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Random Variables with Moment-Matching Staircase Density Functions
This paper proposes a family of random variables for uncertainty modeling. The variables of interest have a bounded support set, and prescribed values for the first four moments. We present the feasibility conditions for the existence of any of such variables, and propose a class of variables that conforms to such constraints. This class is called staircase because the density of its members is a piecewise constant function. Convex optimization is used to calculate their distributions according to several optimality criteria, including maximal entropy and maximal log-likelihood. The flexibility and efficiency of staircases enable modeling phenomena having a possibly skewed and/or multimodal response at a low computational cost. Furthermore, we provide a means to account for the uncertainty in the distribution caused by estimating staircases from data. These ideas are illustrated by generating empirical staircase predictor models. We consider the case in which the predictor matches the sample moments exactly (a setting applicable to large datasets), as well as the case in which the predictor accounts for the sampling error in such moments (a setting applicable to sparse datasets). A predictor model for the dynamics of an aeroelastic airfoil subject to flutter instability is used as an example. The resulting predictor not only describes the system's response accurately, but also enables carrying out a risk analysis for safe flight.
A relation between ELF hiss amplitude and plasma density in the outer plasmasphere
Simultaneous observations of ELF hiss amplitude and plasma density on Ogo 5 have been investigated. Passes through the region of variable plasma density in the outer plasmasphere have yielded a quantitative relation between the hiss amplitude, the plasma density, and the plasma density corresponding to the threshold of wave detection. It is suggested that this dependence of wave amplitude on plasma density is a source effect and is related to the wave-particle interaction in the outer plasmasphere that gives rise to hiss.
Thermodynamically consistent semi-compressible fluids: a variational perspective
This paper presents (Lagrangian) variational formulations for single and multicomponent semi-compressible fluids with both reversible (entropy-conserving) and irreversible (entropy-generating) processes. Semi-compressible fluids are useful in describing low-Mach dynamics, since they are soundproof. These models find wide use in many areas of fluid dynamics, including both geophysical and astrophysical fluid dynamics. Specifically, the Boussinesq, anelastic and pseudoincompressible equations are developed through a unified treatment valid for arbitrary Riemannian manifolds, thermodynamic potentials and geopotentials. By design, these formulations obey the 1st and 2nd laws of thermodynamics, ensuring their thermodynamic consistency. This general approach extends and unifies existing work, and helps clarify the thermodynamics of semi-compressible fluids. To further this goal, evolution equations are presented for a wide range of thermodynamic variables: entropy density s, specific entropy η, buoyancy b, temperature T, potential temperature θ and a generic entropic variable χ; along with a general definition of buoyancy valid for all three semicompressible models and arbitrary geopotentials. Finally, the elliptic equation for the pressure perturbation (the Lagrange multiplier that enforces semi-compressibility) is developed for all three equation sets in the case of reversible dynamics, and for the Boussinesq/anelastic equations in the case of irreversible dynamics; and some discussion is given of the difficulty in formulating it for the pseudoincompressible equations with irreversible dynamics.
Living With a Star, the Geospace Mission Definition Team and Aeronomy
To gain an understanding of the Sun-Earth system, including how and why the sun varies, how the earth responds, and the impacts on humanity, research is needed that has a integrated and systematic approach. The Living With a Star (LWS) program represents an important element in this regard both to continued progress in space science in general and in Aeronomy in particular. A fundamental question in Aeronomy is how the variable sun affects the ionosphere, thermosphere, and mesosphere. The LWS program focuses on those areas of scientific understanding that promote progress in areas that have human impact and can be investigated with space borne instruments. The Geospace Mission Definition Team is charged with investigating the science priorities identified by the LWS Science Architecture Team and developing an approach to making the necessary measurements in concert with other missions and programs. An important aspect of this approach is that all LWS measurement programs are operating simultaneously for several years. We will review some of the areas that the LWS SAT have emphasized in Aeronomy, including understanding the effects of solar variability on ionospheric density and irregularities, the effects of solar variability on the mass density of the atmosphere at LEO altitudes, and the effects of solar variability on near-surface temperatures and on ozone distribution.
Characterizing natural fractures and sub-seismic faults for well completion of Marcellus shale in the MSEEL Consortium project, West Virginia, USA
The Middle Devonian Marcellus shale play has emerged as a major world-class hydrocarbon accumulation and represents one of the largest and most prolific shale plays in the world. According to many outcrop studies in the region, natural fractures are well developed in the Marcellus Shale. However, evaluating fractures in the subsurface is often a significant challenge due to a lack of sufficient data. Therefore, in the Marcellus Shale Energy and Environment Laboratory (MSEEL) consortium project, significant efforts have been made to acquire high-quality image logs in the Marcellus laterals. The project provided tremendous opportunities to characterize the natural fractures and sub-seismic faults and to evaluate their impact on well stimulation. In this study, about 70,000 ft of acquired high-resolution logging while drilling (LWD) acoustic images from five long laterals located in Monongalia County, West Virginia, were processed and interpreted. In addition, the study used high-quality micro-resistivity images from a pilot well, allowing the evaluation of natural fractures in the entire Marcellus vertical sequence. Based on the available acoustic images, the natural fractures were classified into three basic categories: high-amplitude fractures, low-amplitude fractures, and faults. Further, larger open fractures can also be determined when a low-amplitude fracture is evident on caliper images. The fractures in the Marcellus usually have a medium to high angle dip; however, multiple fracture sets in terms of strike orientation were clearly observed in all the laterals. The fracture set with a strike at NE-SW (or 60-240 deg) seems to be the predominant one in all the wells. A few other sets, including those with N-S, NWW-SEE, and E-W strikes, were also observed. Several sub-seismic faults, with mostly a low dip angle and a NE-SW strike, have also been seen in two of the laterals. The fracture density is variable across all the laterals, ranging from very low (or none) to very high (up to 5 fractures per ft). The average fracture density for all the laterals is about 1 fracture per 10 ft. In the vertical sequence, the natural fracture development showed a clear preference for shale or shaly facies over carbonate-rich or thin limestone layers. The interpreted fracture and fault data were used as input data for the stimulation design with the purpose of better understanding the fractures’ impact on well stimulation. Production data from the laterals were also used to evaluate the natural fractures’ influence on well performance. The quality image database and the consistent interpretation results for the entire project enabled a systematic approach to characterizing fractures and, more importantly, to evaluating the impact of fractures on well stimulation and production.
Effects of CO2 Addition on the Turbulent Flame Front Dynamics and Propagation Speeds of Methane/Air Mixtures
Exhaust gas recirculation (EGR) is one of the most promising methods of improving the performance of power-generating gas turbines. CO2 is known to have the largest impact on flame behavior of any major exhaust species, but few studies have specified its thermal, kinetic, and transport effects on turbulent flames. Therefore, in this study, methane/air mixtures diluted with CO2 are experimentally investigated in a reactor-assisted turbulent slot (RATS) burner using OH planar laser-induced fluorescence (PLIF) measurements. CO2 addition is tested under both constant adiabatic flame temperature and variable adiabatic flame temperature conditions in order to elucidate its thermal, kinetic, and transport effects. Particular attention is paid to CO2's effects on the flame surface density, progress variable, turbulent burning velocity, and flame wrinkling. The experimental measurements reveal that CO2's thermal effects are the dominant factor in elongating the turbulent flame brush and decreasing the turbulent burning velocity. When thermal effects are removed by holding the adiabatic flame temperature constant, CO2's kinetic effects are the next most important factor, producing an approximately 5% decrease in the global consumption speed for each 5% of CO2 addition. The transport effects of CO2, however, tend to increase the global consumption speed, counteracting 30–50% of the kinetic effects when the adiabatic flame temperature is fixed. It is also seen that CO2 addition increases the normalized global consumption speed primarily through an enhancement of the stretch factor.
Growth and Morphology of Supercritical Fluids Studied in Microgravity on Mir
The Growth and Morphology of Supercritical Fluids (GMSF) is an international experiment facilitated by the NASA Glenn Research Center at Lewis Field and under the guidance of U.S. principal investigator Professor John Hegseth of the University of New Orleans and three French coinvestigators Daniel Beysens, Yves Garrabos, and Carole Chabot. In early 1999, GMSF experiments were operated for 20 days on the Russian Space Station Mir. Mir astronauts performed experiments One through Seven, which spanned the three science themes of near-critical phase separation rates, interface dynamics in near-critical boiling, and measurement of the spectrum of density fluctuation length scales very close to the critical point. The fluids used were pure CO2 or SF6. Three of the five thermostats used could adjust the sample volume with the scheduled crew time. Such a volume adjustment enabled variable sample densities around the critical density as well as pressure steps (as distinct from the usual temperature steps) to be applied to the sample.
Growth and Morphology of Supercritical Fluids, a Fluid Physics Experiment Conducted on Mir, Complete
The Growth and Morphology of Supercritical Fluids (GMSF) is an international experiment facilitated by the NASA Glenn Research Center and under the guidance of U.S. principal investor Professor Hegseth of the University of New Orleans and three French coinvestigators: Daniel Beysens, Yves Garrabos, and Carole Chabot. The GMSF experiments were concluded in early 1999 on the Russian space station Mir. The experiments spanned the three science themes of near-critical phase separation rates, interface dynamics in near-critical boiling, and measurement of the spectrum of density fluctuation length scales very close to the critical point. The fluids used were pure CO2 or SF6. Three of the five thermostats used could adjust the sample volume with the scheduled crew time. Such a volume adjustment enabled variable sample densities around the critical density as well as pressure steps (as distinct from the usual temperature steps) applied to the sample. The French-built ALICE II facility was used for these experiments. It allows tightly thermostated (left photograph) samples (right photograph) to be controlled and viewed/measured. Its diagnostics include interferometry, shadowgraph, high-speed pressure measurements, and microscopy. Data were logged on DAT tapes, and PCMCIA cards and were returned to Earth only after the mission was over. The ground-breaking near critical boiling experiment has yielded the most results with a paper published in Physical Review Letters (ref. 1). The boiling work also received press in Science Magazine (ref. 2). This work showed that, in very compressible near-critical two-phase pure fluids, a vapor bubble was induced to temporarily overheat during a rapid heating of the sample wall. The temperature rise in the vapor was 23-percent higher than the rise in the driving container wall. The effect is due to adiabatic compression of the vapor bubble by the rapid expansion of fluid near the boundary during heatup. Thermal diffusivity is low near the critical point, so getting heat out of the compressed bubble is observably slow. This gives the appearance of a backward heat flow, or heat flow from a cold surface to a warm fluid.
Fabrication and characterization of a full-size ultra-precise lamellar grating for the Cosmic beamline at ALS-U
We have developed a new process for the production of ultra-precise variable line spacing (VLS) lamellar diffraction gratings through nanofabrication. The process enables the fabrication of full-size X-ray gratings with sub-nanometre accuracy in groove depth, an optimal land-to-groove ratio, and uniform groove depth across the entire grating area. We also established a method for evaluating VLS groove density variation using stitched Fizeau interferometry. The measurements confirmed the exceptionally high accuracy of the VLS groove density in the fabricated gratings, which is well within the specification tolerances while the residual groove density errors are vanishingly small. The gold-coated grating demonstrated near-theoretical diffraction efficiency across the energy range of 100–1200 eV.
The Galex Time Domain Survey. I. Selection And Classification of Over a Thousand Ultraviolet Variable Sources
We present the selection and classification of over a thousand ultraviolet (UV) variable sources discovered in approximately 40 deg(exp 2) of GALEX Time Domain Survey (TDS) NUV images observed with a cadence of 2 days and a baseline of observations of approximately 3 years. The GALEX TDS fields were designed to be in spatial and temporal coordination with the Pan-STARRS1 Medium Deep Survey, which provides deep optical imaging and simultaneous optical transient detections via image differencing. We characterize the GALEX photometric errors empirically as a function of mean magnitude, and select sources that vary at the 5 sigma level in at least one epoch. We measure the statistical properties of the UV variability, including the structure function on timescales of days and years. We report classifications for the GALEX TDS sample using a combination of optical host colors and morphology, UV light curve characteristics, and matches to archival X-ray, and spectroscopy catalogs. We classify 62% of the sources as active galaxies (358 quasars and 305 active galactic nuclei), and 10% as variable stars (including 37 RR Lyrae, 53 M dwarf flare stars, and 2 cataclysmic variables). We detect a large-amplitude tail in the UV variability distribution for M-dwarf flare stars and RR Lyrae, reaching up to absolute value(Δm) = 4.6 mag and 2.9 mag, respectively. The mean amplitude of the structure function for quasars on year timescales is five times larger than observed at optical wavelengths. The remaining unclassified sources include UV-bright extragalactic transients, two of which have been spectroscopically confirmed to be a young core-collapse supernova and a flare from the tidal disruption of a star by dormant supermassive black hole. We calculate a surface density for variable sources in the UV with NUV less than 23 mag and absolute value(Δm) greater than 0.2 mag of approximately 8.0, 7.7, and 1.8 deg(exp −2) for quasars, active galactic nuclei, and RR Lyrae stars, respectively. We also calculate a surface density rate in the UV for transient sources, using the effective survey time at the cadence appropriate to each class, of approximately 15 and 52 deg(exp −2 yr−1 for M dwarfs and extragalactic transients, respectively.
Impact of Grafting Density on the Assembly and Mechanical Properties of Self-Assembled Metal–Organic Framework Monolayers
Polymer-grafted metal–organic frameworks (MOFs) can be used to form free-standing self-assembled MOF monolayers (SAMMs). Polymer chains can be introduced onto MOF surfaces through either the ligands or metal nodes using both grafting-to and grafting-from approaches. However, controlling the grafting density of polymer-grafted MOFs has not yet been achieved, because a means to control the density of grafting sites on the MOF surface has not been developed. In this study, the grafting density of polymer-grafted UiO-66 (UiO = University of Oslo) was controlled by functionalizing a portion of the Zr(IV) secondary building units (SBUs) on a UiO-66 surface with a so-called blocking agent. The remaining sites on the UiO-66 SBUs were functionalized with polymerization initiation groups, and polymers were grown from these sites to obtain particles with variable grafting densities and chain lengths that form SAMMs at an air–water interface. Even under conditions of low grafting density, these materials retain the ability to form SAMMs and their free-standing ability. Changes in particle arrangement within the monolayers were investigated using SEM imaging, and the toughness of the monolayers was evaluated using a film-on-water (FOW) method. Furthermore, coarse-grained molecular dynamics simulations were carried out to elucidate the morphology and mechanical properties of the monolayers. Findings from both experiments and simulations indicate that the toughness of SAMMs is more heavily influenced by the chain length of the grafted polymers than by the overall polymer content in the composite.
A rigorous framework for an improved Messinger/Myers model of ice accretion under conditions of variable property and unsteady aircraft icing
We analyse the Messinger/Myers model by critically evaluating simplifying assumptions through a rigorous formulation of the rime ice accretion process. We explore the effects of both constant and variable ice density and thermal conductivity, along with the effects of sublimation from the ice surface. The effects of key factors such as droplet impact rate, ambient temperature relative to the freezing temperature and the temperature difference between the ambient air and the airfoil surface are examined. Under these varying conditions, the present rigorous formulation is used to assess the significance of unsteady effects, variable ice properties and sublimation. We observe that the Myers model performs remarkably well in certain icing situations and analyse the reasons for this strong performance. We also show that partially relaxing the model’s assumptions can lead to poorer performance. The Myers model can lead to overprediction of ice surface temperature and correspondingly underprediction of transition time under conditions of relatively weak sublimation and surface cooling. A modified Myers model is presented, which can be used to recover near-perfect results under widely varying icing conditions of relevance. This article is part of the theme issue ‘Heat and mass transfer in frost and ice’.
Role of water model on ion dissociation at ambient conditions
In this work, we study ion pair dissociation in water at ambient conditions using a combination of classical and ab initio approaches. The goal of this study is to disentangle the sources of discrepancy observed in computed potentials of mean force. In particular, we aim to understand why some models favor the stability of solvent-separated ion pairs vs contact ion pairs. We found that some observed differences can be explained by non-converged simulation parameters. However, we also unveil that for some models, small changes in the solution density can have significant effects on modifying the equilibrium balance between the two configurations. We conclude that the thermodynamic stability of contact and solvent-separated ion pairs is very sensitive to the dielectric properties of the underlying simulation model. In general, classical models are very robust in providing a similar estimation of the contact ion pair stability, while this is much more variable in density functional theory-based models. The barrier to transition from the solvent-separated to contact ion pair is fundamentally dependent on the balance between electrostatic potential energy and entropy. This reflects the importance of water intra- and inter-molecular polarizability in obtaining an accurate description of the screened ion–ion interactions.
Modeling of dense sprays from LOX/H2 coaxial injectors under supercritical conditions
Assumptions commonly employed in the analytical description of a thin spray become unacceptable as the droplet density and droplet volume displacement become large. Changes in the semiempirical models describing drop-drop or drop-gas interactions as well as in the basic modeling approach itself may be necessary. A number of efforts undertaken to improve such models of the atomization-evaporation process to render them applicable in the dense-spray, supercritical regime are described. The improvements include those for variable drop density, supercritical properties, stripping evaporation and drop reincorporation into the liquid stream. The models are developed for use with the ARICC three-phase finite difference combustion code. Selected results from a sample calculation are presented, demonstrating the enhanced realism achievable with the upgraded models.
Space Technology 5 Multipoint Observations of Temporal and Spatial Variability of Field-Aligned Currents
Space Technology 5 (ST5) is a constellation mission consisting of three microsatellites. It provides the first multipoint magnetic field measurements in low Earth orbit, which enables us to separate spatial and temporal variations. In this paper, we present a study of the temporal variability of field-aligned currents using the ST5 data. We examine the field-aligned current observations during and after a geomagnetic storm and compare the magnetic field profiles at the three spacecraft. The multipoint data demonstrate that mesoscale current structures, commonly embedded within large-scale current sheets, are very dynamic with highly variable current density and/or polarity in approx.10 min time scales. On the other hand, the data also show that the time scales for the currents to be relatively stable are approx.1 min for mesoscale currents and approx.10 min for large-scale currents. These temporal features are very likely associated with dynamic variations of their charge carriers (mainly electrons) as they respond to the variations of the parallel electric field in auroral acceleration region. The characteristic time scales for the temporal variability of mesoscale field-aligned currents are found to be consistent with those of auroral parallel electric field.
Space Technology 5 Multi-point Observations of Field-aligned Currents: Temporal Variability of Meso-Scale Structures
Space Technology 5 (ST5) is a three micro-satellite constellation deployed into a 300 x 4500 km, dawn-dusk, sun-synchronous polar orbit from March 22 to June 21, 2006, for technology validations. In this paper, we present a study of the temporal variability of field-aligned currents using multi-point magnetic field measurements from ST5. The data demonstrate that meso-scale current structures are commonly embedded within large-scale field-aligned current sheets. The meso-scale current structures are very dynamic with highly variable current density and/or polarity in time scales of - 10 min. They exhibit large temporal variations during both quiet and disturbed times in such time scales. On the other hand, the data also shown that the time scales for the currents to be relatively stable are approx. 1 min for meso-scale currents and approx. 10 min for large scale current sheets. These temporal features are obviously associated with dynamic variations of their particle carriers (mainly electrons) as they respond to the variations of the parallel electric field in auroral acceleration region. The characteristic time scales for the temporal variability of meso-scale field-aligned currents are found to be consistent with those of auroral parallel electric field.
Space Technology 5 Multi-Point Observations of Temporal Variability of Field-Aligned Currents
Space Technology 5 (ST5) is a three micro-satellite constellation deployed into a 300 x 4500 km, dawn-dusk, sun-synchronous polar orbit from March 22 to June 21, 2006, for technology validations. In this paper, we present a study of the temporal variability of field-aligned currents using multi-point magnetic field measurements from ST5. The data demonstrate that meso-scale current structures are commonly embedded within large-scale field-aligned current sheets. The meso-scale current structures are very dynamic with highly variable current density and/or polarity in time scales of approximately 10 min. They exhibit large temporal variations during both quiet and disturbed times in such time scales. On the other hand, the data also shown that the time scales for the currents to be relatively stable are approximately 1 min for meso-scale currents and approximately 10 min for large scale current sheets. These temporal features are obviously associated with dynamic variations of their particle carriers (mainly electrons) as they respond to the variations of the parallel electric field in auroral acceleration region. The characteristic time scales for the temporal variability of meso-scale field-aligned currents are found to be consistent with those of auroral parallel electric field.