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At least 91 records · Page 5

High-Frequency Testing of Composite Fan Vanes With Erosion-Resistant Coating Conducted

The mechanical integrity of hard, erosion-resistant coatings were tested using the Structural Dynamics Laboratory at the NASA Glenn Research Center. Under the guidance of Structural Mechanics and Dynamics Branch personnel, fixturing and test procedures were developed at Glenn to simulate engine vibratory conditions on coated polymer-matrix- composite bypass vanes using a slip table in the Structural Dynamics Laboratory. Results from the high-frequency mechanical bench testing, along with concurrent erosion testing of coupons and vanes, provided sufficient confidence to engine-endurance test similarly coated vane segments. The knowledge gained from this program will be applied to the development of oxidation- and erosion-resistant coatings for polymer matrix composite blades and vanes in future advanced turbine engines. Fan bypass vanes from the AE3007 (Rolls Royce America, Indianapolis, IN) gas turbine engine were coated by Engelhard (Windsor, CT) with compliant bond coatings and hard ceramic coatings. The coatings were developed collaboratively by Glenn and Allison Advanced Development Corporation (AADC)/Rolls Royce America through research sponsored by the High-Temperature Engine Materials Technology Project (HITEMP) and the Higher Operating Temperature Propulsion Components (HOTPC) project. High-cycle fatigue was performed through high-frequency vibratory testing on a shaker table. Vane resonant frequency modes were surveyed from 50 to 3000 Hz at input loads from 1g to 55g on both uncoated production vanes and vanes with the erosion-resistant coating. Vanes were instrumented with both lightweight accelerometers and strain gauges to establish resonance, mode shape, and strain amplitudes. Two high-frequency dwell conditions were chosen to excite two strain levels: one approaching the vane's maximum allowable design strain and another near the expected maximum strain during engine operation. Six specimens were tested per dwell condition. Pretest and posttest inspections were performed optically at up to 60 magnification and using a fluorescent-dye penetrant. Accumulation of 10 million cycles at a strain amplitude of two to three times that expected in the engine (approximately 670 Hz and 20g) led to the development of multiple cracks in the coating that were only detectable using fluorescent-dye penetrant inspection. Cracks were prevalent on the trailing edge and on the convex side of the midsection. No cracking or spalling was evident using standard optical inspection at up to 60 magnification. Further inspection may reveal whether these fine cracks penetrated the coating or were strictly on the surface. The dwell condition that simulated actual engine conditions produced no obvious surface flaws even after up to 80 million cycles had been accumulated at strain amplitudes produced at approximately 1500 Hz and 45g.

Bowman, Cheryl L.↗

The radial phase variation of reversed-shear and toroidicity-induced Alfvén eigenmodes in DIII-D

The eigenfunction of an instability contains information about energy flow in the wave. Here, the amplitude and phase of electron cyclotron emission radiometer data from hundreds of DIII-D reversed shear Alfvén eigenmodes (RSAE) and toroidicity-induced Alfvén eigenmodes (TAE) are analyzed along the outboard horizontal midplane. The radial phase profile can be flat, linearly rising or falling, convex or concave; in other words, a wide variety of shapes is observed. For a particular mode, often the radial phase profile remains approximately constant as the mode evolves in time but sometimes it changes rapidly. Many TAEs and some RSAEs have phase profiles that are rather flat where the mode amplitude is largest but rise steadily by ~2π at large major radius. Rapid phase changes are observed when the frequencies of an RSAE and TAE overlap and the modes couple. The phase profile depends weakly on the fast-ion gradient that would appear in the absence of wave-induced transport. Linear and quadratic fits to the phase profiles, together with many plasma parameters, are assembled into RSAE and TAE databases. In both cases, large variability is observed. For RSAEs, the strongest phase dependencies are on electron temperature T e , RSAE mode frequency, and the density of carbon impurities. For TAEs, the strongest dependencies are on beam power and major radius of the mode. In general, the average RSAE radial phase profile is essentially flat but the TAE profile has non-zero slope and curvature.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

An application of the WKBJ technique to the on-surface radiation condition

The on-surface radiation-condition method and the WKBJ method for approximating solutions to differential equations are used to derive an analytic formula for the surface currents on a two-dimensional perfectly conducting convex target. The currents are induced by an incident TE-polarized plane wave. The case of a circular cylinder is used to demonstrate the usefulness of the combined methods. It is shown that a two-term expansion yields good results for the surface currents and excellent results for the ensuing bistatic radar cross section.

Moore, Thomas G.↗

Quantum mixed state compiling

The task of learning a quantum circuit to prepare a given mixed state is a fundamental quantum subroutine. We present a variational quantum algorithm (VQA) to learn mixed states which is suitable for near-term hardware. Our algorithm represents a generalization of previous VQAs that aimed at learning preparation circuits for pure states. We consider two different ansätze for compiling the target state; the first is based on learning a purification of the state and the second on representing it as a convex combination of pure states. In both cases, the resources required to store and manipulate the compiled state grow with the rank of the approximation. Thus, by learning a lower rank approximation of the target state, our algorithm provides a means of compressing a state for more efficient processing. As a byproduct of our algorithm, one effectively learns the principal components of the target state, and hence our algorithm further provides a new method for principal component analysis. We investigate the efficacy of our algorithm through extensive numerical implementations, showing that typical random states and thermal states of many body systems may be learnt this way. Additionally, we demonstrate on quantum hardware how our algorithm can be used to study hardware noise-induced states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Variational Quantum Algorithms for Semidefinite Programming

A semidefinite program (SDP) is a particular kind of convex optimization problem with applications in operations research, combinatorial optimization, quantum information science, and beyond. In this work, we propose variational quantum algorithms for approximately solving SDPs. For one class of SDPs, we provide a rigorous analysis of their convergence to approximate locally optimal solutions, under the assumption that they are weakly constrained (i.e., N " M, where N is the dimension of the input matrices and M is the number of constraints). We also provide algorithms for a more general class of SDPs that requires fewer assumptions. Finally, we numerically simulate our quantum algorithms for applications such as MaxCut, and the results of these simulations provide evidence that convergence still occurs in noisy settings.

97 MATHEMATICS AND COMPUTING↗

Variational Quantum Algorithms for Semidefinite Programming

A semidefinite program (SDP) is a particular kind of convex optimization problem with applications in operations research, combinatorial optimization, quantum information science, and beyond. In this work, we propose variational quantum algorithms for approximately solving SDPs. For one class of SDPs, we provide a rigorous analysis of their convergence to approximate locally optimal solutions, under the assumption that they are weakly constrained (i.e., N$\gg$M, where N is the dimension of the input matrices and M is the number of constraints). We also provide algorithms for a more general class of SDPs that requires fewer assumptions. Finally, we numerically simulate our quantum algorithms for applications such as MaxCut, and the results of these simulations provide evidence that convergence still occurs in noisy settings.

97 MATHEMATICS AND COMPUTING↗

Effect of curvature on stationary crossflow instability of a three-dimensional boundary layer

An incompressible three-dimensional laminar boundary-layer flow over a swept wing is used as a model to study both the wall-curvature and streamline-curvature effects on the stationary crossflow instability. The basic state is obtained by solving the full Navier-Stokes (N-S) equations numerically. The linear disturbance equations are cast on a fixed, body-intrinsic, curvilinear coordinate system. Those nonparallel terms which contribute mainly to the streamline-curvature effect are retained in the formulation of the disturbance equations and approximated by their local finite difference values. The resulting eigenvalue problem is solved by a Chebyshev collocation method. The present results indicate that the convex wall curvature has a stabilizing effect, whereas the streamline curvature has a destabilizing effect. A validation of these effects with an N-S solution for the linear disturbance flow is provided.

Lin, Ray-Sing↗

An optimization method for chaotic turbulent flow

Evidence indicates that quantities-of-interest in some turbulent flows can be controlled despite the overall chaotic dynamics. It is typically thought that this is via relatively deterministic, larger-scale components of the turbulence. However, finding such controls, if they exist, is challenging because chaos causes sensitivity gradients to explode and the search space to become intractably non-convex. This challenge is analyzed, and a penalty method is introduced to cope with it. In the new approach, the time domain is broken into segments approximately matching the chaos time scales, so that the solution within each segment is both physical and relatively deterministic. The initial condition of each segment is included in an adjoint-based gradient optimization, which temporarily introduces artificial Δq discontinuities in the overall solution. The optimization then proceeds in stages with increasing penalization of Δq. The method is developed and illustrated for a logistic map, the Lorenz Equation, and an advection augmented Kuramoto–Sivashinsky Equation. These examples show how the Δq temporarily increases the search scale prior to the strong Δq → 0 penalization that recovers a physical solution. It is then applied to turbulent Kolmogorov flow, for which it also far outperforms a standard adjoint-based gradient search. Finally, the utility of such an optimized chaotic solution is discussed.

97 MATHEMATICS AND COMPUTING↗

Monolithic afocal telescope

An afocal monolithic optical element formed of a shallow cylinder of optical material (glass, polymer, etc.) with fast aspheric surfaces, nominally confocal paraboloids, configured on the front and back surfaces. The front surface is substantially planar, and this lends itself to deposition of multi-layer stacks of thin dielectric and metal films to create a filter for rejecting out-of-band light. However, an aspheric section (for example, a paraboloid) can either be ground into a small area of this surface (for a Cassegrain-type telescope) or attached to the planar surface (for a Gregorian-type telescope). This aspheric section of the surface is then silvered to create the telescope's secondary mirror. The rear surface of the cylinder is figured into a steep, convex asphere (again, a paraboloid in the examples), and also made reflective to form the telescope's primary mirror. A small section of the rear surface (approximately the size of the secondary obscuration, depending on the required field of the telescope) is ground flat to provide an unpowered surface through which the collimated light beam can exit the optical element. This portion of the rear surface is made to transmit the light concentrated by the reflective surfaces, and can support the deposition of a spectral filter.

Roberts, William T.↗

An evaluation of nozzle relaminarization using Low Reynolds Number k-epsilon turbulence models

Two nozzle flowfields are evaluated numerically using a Low Reynolds k-epsilon turbulence model to examine possible boundary layer relaminarization. Flow enters the scramjet-like nozzles at a Mach Number of approximately 4.5 and is expanded around smooth shoulders to an exit Mach number of about 6.5. The strong streamwise acceleration and large favorable pressure gradients act with the convex curvature to form small regions of laminar-like boundary layer behavior along the expansion surface. Two relaminarization criteria are evaluated and they both predict relaminarization to be occurring, with the trends accurately modeled by the Low-Reynolds Number turbulence model that is used. The Baldwin-Lomax turbulence model cannot model the near-wall changes that take place in the rapidly accelerating boundary layer, but it proves to be useful in providing the acceleration parameters used in predicting the potential for relaminarization.

Jentink, Thomas N.↗

The Effect of Curvature on the Transition from Laminar to Turbulent Boundary Layer

In the flow over the upper surface of a wing, a discrepancy between the predicted and actual point of transition from laminar to turbulent boundary layer was found. This effect may be due to the comparatively small radius of curvature of the upper surface of the wing. Tests were undertaken to investigate this effect. As far as the authors know, the present investigation is the first to show that curvature has a pronounced effect on the transition of the boundary layer from the laminar to the turbulent state. It appears that three important results have been obtained thus far. First, the experimental points for the convex and concave side of the sheet are consistent with each other and, with the experimental accuracy involved, lie on the same curve. Second, this curve can be approximated by a straight line. Third, the order of magnitude of the variation is such that the curvature ordinarily used on the upper surface of an airplane wing might double the critical Reynolds number.

Clauser, Milton↗

FedOSAA: Improving Federated Learning with One-Step Anderson Acceleration

Federated learning (FL) is a distributed machine learning approach that enables multiple local clients and a central server to collaboratively train a model while keeping the data on their own devices. First-order methods, particularly those incorporating variance reduction techniques, are the most widely used FL algorithms due to their simple implementation and stable performance. However, these methods tend to be slow and require a large number of communication rounds to reach the global minimizer. We propose FedOSAA, a novel approach that preserves the simplicity of first-order methods while achieving the rapid convergence typically associated with second-order methods. Our approach applies one Anderson acceleration (AA) step following classical local updates based on first-order methods with variance reduction, such as FedSVRG and SCAFFOLD, during local training. This AA step is able to leverage curvature information from the history points and gives a new update that approximates the Newton-GMRES direction, thereby significantly improving the convergence. We establish a local linear convergence rate to the global minimizer of FedOSAA for smooth and strongly convex loss functions. Numerical comparisons show that FedOSAA substantially improves the communication and computation efficiency of the original first-order methods, achieving performance comparable to second-order methods like GIANT.

Feng, Xue [University of California, Davis]↗

Multiscale Morphological Filtering for Analysis of Noisy and Complex Images

Images acquired with passive sensing techniques suffer from illumination variations and poor local contrasts that create major difficulties in interpretation and identification tasks. On the other hand, images acquired with active sensing techniques based on monochromatic illumination are degraded with speckle noise. Mathematical morphology offers elegant techniques to handle a wide range of image degradation problems. Unlike linear filters, morphological filters do not blur the edges and hence maintain higher image resolution. Their rich mathematical framework facilitates the design and analysis of these filters as well as their hardware implementation. Morphological filters are easier to implement and are more cost effective and efficient than several conventional linear filters. Morphological filters to remove speckle noise while maintaining high resolution and preserving thin image regions that are particularly vulnerable to speckle noise were developed and applied to SAR imagery. These filters used combination of linear (one-dimensional) structuring elements in different (typically four) orientations. Although this approach preserves more details than the simple morphological filters using two-dimensional structuring elements, the limited orientations of one-dimensional elements approximate the fine details of the region boundaries. A more robust filter designed recently overcomes the limitation of the fixed orientations. This filter uses a combination of concave and convex structuring elements. Morphological operators are also useful in extracting features from visible and infrared imagery. A multiresolution image pyramid obtained with successive filtering and a subsampling process aids in the removal of the illumination variations and enhances local contrasts. A morphology-based interpolation scheme was also introduced to reduce intensity discontinuities created in any morphological filtering task. The generality of morphological filtering techniques in extracting information from a wide variety of images obtained with active and passive sensing techniques is discussed. Such techniques are particularly useful in obtaining more information from fusion of complex images by different sensors such as SAR, visible, and infrared.

Kher, A.↗

Nonlinear Matrix Approximation with Radial Basis Function Components

We introduce and investigate matrix approximation by decomposition into a sum of radial basis function (RBF) components. An RBF component is a generalization of the outer product between a pair of vectors, where an RBF function replaces the scalar multiplication between individual vector elements. Even though the RBF functions are positive definite, the summation across components is not restricted to convex combinations and allows us to compute the decomposition for any real matrix that is not necessarily symmetric or positive definite. We formulate the problem of seeking such a decomposition as an optimization problem with a nonlinear and non-convex loss function. Several modern versions of the gradient descent method, including their scalable stochastic counterparts, are used to solve this problem. We provide extensive empirical evidence of the effectiveness of the RBF decomposition and that of the gradient-based fitting algorithm. While being conceptually motivated by singular value decomposition (SVD), our proposed nonlinear counterpart outperforms SVD by drastically reducing the memory required to approximate a data matrix with the same L2 error for a wide range of matrix types. For example, it leads to 2 to 6 times memory save for Gaussian noise, graph adjacency matrices, and kernel matrices. Moreover, this proximity-based decomposition can offer additional interpretability in applications that involve, e.g., capturing the inner low-dimensional structure of the data, retaining graph connectivity structure, and preserving the acutance of images.

Rebrova, Elizaveta↗

Geomorphology of Ma'adim Vallis, Mars,and Associated Paleolake Basins

Ma'adim Vallis, one of the largest valleys in the Martian highlands, appears to have originated by catastrophic overflow of a large paleola ke located south of the valley heads. Ma'adim Vallis debouched to Gus ev crater, 900 km to the north, the landing site for the Spirit Mars Exploration Rover. Support for the paleolake overflow hypothesis come s from the following characteristics: (I) With a channel width of 3 km at its head, Ma'adim Vallis originates at two (eastern and western) gaps incised into the divide of the approximately 1.1 M km(exp 2) enc losed Eridania head basin, which suggests a lake as the water source. (2) The sinuous course of Ma'adim Vallis is consistent with overland flow controlled by preexisting surface topography, and structural con trol is not evident or required to explain the valley course. (3) The nearly constant approximately 5 km width of the inner channel through crater rim breaches, the anastomosing course of the wide western tri butary, the migration of the inner channel to the outer margins of be nds in the valley's lower reach, a medial sedimentary bar approximate ly 200 m in height, and a step-pool" sequence are consistent with modeled flows of 1-5 x l0 (exp 6) m(exp 3)/s. Peak discharges were likely higher but are poorly constrained by the relict channel geometry. (4 ) Small direct tributary valleys to Ma'adim Vallis have convex-up lon gitudinal profiles, suggesting a hanging relationship to a valley that was incised quickly relative to the timescales of tributary developm ent. (5) The Eridania basin had adequate volume between the initial d ivide and the incised gap elevations to carve Ma'adim Vallis during a single flood. (6) The Eridania basin is composed of many overlapping , highly degraded and deeply buried impact craters. The floor materials of the six largest craters have an unusually high internal relief ( approximately 1 km) and slope (approximately 0.5-1.5 degrees) among d egraded Martian craters, which are usually flat-floored. Long-term, fluvial sediment transport appears to have been inhibited within these craters, and the topography is inconsistent with basaltic infilling. (7) Fluvial valleys do not dissect the slopes of these deeper crater floor depressions, unlike similar slopes that are dissected at higher levels in the watershed. These characteristics (6, 7) suggest that wa ter mantled at least the lower parts of the Eridania basin floor thro ughout the period of relatively intense erosion early in Martian hist ory. The lake level increased and an overflow occurred near the close of the Noachian (age determined using >5 km crater counts). Initially , the Eridania basin debouched northward at two locations into the in termediate basin, a highly degraded impact crater approximately 500 k m in diameter. As this intermediate basin was temporarily filled with water, erosion took place first along the lower (northern) reach of Ma'adim Vallis, debouching to Gusev crater. The western overflow point was later abandoned, and erosion of the intermediate basin interior was concentrated along the eastern pathway. Subsequent air fall depos ition, impact gardening, tectonism, and limited fluvial erosion modified the Eridania basin region, so evidence for a paleolake is restrict ed to larger landforms that could survive post-Noachian degradation p rocesses.

Irwin, Rossman, P., III↗

The shape of asteroid 1917 Cuyo

Lightcurves obtained for 1917 Cuyo at solar phase angles near 54 degrees have an amplitude delta m = 0.44 mag. However, convex-profile inversion of the lightcurves yields an estimate of the asteroid's mean cross section (C, a 2-D average of the 3-D shape) that is only slightly noncircular, with an elongation approximately 1.15. The estimate of C undoubtedly contains systematic errors, the most severe of which could arise from non-equatorial viewing/illumination geometry. However, Cuyo's radar echo shows very little variation in bandwidth vs. rotation phase, supporting the hypothesis that this asteroid's elongation is rather modest.

Ostro, Steven J.↗

Optical Testing of Diamond Machined, Aspheric Mirrors for Groundbased, Near-IR Astronomy

The Infrared Multi-Object Spectrometer (IRMOS) is a facility-class instrument for the Kitt Peak National Observatory 4 and 2.1 meter telescopes. IRMOS is a near-IR (0.8-2.5 micron) spectrometer and operates at approximately 80 K. The 6061-T651 aluminum bench and mirrors constitute an athermal design. The instrument produces simultaneous spectra at low- to mid-resolving power (R=lambda/delta lambda= 300-3000) of approximately 100 objects in its 2.8 x 2.0 arcmin field. We describe ambient and cryogenic optical testing of the IRMOS mirrors across a broad range in spatial frequency (figure error, mid-frequency error, and microroughness). The mirrors include three rotationally symmetric, off-axis conic sections, one off-axis biconic, and several flat fold mirrors. The symmetric mirrors include convex and concave prolate and oblate ellipsoids. They range in aperture from 94x86 mm to 286x269 mm and in f-number from 0.9 to 2.4. The biconic mirror is concave and has a 94x76 mm aperture, R(sub x)=377 mm, k(sub x)=0.0778, R(sub y)=407 mm, and k(sub y)=0.1265 and is decentered by -2 mm in X and 227 mm in Y. All of the mirrors have an aspect ratio of approximately 6:1. The surface error fabrication tolerances are less than 10 nm RMS microroughness, 'best effort' for mid-frequency error, and less than 63.3 nm RMS figure error. Ambient temperature (approximately 293 K) testing is performed for each of the three surface error regimes, and figure testing is also performed at approximately 80 K. Operation of the ADE Phaseshift MicroXAM white light interferometer (micro-roughness) and the Bauer Model 200 profilometer (mid-frequency error) is described. Both the sag and conic values of the aspheric mirrors make these tests challenging. Figure testing is performed using a Zygo GPI interferometer, custom computer generated holograms (CGH), and optomechanical alignment fiducials. Cryogenic CGH null testing is discussed in detail. We discuss complications such as the change in prescription with temperature and thermal gradients. Correction for the effect of the dewar window is also covered. We discuss the error budget for the optical test and alignment procedure. Data reduction is accomplished using commercial optical design and data analysis software packages. Results from CGH testing at cryogenic temperatures are encouraging thus far.

Chambers, V. John↗

The Li–F–H ternary system at high pressures

Evolutionary crystal structure prediction searches have been employed to explore the ternary Li-F-H system at 300 GPa. Metastable phases were uncovered within the static lattice approximation, with LiF 3 H 2 , LiF 2 H, Li 3 F 4 H, LiF 4 H 4 , Li 2 F 3 H and LiF 3 H lying within 50 meV/atom of the 0 K convex hull. All of these phases contain H n F¯ n+1 (n = 1; 2) anions, and Li + cations. Other structural motifs such as LiF slabs, $H$ $^{+}_{3}$ molecules and F δ- ions are present in some of the low enthalpy Li-F-H structures. The bonding within the H n F¯ n+1 molecules, which may be bent or linear, symmetric or asymmetric, is analyzed. The five phases closest to the hull are insulators, while LiF 3 H is metallic and predicted to have a vanishingly small superconducting critical temperature. Li 3 F 4 H is predicted to be stable at zero pressure. Furthermore, this study lays the foundation for future investigations of the role of temperature and anharmonicity on the stability and properties of compounds and alloys in the Li-F-H ternary system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗