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NASA NTRS2008

Energetic Consistency and Coupling of the Mean and Covariance Dynamics

The dynamical state of the ocean and atmosphere is taken to be a large dimensional random vector in a range of large-scale computational applications, including data assimilation, ensemble prediction, sensitivity analysis, and predictability studies. In each of these applications, numerical evolution of the covariance matrix of the random state plays a central role, because this matrix is used to quantify uncertainty in the state of the dynamical system. Since atmospheric and ocean dynamics are nonlinear, there is no closed evolution equation for the covariance matrix, nor for the mean state. Therefore approximate evolution equations must be used. This article studies theoretical properties of the evolution equations for the mean state and covariance matrix that arise in the second-moment closure approximation (third- and higher-order moment discard). This approximation was introduced by EPSTEIN [1969] in an early effort to introduce a stochastic element into deterministic weather forecasting, and was studied further by FLEMING [1971a,b], EPSTEIN and PITCHER [1972], and PITCHER [1977], also in the context of atmospheric predictability. It has since fallen into disuse, with a simpler one being used in current large-scale applications. The theoretical results of this article make a case that this approximation should be reconsidered for use in large-scale applications, however, because the second moment closure equations possess a property of energetic consistency that the approximate equations now in common use do not possess. A number of properties of solutions of the second-moment closure equations that result from this energetic consistency will be established.

Cohn, Stephen E.↗

NASA NTRS1985

A Kalman filter for a two-dimensional shallow-water model

A two-dimensional Kalman filter is described for data assimilation for making weather forecasts. The filter is regarded as superior to the optimal interpolation method because the filter determines the forecast error covariance matrix exactly instead of using an approximation. A generalized time step is defined which includes expressions for one time step of the forecast model, the error covariance matrix, the gain matrix, and the evolution of the covariance matrix. Subsequent time steps are achieved by quantifying the forecast variables or employing a linear extrapolation from a current variable set, assuming the forecast dynamics are linear. Calculations for the evolution of the error covariance matrix are banded, i.e., are performed only with the elements significantly different from zero. Experimental results are provided from an application of the filter to a shallow-water simulation covering a 6000 x 6000 km grid.

Parrish, D. F.↗

NASA NTRS1982

Dynamic modeling of structures from measured complex modes

A technique is presented to use a set of identified complex modes together with an analytical mathematical model of a structure under test to compute improved mass, stiffness and damping matrices. A set of identified normal modes, computed from the measured complex modes, is used in the mass orthogonality equation to compute an improved mass matrix. This eliminates possible errors that may result from using approximated complex modes as normal modes. The improved mass matrix, the measured complex modes and the higher analytical modes are then used to compute the improved stiffness and damping matrices. The number of degrees-of-freedom of the improved model is limited to equal the number of elements in the measured modal vectors. A simulated experiment shows considerable improvements, in the system's analytical dynamic model, over the frequency range of the given measured modal information.

Ibrahim, s. R.↗

NASA NTRS1985

Dynamic Modeling of Structures from Measured Complex Modes

Ibrahim, S. R.↗

NASA NTRS1996

Geochemical Comparison of Four Cores from the Manson Impact Structure

Concentrations of 33 elements were determined in relatively unaltered, matrix-rich samples of impact breccia at approximately 3-m-depth intervals in the M-1 core from the Manson impact structure, Iowa. In addition, 46 matrix-rich samples from visibly altered regions of the M-7, M-8, and M-10 cores were studied, along with 42 small clasts from all four cores. Major element compositions were determined for a subset of impact breccias from the M-1 core, including matrix-rich impact-melt breccia. Major- and trace-element compositions were also determined for a suite of likely target rocks. In the M-1 core, different breccia units identified from lithologic examination of cores are compositionally distinct. There is a sharp compositional discontinuity at the boundary between the Keweenawan-shale-clast breccia and the underlying unit of impact-melt breccia (IMB) for most elements, suggesting minimal physical mixing between the two units during emplacement. Samples from the 40-m-thick IMB (M-1) are all similar to each other in composition, although there are slight increases in concentration with depth for those elements that have high concentrations in the underlying fragmental-matrix suevite breccia (SB) (e.g., Na, Ca, Fe, Sc), presumably as a result of greater clast proportions at the bottom margin of the unit of impact-melt breccia. The high degree of compositional similarity we observe in the impact-melt breccias supports the interpretation that the matrix of this unit represents impact melt. That our analyses show such compositional similarity results in part from our technique for sampling these breccias: for each sample we analyzed a few small fragments (total mass: approximately 200 mg) selected to be relatively free of large clasts and visible signs of alteration instead of subsamples of powders prepared from a large mass of breccia. The mean composition of the matrix-rich part of impact-melt breccia from the M-1 core can be modeled as a mixture of approximately 35% shale and siltstone (Proterozoic "Red Clastics"), 23% granite, 40% hornblende-biotite gneiss, and a small component (less than 2%) of mafic-dike rocks.

Korotev, Randy L.↗

NASA NTRS1995

CVD silicon carbide monofilament reinforced SrO-Al2O3-2SiO2 (SAS) glass-ceramic composites

Unidirectional CVD SiC fiber-reinforced SrO.Al2O3.2SiO2 (SAS) glass-ceramic matrix composites have been fabricated by hot pressing at various combinations of temperature, pressure and time. Both carbon-rich surface coated SCS-6 and uncoated SCS-0 fibers were used as reinforcements. Almost fully dense composites have been obtained. Monoclinic celsian, SrAl2Si2O8, was the only crystalline phase observed in the matrix from x-ray diffraction. During three point flexure testing of composites, a test span to thickness ratio of approximately 25 or greater was necessary to avoid sample delamination. Strong and tough SCS-6/SAS composites having a first matrix crack stress of approximately 300 MPa and an ultimate bend strength of approximately 825 MPa were fabricated. No chemical reaction between the SCS-6 fibers and the SAS matrix was observed after high temperature processing. The uncoated SCS-0 fiber-reinforced SAS composites showed only limited improvement in strength over SAS monolithic. The SCS-0/SAS composite having a fiber volume fraction of 0.24 and hot pressed at 1400 deg C exhibited a first matrix cracking stress of approximately 231 +/- 20 MPa and ultimate strength of 265 +/- 17 MPa. From fiber push-out tests, the fiber/matrix interfacial debonding strength (tau(sub debond)) and frictional sliding stress (tau(sub friction)) in the SCS-6/SAS system were evaluated to be approximately 6.7 +/- 2.3 MPa and 4.3 +/- 0.6 MPa, respectively, indicating a weak interface. However, for the SCS-0/SAS composite, much higher values of approximately 17.5 +/- 2.7 MPa for tau(sub debond) and 11.3 +/- 1.6 MPa for tau(sub friction) respectively, were observed; some of the fibers were so strongly bonded to the matrix that they could not be pushed out. Examination of fracture surfaces revealed limited short pull-out length of SCS-0 fibers. The applicability of various micromechanical models for predicting the values of first matrix cracking stress and ultimate strength of these composites were examined.

Bansal, Narottam P.↗

NASA NTRS1977

Failure detection and correction for turbofan engines

In this paper, a failure detection and correction strategy for turbofan engines is discussed. This strategy allows continuing control of the engines in the event of a sensor failure. An extended Kalman filter is used to provide the best estimate of the state of the engine based on currently available sensor outputs. Should a sensor failure occur the control is based on the best estimate rather than the sensor output. The extended Kalman filter consists of essentially two parts, a nonlinear model of the engine and up-date logic which causes the model to track the actual engine. Details on the model and up-date logic are presented. To allow implementation, approximations are made to the feedback gain matrix which result in a single feedback matrix which is suitable for use over the entire flight envelope. The effect of these approximations on stability and response is discussed. Results from a detailed nonlinear simulation indicate that good control can be maintained even under multiple failures.

Corley, R. C.↗

NASA NTRS1996

Effects of Fiber Content on Mechanical Properties of CVD SiC Fiber-Reinforced Strontium Aluminosilicate Glass-Ceramic Composites

Unidirectional CVD SiC(f)(SCS-6) fiber-reinforced strontium aluminosilicate (SAS) glass-ceramic matrix composites containing various volume fractions, approximately 16 to 40 volume %, of fibers were fabricated by hot pressing at 1400 C for 2 h under 27.6 MPa. Monoclinic celsian, SrAl2Si2O8, was the only crystalline phase formed, with complete absence of the undesired hexacelsian phase, in the matrix. Room temperature mechanical properties were measured in 3-point flexure. The matrix microcracking stress and the ultimate strength increased with increase in fiber volume fraction, reached maximum values for V(sub f) approximately equal to 0.35, and degraded at higher fiber loadings. This degradation in mechanical properties is related to the change in failure mode, from tensile at lower V(sub f) to interlaminar shear at higher fiber contents. The extent of fiber loading did not have noticeable effect on either fiber-matrix debonding stress, or frictional sliding stress at the interface. The applicability of micromechanical models in predicting the mechanical properties of the composites was also examined. The currently available theoretical models do not appear to be useful in predicting the values of the first matrix cracking stress, and the ultimate strength of the SCS-6/SAS composites.

Bansal, Narottam P.↗

NASA NTRS1977

Structured estimation - Sample size reduction for adaptive pattern classification

The Gaussian two-category classification problem with known category mean value vectors and identical but unknown category covariance matrices is considered. The weight vector depends on the unknown common covariance matrix, so the procedure is to estimate the covariance matrix in order to obtain an estimate of the optimum weight vector. The measure of performance for the adapted classifier is the output signal-to-interference noise ratio (SIR). A simple approximation for the expected SIR is gained by using the general sample covariance matrix estimator; this performance is both signal and true covariance matrix independent. An approximation is also found for the expected SIR obtained by using a Toeplitz form covariance matrix estimator; this performance is found to be dependent on both the signal and the true covariance matrix.

Morgera, S.↗

NASA NTRS2016

Hydrogen Isotopic Composition of Apatite in Northwest Africa 7034: A Record of the "Intermediate" H-Isotopic Reservoir in the Martian Crust?

Northwest Africa (NWA) 7034 and its pairings comprise a regolith breccia with a basaltic bulk composition [1] that yields a better match than any other martian meteorite to visible-infrared reflectance spectra of the martian surface measured from orbit [2]. The composition of the fine-grained matrix within NWA 7034 bears a striking resemblance to the major element composition estimated for the martian crust, with several exceptions. The NWA 7034 matrix is depleted in Fe, Ti, and Cr and enriched in Al, Na, and P [3]. The differences in Al and Fe are the most substantial, but the Fe content of NWA 7034 matrix falls within the range reported for the southern highlands crust [6]. It was previously suggested by [4] that NWA 7034 was sourced from the southern highlands based on the ancient 4.4 Ga ages recorded in NWA 7034/7533 zircons [4, 5]. In addition, the NWA 7034 matrix material is enriched in incompatible trace elements by a factor of 1.2-1.5 [7] relative to estimates of the bulk martian crust. The La/Yb ratio of the bulk martian crust is estimated to be approximately 3 [7], and the La/Yb of the NWA 7034 matrix materials ranges from approximately 3.9 to 4.4 [3, 8], indicating a higher degree of LREE enrichment in the NWA 7034 matrix materials. This elevated La/Yb ratio and enrichment in incompatible lithophile trace elements is consistent with NWA 7034 representing a more geochemically enriched crustal terrain than is represented by the bulk martian crust, which would be expected if NWA 7034 represents the bulk crust from the southern highlands. Given the similarities between NWA 7034 and the martian crust, NWA 7034 may represent an important sample for constraining the composition of the martian crust, particularly the ancient highlands. In the present study, we seek to constrain the H isotopic composition of the martian crust using Cl-rich apatite in NWA 7034. Usui et al., [9] recently proposed that a H isotopic reservoir exists within the martian crust that has a H-isotopic composition that is intermediate (δD of 1000-2000per mille) between an isotopically light mantle (Delta D is less than 275per mille [10]) and an isotopically heavy atmosphere (δD of 2500-6100per mille [11, 12]). Apatites in NWA 7034 occur in a number of lithologic domains, however apatites across all lithologic domains have been affected by a Pb-loss event at about 1.5 Ga before present [5], so they are unlikely to have retained a primary composition and are more likely to have equilibrated with fluids within the martian crust that may or may not have exchanged with the martian atmosphere. Equilibration of apatite with crustal fluids is further supported by the chlorine-rich compositions exhibited by apatites in NWA 7034 in comparison to apatites from other martian meteorites (Figure 1; [13]). Cl is more hydrophilic than F, which promotes formation of Cl-rich apatite compositions in fluid-rich systems [e.g., 14, 15-17].

McCubbin, F. M.↗

NASA NTRS1988

Statistical analysis of effective singular values in matrix rank determination

A major problem in using SVD (singular-value decomposition) as a tool in determining the effective rank of a perturbed matrix is that of distinguishing between significantly small and significantly large singular values to the end, conference regions are derived for the perturbed singular values of matrices with noisy observation data. The analysis is based on the theories of perturbations of singular values and statistical significance test. Threshold bounds for perturbation due to finite-precision and i.i.d. random models are evaluated. In random models, the threshold bounds depend on the dimension of the matrix, the noisy variance, and predefined statistical level of significance. Results applied to the problem of determining the effective order of a linear autoregressive system from the approximate rank of a sample autocorrelation matrix are considered. Various numerical examples illustrating the usefulness of these bounds and comparisons to other previously known approaches are given.

Konstantinides, Konstantinos↗

NASA NTRS1974

A computational procedure to analyze metal matrix laminates with nonlinear lamination residual strains

An approximate computational procedure is described for the analysis of angleplied laminates with residual nonlinear strains. The procedure consists of a combination of linear composite mechanics and incremental linear laminate theory. The procedure accounts for initial nonlinear strains, unloading, and in-situ matrix orthotropic nonlinear behavior. The results obtained in applying the procedure to boron/aluminum angleplied laminates show that this is a convenient means to accurately predict the initial tangent properties of angleplied laminates in which the matrix has been strained nonlinearly by the lamination residual stresses. The procedure predicted initial tangent properties results which were in good agreement with measured data obtained from boron/aluminum angleplied laminates.

Chamis, C. C.↗

NASA NTRS1974

A computational procedure to analyze metal matrix laminates with nonlinear lamination residual strains

An approximate computational procedure is described for the analysis of angleplied laminates with residual nonlinear strains. The procedure consists of a combination of linear composite mechanics and incremental linear laminate theory. The procedure accounts for initial nonlinear strains, unloading, and in-situ matrix orthrotropic nonlinear behavior. The results obtained in applying the procedure to boron/aluminum angleplied laminates show that this is a convenient means to accurately predict the initial tangent properties of angleplied laminates in which the matrix has been strained nonlinearly by the lamination residual stresses. The procedure predicted initial tangent properties results which were in good agreement with measured data obtained from boron/aluminum angleplied laminates.

Chamis, C. C.↗

NASA NTRS2007

Spatial Pattern of Cell Damage in Tissue from Heavy Ions

A new Monte Carlo algorithm was developed that can model passage of heavy ions in a tissue, and their action on the cellular matrix for 2- or 3-dimensional cases. The build-up of secondaries such as projectile fragments, target fragments, other light fragments, and delta-rays was simulated. Cells were modeled as a cell culture monolayer in one example, where the data were taken directly from microscopy (2-d cell matrix). A simple model of tissue was given as abstract spheres with close approximation to real cell geometries (3-d cell matrix), as well as a realistic model of tissue was proposed based on microscopy images. Image segmentation was used to identify cells in an irradiated cell culture monolayer, or slices of tissue. The cells were then inserted into the model box pixel by pixel. In the case of cell monolayers (2-d), the image size may exceed the modeled box size. Such image was is moved with respect to the box in order to sample as many cells as possible. In the case of the simple tissue (3-d), the tissue box is modeled with periodic boundary conditions, which extrapolate the technique to macroscopic volumes of tissue. For real tissue, specific spatial patterns for cell apoptosis and necrosis are expected. The cell patterns were modeled based on action cross sections for apoptosis and necrosis estimated based on BNL data, and other experimental data.

Ponomarev, Artem L.↗

NASA NTRS2002

Charge Resolution of the Silicon Matrix of the ATIC Experiment

ATIC (Advanced Thin Ionization Calorimeter) is a balloon borne experiment designed to measure the cosmic ray composition for elements from hydrogen to iron and their energy spectra from approx.50 GeV to near 100 TeV. It consists of a Si-matrix detector to determine the charge of a CRT particle, a scintillator hodoscope for tracking, carbon interaction targets and a fully active BGO calorimeter. ATIC had its first flight from McMurdo, Antarctica from 28/12/2000 to 13/01/2001. The ATIC flight collected approximately 25 million events. The silicon matrix of the ATIC spectrometer is designed to resolve individual elements from proton to iron. To provide this resolution careful calibration of each pixel of the silicon matrix is required. Firstly, for each electronic channel of the matrix the pedestal value was subtracted taking into account its drift during the flight. The muon calibration made before the flight was used then to convert electric signals (in ADC channel number) to energy deposits in each pixel. However, the preflight muon calibration was not accurate enough for the purpose, because of lack of statistics in each pixel. To improve charge resolution the correction was done for the position of Helium peak in each pixel during the flight . The other way to set electric signals in electronics channels of the Si-matrix to one scale was correction for electric channel gains accurately measured in laboratory. In these measurements it was found that small different nonlinearities for different channels are present in the region of charge Z > 20. The correction for these non-linearities was not done yet. In linear approximation the method provides practically the same resolution as muon calibration plus He-peak correction. For searching a pixel with the signal of primary particle an indication from the cascade in the calorimeter was used. For this purpose a trajectory was reconstructed using weight centers of energy deposits in BGO layers. The point of intersection of this trajectory with Si-matrix and its RMS was determined. The pixel with maximal signal in 3sigma region was taken as sought. The signal in this pixel was corrected by trajectory zenith angle. The preliminary results on charge resolution of the Si-matrix in the range from protons to iron are presented.

Zatsepin, V. I.↗

NASA NTRS1980

Spectral methods for problems in complex geometries

The properties of spectral methods are surveyed and their extension to solve problems in complex geometries is developed. A new iteration procedure is introduced to solve efficiently the full matrix equations resulting from spectral approximations to nonconstant coefficient boundary-value problems in complex geometries. It is shown that the work required to solve these spectral equations exceeds that of solving the lowest-order finite-difference approximation to the same problem by only O(N log N).

Orszag, S. A.↗

NASA NTRS1981

Detection of strength limiting defects in cellular glasses by dielectric measurements

The foamed glasses that are being considered for structural support in solar thermal energy system silvered glass concentrator mirrors are assessed for strength-limiting defects by a nondestructive technique which measures the capacitance of well defined regions. The feasibility of locating large defects is demonstrated for the case of one type of cellular mass. Observed capacitance variations are believed to be due to small voids or other irregularities in the material. If the defects are equal to or greater than approximately 20 times the glass matrix pore size, they can be resolved with sufficient accuracy to delineate their spatial extent.

Gammell, P. M.↗

NASA NTRS1984

A finite element method for nonlinear forced vibrations of beams

Techniques for defining a finite element model (FEM) for analysis of nonlinear vibrations in beam structures subjected to harmonic excitation are presented. The resulting model covers longitudinal deformation and inertial effects. The nonlinear oscillations of a beam element under forced excitation are modeled by a harmonic force matrix based on first order approximations of the Jacobian elliptic forcing function. Harmonic force and nonlinear stiffness matrices are derived and the nonlinear forced responses of beams are calculated under various boundary conditions. The results of FEM computations for simply-supported and clamped beams show that midplane stretching caused by large deflections increases the nonlinearity. Axially-restrained beams experience only hardening nonlinearity, while axially-free beams have reduced nonlinearity in deformation and inertia and an increase in linearity due to large deflection.

Mei, C.↗