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A derivation of the Fokker-Planck equation, based on the central limit theorem, is presented which clearly illustrates the conditions for its validity. It is reiterated that previous use of the Fokker-Planck equation in cosmic-ray transport is correct. Higher-order effects associated with magnetic mirroring and field line random walk at low energies are discussed heuristically.
Applying the parabolic approximation, the equations for two-frequency symmetric and antisymmetric mutual intensity functions for waves propagating through a random medium are derived, including the multiple scattering effects. These functions are applied to derive the general formulas for the covariance functions of narrow-band pulses. They are used to compute the signal intensities for pulse trains passing through an ionospheric irregularity slab.
A multiple high order derivative spectroscopy technique has been developed for deriving wavelength positions, half widths, and heights of absorption bands in reflectance spectra. The technique is applicable to laboratory spectra as well as medium resolution (100-200/cm) telescope or spacecraft spectra with moderate (few percent) noise. The technique permits absorption band positions to be detected with an accuracy of better than 3%, and often better than 1%. The high complexity of radiative transfer processes in diffusely reflected spectra can complicate the determination of absorption band positions. Continuum reflections, random illumination geometries within the material, phase angle effects, composite overlapping bands, and calibration uncertainties can shift apparent band positions by 20% from their actual positions or mask them beyond detection. Using multiple high order derivative analysis, effects of scattering continua, phase angle, and calibration (smooth features) are suppressed. Inflection points that characterize the positions and half widths of constituent bands are enhanced by the process and directly detected with relatively high sensitivity.
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 recently developed storm electrification model (SEM) is used to investigate the operating environment of the F-106 airplane during the NASA Storm Hazards Project. The model is 2-D, time dependent and uses a bulkwater microphysical parameterization scheme. Electric charges and fields are included, and the model is fully coupled dynamically, microphysically and electrically. One flight showed that a high electric field was developed at the aircraft's operating altitude (28 kft) and that a strong electric field would also be found below 20 kft; however, this low-altitude, high-field region was associated with the presence of small hail, posing a hazard to the aircraft. An operational procedure to increase the frequency of low-altitude lightning strikes was suggested. To further the understanding of lightning within the cloud environment, a parameterization of the lightning process was included in the SEM. It accounted for the initiation, propagation, termination, and charge redistribution associated with an intracloud discharge. Finally, a randomized lightning propagation scheme was developed, and the effects of cloud particles on the initiation of lightning investigated.
Two hybrid infrared (IR) detector arrays of antimony-doped silicon (Si:Sb) were produced and tested to evaluate their potential for use in low-background IR astronomy applications. The format of the arrays is 58 x 62 elements, with 76 micron-square pixels. A random-access, switched metal-oxide semiconductor field effect transistor (MOSFET) silicon multiplexer is used to read out the array elements. Reduced-background tests of signal, noise, and noise equivalent power were conducted over the temperature range 3.2 to 12 K. The arrays were found to have good sensitivity and good uniformity.
Report describes experimental and computer-simulation study of multiple-bit errors caused by impingement of single energetic ions on 256-Kb dynamic random-access memory (DRAM) integrated circuit. Studies illustrate effects of different mechanisms for transport of charge from ion tracks to various elements of integrated circuits. Shows multiple-bit errors occur in two different types of clusters about ion tracks causing them.
Simulated annealing is used to solve a minimum fuel trajectory problem in the space station environment. The environment is special because the space station will define a multivehicle environment in space. The optimization surface is a complex nonlinear function of the initial conditions of the chase and target crafts. Small permutations in the input conditions can result in abrupt changes to the optimization surface. Since no prior knowledge about the number or location of local minima on the surface is available, the optimization must be capable of functioning on a multimodal surface. It was reported in the literature that the simulated annealing algorithm is more effective on such surfaces than descent techniques using random starting points. The simulated annealing optimization was found to be capable of identifying a minimum fuel, two-burn trajectory subject to four constraints which are integrated into the optimization using a barrier method. The computations required to solve the optimization are fast enough that missions could be planned on board the space station. Potential applications for on board planning of missions are numerous. Future research topics may include optimal planning of multi-waypoint maneuvers using a knowledge base to guide the optimization, and a study aimed at developing robust annealing schedules for potential on board missions.
Three major additions or modifications were made to the Mars Global Reference Atmospheric Model (Mars-GRAM): (1) in addition to the interactive version, a new batch version is available, which uses NAMELIST input, and is completely modular, so that the main driver program can easily be replaced by any calling program, such as a trajectory simulation program; (2) both the interactive and batch versions now have an option for treating local-scale dust storm effects, rather than just the global-scale dust storms in the original Mars-GRAM; and (3) the Zurek wave perturbation model was added, to simulate the effects of tidal perturbations, in addition to the random (mountain wave) perturbation model of the original Mars-GRAM. A minor modification has also been made which allows heights to go below local terrain height and return realistic pressure, density, and temperature (not the surface values) as returned by the original Mars-GRAM. This feature will allow simulations of Mars rover paths which might go into local valley areas which lie below the average height of the present, rather coarse-resolution, terrain height data used by Mars-GRAM. Sample input and output of both the interactive and batch version of Mars-GRAM are presented.
Three major additions or modifications were made to the Mars Global Reference Atmospheric Model (Mars-GRAM): (1) in addition to the interactive version, a new batch version is available, which uses NAMELIST input, and is completely modular, so that the main driver program can easily be replaced by any calling program, such as a trajectory simulation program; (2) both the interactive and batch versions now have an option for treating local-scale dust storm effects, rather than just the global-scale dust storms in the original Mars-GRAM; and (3) the Zurek wave perturbation model was added, to simulate the effects of tidal perturbations, in addition to the random (mountain wave) perturbation model of the original Mars-GRAM. A minor modification was also made which allows heights to go 'below' local terrain height and return 'realistic' pressure, density, and temperature, and not the surface values, as returned by the original Mars-GRAM. This feature will allow simulations of Mars rover paths which might go into local 'valley' areas which lie below the average height of the present, rather coarse-resolution, terrain height data used by Mars-GRAM. Sample input and output of both the interactive and batch versions of Mars-GRAM are presented.
Passive depth and displacement map determinations have become an important part of computer vision processing. Applications that make use of this type of information include autonomous navigation, robotic assembly, image sequence compression, structure identification, and 3-D motion estimation. With the reliance of such systems on visual image characteristics, a need to overcome image degradations, such as random image-capture noise, motion, and quantization effects, is clearly necessary. Many depth and displacement estimation algorithms also introduce additional distortions due to the gradient operations performed on the noisy intensity images. These degradations can limit the accuracy and reliability of the displacement or depth information extracted from such sequences. Recognizing the previously stated conditions, a new method to model and estimate a restored depth or displacement field is presented. Once a model has been established, the field can be filtered using currently established multidimensional algorithms. In particular, the reduced order model Kalman filter (ROMKF), which has been shown to be an effective tool in the reduction of image intensity distortions, was applied to the computed displacement fields. Results of the application of this model show significant improvements on the restored field. Previous attempts at restoring the depth or displacement fields assumed homogeneous characteristics which resulted in the smoothing of discontinuities. In these situations, edges were lost. An adaptive model parameter selection method is provided that maintains sharp edge boundaries in the restored field. This has been successfully applied to images representative of robotic scenarios. In order to accommodate image sequences, the standard 2-D ROMKF model is extended into 3-D by the incorporation of a deterministic component based on previously restored fields. The inclusion of past depth and displacement fields allows a means of incorporating the temporal information into the restoration process. A summary on the conditions that indicate which type of filtering should be applied to a field is provided.
A transfer matrix approach to the analysis of the dynamics of mistuned bladed disks is presented. The study focuses on mono-coupled systems, in which each blade is coupled to its two neighboring blades, and bi-coupled systems, where each blade is coupled to its four nearest neighbors. Transfer matrices yield the free dynamics, both the characteristic free wave and the normal modes - in closed form for the tuned assemblies. Mistuned assemblies are represented by random transfer matrices and an examination of the effect of mistuning on harmonic wave propagation yields the localization factor - the average rate of spatial wave amplitude decay per blade - in the mono-coupled assembly. Based on a comparison of the wave propagation characteristics of the mono- and bi-coupled assemblies, important conclusions are drawn about the effect of the additional coupling coordinate on the sensitivity to mistuning and the strength of mode localization predicted by a mono-coupled analysis.
In assessing the reliability of a space nuclear propulsion system (SNPS) nozzle, uncertainties associated with the following design parameters were considered: geometry, boundary conditions, material behavior, and thermal and pressure loads. A preliminary assessment of the reliability was performed using NESSUS (Numerical Evaluation of Stochastic Structures Under Stress), a finite-element computer code developed at the NASA Lewis Research Center. The sensitivity of the nozzle reliability to the uncertainties in the random variables was quantified. With respect to the effective stress, preliminary results showed that the nozzle spatial geometry uncertainties have the most significant effect at low probabilities whereas the inner wall temperature has the most significant effect at higher probabilities.
Two experiments were carried out to investigate the consequences of exposure to proton radiation, such as might occur for astronauts during space flight. C57BL/6 mice were exposed, either with or without 15-g/cm2 aluminum shielding, to 0-, 3-, or 4-Gy proton irradiation mimicking features of a solar particle event. Irradiation produced transient direct deficits in open-field exploratory behavior and acoustic startle habituation. Rotorod performance at 18 rpm was impaired by exposure to proton radiation and was impaired at 26 rpm, but only for mice irradiated with shielding and at the 4-Gy dose. Long-term (>2 weeks) indirect deficits in open-field activity appeared as a result of impaired experiential encoding immediately following exposure. A 2-week recovery prior to testing decreased most of the direct effects of exposure, with only rotorod performance at 26 rpm being impaired. These results suggest that the performance deficits may have been mediated by radiation damage to hippocampal, cerebellar, and possibly, forebrain dopaminergic function.
Optical observations of rotating space debris near GEO contain important information on size, shape, composition, and rotational states, but these aspects are difficult to extract due to data limitations and the high number of degrees of freedom in the modeling process. For tri-axial rigid debris objects created by satellite fragmentations, the most likely initial rotation state has a large component of initial angular velocity directed along the intermediate axis of inertia, leading to large angular reorientations of the body on the timescale of the rotation period. This lends some support to the simplest possible interpretation of light curves -- that they represent sets of random orientations of the objects of study. However, effects of internal friction and solar radiation are likely to cause significant modification of rotation states within a time as short as a few orbital periods. In order to examine the rotational dynamics of debris objects under the influences of these effects, a set of seven first-order coupled equations of motion were assembled in state form: three are Euler equations describing the rates of change of the components of angular velocity in the body frame, and four describe the rates of change of the components of the unit quaternion. Quaternions are a four-dimensional extension of complex numbers that form a seamless, singularity-free representation of body orientation on S3. The Euler equations contain explicit terms describing torque from solar radiation in terms of spherical harmonics, and terms representing effects of a prescribed rate of internal friction. Numerical integrations of these equations of motion are being performed, and results will be presented. Initial tests show that internal friction without solar radiation torque leads to rotation about the maximum principal axis of inertia, as required, and solar radiation torque is expected to lead to spin-up of objects. Because the axis of maximum rotational inertia tends to be roughly coincident with the normal to the largest projected cross-sectional area, internal friction is expected to lead to reduced variation of light curve amplitudes at a given phase angle, but a large dependence of the same on phase angle. At a given phase angle, databases are generated which contain reflected intensities for comprehensive sets of equally-likely orientations, represented as unit quaternions. When projected onto three dimensions (S2) and color-coded by intensity, the set is depicted as points within a solid, semi-transparent unit sphere, within which all possible reflected intensities for an object at a given phase angle may be inspected simultaneously. Rotational sequences are represented by trajectories through the sphere. Databases are generated for each of a set of phase angles separately, forming a comprehensive dataset of reflected intensities spanning all object orientations and solar phase angles. Symmetries in the problem suggest that preferred rotation states are likely, defined relative to the object-sun direction in inertial space and relative to the maximum principal axis of inertia in the body coordinate system. Such rotation states may greatly simplify the problem of light curve interpretation by reducing the number of degrees of freedom in the problem.
Analysis of more than 36 years of time series of seven parameters measured in the NSO/AFRL/Sac Peak K-line monitoring program elucidates five elucidates five components of the variation: (1) the solar cycle (period approx. 11 years), (2) quasi-periodic variations (periods approx 100 days), (3) a broad band stochastic process (wide range of periods), (4) rotational modulation, and (5) random observational errors. Correlation and power spectrum analyses elucidate periodic and aperiodic variation of the chromospheric parameters. Time-frequency analysis illuminates periodic and quasi periodic signals, details of frequency modulation due to differential rotation, and in particular elucidates the rather complex harmonic structure (1) and (2) at time scales in the range approx 0.1 - 10 years. These results using only full-disk data further suggest that similar analyses will be useful at detecting and characterizing differential rotation in stars from stellar light-curves such as those being produced by NASA's Kepler observatory. Component (3) consists of variations over a range of timescales, in the manner of a 1/f random noise process. A timedependent Wilson-Bappu effect appears to be present in the solar cycle variations (1), but not in the stochastic process (3). Component (4) characterizes differential rotation of the active regions, and (5) is of course not characteristic of solar variability, but the fact that the observational errors are quite small greatly facilitates the analysis of the other components. The recent data suggest that the current cycle is starting late and may be relatively weak. The data analyzed in this paper can be found at the National Solar Observatory web site http://nsosp.nso.edu/cak_mon/, or by file transfer protocol at ftp://ftp.nso.edu/idl/cak.parameters.
Ground-based reception of optical signals from space suffers from degradation of the optical phase-front caused by atmospheric turbulence, leading to a reduction in the effective diameter of the receiving aperture and to random fluctuations of the point spread function in the focal plane.
The Loss of Coolant Accident (LOCA) is a design basis accident that is included as part of the safety analysis of nuclear power plants. As the nuclear industry desires to increase the cycle length and discharge burnup of existing nuclear power plants they must demonstrate safe operation during a LOCA on high burnup fuel. During a LOCA transient on high burnup fuel rods, the rods may undergo a process known as fuel fragmentation, relocation, and dispersal (FFRD). To permit dispersal, the cladding encapsulating the fuel must rupture with an opening size large enough to allow the fragmented fuel particles to release. Current licensing tools used by industry and the United States Nuclear Regulatory Commission are limited in geometric fidelity and materials that can be analyzed. These simulation tools generally employ a quasi-two-dimensional (1.5D or Layered1D) or 2D-RZ axisymmetric geometric representations exclusively. While a valid approach under some instances, there are times when important physics have an asymmetric behavior in the fuel rod. Examples include fuel fragmentation, thermal-hydraulic boundary conditions, and cladding rupture, all of which are important for LOCA analysis. As industry pursues burnup extensions it must be demonstrated that fuel dispersal can be mitigated or eliminated. To do this, an understanding of the rupture opening after cladding failure is required. This work presents the development of a model for predicting the size and location of the rupture opening in failed fuel rods during LOCA conditions using advanced modeling and simulation tools. In order to supply the rupture model with appropriate boundary conditions, improvements to fuel fragmentation, axial relocation and oxidation modeling were required. First, the eXtended Finite Element Method (XFEM) is used to mechanistically predict the number of fuel fragments that form due to material strength randomization, criteria for strength randomization, mesh density, power ramping rates and irradiation effects. These predictions with associated uncertainty were compared to empirical correlations developed for UO2 verifying that they can be used with increased confidence in subsequent axial relocation analyses. Secondly, a new first-of-its-kind Layered2D computational framework was developed that provides the ability to apply azimuthally varying boundary conditions while providing discrete layers to track fuel movement during the LOCA. An existing fuel axial relocation model developed for Layered1D was extended to work within the Layered2D framework. A large sensitivity study was performed on the initial version of the model to identify modeling parameters of particular importance, with the emissivity used for radiation after blowdown being the primary source of uncertainty. Then, a simplistic approach to incorporate mechanical degradation of the cladding due to oxidation was also developed to investigate the impact of reduced cladding thickness on predictions of the time to failure of cladding tubes. It was found that the cladding will typically rupture prior to a reduction in thickness that is sufficient to impact the rupture behavior. A model was then developed for predicting cladding rupture that transfers the cladding surface temperatures, rod internal and external pressures, fast neutron fluence, and fast neutron flux from a more detailed Layered1D, Layered2D, or 2D-RZ analysis to a 3D cladding only analysis. Comparisons of the rupture model to a few experiments indicate reasonable predictions. The rupture model was then applied to two accident tolerant fuel concepts (FeCrAl and Cr-coated Zircaloy) where it predicted that both ATF concepts would have smaller rupture openings and delayed rupture times than the standard Zircaloy-4 cladding material under identical loading conditions.