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NASA NTRS2004

A Universal Formula for Extracting the Euler Angles

Recently, the authors completed a study of the Davenport angles, which are a generalization of the Euler angles for which the initial and final Euler axes need not be either mutually parallel or mutually perpendicular or even along the coordinate axes. During the conduct of that study, those authors discovered a relationship which can be used to compute straightforwardly the Euler angles characterizing a proper-orthogonal direction-cosine matrix for an arbitrary Euler-axis set satisfying n(sub 1) x n(sub 2) = 0 and n(sub 3) x n(sub 1) = 0, which is also satisfied by the more usual Euler angles we encounter commonly in the practice of Astronautics. Rather than leave that relationship hidden in an article with very different focus from the present Engineering note, we present it and the universal algorithm derived from it for extracting the Euler angles from the direction-cosine matrix here. We also offer literal "code" for performing the operations, numerical examples, and general considerations about the extraction of Euler angles which are not universally known, particularly, the treatment of statistical error.

Shuster, Malcolm D.↗

NASA NTRS2004

A New Approach to Micro-arcsecond Astrometry with SIM Allowing Early Mission Narrow Angle Measurements of Compelling Astronomical Targets

The Space Interferometry Mission (SIM) is capable of detecting and measuring the mass of terrestrial planets around stars other than our own. It can measure the mass of black holes and the visual orbits of radio and x-ray binary sources. SIM makes possible a new level of understanding of complex astrophysical processes. SIM achieves its high precision in the so-called narrow-angle regime. This is defined by a 1 degree diameter field in which the position of a target star is measured with respect to a set of reference stars. The observation is performed in two parts: first, SIM observes a grid of stars that spans the full sky. After a few years, repeated observations of the grid allow one to determine the orientation of the interferometer baseline. Second, throughout the mission, SIM periodically observes in the narrow-angle mode. Every narrow-angle observation is linked to the grid to determine the precise attitude and length of the baseline. The narrow angle process demands patience. It is not until five years after launch that SIM achieves its ultimate accuracy of 1 microarcsecond. The accuracy is degraded by a factor of approx. 2 at mid-mission. Our work proposes a technique for narrow angle astrometry that does not rely on the measurement of grid stars. This technique, called Gridless Narrow Angle Astrometry (GNAA) can obtain microarcsecond accuracy and can detect extra-solar planets and other exciting objects with a few days of observation. It can be applied as early as during the first six months of in-orbit calibration (IOC). The motivations for doing this are strong. First, and obviously, it is an insurance policy against a catastrophic mid-mission failure. Second, at the start of the mission, with several space-based interferometers in the planning or implementation phase, NASA will be eager to capture the public's imagination with interferometric science. Third, early results and a technique that can duplicate those results throughout the mission will give the analysts important experience in the proper use and calibration of SIM.

Shaklan, Stuart↗

NASA NTRS2006

Effect of EMIC Wave Normal Angle Distribution on Relativistic Electron Scattering

The flux level of outer-zone relativistic electrons (above 1 MeV) is extremely variable during geomagnetic storms, and controlled by a competition between acceleration and loss. Precipitation of these electrons due to resonant pitch-angle scattering by electromagnetic ion cyclotron (EMIC) waves is considered one of the major loss mechanisms. This mechanism was suggested in early theoretical studies more than three decades ago. However, direct experimental evidence of the wave role in relativistic electrons precipitation is difficult to obtain because of lack of concurrent measurements of precipitating electrons at low altitudes and the waves in a magnetically conjugate equatorial region. Recently, the data from balloon-borne X-ray instruments provided indirect but strong evidence on an efficiency of the EMIC wave induced loss for the outer-zone relativistic electrons. These observations stimulated theoretical studies that, particularly, demonstrated that EMIC wave induced pitch-angle diffusion of MeV electrons can operate in the strong diffusion limit and this mechanism can compete with relativistic electron depletion caused by the Dst effect during the initial and main phases of storm. Although an effectiveness of relativistic electron scattering by EMIC waves depends strongly on the wave spectral properties, the most favorable assumptions regarding wave characteristics has been made in all previous theoretical studies. Particularly, only quasi field-aligned EMIC waves have been considered as a driver for relativistic electron loss. At the same time, there is growing experimental and theoretical evidence that these waves can be highly oblique; EMIC wave energy can occupy not only the region of generation, i.e. the region of small wave normal angles, but also the entire wave normal angle region, and even only the region near 90 degrees. The latter can dramatically change he effectiveness of relativistic electron scattering by EMIC waves. In the present study, we calculate the pitch-angle diffusion coefficients using the typical wave normal distributions obtained from our self-consistent ring current-EMIC wave model, and try to quantify the effect of EMIC wave normal angle characteristics on relativistic electron scattering.

Gamayunov, K. V.↗

NASA NTRS2007

Effect of EMIC Wave Normal Angle Distribution on Relativistic Electron Scattering in Outer RB

We present the equatorial and bounce average pitch angle diffusion coefficients for scattering of relativistic electrons by the H+ mode of EMIC waves. Both the model (prescribed) and self consistent distributions over the wave normal angle are considered. The main results of our calculation can be summarized as follows: First, in comparison with field aligned waves, the intermediate and highly oblique waves reduce the pitch angle range subject to diffusion, and strongly suppress the scattering rate for low energy electrons (E less than 2 MeV). Second, for electron energies greater than 5 MeV, the |n| = 1 resonances operate only in a narrow region at large pitch-angles, and despite their greatest contribution in case of field aligned waves, cannot cause electron diffusion into the loss cone. For those energies, oblique waves at |n| greater than 1 resonances are more effective, extending the range of pitch angle diffusion down to the loss cone boundary, and increasing diffusion at small pitch angles by orders of magnitude.

Khazanov, G. V.↗

NASA NTRS1991

Aircraft flight path angle display system

A display system for use in an aircraft control wheel steering system provides the pilot with a single, quickened flight path angle display to overcome poor handling qualities due to intrinsic flight path angle response lags, while avoiding multiple information display symbology. The control law for the flight path angle control system is designed such that the aircraft's actual flight path angle response lags the pilot's commanded flight path angle by a constant time lag .tau., independent of flight conditions. The synthesized display signal is produced as a predetermined function of the aircraft's actual flight path angle, the time lag .tau. and command inputs from the pilot's column.

Lambregts, Antonius A.↗

NASA NTRS2009

Angle of Attack Modulation for Mars Entry Terminal State Optimization

From the perspective of atmospheric entry, descent, and landing (EDL), one of the most foreboding destinations in the solar system is Mars due in part to its exceedingly thin atmosphere. To benchmark best possible scenarios for evaluation of potential Mars EDL system designs, a study is conducted to optimize the entry-to-terminal-state portion of EDL for a variety of entry velocities and vehicle masses, focusing on the identification of potential benefits of enabling angle of attack modulation. The terminal state is envisioned as one appropriate for the initiation of terminal descent via parachute or other means. A particle swarm optimizer varies entry flight path angle, ten bank profile points, and ten angle of attack profile points to find maximum-final-altitude trajectories for a 10 30 m ellipsled at 180 different combinations of values for entry mass, entry velocity, terminal Mach number, and minimum allowable altitude. Parametric plots of maximum achievable altitude are shown, as are examples of optimized trajectories. It is shown that appreciable terminal state altitude gains (2.5-4.0 km) over pure bank angle control may be possible if angle of attack modulation is enabled for Mars entry vehicles. Gains of this magnitude could prove to be enabling for missions requiring high-altitude landing sites. Conclusions are also drawn regarding trends in the bank and angle of attack profiles that produce the optimal trajectories in this study, and directions for future work are identified.

Lafleur, Jarret M.↗

NASA NTRS2015

Determination of the Contact Angle Based on the Casimir Effect

In several crystal growth processed based on capillarity, a melt comes into contact with a crucible wall at an angle defined as the contact angle. For molten metals and semiconductors, this contact angle is dependent upon both the crucible and melt material and typical values fall in the range 80-170deg. However, on a microscopic scale, there does not exist a precise and sharp contact angle but rather the melt and solid surfaces merge smoothly and continuously over a distance of up to several micrometers. Accurate modeling requires a more advanced treatment of this interaction. The interaction between the melt and solid surfaces can be calculated by considering two forces: a short-range repulsive force and a longer range (up to a few micrometers) Casimir force. The Casimir force between the two bodies of complex geometry is calculated using a retarded temperature Green's function (Matsubara type) for the photon in the medium. The governing equations are cast in the form of a set of boundary integral equations which are then solved numerically for the case of molten Ge on SiO2. The shape of the molten surface approaching the flat solid body is determined, and the contact angle is defined as the angle between the two surfaces at the microscopically asymptotic distance of 1-2 micrometers. The formulation of this model and the results of the numerical calculations will be presented and discussed.

Mazuruk, K.↗

NASA NTRS2017

Postlaunch Assessment of the Response Versus Scan Angle for the Thermal Emissive Bands of Visible Infrared Imaging Radiometer Suite On-Board the Suomi National Polar-Orbiting Partnership Satellite

The visible infrared imaging radiometer suite (VIIRS) is a key sensor carried on the Suomi national polar-orbiting partnership (S-NPP) satellite, which was launched in October 2011. It has several on-board calibration components, including a solar diffuser and a solar diffuser stability monitor for the reflective solar bands, a V-groove blackbody for the thermal emissive bands (TEB), and a space view port for background subtraction. These on-board calibrators are located at fixed scan angles. The VIIRS response versus scan angle (RVS) was characterized prelaunch in lab ambient conditions and is currently used to characterize the on-orbit response for all scan angles relative to the calibrator scan angle. Since the RVS is vitally important to the quality of calibrated radiance products, several independent studies were performed to analyze the prelaunch RVS measurement data. A spacecraft level pitch maneuver was scheduled during the first 3 months of intensive Cal/Val. The S-NPP pitch maneuver provided a rare opportunity for VIIRS to make observations of deep space over the entire range of Earth view scan angles, which can be used to characterize the TEB RVS. This study provides our analysis of the pitch maneuver data and assessment of the derived TEB RVS by comparison with prelaunch results. In addition, the stability of the RVS after the first 5 years of operation is examined using observed brightness temperatures (BT) over a clear ocean at various angles of incidence (AOI). To reduce the impact of variations in the BT measurements, the daily overpasses collected over the ocean are screened for cloud contamination, normalized to the results obtained at the blackbody AOI, and averaged each year.

Wu, Aisheng↗

NASA NTRS2019

Retrieving Aerosol Characteristics From the PACE Mission, Part 2: Multi-Angle and Polarimetry

The Plankton, Aerosol, Clouds, ocean Ecosystem (PACE) mission presents new opportunities and new challenges in applying observations of two complementary multi-angle polarimeters for the space-based retrieval of global aerosol properties.Aerosol remote sensing from multi-angle radiometric-only observations enables aerosol characterization to a greater degree than single-view radiometers, as demonstrated by nearly two decades of heritage instruments. Adding polarimetry to the multi-angle observations allows for the retrieval of aerosol optical depth, Angstrom exponent,parameters of size distribution, measures of aerosol absorption, complex refractive index and degree of non-sphericity of the particles, as demonstrated by two independent retrieval algorithms applied to the heritage POLarization and Directionality of the Earth's Reflectance (POLDER) instrument. The reason why this detailed particle characterization is possible is because a multi-angle polarimeter measurement contains twice the number of Degrees of Freedom of Signal (DFS) compared to an observation from a single-view radiometer. The challenges of making use of this information content involve separating surface signal from atmospheric signal, especially when the surface is optically complex and especially in the ultraviolet portion of the spectrum where we show the necessity of polarization in making that separation. The path forward is likely to involve joint retrievalsthat will simultaneously retrieve aerosol and surface properties, although advances will berequired in radiative transfer modeling and in representing optically complex constituents in those models. Another challenge is in having the processing capability that can keep pace with the output of these instruments in an operational environment. Yet, preliminaryalgorithms applied to airborne multi-angle polarimeter observations offer encouraging results that demonstrate the advantages of these instruments to retrieve aerosol layer height, particle single scattering albedo, size distribution and spectral optical depth, and also show the necessity of polarization measurements, not just multi-angle radiometricmeasurements, to achieve these results.

Remer, Lorraine A.↗

NASA NTRS2019

Determination of Response Versus Scan Angle for the NOAA-20 Visible Infrared Imaging Radiometer Suite Thermal Emissive Bands from Emissive Radiation Measurements During the Pitch Maneuver

The visible infrared imaging radiometer suite (VIIRS) is a key sensor onboard the newly launched (November 18, 2017) NOAA-20 satellite and the early launched Suomi National Polar-orbiting Partnership (SNPP) satellite. The two VIIRS sensors are nearly identical in design. Its onboard calibration components include a solar diffuser (SD) and a SD stability monitor for the reflective solar bands, a V-grooved blackbody for the thermal emissive bands (TEBs),and a space view port for background subtraction. These onboard calibrators are located at fixed scan angles. The response versus scan angle (RVS) of the VIIRS scan mirror was characterized prelaunch in lab-ambient conditions and is currently used to calibrate the on-orbit response for all scan angles relative to the calibrator's scan angle. A spacecraft-level pitch maneuver was scheduled during the initial intensive calibration and validation testing for both the NOAA-20 and SNPP. The pitch maneuver provided a rare opportunity for VIIRS to make observations of deep space over the entire range of the scan angle, which can be used to characterize the TEBRVS. We analyze the NOAA-20 pitch maneuver data and assess the derived TEB RVS. A comparison between the RVS determined by the pitch maneuver observations and prelaunch lab measurements is conducted for each band, detector, and mirror side of the half-angle mirror.

Wu, Aisheng↗

NASA NTRSDate not supplied

Influence of Airfoil Angle of Attack on Ice Accretion Roughness

The influence of airfoil angle attack on roughness evolution and spatial variation was investigated in the Icing Research Tunnel (IRT) at the NASA Glenn Research Center. Two airfoil models were used for the study: a 53.34-cm (21-in.) NACA 0012 model and a 152.4-cm (60-in.) HAARP-II model. For the NACA 0012, the angle of attack was varied from 0° to 3°, and the ice accretion roughness was characterized while keeping the other icing parameters such as freestream velocity, freestream stagnation temperature, accumulation parameter, and median volumetric diameter (MVD) constant. For the HAARP-II, the angle of attack was varied from -1.9°, which is the non-lifting angle of attack for the airfoil, to 3°. A series of accumulation time progression cases for the HAARP-II at 2.3° angle of attack was also performed in Appendix C and Appendix O conditions and compared to the measurements presented by McClain et al. (2018) for the non-lifting angle of attack condition. The results demonstrate the strong influence of the changing local static pressure along the surface influencing the roughness characteristics. A correlation approach for the maximum equivalent sand-grain roughness along the surface of an airfoil is presented and considers the scaled accumulation time, the stagnation point freezing fraction, and the surface pressure relative to the static and stagnation pressures of the flow. Finally, an attempt to relate the maximum roughness quantities to local pressure coefficients and local icing quantities is presented and discussed.

Icing↗

DOE OSTI2025

Nonmonotonic Band Flattening near the Magic Angle of Twisted Bilayer MoTe 2

Twisted bilayer MoTe 2 (tMoTe 2 ) is an emergent platform for exploring exotic quantum phases driven by the interplay between nontrivial band topology and strong electron correlations. Direct experimental access to its momentum-resolved electronic structure is essential for uncovering the microscopic origins of the correlated topological phases therein. Here, we report angle-resolved photoemission spectroscopy measurements of tMoTe 2 , revealing pronounced twist-angle-dependent band reconstruction shaped by orbital character, interlayer coupling, and moiré potential modulation. Density functional theory captures the qualitative evolution, yet underestimates key energy scales across twist angles, highlighting the importance of electronic correlations. Notably, the hole effective mass at the 𝐾 point exhibits a nonmonotonic dependence on twist angle, peaking near 2°, consistent with band flattening at the magic angle predicted by continuum models. Via electrostatic gating and surface dosing, we further visualize the evolution of electronic structure versus doping, enabling direct observation of the conduction band minimum and confirm tMoTe 2 as a direct band gap semiconductor. These results establish a spectroscopic foundation for modeling and engineering emergent quantum phases in this moiré platform.

2D materials↗

DOE OSTI2025

Quantifying Twist Angles in Cuprate Heterostructures with Anisotropic Raman Signatures

Artificially engineered twisted van der Waals (vdW) heterostructures have unlocked new pathways for exploring emergent quantum phenomena and strongly correlated electronic states. Many of these phenomena are highly sensitive to the twist angle, which can be deliberately tuned to tailor the interlayer interactions. This makes the twist angle a critical tunable parameter, emphasizing the need for precise control and accurate characterization during device fabrication. In particular, twisted cuprate heterostructures based on Bi 2 Sr 2 CaCu 2 O 8 + x (BSCCO) have demonstrated angle-dependent superconducting properties, positioning the twist angle as a key tunable parameter. However, the twisted interface is highly unstable under ambient conditions and vulnerable to damage from conventional characterization tools such as electron microscopy or scanning probe techniques. In this work, a fully non-invasive, polarization-resolved Raman spectroscopy approach is introduced for determining twist angles in artificially stacked BSCCO heterostructures. By analyzing twist-dependent anisotropic vibrational Raman modes, particularly utilizing the out-of-plane A 1g vibrational mode of Bi/Sr at ≈116 cm −1 , clear optical fingerprints of the rotational misalignment between cuprate layers are identified. The high-resolution confocal Raman setup, equipped with polarization control and RayShield filtering down to 10 cm −1 , allows for reliable and reproducible measurements without compromising the material's structural integrity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1994

(abstract) Observation by Clementine of a Hugh Opposition Surge on the Moon at Very Small Solar Phase Angles

The Clementine mission enabled the first quantative observations of the Moon at very small solar phase angles. It is well established from Earth-based observations that the Moon exhibits a non-linear increase in brightness as its face becomes fully illuminated to a terrestrial observer. Because the models of the opposition effect are sensitive indicators of surfical compaction state and particle size, observations at small solar phase angles are important to obtain. A recent model for optical coherent backscatter seeks to explain a narrow opposition spike at very small phase angles (< 1 degree) seen on several icy satellites , including Europa, Icarus 90, and Oberon . Over 90 images of the Moon's surface at phase angles less than 0.5(deg) (the minimum phase angle observable from Earth due to the Moon's angular size) were obtained by the Clementine spacecraft. Our analysis of these images shows the moon exhibits a surge in brightness of approximately 20% below 0.25(deg), comparable to the values observed on icy satellites. No color dependence was detected in the lunar phase curve below 2 degrees.

partical size icy satellites Europa Icarus 90 Ober↗

NASA NTRS2016

Banded Structures in Electron Pitch Angle Diffusion Coefficients from Resonant Wave Particle Interactions

Electron pitch angle (D (alpha)) and momentum (D(pp)) diffusion coefficients have been calculated due to resonant interactions with electrostatic electron cyclotron harmonic (ECH) and whistler mode chorus waves. Calculations have been performed at two spatial locations L = 4.6 and 6.8 for electron energies 10 keV. Landau (n = 0) resonance and cyclotron harmonic resonances n = +/-1, +/-2,...+/-5 have been included in the calculations. It is found that diffusion coefficient versus pitch angle (alpha) profiles show large dips and oscillations or banded structures. The structures are more pronounced for ECH and lower band chorus (LBC) and particularly at location 4.6. Calculations of diffusion coefficients have also been performed for individual resonances. It is noticed that the main contribution of ECH waves in pitch angle diffusion coefficient is due to resonances n = +1 and n = +2. A major contribution to momentum diffusion coefficients appears from n = +2. However, the banded structures in D alpha and Dpp coefficients appear only in the profile of diffusion coefficients for n = +2. The contribution of other resonances to diffusion coefficients is found to be, in general, quite small or even negligible. For LBC and upper band chorus waves, the banded structures appear only in Landau resonance. The Dpp diffusion coefficient for ECH waves is one to two orders smaller than D alpha coefficients. For chorus waves, Dpp coefficients are about an order of magnitude smaller than D alpha coefficients for the case n does not = 0. In case of Landau resonance, the values of Dpp coefficient are generally larger than the values of D alpha coefficients particularly at lower energies. As an aid to the interpretation of results, we have also determined the resonant frequencies. For ECH waves, resonant frequencies have been estimated for wave normal angle 89 deg and harmonic resonances n = +1, +2, and +3, whereas for whistler mode waves, the frequencies have been calculated for angle 10 deg and Landau resonance. Further, in ECH waves, the banded structures appear for electron energies (is) greater than1 keV, and for whistler mode chorus waves, structures appear for energies greater than 2 keV at L = 4.6 and above 200 eV for L = 6.8. The results obtained in the present work will be helpful in the study of diffusion curves and will have important consequences for diffuse aurora and pancake distributions.

diffusion↗

NASA NTRS2021

TLSLEAF: Automatic Leaf Angle Estimates From Single-Scan Terrestrial Laser Scanning

Leaf angle distribution (LAD) in forest canopies affects estimates of leaf area, light interception, and global-scale photosynthesis, but is often simplified to a single theoretical value. Here, we present TLSLeAF (Terrestrial Laser Scanning Leaf Angle Function), an automated open-source method of deriving LADs from terrestrial laser scanning. TLSLeAF produces canopy-scale leaf angle and LADs by relying on gridded laser scanning data. The approach increases processing speed, improves angle estimates, and requires minimal user input. Key features are automation, leaf–wood classification, beta parameter output, and implementation in R to increase accessibility for the ecology community. TLSLeAF precisely estimates leaf angle with minimal distance effects on angular estimates while rapidly producing LADs on a consumer-grade machine. We challenge the popular spherical LAD assumption, showing sensitivity to ecosystem type in plant area index and foliage profile estimates that translate to c. 25% and c. 11% increases in canopy net photosynthesis (c. 25%) and solar-induced chlorophyll fluorescence (c. 11%). TLSLeAF can now be applied to the vast catalog of laser scanning data already available from ecosystems around the globe. The ease of use will enable widespread adoption of the method outside of remote-sensing experts, allowing greater accessibility for addressing ecological hypotheses and large-scale ecosystem modeling efforts.

3D↗

NASA NTRSDate not supplied

Advancements in Force and Angle Measurement by the NFMTC

The National Force Measurement Technology Capability (NFMTC) is a nationwide partnership established in 2008 and sponsored by NASA’s Aeronautics Evaluation and Test Capabilities (AETC) project to maintain and further develop force and angle measurement capabilities primarily for NASA’s ground test facilities. One of the NFMTC’s primary objectives is to develop new force and angle measurement capabilities to meet the needs of researchers testing in NASA’s ground test facilities. This work will highlight several new capabilities that are either at or near operational readiness. A new six-component flow-through balance was designed and fabricated to support an upcoming retropropulsion test campaign at the NASA Langley Unitary Plan Wind Tunnel. The balance employs membranes in place of bellows, which have historically been used, and passes the flow through load bearing parts of the balance. Flow through the balance is optimized via the addition of flow guides, which are manufactured as separate parts, and attached to the balance. Calibration of this new flow-through balance demonstrates that it can suitably characterize the load and pressure ranges it was designed for, which provides aero researchers a new tool to directly measure retropropulsion performance of powered descent vehicles. Balances used in NASA’s ground test facilities are typically either single-piece balances or floating-frame balances. Historically, these two types of balances have generally used different front-end (model) attachments. Single-piece balances generally have a cylindrical front end that is forward of any measuring sections and at a reduced diameter relative to the balance outer diameter. Floating-frame balances generally have front end fits that extend over one or more measuring sections and that engage at the balance outer diameter. Recently, the NFMTC fabricated a single-piece balance with a front end fit that is compatible with the hardware used to calibrate floating-frame balances. Calibration results evaluating this front end fit will be presented. From a recent survey of angle measurement needs, the development of smaller angle measurement packages was identified as one area of improvement. Micro-electromechanical systems (MEMS) are continually being refined to provide high performance accelerometers that are a fraction of the volume of the quartz flexure based accelerometers that are standard in wind tunnels. A survey of commercial off-the-shelf MEMS accelerometers was conducted, and it identified the Safran Colibrys MS lines to be of adequate performance. Single-axis test boards and tri-axis rigid-flex production boards were designed and fabricated with a volume of approximately .18 cubic inches. The boards were designed to provide all the necessary conditioning for the MEMS accelerometers at levels to meet or exceed all requirements for the MS line sensors. Preliminary testing of these assembled sensor packages has demonstrated acceptable performance for wind-tunnel angle measurement. Several new rotating balances are at various stages of completion for NASA Glenn Research Center’s fan drive rigs. These balances provide direct measurement of thrust and torque of a driven fan or fan section to provide an estimate of fan efficiency and net thrust. Three two-component balances have been recently completed, and one six-component balance is in active development. A custom rotating telemetry system has been developed to support testing with these balances, and the telemetry system is integrated into the forward end of each one. The telemetry system is designed to remove mechanical sliprings by using an optical ethernet-based slipring for data transmission.

Force measurement↗

DOE OSTI2025

Estimating QSVT angles for matrix inversion with large condition numbers

Quantum Singular Value Transformation (QSVT) is a state-of-the-art, near-optimal quantum algorithm that can be used for matrix inversion. The QSVT circuit is parameterized by a sequence of angles that must be pre-calculated classically, with the number of angles increasing as the matrix condition number grows. Computing QSVT angles for ill-conditioned problems is a numerically challenging task. Here, we propose a numerical technique for estimating QSVT angles for large condition numbers. This technique allows one to avoid expensive numerical computations of QSVT angles and to emulate QSVT circuits for solving ill-conditioned problems.

97 MATHEMATICS AND COMPUTING↗