Convergence in the mean
Theorem proving for orthogonal systems of functions relative to convergence in mean of series
SERIES EXPANSION↗
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Results for “orthogonal”
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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3-D Deformable Grid Electomagnetic PIC for Parallel Computers
We have developed a three-dimensional non-orthogonal grid electromagnetic PIC code for parallel supercomputers. The numerical formulation is based on hexahedral cells which are logically connected cubic cells but distorted to body-fit complex geometries in physical space. An outstanding area of research is to improve the accuracy of the electromagnetic field solve on distorted meshes.
3D deformable non-orthogonal grid code PIC codes p↗
Taguchi Method Applied in Optimization of Shipley 5740 Positive Resist Deposition
Taguchi Methods of Robust Design Presents a way to optimize output process performance through organized experiments, by using orthogonal arrays for the evaluation of the process controlleable parameters.
Taguchi Method Orthogonal Arrays↗
Taguchi Method Applied in Optimization of Shipley SJR 5740 Positive Resist Deposition
Taguchi Methods of Robust Design presents a way to optimize output process performance through an organized set of experiments by using orthogonal arrays. Analysis of variance and signal-to-noise ratio is used to evaluate the contribution of each of the process controllable parameters in the realization of the process optimization. In the photoresist deposition process, there are numerous controllable parameters that can affect the surface quality and thickness of the final photoresist layer.
Taguchi Method Shipley SJR 5740 orthogonal arrays ↗
The Primordial Inflation Explorer (PIXIE)
The Primordial Inflation Explorer is an Explorer-class mission to measure the gravity-wave signature of primordial inflation through its distinctive imprint on the linear polarization of the cosmic microwave background. PIXIE uses an innovative optical design to achieve background-limited sensitivity in 400 spectral channels spanning 2.5 decades in frequency from 30 GHz to 6 THz (1 cm to 50 micron wavelength). Multi-moded non-imaging optics feed a polarizing Fourier Transform Spectrometer to produce a set of interference fringes, proportional to the difference spectrum between orthogonal linear polarizations from the two input beams. Multiple levels of symmetry and signal modulation combine to reduce the instrumental signature and confusion from unpolarized sources to negligible levels. PIXIE will map the full sky in Stokes I, Q, and U parameters with angular resolution 2.6 deg and sensitivity 0.2 μK per 1 deg square pixel. The principal science goal is the detection and characterization of linear polarization from an inflationary epoch in the early universe, with tensor-to-scalar ratio r less than 10(exp −3) at 5 standard deviations. In addition, PIXIE will measure the absolute frequency spectrum to constrain physical processes ranging from inflation to the nature of the first stars to the physical conditions within the interstellar medium of the Galaxy. We describe the PIXIE instrument and mission architecture with an emphasis on the expected level of systematic error suppression.
Primordial Inflation Explorer is an Explorer-class↗
Detecting Layer Height of Smoke Aerosols over Vegetated Land and Water Surfaces via Oxygen Absorption Bands: Hourly Results from EPIC/DSCOVR in Deep Space
We present an algorithm for retrieving aerosol layer height (ALH) and aerosol optical depth (AOD) for smoke over vegetated land and water surfaces from measurements of the Earth Polychromatic Imaging Camera (EPIC) onboard the Deep Space Climate Observatory (DSCOVR). The algorithm uses Earth-reflected radiances in six EPIC bands in the visible and near-infrared and incorporates flexible spectral fitting that accounts for specifics of land and water surface reflectivity. The fitting procedure first determines AOD using EPIC atmospheric window bands (443 nm, 551 nm, 680nm, and 780 nm), then uses oxygen (O2) A and B bands (688 nm and 764 nm) to derive ALH, which represents an optical centroid altitude. ALH retrieval over vegetated surface primarily takes advantage of measurements in the O2B band. We applied the algorithm to EPIC observations of several biomass burning events over the United States and Canada in August 2017. We found that the algorithm can be used to obtain AOD and ALH multiple times daily over water and vegetated land surface. Validation is performed against aerosol extinction profiles detected by the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) and against AOD observed at nine Aerosol Robotic Network (AERONET) sites, showing, on average, an error of 0.58 km and a bias of -0.13 km in retrieved ALH and an error of 0.05 and a bias of 0.03 in retrieved AOD. Additionally, we show that the aerosol height information retrieved by the present algorithm can potentially benefit the retrieval of aerosol properties from EPIC’s ultraviolet (UV) bands.
Cloud–Aerosol Lidar with Orthogonal Polarization (↗
Satellite-Based Evaluation of AeroCom Model Bias in Biomass Burning Regions
Global models are widely used to simulate biomass burning aerosol (BBA). Exhaustive evaluations on model representation of aerosol distributions and properties are fundamental to assess health and climate impacts of BBA. Here we conducted a comprehensive comparison of Aerosol Comparisons between Observations and Models (AeroCom) project model simulations with satellite observations. A total of 59 runs by 18 models from three AeroCom Phase-III experiments (i.e., biomass burning emissions, CTRL16, and CTRL19) and 14 satellite products of aerosols were used in the study. Aerosol optical depth (AOD) at 550 nm was investigated during the fire season over three key fire regions reflecting different fire dynamics (i.e., deforestation-dominated Amazon, Southern Hemisphere Africa where savannas are the key source of emissions, and boreal forest burning in boreal North America). The 14 satellite products were first evaluated against AErosol RObotic NETwork (AERONET) observations, with large uncertainties found. But these uncertainties had small impacts on the model evaluation that was dominated by modeling bias. Through a comparison with Polarization and Directionality of the Earth’s Reflectances measurements with the Generalized Retrieval of Aerosol and Surface Properties algorithm (POLDER-GRASP), we found that the modeled AOD values were biased by −93 % to 152 %, with most models showing significant underestimations even for the state-of-the-art aerosol modeling techniques (i.e., CTRL19). By scaling up BBA emissions, the negative biases in modeled AOD were significantly mitigated, although it yielded only negligible improvements in the correlation between models and observations, and the spatial and temporal variations in AOD biases did not change much. For models in CTRL16 and CTRL19, the large diversity in modeled AOD was in almost equal measures caused by diversity in emissions, lifetime, and the mass extinction coefficient (MEC). We found that in the AeroCom ensemble, BBA lifetime correlated significantly with particle deposition (as expected) and in turn correlated strongly with precipitation. Additional analysis based on Cloud-Aerosol LIdar with Orthogonal Polarization (CALIOP) aerosol profiles suggested that the altitude of the aerosol layer in the current models was generally too low, which also contributed to the bias in modeled lifetime. Modeled MECs exhibited significant correlations with the Ångström exponent (AE, an indicator of particle size). Comparisons with the POLDER-GRASP-observed AE suggested that the models tended to overestimate the AE (underestimated particle size), indicating a possible underestimation of MECs in models. The hygroscopic growth in most models generally agreed with observations and might not explain the overall underestimation of modeled AOD. Our results imply that current global models contain biases in important aerosol processes for BBA (e.g., emissions, removal, and optical properties) that remain to be addressed in future research.
biomass burning aerosols↗
Application of an Affine Nonlinear Galerkin Reduced-order Model to Compressible Fluid Flows
Galerkin reduced-order models (ROMs) often struggle to accurately capture multiscale fluid physics in challenging flow regimes such as flows experiencing compressibility effects. This in part stems from the global nature of both the basis construction problem and the spectral formulation itself. In this work, a multi-basis ROM is developed in an affine space based on proper orthogonal decomposition (POD) by projecting the full Navier-Stokes equations expressed in terms of the specific volume, velocity, and pressure primitive variables. The model is applied to high-fidelity numerical simulation datasets obtained for a canonical compressible flow configuration: the flow over a backward facing step at different subsonic Mach numbers. It is observed that application of an eigenvalue reassignment (ER) stabilization method is required to avoid early divergence of the ROM predictions for this configuration in the three Mach numbers tested. The sensitivity of the POD-ROM results to the choice of parameters in the stabilization algorithm is discussed.
reduced-order model↗
Application of an Affine Nonlinear Galerkin Reduced-order Model to Compressible Fluid Flows
Galerkin reduced-order models (ROMs) often struggle to accurately capture multiscale fluid physics in challenging flow regimes such as flows experiencing compressibility effects. This in part stems from the global nature of both the basis construction problem and the spectral formulation itself. In this work, a multi-basis ROM is developed in an affine space based on proper orthogonal decomposition (POD) by projecting the full Navier-Stokes equations expressed in terms of the specific volume, velocity, and pressure primitive variables. The model is applied to high-fidelity numerical simulation datasets obtained for a canonical compressible flow configuration: the flow over a backward facing step at different subsonic Mach numbers. It is observed that application of an eigenvalue reassignment (ER) stabilization method is required to avoid early divergence of the ROM predictions for this configuration in the three Mach numbers tested. The sensitivity of the POD-ROM results to the choice of parameters in the stabilization algorithm is discussed.
reduced-order model↗
Solar-angle sensor has no moving parts
To measure the direction of the sun over a spherical field of view, a cube-shaped solar sensor with a photocell on each side is used. The outputs from the six cells are fed into a computer for determining the position of the sun relative to an orthogonal coordinate system.
Exner, D. W., Jr.↗
New anemometer has fast response, measures dynamic pressure directly
A simple anemometer having a fast response to high frequency wind fluctuations by direct measurement of two drag-force components in orthogonal planes is described. It may be used to determine wind profiles to extensive heights and would be helpful in takeoff and landing of light planes.
Lynch, J. W.↗
Results of studies on a twin-gyro attitude- control system for space vehicles
Twin gyroscopic control system for three orthogonal axes of space vehicle attitude control
GYROSCOPE↗
Man's short-time tolerance to sinusoidal vibration.
Mans short time tolerance to sinusoidal vibrations at frequencies between 3 and 20 cps in three orthogonal axes
VIBRATIONAL FREQUENCY↗
Ball and socket joints provide accurate biaxial gimbal
Ball-and-socket joints are used to connect two rotating inputs to orthogonally pivoted outputs. This provides an accurate biaxial gimbal which will operate in continuous motion without backlash.
Rouze, E. R.↗
Coded noncoherent communications.
Binary digits encoding into orthogonal signals with white Gaussian noise for noncoherent communications over Rician channel
DIGITAL COMMUNICATIONS SYSTEM↗
Mount enables precision adjustment of optical-instrumentation mirror
Mirror mount assembly allows the plane of a mirror to be adjusted through small angles about two orthogonal axes. The assembly, which has a mirror mount with two independently adjustable flexure joints, allows independent precise adjustment of the mirror mount with respect to each axis.
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Computer program performs flow analysis through turbines
Computer program based on an equation for the velocity gradient along an arbitrary quasi- orthogonal analyzes flow through a turbomachine. The program obtains meridional solutions for a hub-to-shroud analysis and blade-to-blade analysis at the hub, mean, and shroud surfaces in a single computer run.
Katsanis, T.↗
Developmental instrument supplies accurate attitude and attitude-rate data
Three orthogonal-plane projection provides accuracy of readout of both attitude and attitude-rate information in an easily interpreted, uncluttered arrangement where blind navigation of a moving body is involved. The longitudinal length of the projection is constant, and independent of the pitch and roll attitudes of the moving body.
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