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At least 91 records · Page 5

Speckle in the diffraction patterns of Hendricks-Teller and icosahedral glass models

It is shown that the X-ray diffraction patterns from the Hendricks-Teller model for layered systems and the icosahedral glass models for the icosahedral phases show large fluctuations between nearby scattering wave vectors and from sample to sample, that are quite analogous to laser speckle. The statistics of these fluctuations are studied analytically for the first model and via computer simulations for the second. The observability of these effects is discussed briefly.

Garg, Anupam↗

Proceedings of the Workshop on Change of Representation and Problem Reformulation

The proceedings of the third Workshop on Change of representation and Problem Reformulation is presented. In contrast to the first two workshops, this workshop was focused on analytic or knowledge-based approaches, as opposed to statistical or empirical approaches called 'constructive induction'. The organizing committee believes that there is a potential for combining analytic and inductive approaches at a future date. However, it became apparent at the previous two workshops that the communities pursuing these different approaches are currently interested in largely non-overlapping issues. The constructive induction community has been holding its own workshops, principally in conjunction with the machine learning conference. While this workshop is more focused on analytic approaches, the organizing committee has made an effort to include more application domains. We have greatly expanded from the origins in the machine learning community. Participants in this workshop come from the full spectrum of AI application domains including planning, qualitative physics, software engineering, knowledge representation, and machine learning.

Lowry, Michael R.↗

Accuracy of trace element determinations in alternate fuels

A review of the techniques used at Lewis Research Center (LeRC) in trace metals analysis is presented, including the results of Atomic Absorption Spectrometry and DC Arc Emission Spectrometry of blank levels and recovery experiments for several metals. The design of an Interlaboratory Study conducted by LeRC is presented. Several factors were investigated, including: laboratory, analytical technique, fuel type, concentration, and ashing additive. Conclusions drawn from the statistical analysis will help direct research efforts toward those areas most responsible for the poor interlaboratory analytical results.

Greenbauer-Seng, L. A.↗

Estimation of the accuracy of dynamic flight-determined coefficients

This paper discusses means of assessing the accuracy of maximum likelihood parameter estimates obtained from dynamic flight data. The commonly used analytical predictors of accuracy are compared from both statistical and simplified geometric standpoints. Emphasizing practical considerations, such as modeling error, the accuracy predictions are evaluated with real and simulated data. Improved computations of the Cramer-Rao bound to correct large discrepancies caused by colored noise and modeling error are presented. This corrected Cramer-Rao bound is the best available analytical predictor of accuracy. Engineering judgement, aided by such analytical tools, is the final arbiter of accuracy estimation.

Maine, R. E.↗

Noise produced by turbulent flow into a rotor: Theory manual for atmospheric turbulence prediction and mean flow and turbulence contraction prediction

Prediction of helicopter main rotor noise due to ingestion of atmospheric turbulence was analyzed. The analysis combines several different models that describe the fluid mechanics of the turbulence and the ingestion process. Two models, atmospheric turbulence, and mean flow and turbulence contraction were covered. The third model, covered in a separate report, describes the rotor acoustic mode. The method incorporates the atmospheric turbulence model and a rapid distortion turbulence contraction description to determine the statistics of the anisotropic turbulence at the rotor plane. The analytical basis for a module was provided which was incorporated in NASA's ROTONET helicopter noise prediction program. The mean flow and turbulence statistics associated with the atmospheric boundary layer were modeled including effects of atmospheric stability length, wind speed, and altitude. The turbulence distortion process is modeled as a deformation of vortex filaments (which represent the turbulence field) by a mean flow field due to the rotor inflow.

Simonich, J. C.↗

Combined monitoring, decision and control model for the human operator in a command and control desk

A report is given on the ongoing efforts to mode the human operator in the context of the task during the enroute/return phases in the ground based control of multiple flights of remotely piloted vehicles (RPV). The approach employed here uses models that have their analytical bases in control theory and in statistical estimation and decision theory. In particular, it draws heavily on the modes and the concepts of the optimal control model (OCM) of the human operator. The OCM is being extended into a combined monitoring, decision, and control model (DEMON) of the human operator by infusing decision theoretic notions that make it suitable for application to problems in which human control actions are infrequent and in which monitoring and decision-making are the operator's main activities. Some results obtained with a specialized version of DEMON for the RPV control problem are included.

Muralidharan, R.↗

Long-term risk analysis associated with nuclear waste disposal in space

An assessment and verification of previous analytic results on the long term risk of earth reentry for hazardous payloads is presented. The two areas were studied: (1) stability of nominal, near-circular storage orbits in the regions between Venus and earth and between earth and Mars, and (2) probability of earth reentry for off-nominal planet-crossing orbits resulting from deployment system failures. In the first area, numerical integrations of the equations of motion are compared with stability predications based on secular perturbation theory. The agreement is good in terms of the heliocentric distances covered and the general behavior of the orbital history, although certain near-resonance situations can lead to difficulty. In the second area, a Monte Carlo simulation of orbital evolution is used and the results compared with Opik's analytic theory of planetary encounters and collision statistics, with data verified to within a close order-of-magnitude.

Friedlander, A. L.↗

Wind models for the NSTS ascent trajectory biasing for wind load alleviation

New concepts are presented for aerospace vehicle ascent wind profile biasing. The purpose for wind biasing the ascent trajectory is to provide ascent wind loads relief and thus decrease the probability for launch delays due to wind loads exceeding critical limits. Wind biasing trajectories to the profile of monthly mean winds have been widely used for this purpose. The wind profile models presented give additional alternatives for wind biased trajectories. They are derived from the properties of the bivariate normal probability function using the available wind statistical parameters for the launch site. The analytical expressions are presented to permit generalizations. Specific examples are given to illustrate the procedures. The wind profile models can be used to establish the ascent trajectory steering commands to guide the vehicle through the first stage. For the National Space Transportation System (NSTS) program these steering commands are called I-loads.

Smith, O. E.↗

Wind models for the NSTS ascent trajectory biasing for wind load alleviation

New concepts are presented for aerospace vehicle ascent wind profile biasing. The purpose for wind biasing the ascent trajectory is to provide ascent wind loads relief and thus decrease the probability for launch delays due to wind loads exceeding critical limits. Wind biasing trajectories to the the profile of monthly mean winds have been widely used for this purpose. The wind profile models presented give additional alternatives for wind biased trajectories. They are derived from the properties of the bivariate normal probability function using the available wind statistical parameters for the launch site. The analytical expressions are presented to permit generalizations. Specific examples are given to illustrate the procedures. The wind profile models can be used to establish the ascent trajectory steering commands to guide the vehicle through the first stage. For the National Space Transportation System (NSTS) program these steering commands are called I-loads.

Smith, O. E.↗

Potential, velocity, and density fields from sparse and noisy redshift-distance samples - Method

A method for recovering the three-dimensional potential, velocity, and density fields from large-scale redshift-distance samples is described. Galaxies are taken as tracers of the velocity field, not of the mass. The density field and the initial conditions are calculated using an iterative procedure that applies the no-vorticity assumption at an initial time and uses the Zel'dovich approximation to relate initial and final positions of particles on a grid. The method is tested using a cosmological N-body simulation 'observed' at the positions of real galaxies in a redshift-distance sample, taking into account their distance measurement errors. Malmquist bias and other systematic and statistical errors are extensively explored using both analytical techniques and Monte Carlo simulations.

Dekel, Avishai↗

Mathematical and Computational Challenges in Population Biology and Ecosystems Science

Mathematical and computational approaches provide powerful tools in the study of problems in population biology and ecosystems science. The subject has a rich history intertwined with the development of statistics and dynamical systems theory, but recent analytical advances, coupled with the enhanced potential of high-speed computation, have opened up new vistas and presented new challenges. Key challenges involve ways to deal with the collective dynamics of heterogeneous ensembles of individuals, and to scale from small spatial regions to large ones. The central issues-understanding how detail at one scale makes its signature felt at other scales, and how to relate phenomena across scales-cut across scientific disciplines and go to the heart of algorithmic development of approaches to high-speed computation. Examples are given from ecology, genetics, epidemiology, and immunology.

Levin, Simon A.↗

Progressive Failure And Life Prediction of Ceramic and Textile Composites

An engineering approach to predict the fatigue life and progressive failure of multilayered composite and textile laminates is presented. Analytical models which account for matrix cracking, statistical fiber failures and nonlinear stress-strain behavior have been developed for both composites and textiles. The analysis method is based on a combined micromechanics, fracture mechanics and failure statistics analysis. Experimentally derived empirical coefficients are used to account for the interface of fiber and matrix, fiber strength, and fiber-matrix stiffness reductions. Similar approaches were applied to textiles using Repeating Unit Cells. In composite fatigue analysis, Walker's equation is applied for matrix fatigue cracking and Heywood's formulation is used for fiber strength fatigue degradation. The analysis has been compared with experiment with good agreement. Comparisons were made with Graphite-Epoxy, C/SiC and Nicalon/CAS composite materials. For textile materials, comparisons were made with triaxial braided and plain weave materials under biaxial or uniaxial tension. Fatigue predictions were compared with test data obtained from plain weave C/SiC materials tested at AS&M. Computer codes were developed to perform the analysis. Composite Progressive Failure Analysis for Laminates is contained in the code CPFail. Micromechanics Analysis for Textile Composites is contained in the code MicroTex. Both codes were adapted to run as subroutines for the finite element code ABAQUS and CPFail-ABAQUS and MicroTex-ABAQUS. Graphic user interface (GUI) was developed to connect CPFail and MicroTex with ABAQUS.

Xue, David Y.↗

4.32 Billion Year Old Impact Melts at Apollo 14: Dating the Procellarum Basin?

Introduction: Recent work has improved our understanding of lunar crustal structure and basin evolution on the Moon, but its early impact history and implications for solar system dynamics remain poorly established [1,2]. In particular, there is a derth of absolute ages, especially for the period >4.0 Ga, that could be related to basin-forming events. Here we present U-Pb isotopic data for Zr-rich minerals found in impact-melt fragments from Apollo 14 soil sample 14163 that, when combined with previously published data, dates an impact event at 4324±15 Ma. The compositions and ages of these impact-melt fragments provide unique information about the timing of early impact events and the composition of the lunar crust. Results: Fourteen rocklets ranging in size from 1 to 3 mm were extracted from soil 14163. Most are impactmelt rocks with 10-30% clasts of mostly pyroxene and plagioclase (100 to 500 μm) in a crystalline matrix. Textures of the matrix vary from subophitic, formed by intergrowths of 10-20 μm plagioclase and pyroxene crystals, to poikilitic, with plagioclase and pyroxene reaching 20-50 μm size. Some fragments that contain no visible clasts have similar textures are also interpreted as impact-melt rocks. All fragments contain notably large proportions of euhedral to subhedral ilmenite, zircon, apatite/merrillite and less abundant zirconolite and baddeleyite in the melt matrices. These grains often form intricate intergrowths with each other and rock-forming minerals, indicating their crystallization from the melt (Fig. 1). However, some slightly larger (~50 μm) zircon and phosphate grains can be interpreted as relict clasts based on their granular textures and relationships with the surrounding phases (Fig. 1). This implies that zircon and phosphate minerals were present in the target rocks. Some of these grains were profoundly remelted during the impact, which resulted in an oversaturation of the melt in Zr and P and crystallization of new grains of Zrrich minerals and phosphates during melt solidification. The presence of zircon and phosphates indicates that the melts were significantly enriched in KREEP components and ties their provenance to the Procellarum- KREEP Terrane (PKT) [3]. Combined U-Pb zircon data obtained for all fragments form two main clusters on a concordia diagram (Fig. 2), between about 4.3 and 3.9 Ga. Phosphate data mostly concentrate on the younger end of this age range but some analyses are almost as old as the older zircon grains (Fig. 2). Figure 1: Zircon (Zr) and phosphate (Apt; Mer) grains in impact melt fragments from Apollo 14 soil 14161. A-zircon grains crystallized from impact melt; B-phosphate grain inherited from the target; C- granular zircon grains Our interpretation of these data is that all U-rich minerals experienced variable resetting of the U-Pb system, with phosphate, where closure temperature is significantly lower than that in zircon, affected more profoundly by Pb loss than zircon. Our best estimate of the time of formation of zircon and phosphate is based on statistically valid analysis of grains interpreted texturally as grown from the impact melt (Fig. 2). Ten of these analyses define an age of 4324±15 Ma (MSWD=3.0, probability of fit P=0.002). Our best estimate for the time of resetting is obtained by combining data from phosphates that are statistically indistinguishable from 3.9 Ga within the analytical uncertainties. This group is represented by 18 analyses of 15 phosphate grains from different fragments (Fig. 2) and defines an age of 3922±6 Ma (MSWD=1.2, P=0.23). Conversely, a minimum age of the target lithologies, remelted in the impact that produced the rocklets studied here (Fig. 2), can be determined from the five oldest analyses of zircon clasts at 4338±13 Ma (MSWD=1.5, P=0.2), which is indistinguishable from the age of the impact melt within the uncertainties. The obtained ages, combined with textural evidence, imply that the impact melt was formed at 4324±15 Ma, and that it occurred in a zircon-rich target with a minimum age of 4338±13 Ma. Further reworking occurred during a second impact event at 3922±6 Ma. Discussion: The younger age of 3922±6 Ma can be interpreted as the time of the Imbrium impact. The older age of 4324±15 Ma would then be the time of formation of the impact melt, which was then caught in the Imbrium ejecta either at the Apollo 14 landing site or within the target rocks of the Imbrium impact. The presence of abundant accessory phases such as zircons and phosphates is consistent with a substantial KREEP component in the analyzed particles. The current distribution of KREEP on the lunar surface appears to be strongly influenced by Imbrum ejecta [4] so interpretation of the 4.32 Ga age depends in part on assumed structure of the pre-impact crust and distribution of KREEP within the crust. If KREEP was present only in the deep crust at 4.32 Ga, then a basin-scale impact possibly analogous to Imbrium or larger may be necessary to excavate a KREEPy impact melt at this time. However, if KREEPy materials were present closer to the surface perhaps due to redistribution related to Mg-suite magmatism, then smaller impacts might be able to rework KREEPy compositions at shallower depths. The coherence of the data on the particles analysed here suggests a large volume of melt that has been preserved since 4.32 Ga, consistent with a large impact event. Relict zircons and mineral clasts suggests that the igneous crust in the vicinity of this impact was well developed by at least 4.34 Ga, similar to the model age of KREEP and older than the isochron ages of many Mg-suite cumulates [5]. A problem that confronts all lunar sample studies using the current collection is that the pre-Imbrium geology of the PKT (the source of these 4.32 Ga impact melts) is not well constrained. The South Pole-Aitken basin contains regions that are moderately enriched in Th, but its ejecta is Th-poor [6]; therefore these A14 fragments are probably not SPA ejecta. Alternatively, these fragments may represent formation of a hypothesized Procellarum basin [7] although the lack of a clearly defined basin ejecta signature is a potential problem with that interpretation. In any case, they provide a younger limit on the age of lunar differentiation and formation of KREEP within the lunar crust. Figure 2: U-Pb data for zircon and phosphate grains from impact melt fragments. A-all data; B-data used for age calculations. References: [1] Orgel C., Michael G., Fassett C. I., van der Bogert C. H., Riedel C., Kneissl T., and Hiesinger H. (2018) J. Geophys. Res. Planets 123, 748- 762. [2] Evans A. J., Andrews-Hanna J. C., Head J. W., Soderblom J. M., Solomon S. C., and Zuber M. T. (2018) J. Geophys. Planets. 123, 1596-1617. [3] Jolliff, B.L., Gillis, J.J., Haskin, L.A., Korotev, R.L. and Wieczorek, M.A. (2000) J. Geophys. Res: Planets 105, 4197-4216. [4] Haskin L. A. (1998) J. Geophys. Res. Planets 103, 1679-1689. [5] Borg L.E., Gaffney A.M., and Shearer C.K. (2015) MAPS 50, 715-732. [6] Moriarty, D.P., Watkins, R.N., Valencia, S.N., Kendall, J.D., Evans, A.J., Dygert, N. and Petro, N.E. (2021) J. Geophys. Res. Planets 126. [7] Zhu, M.H., Wünnemann, K., Potter, R.W., Kleine, T. and Morbidelli, A. (2019) J. Geophys. Res: Planets 124, 2117-2140

M D Norman↗

A statistical theory for sound radiation and reflection from a duct

A new analytical method is introduced for the study of the sound radiation and reflection from the open end of a duct. The sound is thought of as an aggregation of the quasiparticles-phonons. The motion of the latter is described in terms of the statistical distribution, which is derived from the classical wave theory. The results are in good agreement with the solutions obtained using the Wiener-Hopf technique when the latter is applicable, but the new method is simple and provides straightforward physical interpretation of the problem. Furthermore, it is applicable to a problem involving a duct in which modes are difficult to determine or cannot be defined at all, whereas the Wiener-Hopf technique is not.

Cho, Y. C.↗

Dynamic remapping of parallel computations with varying resource demands

A large class of computational problems is characterized by frequent synchronization, and computational requirements which change as a function of time. When such a problem must be solved on a message passing multiprocessor machine, the combination of these characteristics lead to system performance which decreases in time. Performance can be improved with periodic redistribution of computational load; however, redistribution can exact a sometimes large delay cost. We study the issue of deciding when to invoke a global load remapping mechanism. Such a decision policy must effectively weigh the costs of remapping against the performance benefits. We treat this problem by constructing two analytic models which exhibit stochastically decreasing performance. One model is quite tractable; we are able to describe the optimal remapping algorithm, and the optimal decision policy governing when to invoke that algorithm. However, computational complexity prohibits the use of the optimal remapping decision policy. We then study the performance of a general remapping policy on both analytic models. This policy attempts to minimize a statistic W(n) which measures the system degradation (including the cost of remapping) per computation step over a period of n steps. We show that as a function of time, the expected value of W(n) has at most one minimum, and that when this minimum exists it defines the optimal fixed-interval remapping policy. Our decision policy appeals to this result by remapping when it estimates that W(n) is minimized. Our performance data suggests that this policy effectively finds the natural frequency of remapping. We also use the analytic models to express the relationship between performance and remapping cost, number of processors, and the computation's stochastic activity.

Nicol, D. M.↗

A Methodology for Determining Statistical Performance Compliance for Airborne Doppler Radar with Forward-Looking Turbulence Detection Capability

The objective of the research developed and presented in this document was to statistically assess turbulence hazard detection performance employing airborne pulse Doppler radar systems. The FAA certification methodology for forward looking airborne turbulence radars will require estimating the probabilities of missed and false hazard indications under operational conditions. Analytical approaches must be used due to the near impossibility of obtaining sufficient statistics experimentally. This report describes an end-to-end analytical technique for estimating these probabilities for Enhanced Turbulence (E-Turb) Radar systems under noise-limited conditions, for a variety of aircraft types, as defined in FAA TSO-C134. This technique provides for one means, but not the only means, by which an applicant can demonstrate compliance to the FAA directed ATDS Working Group performance requirements. Turbulence hazard algorithms were developed that derived predictive estimates of aircraft hazards from basic radar observables. These algorithms were designed to prevent false turbulence indications while accurately predicting areas of elevated turbulence risks to aircraft, passengers, and crew; and were successfully flight tested on a NASA B757-200 and a Delta Air Lines B737-800. Application of this defined methodology for calculating the probability of missed and false hazard indications taking into account the effect of the various algorithms used, is demonstrated for representative transport aircraft and radar performance characteristics.

Bowles, Roland L.↗

Site preferences of Ni/2+/ and Co/2+/ in clinopyroxene and olivine - Limitations of the statistical approach.

Criticism of a statistical approach used by Dasgupta (1972) in analyzing Snyder's (1959) chemical data for minerals from the Duluth Complex in Minnesota. Apart from obvious mathematical objections to citing correlation coefficients to four significant figures from Snyder's relatively inaccurate analytical data, several more fundamental criticisms are leveled at the statistical approach of Dasgupta. These relate to compositional zoning and disequilibrium in the minerals, inhomogeneities of the samples caused by inclusions and exsolved phases, measured site population data for the major cations in olivines and pyroxenes, and the importance of coupled substitutions in the crystal structures. It is concluded that the crystal field predictions of relative enrichments of Ni(2+) and Co(2+) ions in olivine and pyroxene structures have not been disproved by Dasgupta's statistical approach.

Burns, R. G.↗