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The field of stochastic stability is surveyed, with emphasis on the invariance theorems and their potential application to systems with randomly varying coefficients. Some of the basic ideas are reviewed, which underlie the stochastic Liapunov function approach to stochastic stability. The invariance theorems are discussed in detail.
Cells and molecules can be purified by partitioning between the two immiscible liquid phases formed by aqueous solutions of poly/ethylene glycol and dextran. Such purification can be more selective, higher yielding, and less destructive to sensitive biological materials than other available techniques. Earth's gravitational field is a hindering factor as it causes sedimentation of particles to be purified and shear-induced particle randomization. The present proposal is directed toward developing new instrumentation for performing phase partitioning both on Earth and in microgravity.
A software tool for estimating cross-boresight error of a star tracker combined with an inertial measurement unit (IMU) was developed to support trade studies for the Integrated Radio and Optical Communication project (iROC) at the National Aeronautics and Space Administration Glenn Research Center. Typical laser communication systems, such as the Lunar Laser Communication Demonstration (LLCD) and the Laser Communication Relay Demonstration (LCRD), use a beacon to locate ground stations. iROC is investigating the use of beaconless precision laser pointing to enable laser communication at Mars orbits and beyond. Precision attitude knowledge is essential to the iROC mission to enable high-speed steering of the optical link. The preliminary concept to achieve this precision attitude knowledge is to use star trackers combined with an IMU. The Star Tracker Accuracy (STAcc) software was developed to rapidly assess the capabilities of star tracker and IMU configurations. STAcc determines the overall cross-boresight error of a star tracker with an IMU given the characteristic parameters: quantum efficiency, aperture, apparent star magnitude, exposure time, field of view, photon spread, detector pixels, spacecraft slew rate, maximum stars used for quaternion estimation, and IMU angular random walk. This paper discusses the supporting theory used to construct STAcc, verification of the program and sample results.
Nonlinear acoustic propagation of sonic booms in the atmospheric boundary layer is considered in the context of a one-way solution to a third order wave equation. A split-step approach is utilized to compute different physical effects efficiently. Unlike previous approaches, the diffraction effects are computed exactly in the forward direction with no restriction on the angle of propagation. This results in more accurate modelling of sonic boom near the carpet edge. Heterogenous flow effects are incorporated with a wide-angle parabolic approximation. Nonlinear propagation is computed with a Burgers-Hayes method. Turbulence in the medium is constructed by the method of random Fourier modes. The turbulence spectra are constructed using an altitude dependent 3-dimensional von Karman spectrum. The turbulence field is considered frozen, as the eddy turnover time in the atmospheric boundary layer is generally much larger than the propagation time of the acoustic wave. Comparisons with benchmark predictions from the PCBoom software are conducted. The benchmark cases provide insight into the accuracy of the current prediction code for non-turbulent atmospheres. Future work is discussed regarding the prediction of shaped booms, boundary conditions, and predictions near the lateral extent of the boom carpet where previous approaches fail to capture the diffraction effects.
The Hall Effect Rocket with Magnetic Shielding (HERMeS) is a 12.5 kW magnetically shielded Hall thruster presently under development for deep-space missions. A development model HERMeS thruster, TDU-2, with borosilicate channel walls, has successfully undergone proto-qualification testing including random vibration and thermal-vacuum, demonstrating the thruster can survive critical launch and operational environmental requirements. The three-axis random vibrational tests were performed with the thruster body mounted directly to the shaker table using a modified loading schedule to compensate for the vibration isolation dampers under design for the flight thruster. Initial random vibration testing revealed issues with fragmentation of magnetic coil potting material and thruster spool mount fabrication weaknesses that were addressed with an alternate potting material and fabrication revisions that were then successfully retested with an additional round of random vibration tests. Thermal-vacuum testing involved three cycles of full-power 600 V 12.5 kW thruster operation from -121°C to +373°C which included eight hours at peak temperature as well as a hot restart. A thermal model of the test configuration was developed and validated with the experiment results within an average difference of 5°C. Before and after the random vibrational and thermal-vacuum tests, the thruster performance, plasma plume, thrust vector angle, discharge characteristics, and magnetic field profile were measured. The thruster performance, magnetic field, and most other parameters remained invariant throughout the environmental testing campaign. During the thermal testing, an increase in the discharge oscillation amplitude of 11% was observed as well as subtle thrust vector changes of ±0.2° as the thruster warmed from -121°C to +373°C.
Flow fields involving turbulent flames in premixed gases under a variety of conditions are modeled by the use of a numerical technique based on the random vortex method to solve the Navier-Stokes equations and a flame propagation algorithm to trace the motion of the front and implement the Huygens principle, both due to Chorin. A successive over-relaxation hybrid method is applied to solve the Euler equation for flows in an arbitrarily shaped domain. The method of images, conformal transformation, and the integral-equation technique are also used to treat flows in special cases, according to their particular requirements. Salient features of turbulent flame propagation in premixed gases are interpreted by relating them to the aerodynamic properties of the flow field. Included among them is the well-known cellular structure of flames stabilized by bluff bodies, as well as the formation of the characteristic tulip shape of flames propagating in ducts. In its rudimentary form, the mechanism of propagation of a turbulent flame is shown to consist of: (1) rotary motion of eddies at the flame front, (2) self-advancement of the front at an appropriate normal burning speed, and (3) dynamic effects of expansion due to exothermicity of the combustion reaction. An idealized model is used to illustrate these fundamental mechanisms and to investigate basic aerodynamic features of flames in premixed gases. The case of a confined flame stabilized behind a rearward-facing step is given particular care and attention. Solutions are shown to be in satisfactory agreement with experimental results, especially with respect to global properties such as the average velocity profiles and reattachment length.
The consistency of cloud top temperature (Tc) and effective cloud fraction (f) retrieved by the Atmospheric Infrared Sounder (AIRS)/Advanced Microwave Sounding Unit (AMSU) observation suite and the Moderate Resolution Imaging Spectroradiometer (MODIS) on the EOS-Aqua platform are investigated. Collocated AIRS and MODIS TC and f are compared via an 'effective scene brightness temperature' (Tb,e). Tb,e is calculated with partial field of view (FOV) contributions from TC and surface temperature (TS), weighted by f and 1-f, respectively. AIRS reports up to two cloud layers while MODIS reports up to one. However, MODIS reports TC, TS, and f at a higher spatial resolution than AIRS. As a result, pixel-scale comparisons of TC and f are difficult to interpret, demonstrating the need for alternatives such as Tb,e. AIRS-MODIS Tb,e differences ((Delta)Tb,e) for identical observing scenes are useful as a diagnostic for cloud quantity comparisons. The smallest values of DTb,e are for high and opaque clouds, with increasing scatter in (Delta)Tb,e for clouds of smaller opacity and lower altitude. A persistent positive bias in DTb,e is observed in warmer and low-latitude scenes, characterized by a mixture of MODIS CO2 slicing and 11-mm window retrievals. These scenes contain heterogeneous cloud cover, including mixtures of multilayered cloudiness and misplaced MODIS cloud top pressure. The spatial patterns of (Delta)Tb,e are systematic and do not correlate well with collocated AIRS-MODIS radiance differences, which are more random in nature and smaller in magnitude than (Delta)Tb,e. This suggests that the observed inconsistencies in AIRS and MODIS cloud fields are dominated by retrieval algorithm differences, instead of differences in the observed radiances. The results presented here have implications for the validation of cloudy satellite retrieval algorithms, and use of cloud products in quantitative analyses.
Recent studies have suggested that humans cannot estimate their direction of forward translation (heading) from the resulting retinal motion (flow field) alone when rotation rates are higher than approximately 1 deg/sec. It has been argued that either oculomotor or static depth cues are necessary to disambiguate the rotational and translational components of the flow field and, thus, to support accurate heading estimation. We have re-examined this issue using visually simulated motion along a curved path towards a layout of random points as the stimulus. Our data show that, in this curvilinear motion paradigm, five of six observers could estimate their heading relatively accurately and precisely (error and uncertainty < approximately 4 deg), even for rotation rates as high as 16 deg/sec, without the benefit of either oculomotor or static depth cues signaling rotation rate. Such performance is inconsistent with models of human self-motion estimation that require rotation information from sources other than the flow field to cancel the rotational flow.
Ionosphere as anisotropic dissipative medium where charged particles random thermal motion acts as thermal radiation source, noting relation between driven AC conduction current density and applied AC electric field intensity
The existence in the lunar atmosphere of helium, neon, argon, and possibly molecular hydrogen has been confirmed by the Apollo 17 mass spectrometer. The observed helium concentrations and distribution agree closely with model predictions for a non-condensable gas based on a solar wind source, thermal escape and a Monte Carlo random walk calculated longitudinal distribution. Heavier gases are lost by photoionization and subsequent sweeping away by the solar wind electric field. The observed nighttime neon concentration of 80,000 molecules per cu cm is consistent with expected amounts. Argon, however, is adsorbed on the lunar surface late at night when the surface temperature is lowest. It shows the expected predawn enhancement exhibited by condensable gases released into the atmosphere at the sunrise terminator. Hydrogen appears to exist in the molecular rather than atomic state. Its observed concentration is less than a factor of 3 higher than that predicted by a model similar to that used for helium.
This paper presents some exact solutions of problems in random function theory for the purpose of testing the validity of an approximate method known variously in the many different fields of its application as first order smoothing theory, first order cumulant discard, quasilinear theory, or the adiabatic approximation. The hydromagnetic dynamo equations are used here, as particularly appropriate for such an investigation. The calculations show that in one case the exact and approximate solutions agree. In the other case the approximate solution is wrong. Hence, in the absence of a general criterion for validity, a result based on first order smoothing theory is a conjecture rather than a fact. This impacts strongly on much of the recent work on hydromagnetic dynamos.
The polarized reflectance factor, Rq, of sorghum (Sorghum bicolor, L.) leaves from field-grown plants was measured in situ in the summers of 1983 and 1984. In 1983, three leaves of two randomly selected plants were measured at 2-week intervals. The value of Rq varied, depending on leaf and day of measurement. Measured values of Rq for the adaxial leaf surface ranged from 16 to 53; for the abaxial leaf surface the values ranged from 28 to 69. In 1984, measurements consisted of repeated observations made on the same leaf at biweekly intervals. The values of Rq from the adaxial leaf surface ranged from 26 to 38. Values of Rq from the abaxial leaf surface increased throughout the season, from 16 to 45. Differences in Rq were attributed to changes in surface details of the leaf.
The National Meteorological Center Barotropic-Mesh Model has been used to test a statistical correction procedure, designated as M-II, that was developed in Schemm et al. (1981). In the present application, statistical corrections at 12 h resulted in significant reductions of the mean-square errors of both vorticity and the Laplacian of thickness. Predictions to 48 h demonstrated the feasibility of applying corrections at every 12 h in extended forecasts. In addition to these improvements, however, the statistical corrections resulted in a shift of error from smaller to larger-scale motions, improving the smallest scales dramatically but deteriorating the largest scales. This effect is shown to be a consequence of randomization of the residual errors by the regression equations and can be corrected by spatially high-pass filtering the field of corrections before they are applied.
A model of the inner portions of astrophysical jets is constructed in which a relativistic electron beam is injected from the central engine into the jet plasma. This beam drives electrostatic plasma wave turbulence, which leads to the collective emission of electromagnetic waves. The emitted waves are beamed in the direction of the jet axis, so that end-on viewing of the jet yields an extremely bright source (BL Lacertae object). The relativistic electron beam may also drive long-wavelength electromagnetic plasma instabilities (firehose and Kelvin-Helmholtz) that jumble the jet magnetic field lines. After a sufficient distance from the core source, these instabilities will cause the beamed emission to point in random directions and the jet emission can then be observed from any direction relative to the jet axis. This combination of effects may lead to the gap turn-on of astrophysical jets. The collective emission model leads to different estimates for energy transport and the interpretation of radio spectra than the conventional incoherent synchrotron theory.
It is shown how the genus per unit volume of isodensity surfaces in general nonlinear universes is related to the entire hierarchy of correlation functions. The general relation between the correlation function, the probability distribution of densities at several points, and the probability distributions of density and its derivatives at a point are given. Formulas for the area and genus per unit volume of isodensity surfaces are presented. As an application, after first reviewing the case of Gaussian fields, analytic results are reported for one particular example of a thoroughly nonlinear universe, Mandelbrot's Rayleigh-Levy random-walk fractal. While this fractal bears little resemblance to the real universe of galaxies, it possesses the singular and theoretically interesting property that in it cluster-cluster correlations are identically equal to galaxy-galaxy correlations to all orders.
In nonvolatile random-access memory (RAM) circuits of a proposed type, digital data would be stored in analog form in ferroelectric field-effect transistors (FFETs). This type of memory circuit would offer advantages over prior volatile and nonvolatile types: In a conventional complementary metal oxide/semiconductor static RAM, six transistors must be used to store one bit, and storage is volatile in that data are lost when power is turned off. In a conventional dynamic RAM, three transistors must be used to store one bit, and the stored bit must be refreshed every few milliseconds. In contrast, in a RAM according to the proposal, data would be retained when power was turned off, each memory cell would contain only two FFETs, and the cell could store multiple bits (the exact number of bits depending on the specific design). Conventional flash memory circuits afford nonvolatile storage, but they operate at reading and writing times of the order of thousands of conventional computer memory reading and writing times and, hence, are suitable for use only as off-line storage devices. In addition, flash memories cease to function after limited numbers of writing cycles. The proposed memory circuits would not be subject to either of these limitations. Prior developmental nonvolatile ferroelectric memories are limited to one bit per cell, whereas, as stated above, the proposed memories would not be so limited. The design of a memory circuit according to the proposal must reflect the fact that FFET storage is only partly nonvolatile, in that the signal stored in an FFET decays gradually over time. (Retention times of some advanced FFETs exceed ten years.) Instead of storing a single bit of data as either a positively or negatively saturated state in a ferroelectric device, each memory cell according to the proposal would store two values. The two FFETs in each cell would be denoted the storage FFET and the control FFET. The storage FFET would store an analog signal value, between the positive and negative FFET saturation values. This signal value would represent a numerical value of interest corresponding to multiple bits: for example, if the memory circuit were designed to distinguish among 16 different analog values, then each cell could store 4 bits. Simultaneously with writing the signal value in the storage FFET, a negative saturation signal value would be stored in the control FFET. The decay of this control-FFET signal from the saturation value would serve as a model of the decay, for use in regenerating the numerical value of interest from its decaying analog signal value. The memory circuit would include addressing, reading, and writing circuitry that would have features in common with the corresponding parts of other memory circuits, but would also have several distinctive features. The writing circuitry would include a digital-to-analog converter (DAC); the reading circuitry would include an analog-to-digital converter (ADC). For writing a numerical value of interest in a given cell, that cell would be addressed, the saturation value would be written in the control FFET in that cell, and the non-saturation analog value representing the numerical value of interest would be generated by use of the DAC and stored in the storage FFET in that cell. For reading the numerical value of interest stored in a given cell, the cell would be addressed, the ADC would convert the decaying control and storage analog signal values to digital values, and an associated fast digital processing circuit would regenerate the numerical value from digital values.
Low Earth orbit is usually considered a relatively benign environment for internal charging threats due to the low flux of penetrating electrons with energies of a few MeV that are encountered over an orbit. There are configurations, however, where insulators and ungrounded conductors used on the outside of a spacecraft hull may charge when exposed to much lower energy electrons of some 100's keV in a process that is better characterized as internal charging than surface charging. For example, the minimal radiation shielding afforded by thin thermal control materials such as metalized polymer sheets (e.g., aluminized Kapton or Mylar) and multilayer insulation may allow electrons of 100's of keV to charge underlying materials. Yet these same thermal control materials protect the underlying insulators and ungrounded conductors from surface charging currents due to electrons and ions at energies less than a few keV as well as suppress the photoemission, secondary electron, and backscattered electron processes associated with surface charging. We investigate the conditions required for this low Earth orbit "internal charging" to occur and evaluate the environments for which the process may be a threat to spacecraft. First, we describe a simple one-dimensional internal charging model that is used to compute the charge accumulation on materials under thin shielding. Only the electron flux that penetrates exposed surface shielding material is considered and we treat the charge balance in underlying insulation as a parallel plate capacitor accumulating charge from the penetrating electron flux and losing charge due to conduction to a ground plane. Charge dissipation due to conduction can be neglected to consider the effects of charging an ungrounded conductor. In both cases, the potential and electric field is computed as a function of time. An additional charge loss process is introduced due to an electrostatic discharge current when the electric field reaches a prescribed breakdown strength. For simplicity, the amount of charge lost in the discharge is treated as a random percentage of the total charge between a set maximum and minimum amount so a user can consider partial discharges of insulating materials (small loss of charge) or arcing from a conductor (large loss of charge). We apply the model to electron flux measurements from the NOAA-19 spacecraft to demonstrate that charging can reach levels where electrostatic discharges occur and estimate the magnitude of the discharge.
Cheatgrass (Bromus tectorum) is a species of concern across the western United States as it has the potential to outcompete native plant species, reduce biodiversity, and diminish nutrient availability for ungulates. Furthermore, because cheatgrass can quickly dominate disturbed landscapes it has the potential to exacerbate wildfire risk by increasing fuel loads. In 2020, the Cameron Peak fire burned more than 200,000 acres on the Arapaho and Roosevelt National Forests in Colorado. These issues are of imminent concern for our partners at the Forest Service (USFS), as they are tasked with wildfire risk and invasive species mitigation. Disturbances such as wildfires can substantially increase the rate and extent of cheatgrass spread. Current cheatgrass mitigation methods rely on field crews to physically locate cheatgrass on the landscape, which takes time, money, and extensive manpower. Here, we developed two Random Forest models within the Software for Assisted Habitat Modeling (SAHM) using remote sensing predictors derived from Sentinel-2 MultiSpectral Instrument (MSI) and Shuttle Radar Topography Mission (SRTM). The first model identified suitable cheatgrass habitat while the other detected cheatgrass presence during the 2021 growing season. Topographic variables were found to be the most important in driving the habitat suitability model. Cheatgrass detection was also found to be possible within a short timespan with limited imagery surrounding a phenological shift of the plant. Maps produced from these models provide natural resource managers the ability to implement early detection and rapid response to prevent the spread of cheatgrass to new locations.