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At least 37 records · Page 2

Generative learning of densities on manifolds

A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent) spaces in the high-dimensional data (ambient) space. Two approaches for sampling from the latent data density are described. The first is a score-based diffusion model, which is trained to map a standard normal distribution to the latent data distribution using a neural network. The second one involves solving an Itô stochastic differential equation in the latent space. Additional realizations of the data are generated by lifting the samples back to the ambient space using Double Diffusion Maps , a recently introduced technique typically employed in studying dynamical system reduction; here the focus lies in sampling densities rather than system dynamics. The proposed approaches enable sampling high dimensional data densities restricted to low-dimensional, a priori unknown manifolds. The efficacy of the proposed framework is demonstrated through a benchmark problem and a material with multiscale structure.

Double diffusion maps↗

Investigation of the use of an electronic multifunction display and an electromechanical horizontal situation indicator for guidance and control of powered-lift short-haul aircraft

The use which pilots make of a moving map display from en route through the terminal area and including the approach and go-around flight phases was investigated. The content and function of each of three primary STOLAND displays are reviewed from an operational point of view. The primary displays are the electronic attitude director indicator (EADI), the horizontal situation indicator (HSI), and the multifunction display (MFD). Manually controlled flight with both flight director guidance and raw situation data is examined in detail in a simulated flight experiment with emphasis on tracking reference flight plans and maintaining geographic orientation after missed approaches. Eye-point-of-regard and workload measurements, coupled with task performance measurements, pilot opinion ratings, and pilot comments are presented. The experimental program was designed to offer a systematic objective and subjective comparison of pilots' use of the moving map MFD in conjunction with the other displays.

Clement, W. F.↗

Double Diffusion Maps and their Latent Harmonics for scientific computations in latent space

In this work, we introduce a data-driven approach to building reduced dynamical models through manifold learning; the reduced latent space is discovered using Diffusion Maps (a manifold learning technique) on time series data. A second round of Diffusion Maps on those latent coordinates allows the approximation of the reduced dynamical models. This second round enables mapping the latent space coordinates back to the full ambient space (what is called lifting); it also enables the approximation of full state functions of interest in terms of the reduced coordinates. In our work, we develop and test three different reduced numerical simulation methodologies, either through pre-tabulation in the latent space and integration on the fly or by going back and forth between the ambient space and the latent space. The data-driven latent space simulation results, based on the three different approaches, are validated through (a) the latent space observation of the full simulation through the Nyström Extension formula, or through (b) lifting the reduced trajectory back to the full ambient space, via Latent Harmonics. Latent space modeling often involves additional regularization to favor certain properties of the space over others, and the mapping back to the ambient space is then constructed mostly independently from these properties; here, we use the same data-driven approach to construct the latent space and then map back to the ambient space.

97 MATHEMATICS AND COMPUTING↗

Airframe Noise Simulations of a Full-Scale Large Civil Transport in Landing Configuration

This paper summarizes the results obtained from an extensive computational campaign to accurately predict full-scale landing gear noise for large civil transports. A highly accurate digital model of a full-scale Boeing 777-300ER aircraft with as-flown nose and main landing gear components was developed for use in the simulations. Two aircraft configurations were selected: nose and main landing gear deployed with wing high-lift devices retracted, and nose and main landing gear deployed with wing high-lift devices deflected. The two configurations were simulated without and with toboggan fairings installed on the main gear to represent the principal configurations evaluated during the 2005 QTD2 flight test. All simulations were performed with the lattice Boltzmann solver PowerFLOW® to resolve and capture the highly complex, unsteady flow field in the immediate vicinity of the aircraft. The far-field noise sig-nature of the aircraft was computed via a Ffowcs-Williams and Hawkings integral approach, with flow quantities on a permeable surface enclosing the source regions used as input. Synthetic pressure records at ground array microphone locations used during the QDT2 test were employed to generate narrowband acoustic maps and integrated far-field noise spectra. With high-lift devices retracted, the predicted spectra showed that landing gear noise is equivalent to total airframe noise, with no other airframe sources appearing within 10 dB of gear peak levels. Application of a toboggan fairing to the main gear produced modest noise reductions of 1-2 dB across the resolved frequency range. With high-lift devices deflected, undercarriage noise was within 3-4 dB of the total airframe noise, thus comprising nearly half of the total airframe noise. For this configuration, the toboggan fairing did not produce a reduction in noise, corroborating trends previously observed in QTD2 flight test data.

airframe noise↗

Classification of Ascension Island and Natal Ozonesondes Using Self-Organizing Maps

Ozone profiles from balloon-borne ozonesondes are used for development of satellite algorithms and in chemistry-climate model initialization, assimilation and evaluation. An important issue in the application of these profiles is how best to treat variations where varying photochemical and dynamical influences can cause the ozone mixing ratio in the tropospheric segments of the profile to change by of a factor of 2-3 within a day. Clustering techniques are an ideal way to approach the statistical classification of profile data and we apply self-organizing maps to tropical tropospheric SHADOZ data, hypothesizing that the data will sort according to various influences on ozone, namely anthropogenic sources like biomass burning, meteorological conditions, and stratospheric or extra-tropical intrusions. Self-organizing maps, that use a learning algorithm to reveal the most prominent features of a data set according to a specified number of clusters, have been determined for the 1998-2009 SHADOZ profiles over Ascension Island (512 profiles, 7.98 deg. S, 14.42 deg. W) and Natal, Brazil (425 profiles, 5.42degS, 35.38degW). The 2 × 2 self-organizing map, which creates 4 clusters, reveals that deviations from the average ozone in the free troposphere include both increased ozone resulting from seasonal biomass burning in Africa and locally reduced ozone brought about by convective lifting of unpolluted boundary-layer air. Expanding to a 4 × 4 self-organizing map shows how biomass burning influences the yearly cycle of tropospheric ozone at Ascension Island and captures the seasonality of ozone at both Ascension Island and Natal. Comparing Ascension Island and Natal using a 4 × 4 self-organizing map at each site reveals similarities in mid-tropospheric ozone, but shows differences in lower-tropospheric ozone due to Ascension Island being closer to African biomass burning and more affected by descent from the mean Walker circulation, with less convective activity, than Natal.

algorithms↗

Learning Optimal Aerodynamic Designs

This project created a framework for efficient, accurate, and scalable deep neural network representations of design optimization problem solutions. The inputs to these DNN representations are the vector of design requirement parameters, the outputs are the optimal design variables, and the goal is to learn the map from inputs to outputs (i.e., inverse design). The team addressed the problem of the optimal shape design of aerodynamic lifting surfaces—in particular aircraft wings—using a Reynolds-Average Navier Stokes model to govern the CFD-based aerodynamic shape optimization. The inverse design map for such problems is very complex and high-dimensional, involving inputs and outputs on the order of 1000s. To approximate this inverse design map, the team developed algorithms to construct parsimonious DNN architectures, which automatically identify low-dimensional manifolds in which design requirements affect optimal shape parameters, and trained these architectures with multifidelity optimization methods. The resulting methodology accurately and automatically designs optimal aerodynamic lifting surfaces with very high accuracy (99%) at interactive speeds, of the order of milliseconds, resulting in factors of one million or more speedup relative to CFD-based design optimization.

97 MATHEMATICS AND COMPUTING↗

Flying wings / flying fuselages

The present paper has documented the historical relationships between various classes of all lifting vehicles, which includes the flying wing, all wing, tailless, lifting body, and lifting fuselage. The diversity in vehicle focus was to ensure that all vehicle types that map have contributed to or been influenced by the development of the classical flying wing concept was investigated. The paper has provided context and perspective for present and future aircraft design studies that may employ the all lifting vehicle concept. The paper also demonstrated the benefit of developing an understanding of the past in order to obtain the required knowledge to create future concepts with significantly improved aerodynamic performance.

Wood, Richard M.↗

Data-Driven Modeling and Correction of Vehicle Dynamics

We develop a data-driven framework for learning and correcting nonautonomous vehicle dynamics. Physics-based vehicle models are often simplified for tractability and therefore exhibit inherent model-form uncertainty, motivating the need for data-driven correction. Moreover, nonautonomous dynamics are governed by time-dependent control inputs, which pose challenges in learning predictive models directly from temporal snapshot data. To address these, we reformulate the vehicle dynamics via a local parameterization of the time-dependent inputs, yielding a modified system composed ofa sequence of local parametric dynamical systems. Here, we approximate these parametric systems using two complementary approaches. First, we employ the dimension reduction and interpolation in parameter space (DRIPS) methodology to construct efficient linear surrogate models, equipped with lifted observable spaces and manifold-based operator interpolation. This enables data-efficient learning of vehicle models whose dynamics admit accurate linear representations in the lifted spaces. Second, for more strongly nonlinear systems, we employ flow map learning (FML), a deep neural network (DNN) approach that approximates the parametric evolution map without requiring special treatment of nonlinearities. We further extend FML with a transfer-learning-based model correction procedure, enabling the correction of misspecified prior models using only a sparse set of high-fidelity or experimental measurements, without assuming a prescribed form for the correction term. Through a suite of numerical experiments on unicycle, simplified bicycle, and slip-based bicycle models, we demonstrate that DRIPS offers robust and highly data-efficient learning of nonautonomous vehicle dynamics, while FML provides expressive nonlinear modeling and effective correction of model-form errors under severe data scarcity.

data-driven modeling↗

Validation of the NASA Electrical Power System – Sizing and Analysis Tool (EPS-SAT)

The electrification of aircraft propulsion systems has opened the design space for engineers by allowing for unique and highly specialized propulsion system and vehicle designs. NASA developed the Electrical Power System – Sizing and Analysis Tool (EPS-SAT) to conduct high-level trade studies and sensitivity studies on the various propulsion system designs that can be implemented in electrified aircraft. The results of these studies would be used to better direct investment dollars and determine strengths and weaknesses of propulsion system designs. In this paper, the results of the EPS-SAT tool were validated with hardware data extracted from the NASA Revolutionary Vertical Lift Technology (RVLT) Advanced Reconfigurable Electric Aircraft Lab (AREAL). Updated performance maps were added to the EPS-SAT library so that high-fidelity results could be calculated.

Patrick A. Hanlon↗

A two-loop four-point form factor at function level

Recently, the maximally-helicity-violating four-point form factor for the chiral stress-energy tensor in planar $\mathcal{N}$ = 4 super Yang-Mills was computed to three loops at the level of the symbol associated with multiple polylogarithms. It exhibits antipodal self-duality, or invariance under the combined action of a kinematic map and reversing the ordering of letters in the symbol. Here we lift the two-loop form factor from symbol level to function level. We provide an iterated representation of the function’s derivatives (coproducts). In order to do so, we find a three-parameter limit of the five-parameter phase space where the symbol’s letters are all rational. We also use function-level information about dihedral symmetries and the soft, collinear, and factorization limits, as well as limits governed by the form-factor operator product expansion (FFOPE). We provide plots of the remainder function on several kinematic slices, and show that the result is compatible with the FFOPE data. We further verify that antipodal self-duality is valid at two loops beyond the level of the symbol.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Theoretical investigations of high lift aerodynamics

A program which generates a coordinate system for a two element airfoil with the mesh points concentrated in areas of significant vorticity, i.e., boundary layer and wake is operational. The 'imbedded' grid method developed allows a transition from the scale of the main airfoil to the scale of the flap. This requirement is essential for the modeling of viscous flows over the flap and slat of a multielement airfoil. An airfoil mounted in a 2-D wind tunnel was formulated. The program is ready for a fine grid and a large number of planes to explore the characteristics of a Navier-Stokes solver in a quasi-3D case. The program was converted to a form suitable for the STAR computer. Runs were made to map a three dimensional flow field for a wall airfoil intersection with and without lift.

Bennett, G.↗

STS-99 SRTM Lift and Insert into Canister

The primary objective of the STS-99 mission was to complete high resolution mapping of large sections of the Earth's surface using the Shuttle Radar Topography Mission (SRTM), a specially modified radar system. This radar system produced unrivaled 3-D images of the Earth's Surface. The mission was launched at 12:31 on February 11, 2000 onboard the space shuttle Endeavour. and led by Commander Kevin Kregel. The crew was Pilot Dominic L. Pudwill Gorie and Mission Specialists Janet L. Kavandi, Janice E. Voss, Mamoru Mohri from the National Space Development Agency (Japanese Space Agency), and Gerhard P. J. Thiele from DARA (German Space Agency). This videotape shows clean room technicians working on a part of the 200 foot long mast that will hold the SRTM in position during the mission. This videotape also shows the lowering of the SRTM into the canister.

Source record↗

Velocity Measurements in the Wake of the Swept Wing Flow Test Model at the National Transonic Facility

Femtosecond laser electronic excitation tagging (FLEET) was applied to obtain flowfield velocity data for the Swept Wing Flow Test (SWiFT) at the NASA Langley Research Center National Transonic Facility (NTF). Despite numerous challenges associated with performing flow velocimetry measurements within a large-scale cryogenic wind tunnel facility, the experimental campaign was conducted under various conditions, including dry air at 320 K, cool nitrogen at 240 K, and Mach numbers of 0.2 and 0.8. FLEET velocimetry measurements were performed in the downstream wake of the SWiFT model, providing a quantitative dataset. This dataset includes one-dimensional velocity profiles and two-dimensional velocity maps acquired at different angles of attack and Reynolds numbers. The two-dimensional single component velocity maps indicate relatively uniform flow across the 120-mm wide wake flow survey suggesting that the main flow features can be represented by single-position linear velocity profiles. The measured instantaneous velocity profiles at variable angles of attack are compared to model lift coefficient information obtained at Mach 0.2. At high Reynolds numbers, a sudden velocity decrease was observed in the FLEET measurements at the same time as stall in lift coefficient was observed. At a low Reynolds number, both the velocity profiles and the lift coefficient show a smoother transition, without a sudden stall. Furthermore, the two-dimensional, one component velocity map reveals a velocity deficit region at Mach 0.8 at various angles of attack. Both single shot and mean velocity measurements were acquired allowing assessment of flowfield fluctuations and measurement precisions. The uncertainties are within 4 m/s in mean measurements based on repeatability data and about 5 m/s in instantaneous single-shot measurements. Measurements are reported with ~4.8 mm spatial resolution with 32-pixel averaging used to reduce measurement errors.

femtosecond↗

Velocity Measurements in the Wake of the Swept Wing Flow Test (SWIFT) Model at the National Transonic Facility

Femtosecond laser electronic excitation tagging (FLEET) was applied to obtain flowfield velocity data for the Swept Wing Flow Test (SWiFT) at the NASA Langley Research Center National Transonic Facility (NTF). Despite numerous challenges associated with performing flow velocimetry measurements within a large-scale cryogenic wind tunnel facility, the experimental campaign was conducted under various conditions, including dry air at 320 K, cool nitrogen at 240 K, and Mach numbers of 0.2 and 0.8. FLEET velocimetry measurements were performed in the downstream wake of the SWiFT model, providing a quantitative dataset. This dataset includes one-dimensional velocity profiles and two-dimensional velocity maps acquired at different angles of attack and Reynolds numbers. The two-dimensional single component velocity maps indicate relatively uniform flow across the 120-mm wide wake flow survey suggesting that the main flow features can be represented by single-position linear velocity profiles. The measured instantaneous velocity profiles at variable angles of attack are compared to model lift coefficient information obtained at Mach 0.2. At high Reynolds numbers, a sudden velocity decrease was observed in the FLEET measurements at the same time as stall in lift coefficient was observed. At a low Reynolds number, both the velocity profiles and the lift coefficient show a smoother transition, without a sudden stall. Furthermore, the two-dimensional, one component velocity map reveals a velocity deficit region at Mach 0.8 at various angles of attack. Both single shot and mean velocity measurements were acquired allowing assessment of flowfield fluctuations and measurement precisions. The uncertainties are within 4 m/s in mean measurements based on repeatability data and about 5 m/s in instantaneous single-shot measurements. Measurements are reported with ~4.8 mm spatial resolution with 32-pixel averaging used to reduce measurement errors.

Transonic↗

Correlated Hofstadter spectrum and flavour phase diagram in magic-angle twisted bilayer graphene

In magic-angle twisted bilayer graphene, the moiré superlattice potential gives rise to narrow electronic bands that support a multitude of many-body quantum phases. Further richness arises in the presence of a perpendicular magnetic field, where the interplay between moiré and magnetic length scales leads to fractal Hofstadter subbands. In this strongly correlated Hofstadter platform, multiple experiments have identified gapped topological and correlated states, but little is known about the phase transitions between them in the intervening compressible regimes. Here we simultaneously unveil sequences of broken-symmetry Chern insulators and resolve sharp phase transitions between competing states with different topological quantum numbers and different occupations of the spin-valley flavour. Our measurements determine the energy spectrum of interacting Hofstadter subbands in magic-angle twisted bilayer graphene and map out the phase diagram of flavour occupancy. In addition, we observe full lifting of the degeneracy of the zeroth Landau levels together with level crossings, indicating moiré valley splitting. We propose a unified flavour polarization mechanism to understand the intricate interplay of topology, interactions and symmetry breaking as a function of density and applied magnetic field in this system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Optimizing Magnetic Force Microscopy Resolution and Sensitivity to Visualize Nanoscale Magnetic Domains

Magnetic force microscopy (MFM) enables mapping local magnetic fields across a sample surface with nanoscale resolution. To perform MFM, an atomic force microscopy (AFM) probe whose tip has been magnetized vertically (i.e., perpendicular to the probe cantilever) is oscillated at a fixed height above the sample surface. The resultant shifts in the oscillation phase or frequency, which are proportional to the magnitude and sign of the vertical magnetic force gradient at each pixel location, are then tracked and mapped. Although the spatial resolution and sensitivity of the technique increases with decreasing lift height above the surface, this seemingly straightforward path to improved MFM images is complicated by considerations such as minimizing topographical artifacts due to shorter range van der Waals forces, increasing the oscillation amplitude to further improve sensitivity, and the presence of surface contaminants (in particular water due to humidity under ambient conditions). In addition, due to the orientation of the probe's magnetic dipole moment, MFM is intrinsically more sensitive to samples with an out-of-plane magnetization vector. Here, high-resolution topographical and magnetic phase images of single and bicomponent nanomagnet artificial spin-ice (ASI) arrays obtained in an inert (argon) atmosphere glovebox with <0.1 ppm O 2 and H 2 O are reported. Further, optimization of lift height and drive amplitude for high resolution and sensitivity while simultaneously avoiding the introduction of topographical artifacts is discussed, and detection of the stray magnetic fields emanating from either end of the nanoscale bar magnets (~250 nm long and <100 nm wide) aligned in the plane of the ASI sample surface is shown. Likewise, using the example of a Ni-Mn-Ga magnetic shape memory alloy (MSMA), MFM is demonstrated in an inert atmosphere with magnetic phase sensitivity capable of resolving a series of adjacent magnetic domains each ~200 nm wide.

47 OTHER INSTRUMENTATION↗

Application of a Fully Numerical Guidance to Mars Aerocapture

An advanced guidance algorithm, Fully Numerical Predictor-corrector Aerocapture Guidance (FNPAG), has been developed to perform aerocapture maneuvers in an optimal manner. It is a model-based, numerical guidance that benefits from requiring few adjustments across a variety of different hypersonic vehicle lift-to-drag ratios, ballistic co-efficients, and atmospheric entry conditions. In this paper, FNPAG is first applied to the Mars Rigid Vehicle (MRV) mid lift-to-drag ratio concept. Then the study is generalized to a design map of potential Mars aerocapture missions and vehicles, ranging from the scale and requirements of recent robotic to potential human and precursor missions. The design map results show the versatility of FNPAG and provide insight for the design of Mars aerocapture vehicles and atmospheric entry conditions to achieve desired performance.

Matz, Daniel A.↗

NSEG, a segmented mission analysis program for low and high speed aircraft. Volume 1: Theoretical development

A rapid mission analysis code based on the use of approximate flight path equations of motion is presented. Equation form varies with the segment type, for example, accelerations, climbs, cruises, descents, and decelerations. Realistic and detailed characteristics were specified in tabular form. The code also contains extensive flight envelope performance mapping capabilities. Approximate take off and landing analyses were performed. At high speeds, centrifugal lift effects were accounted for. Extensive turbojet and ramjet engine scaling procedures were incorporated in the code.

Hague, D. S.↗