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At least 1,081 records · Page 60

On determining important aspects of mathematical models: Application to problems in physics and chemistry

The use of parametric and functional gradient sensitivity analysis techniques is considered for models described by partial differential equations. By interchanging appropriate dependent and independent variables, questions of inverse sensitivity may be addressed to gain insight into the inversion of observational data for parameter and function identification in mathematical models. It may be argued that the presence of a subset of dominantly strong coupled dependent variables will result in the overall system sensitivity behavior collapsing into a simple set of scaling and self similarity relations amongst elements of the entire matrix of sensitivity coefficients. These general tools are generic in nature, but herein their application to problems arising in selected areas of physics and chemistry is presented.

Rabitz, Herschel↗

Polarimetric clutter modeling: Theory and application

The two-layer anisotropic random medium model is used to investigate fully polarimetric scattering properties of earth terrain media. The polarization covariance matrices for the untilted and tilted uniaxial random medium are evaluated using the strong fluctuation theory and distorted Born approximation. In order to account for the azimuthal randomness in the growth direction of leaves in tree and grass fields, an averaging scheme over the azimuthal direction is also applied. It is found that characteristics of terrain clutter can be identified through the analysis of each element of the covariance matrix. Theoretical results are illustrated by the comparison with experimental data provided by MIT Lincoln Laboratory for tree and grass fields.

Kong, J. A.↗

AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 34th and AIAA/ASME Adaptive Structures Forum, La Jolla, CA, Apr. 19-22, 1993, Technical Papers. Pts. 1-6

Topics addressed include the prediction of helicopter component loads using neural networks, spacecraft on-orbit coupled loads analysis, hypersonic flutter of a curved shallow panel with aerodynamic heating, thermal-acoustic fatigue of ceramic matrix composite materials, transition elements based on transfinite interpolation, damage progression in stiffened composite panels, a direct treatment of min-max dynamic response optimization problems, and sources of helicopter rotor hub inplane shears. Also discussed are dynamics of a layered elastic system, confidence bounds on structural reliability, mixed triangular space-time finite elements, advanced transparency development for USAF aircraft, a low-velocity impact on a graphite/PEEK, an automated mode-tracking strategy, transonic flutter suppression by a passive flap, a nonlinear response of composite panels to random excitation, an optimal placement of elastic supports on a simply supported plate, a probabilistic assessment of composite structures, a model for mode I failure of laminated composites, a residual flexibility approach to multibody dynamics,and multilayer piezoelectric actuators.

Source record↗

Constraints on Mueller matrices of polarization optics

The issue of physical realizability constraints on depolarizing scattering or imaging systems is addressed. In particular, the overpolarization problem, i.e., the problem of ensuring that the output degree of polarization is always smaller than (or equal to) unity, is discussed in detail. A set of necessary conditions for the elements of a Mueller matrix is derived. These conditions can be used to test the accuracy of polarimetric measurements and computations. Several recent experimental examples from polarization optics and radar are discussed.

Kostinski, Alexander B.↗

Monolithic Cu-Cr-Nb Alloys for High Temperature, High Heat Flux Applications

Work during the prior four years of this grant has resulted in significant advances in the development of Cu-8 Cr4 Nb and related Cu-Cr-Nb alloys. The alloys are nearing commercial use in the Reusable Launch Vehicle (RLV) where they are candidate materials for the thrust cell liners of the aerospike engines being developed by Rocketdyne. During the fifth and final year of the grant, it is proposed to complete development of the design level database of mechanical and thermophysical properties and transfer it to NASA Glenn Research Center and Rocketdyne. The database development work will be divided into three main areas: Thermophysical Database Augmentation, Mechanical Testing and Metallography and Fractography. In addition to the database development, work will continue that is focussed on the production of alternatives to the powder metallurgy alloys currently used. Exploration of alternative alloys will be aimed at both the development of lower cost materials and higher performance materials. A key element of this effort will be the use of Thermo-Calc software to survey the solubility behavior of a wide range of alloying elements in a copper matrix. The ultimate goals would be to define suitable alloy compositions and processing routes to produce thin sheets of the material at either a lower cost, or, with improved mechanical and thermal properties compared to the current Cu-Cr-Nb powder metallurgy alloys.

Ellis, David L.↗

Using Dual-wavelength Fiber Bragg Gratings for Temperature and Strain Sensing at Cryogenic Temperature

By using dual-wavelength fiber-optic Bragg gratings, a new technique has been developed for sensing both temperature and strain simultaneously in cryogenic temperature range. Two Bragg gratings with different wavelengths were inscribed at the same location in an optical fiber to form a dual-wavelength sensor. By measuring the wavelength shifts that resulted from the fiber being subjected to different temperatures and strains, the wavelength-dependent thermo-optic coefficients and photoelastic coefficients of the fiber were determined. These coefficients were used to construct the elements of the K matrix, which enables to determine inversely the strain and temperature changes by measuring the wavelength shifts of the dual-wavelength Bragg grating. In this study, measurements were made over the temperature range from room temperature down to about 10 K, addressing much of the low temperature range of cryogenic tanks. A structure transition of the optical fiber during the temperature change was found from about 70 K to 140 K. This transition caused splitting of the waveforms characterizing the Bragg gratings, and the determination of wavelength shifts was consequently complicated. Several alternatives are proposed to resolve this problem. The effectiveness and sensitivities of these measurements in different temperature ranges are discussed. The separation of two wavelengths for the dual-wavelength Bragg grating has been widened to increase the sensitivities of measurement; however, this separation can still be covered in the scanning range from single scanning laser.

Wu, Meng-Chou↗

Comparing Wild 2 Particles to Chondrites and IDPS

We compare the observed composition ranges of olivine, pyroxene and Fe-Ni sulfides in Wild 2 grains, comparing these with chondritic IDPs and chondrite classes to explore whether these data suggest affinities to known hydrous materials in particular. Wild 2 olivine has an extremely wide composition range, from Fo4-100 with a pronounced frequency peak at Fo99. The composition range displayed by the low-calcium pyroxene is also very extensive, from En52 to En100, with a significant frequency peak centered at En95. These ranges are as broad or broader than those reported for any other extraterrestrial material. Wild 2 Fe-Ni sulfides mainly have compositions close to that of FeS, with less than 2 atom % Ni - to date, only two pentlandite grains have been found among the Wild-grains suggesting that this mineral is not abundant. The complete lack of compositions between FeS and pentlandite (with intermediate solid solution compositions) suggests (but does not require) that FeS and pentlandite condensed as crystalline species, i.e. did not form as amorphous phases, which later became annealed. While we have not yet observed any direct evidence of water-bearing minerals, the presence of Ni-bearing sulfides, and magnesium-dominated olivine and low-Ca pyroxene does not rule out their presence at low abundance. We do conclude that modern major and minor element compositions of chondrite matrix and IDPs are needed.

Zolensky, Michael↗

Astrobiology Sample Analysis Program (ASAP) for Advanced Life Detection Instrumentation Development and Calibration

Scientific ground-truth measurements for near-term Mars missions, such as the 2009 Mars Science Laboratory (MSL) mission, are essential for validating current in situ flight instrumentation and for the development of advanced instrumentation technologies for life-detection missions over the next decade. The NASA Astrobiology Institute (NAI) has recently funded a consortium of researchers called the Astrobiology Sample Analysis Program (ASAP) to analyze an identical set of homogenized martian analog materials in a "round-robin" style using both state-of-the-art laboratory techniques as well as in-situ flight instrumentation including the SAM gas chromatograph mass spectrometer and CHEMIN X-ray diffraction/fluorescence instruments on MSL and the Urey and MOMA organic analyzer instruments under development for the 2013 ExoMars missions. The analog samples studied included an Atacama Desert soil from Chile, the Murchison meteorite, a gypsum sample from the 2007 AMASE Mars analog site, jarosite from Panoche Valley, CA, a hydrothermal sample from Rio Tinto, Spain, and a "blind" sample collected during the 2007 MSL slow-motion field test in New Mexico. Each sample was distributed to the team for analysis to: (1) determine the nature and inventory of organic compounds, (2) measure the bulk carbon and nitrogen isotopic composition, (3) investigate elemental abundances, mineralogy and matrix, and (4) search for biological activity. The experimental results obtained from the ASAP Mars analog research consortium will be used to build a framework for understanding the biogeochemistry of martian analogs, help calibrate current spaceflight instrumentation, and enhance the scientific return from upcoming missions.

Glavin, Daniel↗

Modeling Optical Properties of Mineral Aerosol Particles by Using Nonsymmetric Hexahedra

We explore the use of nonsymmetric geometries to simulate the single-scattering properties of airborne dust particles with complicated morphologies. Specifically, the shapes of irregular dust particles are assumed to be nonsymmetric hexahedra defined by using the Monte Carlo method. A combination of the discrete dipole approximation method and an improved geometric optics method is employed to compute the single-scattering properties of dust particles for size parameters ranging from 0.5 to 3000. The primary optical effect of eliminating the geometric symmetry of regular hexahedra is to smooth the scattering features in the phase function and to decrease the backscatter. The optical properties of the nonsymmetric hexahedra are used to mimic the laboratory measurements. It is demonstrated that a relatively close agreement can be achieved by using only one shape of nonsymmetric hexahedra. The agreement between the theoretical results and their measurement counterparts can be further improved by using a mixture of nonsymmetric hexahedra. It is also shown that the hexahedron model is much more appropriate than the "equivalent sphere" model for simulating the optical properties of dust particles, particularly, in the case of the elements of the phase matrix that associated with the polarization state of scattered light.

Bi, Lei↗

Real-Time Principal-Component Analysis

A recently written computer program implements dominant-element-based gradient descent and dynamic initial learning rate (DOGEDYN), which was described in Method of Real-Time Principal-Component Analysis (NPO-40034) NASA Tech Briefs, Vol. 29, No. 1 (January 2005), page 59. To recapitulate: DOGEDYN is a method of sequential principal-component analysis (PCA) suitable for such applications as data compression and extraction of features from sets of data. In DOGEDYN, input data are represented as a sequence of vectors acquired at sampling times. The learning algorithm in DOGEDYN involves sequential extraction of principal vectors by means of a gradient descent in which only the dominant element is used at each iteration. Each iteration includes updating of elements of a weight matrix by amounts proportional to a dynamic initial learning rate chosen to increase the rate of convergence by compensating for the energy lost through the previous extraction of principal components. In comparison with a prior method of gradient-descent-based sequential PCA, DOGEDYN involves less computation and offers a greater rate of learning convergence. The sequential DOGEDYN computations require less memory than would parallel computations for the same purpose. The DOGEDYN software can be executed on a personal computer.

Duong, Vu↗

Handling Qualities of a Large Civil Tiltrotor in Hover using Translational Rate Command

A Translational Rate Command (TRC) control law has been developed to enable low speed maneuvering of a large civil tiltrotor with minimal pitch changes by means of automatic nacelle angle deflections for longitudinal velocity control. The nacelle actuator bandwidth required to achieve Level 1 handling qualities in hover and the feasibility of additional longitudinal cyclic control to augment low bandwidth nacelle actuation were investigated. A frequency-domain handling qualities criterion characterizing TRC response in terms of bandwidth and phase delay was proposed and validated against a piloted simulation conducted on the NASA-Ames Vertical Motion Simulator. Seven experimental test pilots completed evaluations in the ADS-33E-PRF Hover Mission Task Element (MTE) for a matrix of nacelle actuator bandwidths, equivalent rise times and control response sensitivities, and longitudinal cyclic control allocations. Evaluated against this task, longitudinal phase delay shows the Level 1 boundary is around 0.4 0.5 s. Accordingly, Level 1 handling qualities were achieved either with a nacelle actuator bandwidth greater than 4 rad/s, or by employing longitudinal cyclic control to augment low bandwidth nacelle actuation.

Malpica, Carlos A.↗

Observations on the Computation of Eigenvalue and Eigenvector Jacobians

Many scientific and engineering problems benefit from analytic expressions for eigenvalue and eigenvector derivatives with respect to the elements of the parent matrix. While there exists extensive literature on the calculation of these derivatives, which take the form of Jacobian matrices, there are a variety of deficiencies that have yet to be addressed — including the need for both left and right eigenvectors, limitations on the matrix structure, and issues with complex eigenvalues and eigenvectors. This work addresses these deficiencies by proposing a new analytic solution for the eigenvalue and eigenvector derivatives. The resulting analytic Jacobian matrices are numerically efficient to compute and are valid for the general complex case. It is further shown that this new general result collapses to previously known relations for the special cases of real symmetric matrices and real diagonal matrices. Finally, the new Jacobian expressions are validated using forward finite differencing and performance is compared with another technique.

Jacobian↗

Efficient Preconditioning of a High-Order Solver for Multiple Physics

This work addresses preconditioning approaches for an implicit high-order solver frame-work applied to multiple physics. The solver is based on a space-time spectral element method and matrix-free Newton-Krylov solver developed at NASA over the recent years. Within this context, most preconditioning methods are impractical, as the computational time and memory requirements scale poorly with increasing polynomial orders. To improve computational efficiency, we first describe a novel entity-based Block Jacobi preconditioner for the continuous-Galerkin solution of the linear-elasticity and linear-shell equations. Second, we introduce a multigrid algorithm to further reduce time-to-solution on stiff cases arising from continuous-and discontinuous-Galerkin discretizations. Results obtained on relevant single-physics reference solutions, demonstrate the feasibility of the methods, paving the way for high-order solutions of fully coupled multi-physics problems.

STMD↗

The J and K Dependencies of the Line Coupling and Line Mixing Effects: Theoretical Studies of the Relaxation Matrices of N 2 -Broadened Ch 3 D

Line coupling and line mixing effects in parallel and perpendicular bands of CH 3 D perturbed by N 2 have been studied. The work focuses on exhibiting the j and k dependencies of these two processes. The calculations were based on a previously reported anisotropic intermolecular potential including both the long-range multipole, induction, and dispersion forces and a short-range atom-atom model. It is shown that components with L 1 = 3 of the atom-atom model are dominant contributions to the diffusion operator. As a consequence, in comparison with other molecular systems such as the CH 3 Cl-N 2 and CH 3 I-N 2 , theoretically predicted line coupling and line mixing effects exhibit completely new j and k dependencies. In general, the theoretically calculated halfwidths and intra-doublets’ off-diagonal elements of the relaxation matrix are in reasonable agreement with measurements.

Methane-d↗

Fracture-Based Mesh Size Requirements for Matrix Cracks in Continuum Damage Mechanics Models

This paper evaluates the ability of progressive damage analysis (PDA) finite element (FE) models to predict transverse matrix cracks in unidirectional composites. The results of the analyses are compared to closed-form linear elastic fracture mechanics (LEFM) solutions. Matrix cracks in fiber-reinforced composite materials subjected to mode I and mode II loading are studied using continuum damage mechanics and zero-thickness cohesive zone modeling approaches. The FE models used in this study are built parametrically so as to investigate several model input variables and the limits associated with matching the upper-bound LEFM solutions. Specifically, the sensitivity of the PDA FE model results to changes in strength and element size are investigated.

Leone, Frank A.↗

Postbuckling analysis using a general purpose code

A new capability for solving postbuckling problems in shell structures is described. The matrix theory to adapt Newton's method to nonlinear finite element shell analysis is outlined first. The matrix theory is directed at writing consistent linear algebratic equations for problems where the tangent stiffness matrix is singular or nearly singular. The matrix theory suggests a change of variables as part of the usual iterative procedure in Newton's method. The change of variables is shown to be feasible for introduction into the algorithm programmed in general purpose codes for finite element analysis of structures. Numerical results from a new option that has been programmed in an existing general purpose code are presented. The analysis of shell structures for collapse and for branching at bifurcation loads is illustrated by the numerical examples.

Thurston, G. A.↗

Structure of the polysaccharide sheath from the B race of the green microalga Botryococcus braunii

The green microalga Botryococcus braunii forms a colony of cells held together by an intricate extracellular matrix. This extracellular matrix also acts as a storage location for liquid hydrocarbons initially produced inside the cells. These hydrocarbons can be used as feedstocks to produce transportation fuels. In the B race of B. braunii, the extracellular matrix is composed of several elements: a cross-linked hydrocarbon network filled with the liquid hydrocarbons, a retaining wall to hold the hydrocarbons in the extracellular matrix, an arabinogalactan polysaccharide fibrillar sheath that extends outward from the retaining wall, and a single protein known as polysaccharide associated protein is found at the base of the polysaccharide fibers where they connect to the retaining wall. During growth, colonies of the B race of B. braunii shed fragments of the retaining wall with polysaccharide fibrils attached into the media. Here we describe the isolation and structural analysis of these polysaccharides using a series of chemical degradations in combination with glycosyl residue composition and linkage analysis, as well as 2-dimensional nuclear magnetic resonance spectroscopy. The results demonstrate that the polysaccharide is highly branched, consisting of a galactan backbone with short branches comprised of Dgalactopyranose, L-arabinofuranose, 4-O-methyl-D-glucopyranuronic acid, and 6-deoxy-D-altropyranose. To our knowledge, this is the first description of 6-deoxyaltrose in algae or plants.

59 BASIC BIOLOGICAL SCIENCES↗

The bit-error rate performance of a satellite microwave matrix switch

The matrix switch is a critical element of communications satellites employing multiple beam antennas and on-board switching. Two proof-of-concept models of a microwave matrix switch have been developed under NASA-sponsored contracts. These switches have undergone extensive testing at NASA Lewis Research Center to determine their operating characteristics in a system environment. The results of these tests indicate the effect of the matrix switch on the overall system operation.

Kerczewski, Robert J.↗