The minimum for both temperatures occurs near sunrise and LST is found to agree closely with surface-air temperatures a period of hours before sunrise on clear sky nights. The Moderate Resolution Imaging Spectroradiometer (MODIS)-derived LST renders more horizontal temperature structure - with its high spatial resolution (1 km at nadir) compared to the GOES-12 sounder (10 km). Nighttime MODIS-derived LST is extrapolated to the time of minimum temperature for a number of case study days and these are grouped by season and atmospheric conditions. These composites show that the variation in LST mirror the variation in minimum surface-air temperature under similar conditions.

Jones, P. R.↗

NASA NTRS2004

Changes in the Far UV Spectrum of Eta Carinae Near the 2003 Minimum

High resolution 905-1180 spectra of \eta Carinae have been obtained with the Far Ultraviolet Spectroscopic Explorer (FUSE) satellite at nine epochs between February 2000 and June 2003 . This period of time extends from the broad maximum up to the very beginning of the minimum of the 5.52-year period initially discovered by A. Damineli. The flux levels were unchanged between February 2000 through February 2003 with minor spectral differences. The X-Ray minimum started on June 29, 2003 . Three observations were accomplished on June 10, June 17 and June 27 leading up to the minimum. Substantial changes were present in the June 10 and June 17 spectra, but a very significant change occurred by June 27, 2003. Longward of 1100A, the overall flux dropped 10 to 30 %. Shortward of 1100A, there are spectral intervals with NO decrease in flux even down to the shortest wavelengths (920--950 ). This indicates that dust absorption has a negligible role in the observed spectral changes and that line absorptions play a major role. Throughout the spectrum there are intervals ranging in width of 3-10A with strong increased absorption. Significant absorptions may be associated with the red portion of the following stellar wind lines: C III 977, O VI 1031,1037, P V 1117, while other absorption features are much broader, more extended and not clearly associated with well-known spectral transitions. Given the complexity of the STIS echelle spectra taken in this period of time, many of these absorption features are likely due to multiple absorption lines

Iping, R. C.↗

NASA NTRS2005

Eta Carinae: What We have learned recently with HST/STIS, VLT/UVES and VLTI: What We Might Learn with VLT/VLTI across the 2008/9 Minimum

Eta Carinae, the LBV that we have learned to love and hate, has revealed many clues of its character over the past seven years by studies with HST and VLT. Based upon X-Ray, optical and IR observations, Eta Carinae is convincingly a massive binary system that uniquely has major nebular ejecta that are connected with historical outbursts. We have successhlly followed the stellar and nebular changes over the 5.5 year cycle, especially with STIS and RXTE, and across the spectroscopic minimum in 2003.5 with STIS, CHANDRA, RXTE, FUSE, and VLT/UVES. The HST/STIS high spatial resolution, combined with appropriate spectral resolving powers from 1150 to 10300 A, has revealed much about the Central Source and especially the spatially resolved extended stellar atmosphere and the ejecta, known as the Homunculus. Indeed the neutral, dusty outer Homunculus, ejected in the 1840s, envelops the newly discovered ionized Little Homunculus, ejected in the 1890s. In line of sight, multiple hot clumps, both ionized and neutral, are seen in absorption and provide much information on the physical conditions of these massive ejecta. Against the nebular-scattered starlight, wind and nebular absorptions provide views at different angles from line of sight. The VLT/UVES studies from 2002 through 2004 provided very important time-sampled spectra of both the star as seen directly and as seen by the SE lobe viewing the polar region of the star. The VLTI 2.2 micron measures of the central source are consistent with a prolate spheroid with its axis extending along the axis of the Homunculus. This is consistent with the noticeably larger wind mass and higher terminal velocity along the axis of the Homunculus compared to that measured in line of sight at about 45 degrees from the polar axes. We understand the system to be a massive primary with an O or WR companion in a very highly elliptical orbit. The spectroscopic minimum occurs during periastron, when the greatly extended primary atmosphere and wind bottles up the ionizing uv radiation of the companion star. This transient drop in uv photons leads to recombination of much of the wind structure and of the nearby ejecta. Doubly-ionized elements (iron, neon, argon, vanadium) recombine to singly ionized forms and extended structures on the scales of below 0.03 arcseconds to an arcsecond change, appear, or disappear. With the loss of the STIS on HST, ground-based observations, especially with high spatial-resolution facilities, including the VLT and VLTI will be key to further studies across the minimum centered on 2009.0. Now is the time to plan for these studies.

Gull, Theodore R.↗

NASA NTRS2006

NUV Spectroscopic Studies of Eta Car's Weigelt D across the 2003.5 Minimum

HST/STIS high dispersion, high spatial resolution spectra in the near UV (2424-2705A) were recorded of Weigelt D, located 0.25" from Eta Carinae, before, during and after the star's 2003.5 minimum. Most nebular emission, including Lyman-alpha pumped Fe II and [Fe III] lines show phase dependent variations with disappearance at the minimum and reappearance a few months later. Circumstellar absorptions increase at minimum, especially in the Fe II resonance lines originating not only from ground levels but also meta stable levels well above the ground levels. These ionization/excitation effects can be explained by a sudden change in UV flux reaching the blobs, likely due to a line-of-sight obscuration of the hotter companion star, Eta Car B, recently discovered by Iping et al. (poster, this meeting). The scattered starlight seen towards Weigelt D display noticeable different line profiles than the direct starlight from Eta Carinae. P-Cygni absorption profiles in Fe II stellar lines observed directly towards Eta Carinae, show terminal velocities up to -550 km/s. However, scattered starlight of Weigelt D display significant lower velocities ranging from -40 to -150 km/s.We interpret this result to be indicative that no absorbing Fe II wind structure exists between the Central source and Weigelt D. The lower velocity absorption appears to be connected to the outer Fe II wind structure of Eta Car A extending beyond Weigelt D intersecting the observer's line of sight. This result is consistent with the highly extended wind of Eta Car A.

Ivarsson, S.↗

NASA NTRS2010

Polar Chromospheric Signatures of the Subdued Cycle 23/24 Solar Minimum

Coronal holes appear brighter than the quiet Sun in microwave images, with a brightness enhancement of 500 to 2000 K. The brightness enhancement corresponds to the upper chromosphere, where the plasma temperature is about 10000 K. We constructed a microwave butterfly diagram using the synoptic images obtained by the Nobeyama radioheliograph (NoRH) showing the evolution of the polar and low latitude brightness temperature. While the polar brightness reveals the chromospheric conditions, the low latitude brightness is attributed to active regions in the corona. When we compared the microwave butterfly diagram with the magnetic butterfly diagram, we found a good correlation between the microwave brightness enhancement and the polar field strength. The microwave butterfly diagram covers part of solar cycle 22, whole of cycle 23, and part of cycle 24, thus enabling comparison between the cycle 23/24 and cycle 22/23 minima. The microwave brightness during the cycle 23/24 minimum was found to be lower than that during the cycle 22/23 minimum by approximately 250 K. The reduced brightness temperature is consistent with the reduced polar field strength during the cycle 23/24 minimum seen in the magnetic butterfly diagram. We suggest that the microwave brightness at the solar poles is a good indicator of the speed of the solar wind sampled by Ulysses at high latitudes.

Gopalswamy, N.↗

NASA NTRS2010

On the Minimum Induced Drag of Wings

Of all the types of drag, induced drag is associated with the creation and generation of lift over wings. Induced drag is directly driven by the span load that the aircraft is flying at. The tools by which to calculate and predict induced drag we use were created by Ludwig Prandtl in 1903. Within a decade after Prandtl created a tool for calculating induced drag, Prandtl and his students had optimized the problem to solve the minimum induced drag for a wing of a given span, formalized and written about in 1920. This solution is quoted in textbooks extensively today. Prandtl did not stop with this first solution, and came to a dramatically different solution in 1932. Subsequent development of this 1932 solution solves several aeronautics design difficulties simultaneously, including maximum performance, minimum structure, minimum drag loss due to control input, and solution to adverse yaw without a vertical tail. This presentation lists that solution by Prandtl, and the refinements by Horten, Jones, Kline, Viswanathan, and Whitcomb

Bowers, Albion H.↗

NASA NTRS2011

Chromospheric Signatures of the Subdued Cycle 23/24 Solar Minimum in Microwaves

Coronal holes appear brighter than the quiet Sun in microwave images, with a brightness enhancement of 500 to 2000 K. The brightness enhancement corresponds to the upper chromosphere, where the plasma temperature is about 10000 K. We constructed a microwave butterfly diagram using the synoptic images obtained by the Nobeyama radio-heliograph (NoRH) showing the evolution of the polar and low latitude brightness temperature. While the polar brightness reveals the chromospheric conditions, the low latitude brightness is attributed to active regions in the corona. When we compared the microwave butterfly diagram with the magnetic butterfly diagram, we found a good correlation between the microwave brightness enhancement and the polar field strength. The microwave butterfly diagram covers part of solar cycle 22, whole of cycle 23, and part of cycle 24, thus enabling comparison between the cycle 23/24 and cycle 22/23 minima. The microwave brightness during the cycle 23/24 minimum was found to be lower than that during the cycle 22/23 minimum by approx.250 K. The reduced brightness temperature is consistent with the reduced polar field strength during the cycle 23/24 minimum seen in the magnetic butterfly diagram. We suggest that the microwave brightness at the solar poles is a good indicator of the speed of the solar wind sampled by Ulysses at high latitudes.

Yashiro, S.↗

NASA NTRS2011

On the Minimum Induced Drag of Wings

Bowers, Albion H.↗

NASA NTRS2011

On the Minimum Induced Drag of Wings -or- Thinking Outside the Box

Bowers, Albion H.↗

NASA NTRS2012

Rate-compatible protograph LDPC code families with linear minimum distance

Digital communication coding methods are shown, which generate certain types of low-density parity-check (LDPC) codes built from protographs. A first method creates protographs having the linear minimum distance property and comprising at least one variable node with degree less than 3. A second method creates families of protographs of different rates, all having the linear minimum distance property, and structurally identical for all rates except for a rate-dependent designation of certain variable nodes as transmitted or non-transmitted. A third method creates families of protographs of different rates, all having the linear minimum distance property, and structurally identical for all rates except for a rate-dependent designation of the status of certain variable nodes as non-transmitted or set to zero. LDPC codes built from the protographs created by these methods can simultaneously have low error floors and low iterative decoding thresholds, and families of such codes of different rates can be decoded efficiently using a common decoding architecture.

Divsalar, Dariush↗

NASA NTRS2013

Ion-neutral Coupling During Deep Solar Minimum

The equatorial ionosphere under conditions of deep solar minimum exhibits structuring due to tidal forces. Data from instruments carried by the Communication Navigation Outage Forecasting System (CNOFS) which was launched in April 2008 have been analyzed for the first 2 years following launch. The Planar Langmuir Probe (PLP), Ion Velocity Meter (IVM) and Vector Electric Field Investigation (VEFI) all detect periodic structures during the 20082010 period which appear to be tides. However when the tidal features detected by these instruments are compared, there are distinctive and significant differences between the observations. Tides in neutral densities measured by the Gravity Recovery and Climate Experiment (GRACE) satellite were also observed during June 2008. In addition, Broad Plasma Decreases (BPDs) appear as a deep absolute minimum in the plasma and neutral density tidal pattern. These are co-located with regions of large downward-directed ion meridional velocities and minima in the zonal drifts, all on the nightside. The region in which BPDs occur coincides with a peak in occurrence rate of dawn depletions in plasma density observed on the Defense Meterological Satellite Program (DMSP) spacecraft, as well as a minimum in radiance detected by UV imagers on the Thermosphere Ionosphere Mesosphere Energetics and Dynamics (TIMED) and IMAGE satellites

IVM↗

NASA NTRS2013

On the Trend of the Annual Mean, Maximum, and Minimum Temperature and the Diurnal Temperature Range in the Armagh Observatory, Northern Ireland, Dataset, 1844 -2012

Examined are the annual averages, 10-year moving averages, decadal averages, and sunspot cycle (SC) length averages of the mean, maximum, and minimum surface air temperatures and the diurnal temperature range (DTR) for the Armagh Observatory, Northern Ireland, during the interval 1844-2012. Strong upward trends are apparent in the Armagh surface-air temperatures (ASAT), while a strong downward trend is apparent in the DTR, especially when the ASAT data are averaged by decade or over individual SC lengths. The long-term decrease in the decadaland SC-averaged annual DTR occurs because the annual minimum temperatures have risen more quickly than the annual maximum temperatures. Estimates are given for the Armagh annual mean, maximum, and minimum temperatures and the DTR for the current decade (2010-2019) and SC24.

Wilson, Robert M.↗

NASA NTRS2013

Galactic Cosmic-Ray Energy Spectra and Composition during the 2009-2010 Solar Minimum Period

We report new measurements of the elemental energy spectra and composition of galactic cosmic rays during the 2009-2010 solar minimum period using observations from the Cosmic Ray Isotope Spectrometer (CRIS) onboard the Advanced Composition Explorer. This period of time exhibited record-setting cosmic-ray intensities and very low levels of solar activity. Results are given for particles with nuclear charge 5 <= Z <= 28 in the energy range approx. 50-550 MeV / nucleon. Several recent improvements have been made to the earlier CRIS data analysis, and therefore updates of our previous observations for the 1997-1998 solar minimum and 2001-2003 solar maximum are also given here. For most species, the reported intensities changed by less than approx. 7%, and the relative abundances changed by less than approx. 4%. Compared with the 1997-1998 solar minimum relative abundances, the 2009-2010 abundances differ by less than 2sigma, with a trend of fewer secondary species observed in the more recent time period. The new 2009-2010 data are also compared with results of a simple "leaky-box" galactic transport model combined with a spherically symmetric solar modulation model. We demonstrate that this model is able to give reasonable fits to the energy spectra and the secondary-to-primary ratios B/C and (Sc+Ti+V)/Fe. These results are also shown to be comparable to a GALPROP numerical model that includes the effects of diffusive reacceleration in the interstellar medium.

Galactic Cosmic Rays↗

NASA NTRS2015

Minimum deltaV Burn Planning for the International Space Station Using a Hybrid Optimization Technique, Level 1

The International Space Station's (ISS) trajectory is coordinated and executed by the Trajectory Operations and Planning (TOPO) group at NASA's Johnson Space Center. TOPO group personnel routinely generate look-ahead trajectories for the ISS that incorporate translation burns needed to maintain its orbit over the next three to twelve months. The burns are modeled as in-plane, horizontal burns, and must meet operational trajectory constraints imposed by both NASA and the Russian Space Agency. In generating these trajectories, TOPO personnel must determine the number of burns to model, each burn's Time of Ignition (TIG), and magnitude (i.e. deltaV) that meet these constraints. The current process for targeting these burns is manually intensive, and does not take advantage of more modern techniques that can reduce the workload needed to find feasible burn solutions, i.e. solutions that simply meet the constraints, or provide optimal burn solutions that minimize the total DeltaV while simultaneously meeting the constraints. A two-level, hybrid optimization technique is proposed to find both feasible and globally optimal burn solutions for ISS trajectory planning. For optimal solutions, the technique breaks the optimization problem into two distinct sub-problems, one for choosing the optimal number of burns and each burn's optimal TIG, and the other for computing the minimum total deltaV burn solution that satisfies the trajectory constraints. Each of the two aforementioned levels uses a different optimization algorithm to solve one of the sub-problems, giving rise to a hybrid technique. Level 2, or the outer level, uses a genetic algorithm to select the number of burns and each burn's TIG. Level 1, or the inner level, uses the burn TIGs from Level 2 in a sequential quadratic programming (SQP) algorithm to compute a minimum total deltaV burn solution subject to the trajectory constraints. The total deltaV from Level 1 is then used as a fitness function by the genetic algorithm in Level 2 to select the number of burns and their TIGs for the next generation. In this manner, the two levels solve their respective sub-problems separately but collaboratively until a burn solution is found that globally minimizes the deltaV across the entire trajectory. Feasible solutions can also be found by simply using the SQP algorithm in Level 1 with a zero cost function. This paper discusses the formulation of the Level 1 sub-problem and the development of a prototype software tool to solve it. The Level 2 sub-problem will be discussed in a future work. Following the Level 1 formulation and solution, several look-ahead trajectory examples for the ISS are explored. In each case, the burn targeting results using the current process are compared against a feasible solution found using Level 1 in the proposed technique. Level 1 is then used to find a minimum deltaV solution given the fixed number of burns and burn TIGs. The optimal solution is compared with the previously found feasible solution to determine the deltaV (and therefore propellant) savings. The proposed technique seeks to both improve the current process for targeting ISS burns, and to add the capability to optimize ISS burns in a novel fashion. The optimal solutions found using this technique can potentially save hundreds of kilograms of propellant over the course of the ISS mission compared to feasible solutions alone. While the software tool being developed to implement this technique is specific to ISS, the concept is extensible to other long-duration, central-body orbiting missions that must perform orbit maintenance burns to meet operational trajectory constraints.

Brown, Aaron J.↗

NASA NTRS2017

BrO and Inferred Bry Profiles over the Western Pacific: Relevance of Inorganic Bromine Sources and a Bry Minimum in the Aged Tropical Tropopause Layer

We report measurements of bromine monoxide (BrO) and use an observationally constrained chemical box model to infer total gas-phase inorganic bromine (Br(sub y)) over the tropical western Pacific Ocean (tWPO) during the CONTRAST field campaign (January-February 2014). The observed BrO and inferred Bry profiles peak in the marine boundary layer (MBL), suggesting the need for a bromine source from sea-salt aerosol (SSA), in addition to organic bromine (CBry ). Both profiles are found to be C-shaped with local maxima in the upper free troposphere (FT). The median tropospheric BrO vertical column density (VCD) was measured as 1.6 x 10(exp 13) molec cm(exp -2), compared to model predictions of 0.9 x 10(exp 13) molec cm(exp -2) in GEOS-Chem (CBr(sub y) but no SSA source), 0.4 x 10(exp 13) molec cm(exp -2) in CAM-Chem (CBr(sub y) and SSA), and 2.1 x 10(exp 13) molec cm(exp -2) in GEOS-Chem (CBry and SSA). Neither global model fully captures the Cshape of the Br(sun y) profile. A local Br(sub y) maximum of 3.6 ppt (2.9-4.4 ppt; 95% confidence interval, CI) is inferred between 9.5 and 13.5 km in air masses influenced by recent convective outflow. Unlike BrO, which increases from the convective tropical tropopause layer (TTL) to the aged TTL, gas-phase Br(sub y) decreases from the convective TTL to the aged TTL. Analysis of gas-phase Br(sub y) against multiple tracers (CFC-11, H2O/O3 ratio, and potential temperature) reveals a Br(sub y) minimum of 2.7 ppt (2.3-3.1 ppt; 95% CI) in the aged TTL, which agrees closely with a stratospheric injection of 2.6 +/- 0.6 ppt of inorganic Br(sub y) (estimated from CFC-11 correlations), and is remarkably insensitive to assumptions about heterogeneous chemistry. Bry increases to 6.3 ppt (5.6-7.0 ppt; 95% CI) in the stratospheric "middleworld" and 6.9 ppt (6.5-7.3 ppt; 95% CI) in the stratospheric "overworld". The local Br(sub y) minimum in the aged TTL is qualitatively (but not quantitatively) captured by CAM-Chem, and suggests a more complex partitioning of gas-phase and aerosol Br(sub y) species than previously recognized. Our data provide corroborating evidence that inorganic bromine sources (e.g., SSA-derived gas-phase Br(sub y) ) are needed to explain the gas-phase Br(sub y) budget in the upper free troposphere and TTL. They are also consistent with observations of significant bromide in Upper Troposphere-Lower Stratosphere aerosols. The total Br(sub y) budget in the TTL is currently not closed, because of the lack of concurrent quantitative measurements of gas-phase Br(sub y) species (i.e., BrO, HOBr, HBr, etc.) and aerosol bromide. Such simultaneous measurements are needed to (1) quantify SSA-derived Br(sub y) in the upper FT, (2) test Br(sub y) partitioning, and possibly explain the gas-phase Br(sub y) minimum in the aged TTL, (3) constrain heterogeneous reaction rates of bromine, and (4) account for all of the sources of Br(sub y) to the lower stratosphere.

Atmospheric Chemistry; bromine; troposphere; CONTR↗

NASA NTRS2022

CME Evolution in the Structured Heliosphere and Effects at Earth and Mars During Solar Minimum

The activity of the Sun alternates between a solar minimum and a solar maximum, the former corresponding to a period of “quieter” status of the heliosphere. During solar minimum, it is in principle more straightforward to follow eruptive events and solar wind structures from their birth at the Sun throughout their interplanetary journey. In this paper, we report analysis of the origin, evolution, and heliospheric impact of a series of solar transient events that took place during the second half of August 2018, that is, in the midst of the late declining phase of Solar Cycle 24. In particular, we focus on two successive coronal mass ejections (CMEs) and a following high-speed stream (HSS) on their way toward Earth and Mars. We find that the first CME impacted both planets, whilst the second caused a strong magnetic storm at Earth and went on to miss Mars, which nevertheless experienced space weather effects from the stream interacting region preceding the HSS. Analysis of remote-sensing and in-situ data supported by heliospheric modeling suggests that CME–HSS interaction resulted in the second CME rotating and deflecting in interplanetary space, highlighting that accurately reproducing the ambient solar wind is crucial even during “simpler” solar minimum periods. Lastly, we discuss the upstream solar wind conditions and transient structures responsible for driving space weather effects at Earth and Mars.

Space weather↗