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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Use of Fourier transforms for asynoptic mapping: Applications to the Upper Atmosphere Research Satellite microwave limb sounder

Fourier analysis has been applied to data obtained from limb viewing instruments on the Upper Atmosphere Research Satellite. A coordinate system rotation facilitates the efficient computation of Fourier transforms in the temporal and longitudinal domains. Fields such as ozone (O3), chlorine monoxide (ClO), temperature, and water vapor have been transformed by this process. The transforms have been inverted to provide maps of these quantities at selected times, providing a method of accurate time interpolation. Maps obtained by this process show evidence of both horizontal and vertical transport of important trace species such as O3 and ClO. An examination of the polar regions indicates that large-scale planetary variations are likely to play a significant role in transporting midstratospheric O3 into the polar regions. There is also evidence that downward transport occurs, providing a means of moving O3 into the polar vortex at lower altitudes. The transforms themselves show the structure and propagation characteristics of wave variations.

Elson, Lee S.↗
DOE OSTI2024

Learning the boundary-to-domain mapping using Lifting Product Fourier Neural Operators for partial differential equations

Neural operators such as the Fourier Neural Operator (FNO) have been shown to provide resolution-independent deep learning models that can learn mappings between function spaces. For example, an initial condition can be mapped to the solution of a partial differential equation (PDE) at a future time-step using a neural operator. Despite the popularity of neural operators, their use to predict solution functions over a domain given only data over the boundary (such as a spatially varying Dirichlet boundary condition) remains unexplored. In this paper, we refer to such problems as boundary-to-domain problems; they have a wide range of applications in areas such as fluid mechanics, solid mechanics, heat transfer etc. We present a novel FNO-based architecture, named Lifting Product FNO (or LP-FNO) which can map arbitrary boundary functions defined on the lower-dimensional boundary to a solution in the entire domain. Specifically, two FNOs defined on the lower-dimensional boundary are lifted into the higher dimensional domain using our proposed lifting product layer. We demonstrate the efficacy and resolution independence of the proposed LP-FNO for the 2D Poisson equation.

Kashi, Aditya↗
NASA NTRS1994

On determining the spectrum of primordial inhomogeneity from the COBE DMR sky maps: Method

The natural approach to a spectral analysis of data distributed on the sky employs spherical harmonic decomposition. A common problem encountered in practical astronomy is the lack of full sky coverage in the available data. For example, the removal of the Galactic plane data from the Cosmic Background Explorer (COBE) Differential Microwave Radiometer (DMR) sky maps compromises Fourier analysis of the cosmic microwave background (CMB) temperature distribution due to the loss of orthogonality of the spherical harmonics. An explicit method for constructing orthonormal functions on an incomplete (e.g., Galaxy-cut) sphere is presented. These functions should be used in the proper Fourier analysis of the COBE DMR sky maps to provide the correct input for the determination of the spectrum of primordial inhomogeneity. The results of such an analysis are presented in an accompanying Letter. A similar algebraic construction of appropriate functions can be devised for other astronomical applications.

Gorski, Krzysztof M.↗
NASA NTRS1991

Dynamics of the 4-day wave in the Southern Hemisphere polar stratosphere

Horizontal wind and temperature data are employed to investigate the dynamics of the 4-day wave in the Southern Hemisphere polar stratosphere. They were derived from synoptic maps of satellite-measured brightness temperatures, which were generated using the fast Fourier synoptic mapping technique of Salby (1982). Circulation statistics from these data are compared to those from the NMC operational stratospheric analyses, demonstrating improvements afforded by detailed treatment of asynoptic sampling effects. The 40-day wave is isolated using temporally filtered data. Several events of wave growth and decay are observed in the upper stratosphere during August 1980. Derived zonal-mean and eddy statistics suggest that the 4-day wave results from an instability of the zonal-mean flow near 55-60S, at and above 1 mb. It is inferred from climatological data that the source of the instability is the 'double-jet' structure in the upper stratosphere and mesosphere.

Randel, William J.↗
DOE OSTI2024

Crystal structure solution and high-temperature thermal expansion in NaZr 2 (PO 4 ) 3 -type materials

The NaZr 2 P 3 O 12 family of materials have shown low and tailorable thermal expansion properties. In this study, SrZr 4 P 6 O 24 (SrO·4ZrO 2 ·3P 2 O 5 ), CaZr 4 P 6 O 24 (CaO·4ZrO 2 ·3P 2 O 5 ), MgZr 4 P 6 O 24 (MgO·4ZrO 2 ·3P 2 O 5 ), NaTi 2 P 3 O 12 [½(Na 2 O·4TiO 2 ·3P 2 O 5 )], NaZr 2 P 3 O 12 [½(Na 2 O·4ZrO 2 ·3P 2 O 5 )], and related solid solutions were synthesized using the organic–inorganic steric entrapment method. The samples were characterized by in-situ high-temperature X-ray diffraction from 25 to 1500°C at the Advanced Photon Source and National Synchrotron Light Source II. The average linear thermal expansion of SrZr 4 P 6 O 24 and CaZr 4 P 6 O 24 was between −1 × 10 −6 per °C and 6 × 10 −6 per °C from 25 to 1500°C. The crystal structures of the high-temperature polymorphs of CaZr 4 P 6 O 24 and SrZr 4 P 6 O 24 with R 3 c symmetry were solved by Fourier difference mapping and Rietveld refinement. This polymorph is present above ∼1250°C. This work measured thermal expansion coefficients to 1500°C for all samples and investigated the differences in thermal expansion mechanisms between polymorphs and between compositions.

36 MATERIALS SCIENCE↗
NASA NTRS1999

Synoptic Mapping of Chemical Composition, Thermal Structure, and Air Motion from UARS Observations

An operational mapping algorithm was developed to process measurements of individual species observed by different satellite instruments on board UARS. Based on Fast Fourier Synoptic Mapping (FFSM), the algorithm accounts for the precessing orbit of UARS, the error of individual instruments, and gaps associated with instrument duty cycle and the satellite yaw maneuver. It provides synoptic structure and evolution on periods as short as 1 day, derived collectively from all observations of an individual species. The algorithm was applied to synoptically map temperature, thickness, and several chemical constituents observed by the instruments: MLS, CLAES, ISAMS, and HALOE. Each field variable observed by these instruments was mapped twice-daily in continuous global time series several months long. Mapped behavior produced via FFSM was compared against standard archived products generated via Kalman filtering. The standard map products reveal similar behavior, but are limited to features of larger scale. Tracer structure that develops through flow deformation and attending transport is therefore represented in those products more coarsely, eventually being sheared down to scales that are no longer represented properly. The synoptic time series also reveal a diurnal cycle for several of the constituents, one that emerges clearly in their space-time spectra. The zonal and meridional structure of diurnal variability was mapped by filtering the space-time spectrum, an intermediate product of FFSM, to those scales resolved by the UARS sampling. Geographical variations of the diurnal cycle have also been evaluated in its seasonal-mean structure by compositing distributions at individual local times. Both were compared to diurnal variations in chemical models and in dynamical models that account for transport by the diurnal tide. Diurnal variations were found to introduce spurious behavior into the archived products generated via Kalman filtering, behavior that is misrepresented in those synoptic time series. Aliasing by under-sampled diurnal variations introduces a bias into the time-mean structure of archived products. That systematic error is manifested as anomalous wave structure in the time-mean fields. By contrast, synoptic time series generated via FFSM faithfully represent such behavior as varying diurnally, so it does not corrupt time-mean structure. Tracer structure mapped via the above algorithm was being applied to determine the Brewer-Dobson circulation of the stratosphere through Lagrangian considerations. Preliminary results are encouraging: They reveal diabatic ascent in the tropics, balanced by diabatic descent over the winter hemisphere. This Lagrangian description of transport derived from UARS tracer measurements would be potentially valuable for diagnosing interannual changes of transport, specifically, in relation to interannual changes of total ozone. Regrettably, support was reduced to 50% of the approved funding level, leaving this component incomplete.

Salby, Murry L.↗
NASA NTRS1977

Maps of Jovian radio emission

Observations were made of Jupiter with the Westerbork telescope at all three frequencies available: 610 MHz, 1415 MHz, and 4995 MHz. The raw measurements were corrected for position errors, atmospheric extinction, Faraday rotation, clock, frequency, and baseline errors, and errors due to a shadowing effect. The data was then converted into brightness distribution of the sky by Fourier transformation. Maps of both thermal and nonthermal radiation were developed. Results indicate that the thermal disk of Jupiter measured at a wavelength of 6 cm has a temperature of 236 + or - 15 K. The radiation belts have an overall structure governed by the trapping of electrons in the dipolar field of the planet with significant beaming of the synchrotron radiation into the plane of the magnetic equator.

Depater, I.↗
DOE OSTI2015

FEM: Feature-enhanced map

A method is presented that modifies a 2 m F obs - D F model σ A -weighted map such that the resulting map can strengthen a weak signal, if present, and can reduce model bias and noise. The method consists of first randomizing the starting map and filling in missing reflections using multiple methods. This is followed by restricting the map to regions with convincing density and the application of sharpening. The final map is then created by combining a series of histogram-equalized intermediate maps. In the test cases shown, the maps produced in this way are found to have increased interpretability and decreased model bias compared with the starting 2 m F obs - D F model σ A -weighted map.

36 MATERIALS SCIENCE↗
DOE OSTI2013

A fast, high-order solver for the Grad–Shafranov equation

We present a new fast solver to calculate fixed-boundary plasma equilibria in toroidally axisymmetric geometries. By combining conformal mapping with Fourier and integral equation methods on the unit disk, we show that high-order accuracy can be achieved for the solution of the equilibrium equation and its first and second derivatives. Smooth arbitrary plasma cross-sections as well as arbitrary pressure and poloidal current profiles are used as initial data for the solver. Equilibria with large Shafranov shifts can be computed without difficulty. Spectral convergence is demonstrated by comparing the numerical solution with a known exact analytic solution. A fusion-relevant example of an equilibrium with a pressure pedestal is also presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Impedance-Based Detection of NO 2 Using Ni-MOF-74: Influence of Competitive Gas Adsorption

Chemically robust, low-power sensors are needed for the direct electrical detection of toxic gases. Metal–organic frameworks (MOFs) offer exceptional chemical and structural tunability to meet this challenge, though further understanding is needed regarding how coadsorbed gases influence or interfere with the electrical response. To probe the influence of competitive gases on trace NO 2 detection in a simulated flue gas stream, a combined structure–property study integrating synchrotron powder diffraction and pair distribution function analyses was undertaken, to elucidate how structural changes associated with gas binding inside Ni-MOF-74 pores correlate with the electrical response from Ni-MOF-74-based sensors. Data were evaluated for 16 gas combinations of N 2 , NO 2 , SO 2 , CO 2 , and H 2 O at 50 °C. Fourier difference maps from a rigid-body Rietveld analysis showed that additional electron density localized around the Ni-MOF-74 lattice correlated with large decreases in Ni-MOF-74 film resistance of up to a factor of 6 × 10 3 , observed only when NO 2 was present. These changes in resistance were significantly amplified by the presence of competing gases, except for CO 2 . Without NO 2 , H 2 O rapidly (<120 s) produced small (1–3×) decreases in resistance, though this effect could be differentiated from the slower adsorption of NO 2 by the evaluation of the MOF’s capacitance. Furthermore, samples exposed to H 2 O displayed a significant shift in lattice parameters toward a larger lattice and more diffuse charge density in the MOF pore. Evaluating the Ni-MOF-74 impedance in real time, NO 2 adsorption was associated with two electrically distinct processes, the faster of which was inhibited by competitive adsorption of CO 2 . Together, this work points to the unique interaction of NO 2 and other specific gases (e.g., H 2 O, SO 2 ) with the MOF’s surface, leading to orders of magnitude decrease in MOF resistance and enhanced NO2 detection. Finally, understanding and leveraging these coadsorbed gases will further improve the gas detection properties of MOF materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1978

Very long baseline interferometric observations of the hydroxyl masers in VY Canis Majoris

Results are presented for spectral-line VLBI observations of the OH emission from VY CMa. The main-line (1665 and 1667 MHz) emission was mapped with an angular resolution of 0.02 arcsec by analyzing interferometer phase data. The main-line emission comes from many maser components of apparent size less than 0.03 arcsec which are separated by up to 0.5 arcsec. New maser features near the center of the OH spectra were detected and found to lie within the region encompassed by the low-velocity OH emission. The 1612-MHz emission was mapped by Fourier inversion of the VLBI data from two baselines. All spatially isolated maser components appeared smaller than 0.15 arcsec; however, the maser emission is very complex at most velocities. Maser components within a velocity range of 1.3 km/s are often separated by more than 1 arcsec, while components more than 10 km/s apart in each emission complex are often coincident to 0.2 arcsec.

Reid, M. J.↗
NASA NTRS1992

Direct numerical simulations of a spatially developing plane wake

In the present paper, direct numerical methods by which to simulate the spatially developing free shear flows in the transitional region are described and the numerical results of a spatially developing plane wake are presented. The incompressible time-dependent Navier-Stokes equations were solved using Pade finite difference approximations in the streamwise direction, a mapped pseudospectral Fourier method in the cross-stream direction, and a third-order compact Runge-Kutta scheme for time advancement. The unstable modes of the Orr-Sommerfeld equations were used to perturb the inlet of the wake. Statistical analyses were performed and some numerical results were compared with experimental measurements. When only the fundamental mode is forced, the energy spectra show amplification of the fundamental and its higher harmonics. In this case, unperturbed alternate vortices develop in the saturation region of the wake. The phase jitter around the fundamental frequency plays a critical role in generating vortices of random shape and spacing. Large- and small-scale distortions of the fundamental structure are observed. Pairing of vortices of the same sign is observed, as well as vortex coupling of vortices of the opposite sign.

Maekawa, Hiroshi↗
NASA NTRS2003

Optical Tweezers Array and Nimble Tweezers Probe Generated by Spatial- Light Modulator

An optical tweezers is being developed at the NASA Glenn Research Center as a visiblelight interface between ubiquitous laser technologies and the interrogation, visualization, manufacture, control, and energization of nanostructures such as silicon carbide (SiC) nanotubes. The tweezers uses one or more focused laser beams to hold micrometer-sized particles called tools (sometimes called tips in atomic-force-microscope terminology). A strongly focused laser beam has an associated light-pressure gradient that is strong enough to pull small particles to the focus, in spite of the oppositely directed scattering force; "optical tweezers" is the common term for this effect. The objective is to use the tools to create carefully shaped secondary traps to hold and assemble nanostructures that may contain from tens to hundreds of atoms. The interaction between a tool and the nanostructures is to be monitored optically as is done with scanning probe microscopes. One of the initial efforts has been to create, shape, and control multiple tweezers beams. To this end, a programmable spatial-light modulator (SLM) has been used to modify the phase of a laser beam at up to 480 by 480 points. One program creates multiple, independently controllable tweezer beams whose shapes can be tailored by making the SLM an adaptive mirror in an interferometer (ref. 1). The beams leave the SLM at different angles, and an optical Fourier transform maps these beams to different positions in the focal plane of a microscope objective. The following figure shows two arrays of multiple beams created in this manner. The patterns displayed above the beam array control the intensity-to-phase transformation required in programming the SLM. Three of the seven beams displayed can be used as independently controllable beams.

Decker, Arthur J.↗
DOE OSTI2021

Fourier Neural Networks as Function Approximators and Differential Equation Solvers

We present a Fourier neural network (FNN) that can be mapped directly to the Fourier decomposition. The choice of activation and loss function yields results that replicate a Fourier series expansion closely while preserving a straightforward architecture with a single hidden layer. The simplicity of this network architecture facilitates the integration with any other higher-complexity networks, at a data pre- or postprocessing stage. We validate this FNN on naturally periodic smooth functions and on piecewise continuous periodic functions. We showcase the use of this FNN for modeling or solving partial differential equations with periodic boundary conditions. The main advantages of the current approach are the validity of the solution outside the training region, interpretability of the trained model, and simplicity of use.

Fourier decomposition↗
DOE OSTI2013

Quantization maps, algebra representation, and non-commutative Fourier transform for Lie groups

The phase space given by the cotangent bundle of a Lie group appears in the context of several models for physical systems. A representation for the quantum system in terms of non-commutative functions on the (dual) Lie algebra, and a generalized notion of (non-commutative) Fourier transform, different from standard harmonic analysis, has been recently developed, and found several applications, especially in the quantum gravity literature. We show that this algebra representation can be defined on the sole basis of a quantization map of the classical Poisson algebra, and identify the conditions for its existence. In particular, the corresponding non-commutative star-product carried by this representation is obtained directly from the quantization map via deformation quantization. We then clarify under which conditions a unitary intertwiner between such algebra representation and the usual group representation can be constructed giving rise to the non-commutative plane waves and consequently, the non-commutative Fourier transform. The compact groups U(1) and SU(2) are considered for different choices of quantization maps, such as the symmetric and the Duflo map, and we exhibit the corresponding star-products, algebra representations, and non-commutative plane waves.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Synthesis and structure of a stuffed derivative of α-quartz, Mg 0.5 AlSiO 4

A structural derivative of quartz with the composition Mg 0.5 AlSiO 4 has been grown from glass and characterized using synchrotron X-ray diffraction (XRD), transmission electron microscopy (TEM), and 29 Si nuclear magnetic resonance (NMR) spectroscopy. Rietveld analysis of the XRD data indicates that the framework of Mg 0.5 AlSiO 4 is isostructural with α-quartz, rather than β-quartz, as is consistent with previous theoretical modeling (Sternitzke and Müller 1991). Al and Si exhibit long-range disorder over the framework tetrahedral sites, indicated by the absence of the superlattice reflections corresponding to the doubling of c relative to that of quartz. Nevertheless, 29 Si NMR measurements show that Al and Si exhibit partial short-range order with an ordering degree of 56%. Electron diffraction reveals superlattice reflections indicative of doubled periodicities along the a-axes. In conclusion, Fourier electron density maps show that Mg occupies channel sites that each are bonded to six O atoms, in contrast to the tetrahedral coordination of Li in the β-quartz-type framework for β-eucryptite, LiAlSiO 4 . Furthermore, the concentrations of Mg in adjacent channels are different, resulting in framework distortions that generate the superstructures along a.

36 MATERIALS SCIENCE↗
NASA NTRS1992

Fourier/Chebyshev methods for the incompressible Navier-Stokes equations in finite domains

A fully spectral numerical scheme for the incompressible Navier-Stokes equations in domains which are infinite or semi-infinite in one dimension. The domain is not mapped, and standard Fourier or Chebyshev expansions can be used. The handling of the infinite domain does not introduce any significant overhead. The scheme assumes that the vorticity in the flow is essentially concentrated in a finite region, which is represented numerically by standard spectral collocation methods. To accomodate the slow exponential decay of the velocities at infinity, extra expansion functions are introduced, which are handled analytically. A detailed error analysis is presented, and two applications to Direct Numerical Simulation of turbulent flows are discussed in relation with the numerical performance of the scheme.

Corral, Roque↗