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NASA NTRS1953

Impingement of water droplets on wedges and diamond airfoils at supersonic speeds

An analytical solution has been obtained for the equations of motion of water droplets impinging on a wedge in a two-dimensional supersonic flow field with a shock wave attached to the wedge. The closed-form solution yields analytical expressions for the equation of the droplet trajectory, the local rate of impingement and the impingement velocity at any point on the wedge surface, and the total rate of impingement. The analytical expressions are utilized to determine the impingement on the forward surfaces of diamond airfoils in supersonic flow fields with attached shock waves. The results presented include the following conditions: droplet diameters from 2 to 100 microns, pressure altitudes from sea level to 30,000 feet, free-stream static temperatures from 420 degrees to 460 degrees R. Also, free-stream Mach numbers from 1.1 to 2.0, semi-apex angles for the wedge from 1.14 degrees to 7.97 degrees, thickness-to-chord ratios for the diamond airfoil from 0.02 to 0.14, chord lengths from 1 to 20 feet, and angles of attack from zero to the inverse tangent of the airfoil thickness-to-chord ratio.

SURFACE CONDITIONS - WING SECTIONS↗

NASA NTRS1954

Experimental investigation at Mach numbers 1.88, 3.16, and 3.83 of pressure drag of wedge diverters simulating boundary-layer-removal systems for side inlets

The pressure drag coefficients for a number of simulated wedge diverter boundary-layer-removal systems for side inlets were obtained at Mach numbers of 1.88m 3.16, and 3.83. Wedge included angle, wedge height, and wedge axial position relative to the splitter plate were independently varied for unswept and swept splitter plate configurations immersed in the turbulent boundary layer of a flat plate. Friction and total drag coefficients for several configurations were also obtained at Mach number 3.16

Piercy, Thomas G↗

NASA NTRS1952

An Experimental Investigation of Transonic Flow Past Two-Dimensional Wedge and Circular-Arc Sections Using A Mach-Zehnder Interferometer

Report presents the results of interferometer measurements of the flow field near two-dimensional wedge and circular-arc sections of zero angle of attack at high-subsonic and low-supersonic velocities. Both subsonic flow with local supersonic zone and supersonic flow with detached shock wave have been investigated. Pressure distributions and drag coefficients as a function of Mach number have been obtained. The wedge data are compared with the theoretical work on flow past wedge sections of Guderley and Yoshihara, Vincenti and Wagner, and Cole. Pressure distributions and drag coefficients for the wedge and circular-arc sections are presented throughout the entire transonic range of velocities.

Bryson, Arthur Earl, Jr↗

NASA NTRS2009

RANS Analyses of Turbofan Nozzles with Internal Wedge Deflectors for Noise Reduction

Computational fluid dynamics (CFD) was used to evaluate the flow field and thrust performance of a promising concept for reducing the noise at take-off of dual-stream turbofan nozzles. The concept, offset stream technology, reduces the jet noise observed on the ground by diverting (offsetting) a portion of the fan flow below the core flow, thickening and lengthening this layer between the high-velocity core flow and the ground observers. In this study a wedge placed in the internal fan stream is used as the diverter. Wind, a Reynolds averaged Navier-Stokes (RANS) code, was used to analyze the flow field of the exhaust plume and to calculate nozzle performance. Results showed that the wedge diverts all of the fan flow to the lower side of the nozzle, and the turbulent kinetic energy on the observer side of the nozzle is reduced. This reduction in turbulent kinetic energy should correspond to a reduction in noise. However, because all of the fan flow is diverted, the upper portion of the core flow is exposed to the freestream, and the turbulent kinetic energy on the upper side of the nozzle is increased, creating an unintended noise source. The blockage due to the wedge reduces the fan mass flow proportional to its blockage, and the overall thrust is consequently reduced. The CFD predictions are in very good agreement with experimental flow field data, demonstrating that RANS CFD can accurately predict the velocity and turbulent kinetic energy fields. While this initial design of a large scale wedge nozzle did not meet noise reduction or thrust goals, this study identified areas for improvement and demonstrated that RANS CFD can be used to improve the concept.

DeBonis, James R.↗

NASA NTRS2003

Wedge Heat-Flux Indicators for Flash Thermography

Wedge indicators have been proposed for measuring thermal radiation that impinges on specimens illuminated by flash lamps for thermographic inspection. Heat fluxes measured by use of these indicators would be used, along with known thermal, radiative, and geometric properties of the specimens, to estimate peak flash temperatures on the specimen surfaces. These indicators would be inexpensive alternatives to high-speed infrared pyrometers, which would otherwise be needed for measuring peak flash surface temperatures. The wedge is made from any suitable homogenous material such as plastic. The choice of material is governed by the equation given. One side of the wedge is covered by a temperature sensitive compound that decomposes irreversibly when its temperature exceeds a rated temperature (T-rated). The uncoated side would be positioned alongside or in place of the specimen and exposed to the flash, then the wedge thickness at the boundary between the white and blackened portions measured.

Koshti, Ajay M.↗

DOE OSTI2020

Entanglement wedge reconstruction using the Petz map

At the heart of recent progress in AdS/CFT is the question of subregion duality, or entanglement wedge reconstruction: which part(s) of the boundary CFT are dual to a given subregion of the bulk? This question can be answered by appealing to the quantum error correcting properties of holography, and it was recently shown that robust bulk (entanglement wedge) reconstruction can be achieved using a universal recovery channel known as the twirled Petz map. In short, one can use the twirled Petz map to recover bulk data from a subset of the boundary. However, this map involves an averaging procedure over bulk and boundary modular time, and hence it can be somewhat intractable to evaluate in practice. We show that a much simpler channel, the Petz map, is sufficient for entanglement wedge reconstruction for any code space of fixed finite dimension – no twirling is required. Moreover, the error in the reconstruction will always be non-perturbatively small. From a quantum information perspective, we prove a general theorem extending the use of the Petz map as a general-purpose recovery channel to subsystem and operator algebra quantum error correction.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Holographic scattering requires a connected entanglement wedge

In AdS/CFT, there can exist local 2-to-2 bulk scattering processes even when local scattering is not possible on the boundary; these have previously been studied in con- nection with boundary correlation functions. We show that boundary regions associated with these scattering configurations must have O(1/G N ) mutual information, and hence a connected entanglement wedge. One of us previously argued for this statement from the boundary theory using operational tools in quantum information theory. We improve that argument to make it robust to small errors and provide a proof in the bulk using focusing arguments in general relativity. We also provide a direct link to entanglement wedge reconstruction by showing that the bulk scattering region must lie inside the con- nected entanglement wedge. Our construction implies the existence of nonlocal quantum computation protocols that are exponentially more efficient than the optimal protocols currently known.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Entanglement wedge reconstruction and the information paradox

When absorbing boundary conditions are used to evaporate a black hole in AdS/CFT, we show that there is a phase transition in the location of the quantum Ryu-Takayanagi surface, at precisely the Page time. The new RT surface lies slightly inside the event horizon, at an infalling time approximately the scrambling time β/2 π logS BH into the past. We can immediately derive the Page curve, using the Ryu-Takayanagi formula, and the Hayden-Preskill decoding criterion, using entanglement wedge reconstruction. Because part of the interior is now encoded in the early Hawking radiation, the decreasing entanglement entropy of the black hole is exactly consistent with the semiclassical bulk entanglement of the late-time Hawking modes, despite the absence of a firewall.By studying the entanglement wedge of highly mixed states, we can understand the state dependence of the interior reconstructions. A crucial role is played by the existence of tiny, non-perturbative errors in entanglement wedge reconstruction. Directly after the Page time, interior operators can only be reconstructed from the Hawking radiation if the initial state of the black hole is known. As the black hole continues to evaporate, reconstructions become possible that simultaneously work for a large class of initial states. Using similar techniques, we generalise Hayden-Preskill to show how the amount of Hawking radiation required to reconstruct a large diary, thrown into the black hole, depends on both the energy and the entropy of the diary. Finally we argue that, before the evaporation begins, a single, state-independent interior reconstruction exists for any code space of microstates with entropy strictly less than the Bekenstein-Hawking entropy, and show that this is sufficient state dependence to avoid the AMPSS typical-state firewall paradox.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

The connected wedge theorem and its consequences

In the AdS/CFT correspondence, bulk causal structure has consequences for boundary entanglement. In quantum information science, causal structures can be replaced by distributed entanglement for the purposes of information processing. In this work, we deepen the understanding of both of these statements, and their relationship, with a number of new results. Centrally, we present and prove a new theorem, the n-to-n connected wedge theorem, which considers n input and n output locations at the boundary of an asymptotically AdS 2+1 spacetime described by AdS/CFT. When a sufficiently strong set of causal connections exists among these points in the bulk, a set of n associated regions in the boundary will have extensive-in-N mutual information across any bipartition of the regions. The proof holds in three bulk dimensions for classical spacetimes satisfying the null curvature condition and for semiclassical spacetimes satisfying standard conjectures. The n-to-n connected wedge theorem gives a precise example of how causal connections in a bulk state can emerge from large-N entanglement features of its boundary dual. It also has consequences for quantum information theory: it reveals one pattern of entanglement which is sufficient for information processing in a particular class of causal networks. We argue this pattern is also necessary, and give an AdS/CFT inspired protocol for information processing in this setting. Our theorem generalizes the 2-to-2 connected wedge theorem proven in [3]. We also correct some errors in the proof presented there, in particular a false claim that existing proof techniques work above three bulk dimensions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Island for gravitationally prepared state and pseudo entanglement wedge

We consider spacetime initiated by a finite-sized initial boundary as a generalization of the Hartle-Hawking no-boundary state. We study entanglement entropy of matter state prepared by such spacetime. We find that the entanglement entropy for large subregion is given either by the initial state entanglement or the entanglement island, preventing the entropy to grow arbitrarily large. Consequently, the entanglement entropy is always bounded from above by the boundary area of the island, leading to an entropy bound in terms of the island. The island I is located in the analytically continued spacetime, either at the bra or the ket part of the spacetime in Schwinger-Keldysh formalism. The entanglement entropy is given by an average of complex pseudo generalized entropy for each entanglement island. We find a necessary condition of the initial state to be consistent with the strong sub-additivity, which requires that any probe degrees of freedom are thermally entangled with the rest of the system. We then find a large parameter region where the spacetime with finite-sized initial boundary, which does not have the factorization puzzle at leading order, dominates over the Hartle-Hawking no-boundary state or the bra ket wormhole. Due to the absence of a moment of time reflection symmetry, the island in our setup is a generalization of the entanglement wedge, called pseudo entanglement wedge. In pseudo entanglement wedge reconstruction, we consider reconstructing the bulk matter transition matrix on A ∪ I, from a fine-grained state on A. The bulk transition matrix is given by a thermofield double state with a projection by the initial state. We also provide an AdS/BCFT model by considering EOW branes with corners. We also find the exponential hardness of such reconstruction task using a generalization of Python’s lunch conjecture to pseudo generalized entropy.

2D gravity↗

DOE OSTI2020

LoTToR: An Algorithm for Missing-Wedge Correction of the Low-Tilt Tomographic 3D Reconstruction of a Single-Molecule Structure

A single-molecule three-dimensional (3D) structure is essential for understanding the thermal vibrations and dynamics as well as the conformational changes during the chemical reaction of macromolecules. Individual-particle electron tomography (IPET) is an approach for obtaining a snap-shot 3D structure of an individual macromolecule particle by aligning the tilt series of electron tomographic (ET) images of a targeted particle through a focused iterative 3D reconstruction method. The method can reduce the influence on the 3D reconstruction from large-scale image distortion and deformation. Due to the mechanical tilt limitation, 3D reconstruction often contains missing-wedge artifacts, presented as elongation and an anisotropic resolution. Here, we report a post-processing method to correct the missing-wedge artifact. This low-tilt tomographic reconstruction (LoTToR) method contains a model-free iteration process under a set of constraints in real and reciprocal spaces. A proof of concept is conducted by using the LoTToR on a phantom, i.e., a simulated 3D reconstruction from a low-tilt series of images, including that within a tilt range of ±15°. The method is validated by using both negative-staining (NS) and cryo-electron tomography (cryo-ET) experimental data. A significantly reduced missing-wedge artifact verifies the capability of LoTToR, suggesting a new tool to support the future study of macromolecular dynamics, fluctuation and chemical activity from the viewpoint of single-molecule 3D structure determination.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Spatially Averaged Ice Contents of Ice-Wedge Polygon Cross-Sections to 3-m Depth, July 2013, Utqiagvik, Alaska

This dataset contains spatially averaged estimates of ice content (volume percent) for two-dimensional cross-sectional profiles (from trough center to trough center to a depth of 3 meters) of low- and flat-centered ice-wedge polygons (three of each type) located near Utqiagvik, Alaska. A combination of soil pits, trenches, and cores were used to describe, sample, and map the cross-section stratigraphy of soil horizons and ice wedges for each polygon at 6 depth intervals. Observed soil horizons were assigned to four types with increasing amounts of organic components (mineral, mineral/organic, organic/mineral, and organic). The average ice contents of each soil horizon type below the permafrost boundary and wedge ice were weighted by their cross-sectional area fractions to calculate spatially averaged estimates of ice content for each polygon. In the active layer, spatially averaged estimates of volumetric water contents were similarly determined and reported here as “ice” content to enable estimates of the soil’s structurally competent porosity and excess ice in permafrost layers. In this dataset, the file AK13_ice_contents.csv includes cross-sectional area fractions and spatially averaged ice contents for soil layers and horizon types at the six depth intervals. The file AK13_permafrost_ice_fractions.csv contains the calculated partitioning of ice contents into pore ice and excess ice fractions for the three permafrost-dominated depth intervals. In addition, there is a data dictionary file for each of these data files and a file-level metadata file. These data were generated by the Department of Energy’s Soil Carbon Response to Environmental Change Scientific Focus Area and were used as inputs to model simulations examining the consequences of thaw-affected subsidence and microtopography change on active layer thickness of low-relief polygonal tundra landscapes in a warming Arctic.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1965

Wedge immersed thermistor bolometer measures infrared radiation

Wedge immersed-thermistor bolometer measures infrared radiation in the atmosphere. The thermistor flakes are immersed by optical contact on a wedge-shaped germanium lens whose narrow dimension is clamped between two complementary wedge-shaped germanium blocks bonded with a suitable adhesive.

Dreyfus, M. G.↗

NASA NTRS1972

Diffraction by an aperture between two wedges.

An asymptotic solution for large spacing is obtained in the problem of diffraction by an aperture between two conducting wedges. The variation of the wedge angles is shown to have significant effect on the far field amplitude of the transmitted field in certain ranges of angle for E-polarization. The wedge angles are seen to have a greater effect than interaction corrections in some cases but a lesser effect in others. Numerical comparisons are carried out.

Teague, B. R.↗

NASA NTRS1974

Fracture and contact problems for an elastic wedge

The plane elastostatic contact problem for an infinite elastic wedge of arbitrary angle is discussed. The medium is loaded through a frictionless rigid wedge of a given symmetric profile. Using the Mellin transform formulation the mixed boundary value problem is reduced to a singular integral equation with the contact stress as the unknown function. With the application of the results to the fracture of the medium in mind, the main emphasis in the study has been on the investigation of the singular nature of the stress state around the apex of the wedge and on the determination of the contact pressure.

Erdogan, F.↗

NASA NTRS1974

Evaluation of a wedge gas-sampling probe

The performances of a wedge-type gas-sampling probe and pitot probes are compared in applications to flowfield profile studies. The flow structure data obtained by these techniques are found to agree well in flow regions with and without significant gradients. The wedge-type probe showed a good service life and allowed a substantial reduction of the sampling time. The wedge probe design is discussed.

Beach, H. L., Jr.↗

NASA NTRS1975

Flight investigation of installation effects on a wedge nozzle installed on an underwing nacelle

A flight research program was conducted using a modified F-106B aircraft with an underwing-nacelle - engine installation to investigate installation effects on a wedge nozzle with retracted shrouds from Mach 0.70 to 1.10. These configurations simulated the subsonic flight geometries of a variable-geometry wedge nozzle design for Mach 2.70 operation. The nozzle was tested with a J85-GE-13 turbojet engine, and data were compared with that of 0.34-scale isolated wind tunnel model. Data are also compared with the flight results of a boattail plug nozzle and a cylindrical nacelle plug nozzle. A favorable installation effect occurred from Mach 0.82 to 0.96 with a nominal 4-percent corrected secondary weight-flow ratio. This favorable effect resulted from changes in pressure forces on the nozzle surfaces. The wedge nozzle gross thrust coefficient was about the same as the boattail nacelle plug nozzle and 2.50 to 1.30 percent higher than the cylindrical nacelle plug nozzle over the subsonic Mach number range.

Johns, A. L.↗

NASA NTRS1976

Flight velocity effects on exhaust noise of a wedge nozzle installed on an underwing nacelle on an F-106 airplane

It is important to know whether the relatively high takeoff speeds of supersonic transport aircraft will change the exhaust noise levels of nozzles from those measured at static conditions. To gain some insight into this question, a modified F-106B aircraft was used to conduct flyover and static tests on a wedge nozzle. Flight velocity had an adverse effect on exhaust noise when compared with static results at the same relative jet velocity but a beneficial effect when compared with static results at the same absolute jet velocity. The wedge nozzle, which has a two-dimensional wedge surface rather than an axisymmetric plug surface, had a higher peak flyover noise level than the plug nozzle.

Burley, R. R.↗