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DOE OSTI2020

General approaches for shear-correcting coordinate transformations in Bragg coherent diffraction imaging. Part I

This two-part article series provides a generalized description of the scattering geometry of Bragg coherent diffraction imaging (BCDI) experiments, the shear distortion effects inherent in the 3D image obtained from presently used methods and strategies to mitigate this distortion. Part I starts from fundamental considerations to present the general real-space coordinate transformation required to correct this shear, in a compact operator formulation that easily lends itself to implementation with available software packages. Such a transformation, applied as a final post-processing step following phase retrieval, is crucial for arriving at an undistorted, correctly oriented and physically meaningful image of the 3D crystalline scatterer. As the relevance of BCDI grows in the field of materials characterization, the available sparse literature that addresses the geometric theory of BCDI and the subsequent analysis methods are generalized here. This geometrical aspect, specific to coherent Bragg diffraction and absent in 2D transmission CDI experiments, gains particular importance when it comes to spatially resolved characterization of 3D crystalline materials in a reliable nondestructive manner. This series of articles describes this theory, from the diffraction in Bragg geometry to the corrections needed to obtain a properly rendered digital image of the 3D scatterer. Part I of this series provides the experimental BCDI community with the general form of the 3D real-space distortions in the phase-retrieved object, along with the necessary post-retrieval correction method. Part II builds upon the geometric theory developed in Part I with the formalism to correct the shear distortions directly on an orthogonal grid within the phase-retrieval algorithm itself, allowing more physically realistic constraints to be applied. Taken together, Parts I and II provide the X-ray science community with a set of generalized BCDI shear-correction techniques crucial to the final rendering of a 3D crystalline scatterer and for the development of new BCDI methods and experiments.

36 MATERIALS SCIENCE↗

NASA NTRSDate not supplied

Magnetic Mapping in the Inner Magnetosphere using Kamodo

Many models require specialized access and interpolation schemes to effectively extract and interpolate their outputs. In particular, the Block-Adaptive Tree Solarwind Roe Upwind Scheme (BATSRUS) component of the Space Weather Modeling Framework (SWMF) requires Kamodo to take advantage of its block-based adaptive grid structure, and the Lyon-Fedder Mobarry magnetosphere model (or its successor GAMERA) needs a scheme that appreciates the distorted spherical arrangement of grid vertices on a non-orthogonal grid. With the flythrough layer developed by Ringuette et al. (SH42E-2337), the underlying model readers have been adapted to use multiple time steps in a single Python session to perform 4- dimensional interpolations in time and space. Kamodo now utilizes lazy interpolation that loads data only when needed. We present the successful integration of SWMF/BATSRUS magnetosphere access and interpolation into the new 4D Kamodo framework utilizing an external library of C code. Through function composition, Kamodo facilitates the calculation of derived quantities and the transformation of positions and vectors into different coordinate systems. This work is a significant step towards performing field line tracing in Kamodo with SWMF magnetosphere outputs.

Lutz Rastaetter↗

NASA NTRS1989

Direction of movement effects under transformed visual/motor mappings

Performance in a discrete aiming task was compared under several transformed visual/motor mappings: rotations by 45, 90, 135, and 180 deg and reflections about the horizontal and the vertical midlines. Eight aiming targets were used, corresponding to eight directions of movement: up, down, right, left, up-right, down-left, up-left, and down-right. Direction of movements were characterized in terms of separable visual and motor components, and two kinds of direction of movement effects were considered. First, a direction of movement effect paralleling that seen in rapid aiming under the usual nontransformed mapping. Second, because rotations, but not reflections, are physically realizable 2-D transformations, a visual/motor control system which is sensitive to physical constraints should perform reflections, but not rotations, in a piecemeal fashion. Results supported the hypothesis that a motor factor having to do with complexity of limb movement accounts for differences in movement accuracy between right and left oblique directions. Direction of movement effects were more evident in reflections than in rotations, and were consistent with the hypothesis that the visual/motor-control system seeks a physically realizable 2-D rotation solution to reflections. Results also suggested that reversal of two orthogonal basis dimensions is far less difficult than reversing only one and leaving the other intact.

Cunningham, H. A.↗

NASA NTRS1991

IDE spatio-temporal impact fluxes and high time-resolution studies of multi-impact events and long-lived debris clouds

During the first 12 months of the Long Duration Exposure Facility (LDEF) mission, the Interplanetary Dust Experiment (IDE) recorded over 15,000 total impacts on six orthogonal faces with a time resolution on the order of 15 to 20 seconds. When combined with the orbital data and the stabilized configuration of the spacecraft, this permits a detailed analysis of the micro-particulate environment. The functional status of each of the 459 detectors was monitored every 2.4 hours, and post-flight analyses of these data has now permitted an evaluation of the effective active detection area as a function of time, panel by panel and separately for the two sensitivity levels. Thus, total impacts were transformed into areal fluxes, and are presented here for the first time. Also discussed are possible effects of these fluxes on previously announced results: apparent debris events, meteor stream detections, and beta meteoroids in observationally significant numbers.

Mulholland, J. Derral↗

NASA NTRS1967

Differentiating unit orthogonal vectors in a Riemannian space that admits and N-tuply orthogonal system of hypersurfaces.

In a normal coordinate system { y 𝑎 } , the identity 𝜕 2 𝑥 𝑝 /∂y 𝑛 ∂y 𝑚 = ∂ 2 𝑥 𝑝 /∂y 𝑚 ∂y 𝑛 is used to obtain expressions, involving the components of the metric tensor in this coordinate system, for the derivatives of the unit tangent vectors to the parametric curves. An example is given for a normal coordinate system in the De Sitter universe.

Riemann space↗

NASA NTRS1990

Some fundamentals regarding kinematics and generalized forces for multibody dynamics

In order to illustrate the various forms in which generalized forces can arise from diverse subsystem analyses in multibody dynamics, intrinsic dynamical equations for the rotational dynamics of a rigid body are derived from Hamilton's principle. Two types of generalized forces are derived: (1) those associated with the virtual rotation vector in some orthogonal basis, and (2) those associated with varying generalized coordinates. As one physical or kinematical result (such as a frequency or a specific direction cosine) cannot rely on this selection, a 'blind' coupling of two models in which generalized forces are calculated in different ways would be wrong. Both types should use the same rotational coordinates and should denote the virtual rotation on a similar basis according to method 1, or in terms of common rotational coordinates and their diversifications as in method 2. Alternatively, the generalized forces and coordinates of one model may be transformed to those of the other.

Hodges, Dewey H.↗

NASA NTRS1984

MMIC devices for active phased array antennas

The study of printed circuit discontinuities is necessary in order to design, for example, transitions between rectangular waveguides and printed circuits. New developments with respect to the analytical approaches to this problem are discussed. A summary of the progress in the experimental approach is presented. The accurate solution for the modes in various millimeter-wave waveguides is essential in the analysis of many integrated circuit components, such as filters and impedance transformers. Problems associated with the numerical computation of these modes in two frequently used waveguide forms, namely, the finline and microstrip, are presented. The spectral domain method of formulation, with a moment method solution, is considered. This approach can be readily extended to analyze an arbitrary configuration of dielectric and metallized regions in a shielded enclosure. Galerkin's method is used, where the testing and basic functions are the same. It is shown that the mode functions, or eigenfunctions, are more sensitive to errors than the phase constants, or eigenvalues. The approximate mode functions do not satisfy the orthogonality relationship well, resulting in difficulties when these modal solutions are used to form an approximate Green's function or are used in a mode matching analysis.

Mittra, R.↗

NASA NTRS2019

Seasonal and Diurnal Opportunities for XCH4, XCO2, and XCO for the Amazonian Rainforest Region Allowing Sampling and Validation

There is considerable interest in the aggregate methane emissions from the Amazon and similar moist tropical regions, and XCH4 measurements are well suited to constrain sources to the global atmosphere. Similarly, XCO2 measurements constrain CO2 in the region. XCO helps to partition CO2 patterns among burning and respiration processes. GeoCarb may allow these column measurements over the Western Hemisphere, but satellite retrieval require exacting calibration and validation by sun-focused Fourier transform spectrometers (FTS). The rarity of sufficiently large gaps in the cloud cover over the Amazon and similar rainforests restricts the validation opportunities for useful FTS observations and even more the opportunities for accurate retrievals. TropOMI observational statistics are extremely poor for the region. We have used two data sources to evaluate FTS opportunities at Manaus, Brazil, an FTS operated for 8 months near Manaus by Mavendra Dubey, and also sun-photometer measurements at several stations. The promise of using data from other satellites, e.g. GOES-16 ( (Geostationary Operational Environmental Satellite) and CALIOP (Cloud-Aerosol LIdar with Orthogonal Polarization gaps and aerosol layering will be described. We report initial results on five questions: (1) how frequent are observing opportunities of FTS?, (2) What evidence is there that gaps in clouds are wide enough for satellite retrievals at an appropriate accuracy, (3) What is the diurnal and seasonal variability of cloud gaps?, and (4) What limitations are currently suggested for unbiased FTS measurement of XCH4 due to diurnal effects, and (5) What evidence is there for incidence of problematic high aerosol extinction at higher layers of the troposphere (800 hPa to 120 hPa) which alter the XCH4 light-paths?

Chatfield, Robert↗

NASA NTRS1981

Three-axis electron-beam test facility

An electron beam test facility, which consists of a precision multidimensional manipulator built into an ultra-high-vacuum bell jar, was designed, fabricated, and operated at Lewis Research Center. The position within the bell jar of a Faraday cup which samples current in the electron beam under test, is controlled by the manipulator. Three orthogonal axes of motion are controlled by stepping motors driven by digital indexers, and the positions are displayed on electronic totalizers. In the transverse directions, the limits of travel are approximately + or - 2.5 cm from the center with a precision of 2.54 micron (0.0001 in.); in the axial direction, approximately 15.0 cm of travel are permitted with an accuracy of 12.7 micron (0.0005 in.). In addition, two manually operated motions are provided, the pitch and yaw of the Faraday cup with respect to the electron beam can be adjusted to within a few degrees. The current is sensed by pulse transformers and the data are processed by a dual channel box car averager with a digital output. The beam tester can be operated manually or it can be programmed for automated operation. In the automated mode, the beam tester is controlled by a microcomputer (installed at the test site) which communicates with a minicomputer at the central computing facility. The data are recorded and later processed by computer to obtain the desired graphical presentations.

Dayton, J. A., Jr.↗

DOE OSTI2020

Spectral fluctuations in the Sachdev-Ye-Kitaev model

We present a detailed quantitative analysis of spectral correlations in the Sachdev-Ye-Kitaev (SYK) model. We find that the deviations from universal Random Matrix Theory (RMT) behavior are due to a small number of long-wavelength fluctuations (of the order of the number of Majorana fermions N ) from one realization of the ensemble to the next one. These modes can be parameterized effectively in terms of Q-Hermite orthogonal polynomials, the main contribution being due to scale fluctuations for which we give a simple analytical estimate. Our numerical results for N = 32 show that only the lowest eight polynomials are needed to eliminate the nonuniversal part of the spectral fluctuations. The covariance matrix of the coefficients of this expansion can be obtained analytically from low-order double-trace moments. We evaluate the covariance matrix of the first six moments and find that it agrees with the numerics. We also analyze the spectral correlations in terms of a nonlinear σ-model, which is derived through a Fierz transformation, and evaluate the one and two-point spectral correlation functions to two-loop order. The wide correlator is given by the sum of the universal RMT result and corrections whose lowest-order term corresponds to scale fluctuations. However, the loop expansion of the σ-model results in an ill-behaved expansion of the resolvent, and it gives universal RMT fluctuations not only for q= 4 or higher even q-body interactions, but also for the q= 2 SYK model albeit with a much smaller Thouless energy while the correct result in this case should have been Poisson statistics. In our numerical studies we analyze the number variance and spectral form factor for N = 32 and q = 4. We show that the quadratic deviation of the number variance for large energies appears as a peak for small times in the spectral form factor. After eliminating the long-wavelength fluctuations, we find quantitative agreement with RMT up to an exponentially large number of level spacings for the number variance or exponentially short times in the case of the spectral form factor.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1999

The Prospect for Remote Sensing of Cirrus Clouds with a Submillimeter-Wave Spectrometer

Given the substantial radiative effects of cirrus clouds and the need to validate cirrus cloud mass in climate models, it is important to measure the global distribution of cirrus properties with satellite remote sensing. Existing cirrus remote sensing techniques, such as solar reflectance methods, measure cirrus ice water path (IWP) rather indirectly and with limited accuracy. Submillimeter/wave radiometry is an independent method of cirrus remote sensing based on ice particles scattering the upwelling radiance emitted by the lower atmosphere. A new aircraft instrument, the Far Infrared Sensor for Cirrus (FIRSC), is described. The FIRSC employs a Fourier Transform Spectrometer (FTS). which measures the upwelling radiance across the whole submillimeter region (0.1 1.0-mm wavelength). This wide spectral coverage gives high sensitivity to most cirrus particle sizes and allows accurate determination of the characteristic particle size. Radiative transfer modeling is performed to analyze the capabilities of the submillimeter FTS technique. A linear inversion analysis is done to show that cirrus IWP, particle size, and upper-tropospheric temperature and water vapor may be accurately measured, A nonlinear statistical algorithm is developed using a database of 20000 spectra simulated by randomly varying most relevant cirrus and atmospheric parameters. An empirical orthogonal function analysis reduces the 500-point spectrum (20 - 70/cm) to 15 "pseudo-channels" that are then input to a neural network to retrieve cirrus IWP and median particle diameter. A Monte Carlo accuracy study is performed with simulated spectra having realistic noise. The retrieval errors are low for IWP (rms less than a factor of 1.5) and for particle sizes (rins less than 30%) for IWP greater than 5 g/sq m and a wide range of median particle sizes. This detailed modeling indicates that there is good potential to accurately measure cirrus properties with a submillimeter FTS.

Evans, K. Franklin↗

NASA NTRS2002

622-Mbps Orthogonal Frequency Division Multiplexing (OFDM) Digital Modem Implemented

Future generation space communications systems feature significantly higher data rates and relatively smaller frequency spectrum allocations than systems currently deployed. This requires the application of bandwidth- and power-efficient signal transmission techniques. There are a number of approaches to implementing such techniques, including analog, digital, mixed-signal, single-channel, or multichannel systems. In general, the digital implementations offer more advantages; however, a fully digital implementation is very difficult because of the very high clock speeds required. Multichannel techniques are used to reduce the sampling rate. One such technique, multicarrier modulation, divides the data into a number of low-rate channels that are stacked in frequency. Orthogonal frequency division multiplexing (OFDM), a form of multicarrier modulation, is being proposed for numerous systems, including mobile wireless and digital subscriber link communication systems. In response to this challenge, NASA Glenn Research Center's Communication Technology Division has developed an OFDM digital modem (modulator and demodulator) with an aggregate information throughput of 622 Mbps. The basic OFDM waveform is constructed by dividing an incoming data stream into four channels, each using either 16- ary quadrature amplitude modulation (16-QAM) or 8-phase shift keying (8-PSK). An efficient implementation for an OFDM architecture is being achieved using the combination of a discrete Fourier transform (DFT) at the transmitter to digitally stack the individual carriers, inverse DFT at the receiver to perform the frequency translations, and a polyphase filter to facilitate the pulse shaping.

Kifle, Muli↗

NASA NTRS1973

On the theory of group generation of stars

The hypothesis proposed is that topology of a rotating gaseous cloud can be variable in the contraction process. Due to rotation an originally spherical cloud is transformed into a toroidal body. The contraction of a thin torus is considered with different suppositions on cooling the gas. In the determined time the torus will become gravitationally unstable. The excitation of Jeans' waves is shown to result in the disintegration of the torus into fragments. The number of the fragments and their mass distributions are calculated. The proposed hypothesis on toroidal stages in stellar evolution can remove some difficulties in the theory of structure and evolution of stars, such as absence of limitary stars, distribution of rotation velocities of early-type stars, origin of poloidal magnetic fields and decline rotators with the magnetic axis orthogonal to the axis of rotation.

Zhilyayev, B. Y.↗

DOE OSTI2026

Alchemy: A Model-Based Approach for 2D to 3D Autonomous Nuclear System Design

Engineering design of nuclear power plant (NPP) piping and equipment systems frequently bypasses crucial 2D system planning, instead moving straight to 3D modeling. This often leads to designs that exceed building envelope constraints, forcing expensive and time-consuming redesigns. When 2D modeling is employed, it typically involves labor-intensive manual workflows that convert 2D drawings into 3D models, resulting in inefficiencies and errors across design iterations. These workflows further suffer from poor software interoperability and dependence on proprietary software ecosystems, thereby contributing to schedule delays and cost overruns. This paper presents Alchemy, an autonomous framework that transforms 2D system definitions into Industry Foundation Classes (IFC)-compliant 3D building information models (BIMs) for expediting nuclear facility design at the conceptual preliminary phase. Using a model-based approach, the framework treats the 2D system diagram as the central reference model employed to automatically generate all subsequent outputs, ensuring consistency between the system definition and the resulting physical design. A web-based interface enables engineers to define hierarchical system topologies including associated equipment, geometric properties, and connectivity requirements. A two-phase equipment layout optimization algorithm automatically computes collision-free spatial configurations within predefined building envelopes. An artificial intelligence (AI)-assisted pipe routing module then generates orthogonal, collision-free routing paths, allowing the user to select either an A* search-based method or an Ant Colony Optimization (ACO)-based method. All outputs are authored natively in IFC format, relying on open-source technologies and standardized formats in order to ensure extensibility and eliminate proprietary software dependencies. The proposed framework is validated on two representative pressurized-water reactor (PWR)-based case studies, for which it autonomously generates IFC-compliant 3D models in minutes, drastically reducing workflows that typically require hours of manual effort. The generated model demonstrates topologically correct equipment placement, physically plausible spatial relationships, and collision-free pipe routing consistent with known PWR loop configurations. This work represents a foundational step toward digital engineering for nuclear facility preliminary design, with future ongoing development targeting design code compliance and expanded system complexity.

97 - MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Measurement of 2D density profiles using a second-harmonic, dispersion interferometer

A second-harmonic, dispersion interferometer is used to image large-area (≃5 cm 2 ) plasma-jet and gas-jet density profiles. Achromatic telescopes magnify the diameters of the primary-laser beam (1064 nm) and its second-harmonic (532 nm) before probing the sample and de-magnify the beam diameters after the sample, where the primary beam transfers its phase change to a second, second-harmonic beam, allowing the sample’s dispersive-phase change to be measured between two, orthogonally polarized second harmonic beams. The telescopes produce an azimuthally symmetric, dispersive-phase shift in the sample + background phase-change image and in the background phase-change image, which is removed by digital subtraction. The interferometer’s performance was verified using standard-optical components as dispersive elements (BK7 lenses and wedge plates), resolving a minimum, phase-change sensitivity of ΔΦ min ≳ 15 mrad and spatial resolution of Δx res ≃ 100 μm. The phase change produced by unknown-density objects (a pulsed-plasma-jet and a pulsed-gas-jet) was measured, and their data were used to recover the original, 2D density profiles using an inverse Abel transform: peak-number density, N gas ≃ 6 × 10 20 cm –3 and N e ≃ 5 × 10 16 cm –3 ; line-integrated density, ∫N gas dl ~ 2 × 10 19 cm –2 and ∫N e dl ~ 1 × 10 16 cm –2 . The techniques and methods developed here are scalable to even larger probe-beam diameters and frame-capture rates, leading to a diagnostic capability that is well-suited for applications involving the real-time measurement of density.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1986

On realizations of least-squares estimation and Kalman filtering by systolic arrays

Least-squares (LS) estimation is a basic operation in many signal processing problems. Given y = Ax + v, where A is a m x n coefficient matrix, y is a m x 1 observation vector, and v is a m x 1 zero mean white noise vector, a simple least-squares solution is finding the estimated vector x which minimizes the norm of /Ax-y/. It is well known that for an ill-conditioned matrix A, solving least-squares problems by orthogonal triangular (QR) decomposition and back substitution has robust numerical properties under finite word length effect since 2-norm is preserved. Many fast algorithms have been proposed and applied to systolic arrays. Gentleman-Kung (1981) first presented the trianglular systolic array for a basic Givens reduction. McWhirter (1983) used this array structure to find the least-squares estimation errors. Then by geometric approach, several different systolic array realizations of the recursive least-squares estimation algorithms of Lee et al (1981) were derived by Kalson-Yao (1985). Basic QR decomposition algorithms are considered in this paper and it is found that under a one-row time updating situation, the Householder transformation degenerates to a simple Givens reduction. Next, an improved least-squares estimation algorithm is derived by considering a modified version of fast Givens reduction. From this approach, the basic relationship between Givens reduction and Modified-Gram-Schmidt transformation can easily be understood. This improved algorithm also has simpler computational and inter-cell connection complexities while compared with other known least-squares algorithms and is more realistic for systolic array implementation.

Chen, M. J.↗

DOE OSTI2022

Physics-constrained deep learning of nonlinear normal modes of spatiotemporal fluid flow dynamics

In this study, we present a physics-constrained deep learning method to discover and visualize from data the invariant nonlinear normal modes (NNMs) which contain the spatiotemporal dynamics of the fluid flow potentially containing strong nonlinearity. Specifically, we develop a NNM-physics-constrained convolutional autoencoder (NNM-CNN-AE) integrated with a multi-temporal-step dynamics prediction block to learn the nonlinear modal transformation, the NNMs containing the spatiotemporal dynamics of the flow, and reduced-order reconstruction and long-time future-state prediction of the flow fields, simultaneously. In test cases, we apply the developed method to analyze different flow regimes past a cylinder, including laminar flows with low Reynolds number in transient and steady states (RD = 100) and high Reynolds number flow (RD = 1000), respectively. The results indicate that the identified NNMs are able to reveal the nonlinear spatiotemporal dynamics of these flows, and the NNMs-based reduced-order modeling consistently achieves better accuracy with orders of magnitudes smaller errors in construction and prediction of the nonlinear velocity and vorticity fields, compared to the linear proper orthogonal decomposition (POD) method and the Koopman-constrained-CNN-AE using the same number or dimension of modes. We perform an analysis of the modal energy distribution of NNMs and find that compared to POD modes, the few fundamental NNMs capture a very high level of total energy of the flow, which is advantageous for reduced-order modeling and representation of the complex flows. Finally, we discuss the potentials and limitations of the presented method.

Mechanics↗

NASA NTRS2019

Meshless Local Petrov-Galerkin (MLPG) Method with Orthogonal Polynomials for Euler-Bernoulli Beam Problems

In this paper, the feasibility of orthogonal polynomials in the meshless local Petrov Galerkin method (MLPG) method is studied. The orthogonal polynomials, Chebyshev and Legendre polynomials, are used in this MLPG method as trial functions. The test functions used were power functions with smooth derivatives at their ends. The performance of these methods is studied by applying these methods to Euler-Bernoulli beam problems. The MLPG-Galerkin and Legendre methods passed all the patch tests for simple beam problems. Next the formulations are tested on complex beam problems such as beams with partial loadings and continuous beam problems. Problems with load discontinuities and additional supports require special attention. Near discontinuities, judicious choice of number of nodes and nodal placements are needed to obtain accurate deflections, slopes, moments and shear forces. As polynomial functions are used, the large number of nodes can create a transformation matrix that is ill-conditioned, resulting in problems with the inversion of the matrix. The conditioning worsens as the number of nodes are increased beyond 20. Quadruple precision was needed for models to obtain accurate solutions. Even with quadruple precision the accuracy of the method suffers as the number of nodes is increased beyond 20. This appears to be a drawback of the MLPG-Chebyshev and MLPG-Legendre methods.

Raju, Ivatury S.↗