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Results for “Local coordinate transform”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Quantum space, quantum time, and relativistic quantum mechanics

We treat space and time as bona fide quantum degrees of freedom on an equal footing in Hilbert space. Motivated by considerations in quantum gravity, we focus on a paradigm dealing with linear, first-order Hamiltonian and momentum constraints that lead to emergent features of temporal and spatial translations. Unlike the conventional treatment, we show that Klein-Gordon and Dirac equations in relativistic quantum mechanics can be unified in our paradigm by applying relativistic dispersion relations to eigenvalues rather than treating them as operator-valued equations. With time and space being treated on an equal footing in Hilbert space, we show symmetry transformations to be implemented by unitary basis changes in Hilbert space, giving them a stronger quantum mechanical footing. Global symmetries, such as Lorentz transformations, modify the decomposition of Hilbert space; and local symmetries, such as U(1) gauge symmetry are diagonal in coordinate basis and do not alter the decomposition of Hilbert space. Here, we briefly discuss extensions of this paradigm to quantum field theory and quantum gravity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1977

Instantaneous relationship between solar inertial and local vertical local horizontal attitudes

The instantaneous relationship between the Solar Inertial (SI) and Local Vertical Local Horizontal (LVLH) coordinate systems is derived. A method is presented for computation of the LVLH to SI rotational transformation matrix as a function of an input LVLH attitude and the corresponding look angles to the sun. Logic is provided for conversion between LVLH and SI attitudes expressed in terms of a pitch, yaw, roll Euler sequence. Documentation is included for a program which implements the logic on the Hewlett-Packard 97 programmable calculator.

Vickery, S. A.↗
NASA NTRS1976

ISIS-2 satellite imagery and auroral morphology

Auroral morphology is emphasized over auroral dynamics in a paper describing conspicuous auroral features picked up by the ISIS-2 scanning photometer. Results of improved programs designed to transform the data into a corrected geomagnetic coordinate frame and generate latitude profiles of auroral intensities at different magnetic local times are reported. The diffuse aurora and its relation to the morphology of discrete aurorae is given special attention.

Anger, C. D.↗
NASA NTRS1993

Burnett solutions along the stagnation line of a cooled cylinder in low-density hypersonic flows

The Burnett equations in the cylindrical coordinate system have been applied to the hypersonic flow over a cylinder in low density environments. Through a local similarity transformation, the Burnett equations are degenerated into nonlinear third-order ordinary differential equations which are only valid along the stagnation line. These equations are solved by the multi-staged Runge-Kutta integration technique. Steady state solutions are asymptotically reached by the time-marching procedure. A newly-developed computer code is used to solve both the Navier-Stokes and the Burnett equations within the shock layer. The computed heat transfer coefficients are consistent with wind-tunnel and STS flight data. Comparisons with the DSMC solutions and the Boltzmann solutions show that the Burnett equations are more appropriate as the governing equations than the Navier-Stokes equations in the transitional flow regime.

Liaw, G. S.↗
DOE OSTI2024

Resolving local ordering and structure in Mn x Ge 1- x Te alloys through thermodynamic ensembles of pair distribution functions

Characterizing local bonding environments in complex materials is essential for understanding and optimizing their properties. Equally as important is the ability to predict local motifs as a function of synthesis conditions, enhancing chemists’ ability to design properties into materials. In this study, we present an approach to leverage statistical mechanics to generate temperature- and energy-informed ensemble averaged pair distribution functions (PDFs). This method, which we have named Thermodynamic Ensemble Averages of PDFs for Ordering and Transformations (TEAPOT), utilizes density functional theory (DFT) to relax supercells while incorporating energetic penalties for local order, enabling accurate and computationally efficient analysis of local structure. We apply this method to the neutron PDF measurements of the pseudobinary MnTe–GeTe (MGT) alloy, demonstrating its capability to resolve complex local distortions and chemical ordering. Our results reveal detailed insights into phase transformations and local distortions driven by Mn substitution. For compositions that globally present as rock salt, our analysis reveals that Ge coordination geometry is heavily impacted by synthesis temperature. We propose that high temperature synthesis conditions promote a lowered Ge polyhedra distortion, promoting high charge carrier mobility due to the alignment of local and global structure. Incorporating statistical mechanics and computation into experimental analysis thus guides synthesis of tailored local structure.

36 MATERIALS SCIENCE↗
NASA NTRS1992

A method of smooth bivariate interpolation for data given on a generalized curvilinear grid

A method of locally bicubic interpolation is presented for data given at the nodes of a two-dimensional generalized curvilinear grid. The physical domain is transformed to a computational domain in which the grid is uniform and rectangular by a generalized curvilinear coordinate transformation. The metrics of the transformation are obtained by finite differences in the computational domain. Metric derivatives are determined by repeated application of the chain rule for partial differentiation. Given the metrics and the metric derivatives, the partial derivatives required to determine a locally bicubic interpolant can be estimated at each data point using finite differences in the computational domain. A bilinear transformation is used to analytically transform the individual quadrilateral cells in the physical domain into unit squares, thus allowing the use of simple formulas for bicubic interpolation.

Zingg, David W.↗
NASA NTRS1989

Quasi-conformal remapping for compensation of human visual field defects - Advances in image remapping for human field defects

Image coordinate transformations are investigated for possible use in a low vision aid for human patients. These patients typically have field defects with localized retinal dysfunction predominately central (age related maculopathy) or peripheral (retinitis pigmentosa). Previously simple eccentricity-only remappings which do not maintain conformality were shown. Initial attempts on developing images which hold quasi-conformality after remapping are presented. Although the quasi-conformal images may have less local distortion, there are discontinuities in the image which may counterindicate this type of transformation for the low vision application.

Juday, Richard D.↗
DOE OSTI2024

Anatase TiO 2 Surface Hydration: Infrared Vibrational Assignment and Facet-Specific Stability

Anatase TiO 2 nanoparticles support a subtle diversity of surface aqua and hydroxy coordination environments that are characteristic of distinct facets and defect sites. The disparate properties and stability of each molecularly or dissociatively absorbed water environment may provide unique reactivity for facet- and site-selective atomic layer deposition (ALD). Here we probe the temperature-dependent and facet-specific stretching frequency and stability of surface hydroxyls on faceted anatase TiO 2 nanoparticles via in situ diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS). Well-defined truncated octahedra, disks, and rods fabricated through hydrothermal synthesis present dominant (101), (001), and (010) facets, respectively. The selective dehydration of discrete local coordination environments as a function of temperature provides a potential pathway to site-selective and facet-selective ALD on metal oxide nanomaterials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Electrical and structural properties of binary Ga–Sb phase change memory alloys

Material properties of Ga–Sb binary alloy thin films deposited under ultra-high vacuum conditions were studied for analog phase change memory (PCM) applications. Crystallization of this alloy was shown to occur in the temperature range of 180–264 °C, with activation energy >2.5 eV depending on the composition. X-ray diffraction (XRD) studies showed phase separation upon crystallization into two phases, Ga-doped A7 antimony and cubic zinc-blende GaSb. Synchrotron in situ XRD analysis revealed that crystallization into the A7 phase is accompanied by Ga out-diffusion from the grains. X-ray absorption fine structure studies of the local structure of these alloys demonstrated a bond length decrease with a stable coordination number of 4 upon amorphous-to-crystalline phase transformation. Mushroom cell structures built with Ga–Sb alloys on ø110 nm TiN heater show a phase change material resistance switching behavior with resistance ratio >100 under electrical pulse measurements. TEM and Energy Dispersive Spectroscopy (EDS) studies of the Ga–Sb cells after ∼100 switching cycles revealed that partial SET or intermediate resistance states are attained by the variation of the grain size of the material as well as the Ga content in the A7 phase. A mechanism for a reversible composition control is proposed for analog cell performance. These results indicate that Te-free Ga–Sb binary alloys are potential candidates for analog PCM applications.

Ume, Rubab (ORCID:0000000324766900)↗
NASA NTRS1979

Logarithmic spiral grids for image processing

A picture digitization grid based on logarithmic spirals rather than Cartesian coordinates is presented. Expressing this curvilinear grid as a conformal exponential mapping reveals useful image processing properties. The mapping induces a computational simplification that suggests parallel architectures in which most geometric transformations are effected by data shifting in memory rather than arithmetic on coordinates. These include fast, parallel noise-free rotation, scaling, and some projective transformations of pixel defined images. Conformality of the mapping preserves local picture-processing operations such as edge detection.

Weiman, C. F. R.↗
NASA NTRS1987

Loran-C approach guidance project current status

There are four areas of work in the Loran-C flight test project. Current results provide performance data on the effects of Signal Noise Ratio (SNR) on the dynamic performance of the receiver filters for Loran-C data, and data on Loran-C grid deformation at a microscale of 100 meters. The Loran-C receiver provides a line of position (LOP) Master and Slave transmitter at an angle 0 to magnetic north. No transformation to latitude-longitude reference frame is required since this is the major source of Loran-C navigation errors. A local coordinate frame is established centered at touchdown point on the runway with directions along and across the runway. A Loran-C data collection system was set up. The Loran-C data are sent directly to an Apple II computer with a 12 inch monitor. The effect of SNR on Loran-C precision is shown for two receiver filters of different frequency response. A set of ground level static readings of touchdown was taken around Hanscom Field and transferred to an accurate detailed layout drawing; this showed local distortions of the average touchdown values.

Elias, A. L.↗
NASA NTRS1992

Klein-Gordon equation and reflection of Alfven waves in nonuniform media

A new analytical approach is presented for assessing the reflection of linear Alfven waves in smoothly nonuniform media. The general one-dimensional case in Cartesian coordinates is treated. It is shown that the wave equations, upon transformation into the form of the Klein-Gordon equation, display a local critical frequency for reflection. At any location in the medium, reflection becomes strong as the wave frequency descends past this characteristic frequency set by the local nonuniformity of the medium. This critical frequecy is given by the transformation as an explicit function of the Alfven velocity and its first and second derivatives, and hence as an explicit spatial function. The transformation thus directly yields, without solution of the wave equations, the location in the medium at which an Alfven wave of any given frequency becomes strongly reflected and has its propagation practically cut off.

Musielak, Z. E.↗
NASA NTRS1972

Analysis of heat transfer in a porous cooled wall with variable pressure and temperature along the coolant exit boundary

Fluid from a reservior at constant pressure and temperature is forced through a porous wall of uniform thickness. The boundary through which the fluid exits has specified variations in pressure and temperature along it in one direction so that the flow and heat transfer are two-dimensional. The local fluid and matrix temperatures are assumed to be equal and therefore a single energy equation governs the temperature distribution within the wall. The solution is obtained by transforming this energy equation into potential plane coordinates, which results in a separable equation. A technique yielding an integral equation is used to adapt the general solution so that it satisfies the variable-pressure boundary condition. Analytical expressions are given for the normal exit velocity and heat flux along the exit boundary. Illustrative examples are carried out which indicate to what extent the solution is locally one-dimensional.

Siegel, R.↗
NASA NTRS1987

A combined Eulerian-Lagrangian analysis for computation of two-phase flows

A combined Eulerian-Lagrangian analysis, which combines a linearized block implicit Navier-Stokes analysis for the continuous phase with a Lagrangian analysis for the motion of the droplet phase to simulate evaporating two-phase flows, has been developed. A unique aspect of this analysis is that the Lagrangian equations for the droplet motion have been transformed into the Eulerian computational space using coordinate transformation resulting in better computational efficiency. Use of the present implicit procedure for the continuous phase makes it possible to efficiently use a locally highly refined mesh. The coupling of the continuous phase and the droplet phase analyses is such that it allows the use of convergence acceleration techniques for steady-state problems, as well as making it possible to simulate transient flows. A rapidly evaporating two-phase flow caused by spray of liquid nitrogen in gaseous nitrogen has been used as a test problem to demonstrate the computer code using this analysis.

Sabnis, J. S.↗
NASA NTRS1973

Conformal mapping technique for two-dimensional porous media and jet impingement heat transfer

Transpiration cooling and liquid metals both provide highly effective heat transfer. Using Darcy's law in porous media, and the inviscid approximation for liquid metals, the local fluid velocity in these flows equals the gradient of a potential, The energy equation and flow region are simplified when transformed into potential plane coordinates. In these coordinates the present problems are reduced to heat conduction solutions which are mapped into the physical geometry. Results are obtained for a porous region with simultaneously prescribed surface temperature and heat flux, heat transfer in a two-dimensional porous bed, and heat transfer for two liquid metal slot jets impinging on a heated plate.

Siegel, R.↗
NASA NTRS1974

Conformal mapping technique for two-dimensional porous media and jet impingement heat transfer

Transpiration cooling and liquid metals both provide highly effective heat transfer. Using Darcy's law in porous media and the inviscid approximation for liquid metals, the local fluid velocity in these flows equals the gradient of a potential. The energy equation and flow region are simplified when transformed into potential plane coordinates. In these coordinates, the present problems are reduced to heat conduction solutions which are mapped into the physical geometry. Results are obtained for a porous region with simultaneously prescribed surface temperature and heat flux, heat transfer in a two-dimensional porous bed, and heat transfer for two liquid metal slot jets impinging on a heated plate.

Siegel, R.↗
DOE OSTI2024

Atomically Precise Single-Site Catalysts via Exsolution in a Polyoxometalate–Metal–Organic-Framework Architecture

Single-site catalysts (SSCs) achieve a high catalytic performance through atomically dispersed active sites. A challenge facing the development of SSCs is aggregation of active catalytic species. Reducing the loading of these sites to very low levels is a common strategy to mitigate aggregation and sintering; however, this limits the tools that can be used to characterize the SSCs. Here we report a sintering-resistant SSC with high loading that is achieved by incorporating Anderson–Evans polyoxometalate clusters (POMs, MMo 6 O 24 , M = Rh/Pt) within NU-1000, a Zr-based metal–organic framework (MOF). The dual confinement provided by isolating the active site within the POM, then isolating the POMs within the MOF, facilitates the formation of isolated noble metal sites with low coordination numbers via exsolution from the POM during activation. The high loading (up to 3.2 wt %) that can be achieved without sintering allowed the local structure transformation in the POM cluster and the surrounding MOF to be evaluated using in situ X-ray scattering with pair distribution function (PDF) analysis. Notably, the Rh/Pt···Mo distance in the active catalyst is shorter than the M···M bond lengths in the respective bulk metals. Furthermore, models of the active cluster structure were identified based on the PDF data with complementary computation and X-ray absorption spectroscopy analysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2004

Science Using an Electrostatic Levitation Furnace in the MUCAT Sector at the APS

The original motivation for the construction of the BESL prototype was to obtain the first proof of a 50-year-old hypothesis regarding the solidification of liquid metals. Since the 1950s it has been known that under proper conditions liquid metals can be cooled below their melting temperature (undercooled) without crystallizing to the stable solid phase. In 1952 Frank proposed that this was because the atoms in the metallic liquid were arranged with the symmetry of an icosahedron, a Platonic solid consisting of 20 tetrahedra (4-sided pyramid-shaped polyhedra) arranged around a common center. Since this local atomic order is incompatible with the long-range translational periodicity of crystal phases, a barrier is formed to the formation of small regions of the crystal phase, the nucleation barrier. A proof of Frank's hypothesis required a direct correlation between measured icosahedral order in the undercooled liquid and the nucleation barrier. The tendency of sample containers to catalyze nucleation obscured this relation, requiring containerless techniques. Combining containerless processing techniques for electrostatically levitated droplets (ESL) with x-ray synchrotron methods, a team from Washington University, St. Louis, MO, NASA Marshall Space Flight Center, and MUCAT at the APS demonstrated an increasing icosahedral order in TiZrNi liquids with decreasing temperature below the melting temperature. The increased icosahedral order caused the transformation of the liquid to a metastable icosahedral quasicrystal phase, instead of the stable tetrahedrally-coordinated crystal intermetallic, giving the first clear demonstration of the connection between the nucleation barrier and the local structure of the liquid, verifying Frank's hypothesis for this alloy.

Goldman, A.↗