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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
DOE OSTI2023

Geodesic-based relaxation for deep canonical correlation analysis

Deep canonical correlation analysis (DCCA) is often applied to paired data samples from diverse sources to extract meaningful common information. However, when the data sources are heterogeneous, some of the useful information may be complementary but not exactly common. In spite of this fact, existing techniques learn maximally correlated representations from multiple views and are formulated so that they aim to yield identical latent subspaces for each view. This approach is sub-optimal in estimating the true signal subspaces for heterogeneous data sources. We propose a residual relaxation for deep canonical correlation analysis (RDCCA) based on a subspace distance metric, which generalizes the existing problem formulation and extracts representations that are better estimates of the actual, non-identical subspaces. We demonstrate that when using such a relaxation, the learned representations are closer to the true ones and that RDCCA outperforms CCA and DCCA in scenarios with heterogeneous data.

Kuschel, Maurice↗
NASA NTRS1973

Vector and tensor radiation from Schwarzschild relativistic circular geodesics.

A technique developed by Regge and Wheeler (1957) is applied in the Schwarzschild background geometry to treat the radiation emitted by a test particle moving at a speed close to the local speed of light in the vicinity of a black hole. An analytic expression is obtained for the gravitational and electromagnetic radiation spectrum of a particle traveling in a highly relativistic orbit around a Schwarzschild blac hole.

Breuer, R. A.↗
NASA NTRS1974

Radiation from highly relativistic geodesics

A number of recent works are reviewed concerning the generation and emission of gravitational waves. It is shown that at high frequencies, the generation of gravitational radiation is a local phenomenon. Two examples are described illustrating this generation when a high-energy particle collides against the space-time curvature. One, after Matzner and Nutku, uses a method of virtual photons; the other, after Chrzanowski and Misner, is based on the W.K.B. approximation, corresponding to geometric optics, for the inhomogeneous wave equation. This method uses a factorized integral representation of the Green function which is valid asymptotically to infinity in space.

Misner, C. W.↗
NASA NTRS1976

Effects of edge-rounding on geodesic lenses

A method that eliminates the need for a mathematical model is described for measuring the absolute light intensity radiated from volume chemiluminescent and fluorescent sources. This technique applies to a uniform cylindrical luminous volume, which is the geometry most often practical for the study of flowing chemiluminescent and fluorescent fluids. In this method, the necessary integration over a luminous volume is carried out experimentally, using a calibrated piston source that has as its head a disk of uniform luminosity. The relatively small total error in absolute light intensity measurements with the piston source technique represents a significant improvement over competing comparison methods. The construction of a piston source to fit the cross section of a particular cylindrical volume is straightforward, and its calibration against a standard source can be readily made while exercising normal precautions.

Wood, V. E.↗
NASA NTRS1985

Deployable Geodesic Truss

Efficiently packaged structure deployed or retracted easily. In preliminary two-bay model each bay has sets of battens connected by two longitudinal crossed members that give bay axial and torsional stiffness. Cross-members hinged in center to fold for packaging. Bays deployed and stabilized by actuators connected between center hinges of cross-members.

Mikulas, M. M., Jr.↗
NASA NTRS1988

Optimum design of geodesically stiffened composite plates

With the goal of tailorability in mind, the in-plane stiffness characteristics of a particular grid stiffened plate configuration under axial and shear loads have been studied. The contribution of the skin to the stiffener network and the resultant skin/rib interaction is analyzed. For the given plate geometry and loads, it is shown that an optimum configuration does exist. To achieve optimally designed practical plate configurations, buckling constraints need to be included in the design. Due to the complex geometry and loading of the plates, a simplified local buckling analysis of isolated stiffeners and triangular skin elements between the stiffeners is considered. Development of a stiffener buckling analysis represent stiffeners as shear deformable plate elements is presented.

Guerdal, Zafer↗
DOE OSTI2021

Complexity growth in integrable and chaotic models

We use the SYK family of models with N Majorana fermions to study the complexity of time evolution, formulated as the shortest geodesic length on the unitary group manifold between the identity and the time evolution operator, in free, integrable, and chaotic systems. Initially, the shortest geodesic follows the time evolution trajectory, and hence complexity grows linearly in time. We study how this linear growth is eventually truncated by the appearance and accumulation of conjugate points, which signal the presence of shorter geodesics intersecting the time evolution trajectory. By explicitly locating such “shortcuts” through analytical and numerical methods, we demonstrate that: (a) in the free theory, time evolution encounters conjugate points at a polynomial time; consequently complexity growth truncates at O($\sqrt{N}$), and we find an explicit operator which “fast-forwards” the free N-fermion time evolution with this complexity, (b) in a class of interacting integrable theories, the complexity is upper bounded by O(poly(N)), and (c) in chaotic theories, we argue that conjugate points do not occur until exponential times O(e N ), after which it becomes possible to find infinitesimally nearby geodesics which approximate the time evolution operator. Finally, we explore the notion of eigenstate complexity in free, integrable, and chaotic models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Chaotic LLM billiards

Abstract We study null geodesics of the ten-dimensional LLM geometries. In particular, we show that there are a subset of these null geodesics that are confined to the LLM plane. The effective dynamics of these in-plane geodesics is that of a Hamiltonian system with two degrees of freedom (a phase space of dimension 4). We show that these are chaotic. In the two-coloring of the LLM plane, if they start in the empty region, they cannot penetrate the filled region and viceversa. The dynamical problem is therefore very similar to that of a billiards problem with fixed obstacles. We study to what extent LLM geometries with many droplets may be treated as an incipient black hole and draw analogies with the fuzzball proposal. We argue that for in-plane null geodesics deep in the interior of a region with a lot of droplets, in order to exit towards theAdSboundary they will need to undergo a process that resembles diffusion. This mechanism can account for signals getting lost in the putative black hole for a very long time.

Physics↗
DOE OSTI2023

Past-completeness of inflationary spacetimes

Here, we discuss the question of whether or not inflationary spacetimes can be geodesically complete in the infinite past. Geodesic completeness is a necessary condition for averting an initial singularity during eternal inflation. It is frequently argued that cosmological models which are expanding sufficiently fast (having average Hubble expansion rate H avg > 0) must be incomplete in null and timelike past directions. This well-known conjecture relies on specific bounds on the integral of the Hubble parameter over a past- directed timelike or null geodesic. As stated, we show this claim is an open issue. We show that the calculation of H avg yields a continuum of results for a given spacetime predicated upon the underlying topological assumptions. We present an improved definition for H avg and introduce an uncountably infinite cohort of cosmological solutions which are geodesically complete despite having H avg > 0. We discuss a standardized definition for inflationary spacetimes as well as quantum (semiclassical) cosmological concerns over physically reasonable scale factors.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2012

Strong Magnetic Field Fluctuations within Filamentary Auroral Density Cavities Interpreted as VLF Saucer Sources

The Geoelectrodynamics and Electro-Optical Detection of Electron and SuprathermalIon Currents (GEODESIC) sounding rocket encountered more than 100 filamentary densitycavities associated with enhanced plasma waves at ELF (3 kHz) and VLF (310 kHz)frequencies and at altitudes of 800990 km during an auroral substorm. These cavities weresimilar in size (20 m diameter in most cases) to so-called lower-hybrid cavities (LHCs)observed by previous sounding rockets and satellites; however, in contrast, many of theGEODESIC cavities exhibited up to tenfold enhancements in magnetic wave powerthroughout the VLF band. GEODESIC also observed enhancements of ELF and VLFelectric fields both parallel and perpendicular to the geomagnetic field B0 within cavities,though the VLF E field increases were often not as large proportionally as seen in themagnetic fields. This behavior is opposite to that predicted by previously published theoriesof LHCs based on passive scattering of externally incident auroral hiss. We argue thatthe GEODESIC cavities are active wave generation sites capable of radiating VLF wavesinto the surrounding plasma and producing VLF saucers, with energy supplied by cold,upward flowing electron beams composing the auroral return current. This interpretation issupported by the observation that the most intense waves, both inside and outside cavities,occurred in regions where energetic electron precipitation was largely inhibited orabsent altogether. We suggest that the wave-enhanced cavities encountered by GEODESICwere qualitatively different from those observed by earlier spacecraft because of thefortuitous timing of the GEODESIC launch, which placed the payload at apogee within asubstorm-related return current during its most intense phase, lasting only a few minutes.

Knudsen, D. L.↗
NASA NTRS2017

Map Projection Induced Variations in Locations of Polygon Geofence Edges

This Paper under-estimates answers to the following question under various constraints: If a geofencing algorithm uses a map projection to determine whether a position is inside/outside a polygon region, how far outside/inside the polygon can the point be and the algorithm determine that it is inside/outside (the opposite and therefore incorrect answer)? Geofencing systems for unmanned aircraft systems (UAS) often model stay-in and stay-out regions using 2D polygons with minimum and maximum altitudes. The vertices of the polygons are typically input as latitude-longitude pairs, and the edges as paths between adjacent vertices. There are numerous ways to generate these paths, resulting in numerous potential locations for the edges of stay-in and stay-out regions. These paths may be geodesics on a spherical model of the earth or geodesics on the WGS84 reference ellipsoid. In geofencing applications that use map projections, these paths are inverse images of straight lines in the projected plane. This projected plane may be a projection of a spherical earth model onto a tangent plane, called an orthographic projection. Alternatively, it may be a projection where the straight lines in the projected plane correspond to straight lines in the latitudelongitude coordinate system, also called a Plate Carr´ee projection. This paper estimates distances between different edge paths and an oracle path, which is a geodesic on either the spherical earth or the WGS84 ellipsoidal earth. This paper therefore estimates how far apart different edge paths can be rather than comparing their path lengths, which are not considered. Rather, the comparision is between the actual locations of the edges between vertices. For edges drawn using orthographic projections, this maximum distance increases as the distance from the polygon vertices to the projection point increases. For edges drawn using Plate Carr´ee projections, this maximum distance increases as the vertices become further from the equator. Distances between geodesics on a spherical earth and a WGS84 ellipsoidal earth are also analyzed, using the WGS84 ellipsoid as the oracle. Bounds on the 2D distance between a straight line and a great circle path, in an orthographically projected plane rather than on the surface of the earth, have been formally verified in the PVS theorem prover, meaning that they are mathematically correct in the absence of floating point errors.

Neeley, Paula↗
DOE OSTI2020

Canonical Transformation of Potential Model Hamiltonian Mechanics to Geometrical Form I

Using the methods of symplectic geometry, we establish the existence of a canonical transformation from potential model Hamiltonians of standard form in a Euclidean space to an equivalent geometrical form on a manifold, where the corresponding motions are along geodesic curves. The advantage of this representation is that it admits the computation of geodesic deviation as a test for local stability, shown in recent previous studies to be a very effective criterion for the stability of the orbits generated by the potential model Hamiltonian. We describe here an algorithm for finding the generating function for the canonical transformation and describe some of the properties of this mapping under local diffeomorphisms. We give a convergence proof for this algorithm for the one-dimensional case, and provide a precise geometric formulation of geodesic deviation which relates the stability of the motion in the geometric form to that of the Hamiltonian standard form. We apply our methods to a simple one-dimensional harmonic oscillator and conclude with a discussion of the relation of bounded domains in the two representations for which Morse theory would be applicable.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Optical analogues to the equatorial Kerr–Newman black hole

Optical analogues to black holes allow the investigation of general relativity in a laboratory setting. Previous works have considered analogues to Schwarzschild black holes in an isotropic coordinate system; the major drawback is that required material properties diverge at the horizon. We present the dielectric permittivity and permeability tensors that exactly reproduce the equatorial Kerr–Newman metric, as well as the gradient-index material that reproduces equatorial Kerr–Newman null geodesics. Importantly, the radial profile of the scalar refractive index is finite along all trajectories except at the point of rotation reversal for counter-rotating geodesics. Construction of these analogues is feasible with available ordinary materials. A finite-difference frequency-domain solver of Maxwell’s equations is used to simulate light trajectories around a variety of Kerr–Newman black holes. For reasonably sized experimental systems, ray tracing confirms that null geodesics can be well-approximated in the lab, even when allowing for imperfect construction and experimental error.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Path-Based Dictionary Augmentation: A Framework for Improving $k$ -Sparse Image Processing

In this study, we have previously shown that augmenting orthogonal matching pursuit (OMP) with an additional step in the identification stage of each pursuit iteration yields improved $k$ -sparse reconstruction and denoising performance relative to baseline OMP. At each iteration a “path” or geodesic, is generated between the two dictionary atoms that are most correlated with the residual and from this path a new atom that has a greater correlation to the residual than either of the two bracketing atoms is selected. Here, we provide new computational results illustrating improvements in sparse coding and denoising on canonical datasets using both learned and structured dictionaries. The two methods of constructing a path are investigated for each dictionary type: the Euclidean geodesic formed by a linear combination of the two atoms and the 2-Wasserstein geodesic corresponding to the optimal transport map between the atoms. We prove here the existence of a higher-correlation atom in the Euclidean case under assumptions on the two bracketing atoms and introduce algorithmic modifications to improve the likelihood that the bracketing atoms meet those conditions. Although, we demonstrate our augmentation on OMP alone, in general it may be applied to any reconstruction algorithm that relies on the selection and sorting of high-similarity atoms during an analysis or identification phase.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1977

Feasibility investigation of integrated optics Fourier transform devices

The possibility of producing an integrated optics data processing device based upon Fourier transformations or other parallel processing techniques, and the ways in which such techniques may be used to upgrade the performance of present and projected NASA systems were investigated. Activities toward this goal include; (1) production of near-diffraction-limited geodesic lenses in glass waveguides; (2) development of grinding and polishing techniques for the production of geodesic lenses in LiNbO3 waveguides; (3) development of a characterization technique for waveguide lenses; and (4) development of a theory for corrected aspheric geodesic lenses. A holographic subtraction system was devised which should be capable of rapid on-board preprocessing of a large number of parallel data channels. The principle involved is validated in three demonstrations.

Verber, C. M.↗