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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Iterative Stability Enforcement in Adaptive Antoulas–Anderson Algorithms for \({\boldsymbol{\mathcal{H}_2}}\) Model Reduction

This paper presents an extension of the Adaptive-Antoulas-Anderson (AAA) algorithm for rational modelling. Specifically, our new stable multi-input multi-output AAA (smiAAA) algorithm builds rational approximations of multi-input signals with a common set of stable poles. A new methodology is presented for iteratively enforcing stability constraints on the poles. We demonstrate the strengths of this approach compared to the stability enforcement in the FastAAA algorithm. Results using the smiAAA algorithm are compared with the commonly used Vector Fitting algorithm and the more recently published RKFIT algorithm. Vector Fitting and RKFIT both require the user to input the number of poles to use in the approximations. If the final approximation is not accurate enough, the user must re-start Vector Fitting or RKFIT with a larger number of poles and/or a new starting location for the poles. In contrast, the smiAAA algorithm is designed to allow the user to simply input the desired accuracy of the approximations, and the necessary number of poles is detected automatically. This permits users to produce approximations of a desired accuracy with no knowledge about the underlying order of the system being approximated, preventing the algorithm from ever needing to be rerun. An additional feature for preventing extraneous poles from being returned by AAA is also discussed. The cause of these extraneous poles is efficiently detected and removed by our presented methodology. In conclusion, the examples presented demonstrate that smiAAA can efficiently produce approximations of similar or better accuracy than Vector Fitting and RKFIT while requiring less input from the user.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A MIMO AAA Agorithm for Frequency Dependent Line Modeling

Modeling of power distribution system components that are valid for a wide range of frequencies are crucial for highly accurate modeling of electromagnetic transient (EMT) events. This has recently become of interest due to the improvements needed for the resilient operation of distribution systems. Vector fitting (VF) is a very popular and commonly used algorithm for wide band representations of power system components in EMT simulations. In this research, we present a new multi-input rational approximation algorithm (MIAAA) and illustrate its advantages with respect to VF using examples of approximations of admittance matrices discussed in the literature. We show that MIAAA not only outperforms VF in terms of achieving better accuracy using lesser number of poles, but also has no numerical issues achieving convergence. In contrast to VF, MIAAA is not sensitive to the location of input sample points and it does not require good estimates for the location of the desired approximation poles. The novelty of this research work is the use of recent mathematical results to solve existing challenges in distribution system modeling and to develop rational approximations for power system models that intend to be optimal in terms of accuracy and performance.

AAA algorithm↗
DOE OSTI2024

Physically interpretable approximations of many-body spectral functions

The rational function approximation provides a natural and interpretable representation of response functions such as the many-body spectral functions. We apply the vector fitting (VFIT) algorithm to fit a variety of spectral functions calculated from the Holstein model of electron-phonon interactions. We show that the resulting rational functions are highly efficient in their fitting of sharp features in the spectral functions, and could provide a means to infer physically relevant information from a spectral data set. The position of the peaks in the approximated spectral function are determined by the location of poles in the complex plane. Additionally, we developed a variant of VFIT that incorporates regularization to improve the quality of fits. With this procedure, we demonstrate it is possible to achieve accurate spectral function fits that vary smoothly as a function of physical conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRSDate not supplied

On the Implementation and Further Validation of a Time Domain Boundary Element Method Broadband Impedance Boundary Condition

A time domain boundary integral equation with Burton-Miller reformulation is presented for acoustic scattering by surfaces with liners in a uniform mean flow. The Ingard-Myers impedance boundary condition is implemented using a broadband multipole impedance model and converted into time domain differential equations to augment the boundary integral equation. The coupled integral-differential equations are solved numerically by a March-On-in-Time (MOT) scheme. While the Ingard-Myers condition is known to support Kelvin-Helmholtz instability due to its use of a vortex sheet interface between the flow and the liner surface, it is found that by neglecting a second derivative term in the current time domain impedance boundary condition formulation, the instability an be effectively suppressed in computation. The proposed formulation and implementation are validated using a NASA Langley Research Center Grazing Flow Impedance Tube (GFIT) experimental dataset with satisfactory results. Moreover, a minimization procedure for finding the poles and coefficients of the broadband multiple impedance model is formulated in this paper by which, unlike the commonly used vector-fitting method, passivity of the model is ensured. Numerical tests show the proposed minimization approach is effective for modeling liners that are commonly used in aeroacoustic applications.

Time Domain Impedance Boundary Condition↗
NASA NTRS1993

Vector formulation for interferogram surface fitting

Interferometry is an optical testing technique that quantifies the optical path difference (OPD) between a reference wave front and a test wave front based on the interference of light. Fringes are formed when the OPD is an integral multiple of the illuminating wavelength. The resultant two-dimensional pattern is called an interferogram. The function of any interferogram analysis program is to extract this OPD and to produce a representation of the test wave front (or surface). This is accomplished through a three-step process of sampling, ordering, and fitting. We develop a generalized linear-algebra vector-notation model of the interferogram sampling and fitting process.

Fischer, David J.↗
NASA NTRS1993

Encoding of head acceleration in vestibular neurons. I. Spatiotemporal response properties to linear acceleration

1. Extracellular recordings were made in and around the medial vestibular nuclei in decerebrated rats. Neurons were functionally identified according to their semicircular canal input on the basis of their responses to angular head rotations around the yaw, pitch, and roll head axes. Those cells responding to angular acceleration were classified as either horizontal semicircular canal-related (HC) or vertical semicircular canal-related (VC) neurons. The HC neurons were further characterized as either type I or type II, depending on the direction of rotation producing excitation. Cells that lacked a response to angular head acceleration, but exhibited sensitivity to a change in head position, were classified as purely otolith organ-related (OTO) neurons. All vestibular neurons were then tested for their response to sinusoidal linear translation in the horizontal head plane. 2. Convergence of macular and canal inputs onto central vestibular nuclei neurons occurred in 73% of the type I HC, 79% of the type II HC, and 86% of the VC neurons. Out of the 223 neurons identified as receiving macular input, 94 neurons were further studied, and their spatiotemporal response properties to sinusoidal stimulation with pure linear acceleration were quantified. Data were obtained from 33 type I HC, 22 type II HC, 22 VC, and 17 OTO neurons. 3. For each neuron the angle of the translational stimulus vector was varied by 15, 30, or 45 degrees increments in the horizontal head plane. In all tested neurons, a direction of maximum sensitivity was identified. An interesting difference among neurons was their response to translation along the direction perpendicular to that that produced the maximum response ("null" direction). For the majority of neurons tested, it was possible to evoke a nonzero response during stimulation along the null direction always had response phases that varied as a function of stimulus direction. 4. These spatiotemporal response properties were quantified in two independent ways. First, the data were evaluated on the basis of the traditional one-dimensional principle governed by the "cosine gain rule" and constant response phase at different stimulus orientations. Second, the response gain and phase values that were empirically determined for each orientation of the applied linear stimulus vector were fitted on the basis of a newly developed formalism that treats neuronal responses as exhibiting two-dimensional spatial sensitivity. Thus two response vectors were determined for each neuron on the basis of its response gain and phase at different stimulus directions in the horizontal head plane.(ABSTRACT TRUNCATED AT 400 WORDS).

NASA Discipline Neuroscience↗
NASA NTRS1989

Minimizing distortion and internal forces in truss structures by simulated annealing

Inaccuracies in the length of members and the diameters of joints of large truss reflector backup structures may produce unacceptable levels of surface distortion and member forces. However, if the member lengths and joint diameters can be measured accurately it is possible to configure the members and joints so that root-mean-square (rms) surface error and/or rms member forces is minimized. Following Greene and Haftka (1989) it is assumed that the force vector f is linearly proportional to the member length errors e(sub M) of dimension NMEMB (the number of members) and joint errors e(sub J) of dimension NJOINT (the number of joints), and that the best-fit displacement vector d is a linear function of f. Let NNODES denote the number of positions on the surface of the truss where error influences are measured. The solution of the problem is discussed. To classify, this problem was compared to a similar combinatorial optimization problem. In particular, when only the member length errors are considered, minimizing d(sup 2)(sub rms) is equivalent to the quadratic assignment problem. The quadratic assignment problem is a well known NP-complete problem in operations research literature. Hence minimizing d(sup 2)(sub rms) is is also an NP-complete problem. The focus of the research is the development of a simulated annealing algorithm to reduce d(sup 2)(sub rms). The plausibility of this technique is its recent success on a variety of NP-complete combinatorial optimization problems including the quadratic assignment problem. A physical analogy for simulated annealing is the way liquids freeze and crystallize. All computational experiments were done on a MicroVAX. The two interchange heuristic is very fast but produces widely varying results. The two and three interchange heuristic provides less variability in the final objective function values but runs much more slowly. Simulated annealing produced the best objective function values for every starting configuration and was faster than the two and three interchange heuristic.

Kincaid, Rex K.↗
NASA NTRS2023

X-Ray Polarimetry of X-Ray Pulsar X Persei: Another Orthogonal Rotator?

X Persei is a persistent low-luminosity X-ray pulsar of period of ≈ 835 s in a Be binary system. The field strength at the neutron star surface is not known precisely, but indirect signs indicate a magnetic field above 10 13 G, which makes the object one of the most magnetized known X-ray pulsars. Here we present the results of observations X Persei performed with the Imaging X-ray Polarimetry Explorer (IXPE). The X-ray polarization signal was found to be strongly dependent on the spin phase of the pulsar. The energy-averaged polarization degree in 3–8 keV band varied from several to ∼20 per cent over the pulse with a phase dependence resembling the pulse profile. The polarization angle shows significant variation and makes two complete revolutions during the pulse period, resulting in nearly nil pulse-phase averaged polarization. Applying the rotating vector model to the IXPE data we obtain the estimates for the rotation axis inclination and its position angle on the sky, as well as for the magnetic obliquity. The derived inclination is close to the orbital inclination, reported earlier for X Persei. The polarimetric data imply a large angle between the rotation and magnetic dipole axes, which is similar to the result reported recently for the X-ray pulsar GRO J1008−57. After eliminating the effect of polarization angle rotation over the pulsar phase using the best-fitting rotating vector model, the strong dependence of the polarization degree with energy was discovered, with its value increasing from 0 at ∼2 keV to 30per cent at 8 keV.

X-Persei↗
DOE OSTI2023

An SU(5) × U(1)' SUSY GUT with a “vector-like chiral” fourth family to fit all low energy data, including the muon g – 2

An additional generation of quarks and leptons and their SUSY counterparts, which are vector-like under the Standard Model gauge group but are chiral with respect to the new U(1) 3–4 gauge symmetry, are added to the Minimal Supersymmetric Standard Model (MSSM). We show that this model is a GUT and unifies the three SM gauge couplings and also the additional U(1) 3–4 coupling at a GUT scale of ≈ 5 × 10 16 GeV and explains the experimentally observed deviation of the muon g – 2. We also fit the quark flavor changing processes consistent with the latest experimental data and look at the effect of the new particles on the W boson mass without obviously conflicting with the observed masses of particles, CKM matrix elements, neutrino mixing angles, their mass differences, and the lepton-flavor violating bounds. This model predicts sparticle masses less than 25 TeV, with a gluino mass ≈ 2.3 – 3 TeV consistent with constraints, and one of the neutralinos as the LSP with a mass of ≈ 480 – 580 GeV, which is a potential dark matter candidate. The model is string theory motivated and predicts the VL quarks, leptons, a massive Z' and two Dirac neutrinos at the TeV scale and the branching ratios of μ → eγ, τ → μγ and τ → 3μ with BR(μ → eγ) within reach of future experiments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1992

A test of present-day plate geometries for northeast Asia and Japan

Alternative geometries for the present-day configuration of plate boundaries in northeast Asia and Japan are tested using NUVEL-1 and 256 horizontal earthquake slip vectors from the Japan and northern Kuril trenches. Statistical analysis of the slip vectors is used to determine whether the North American, Eurasian, or Okhotsk plate overlies the trench. Along the northern Kuril trench, slip vectors are well-fit by the NUVEL-1 Pacific-North America Euler pole, but are poorly fit by the Pacific-Eurasia Euler pole. Results for the Japan trench are less conclusive, but suggest that much of Honshu and Hokkaido are also part of the North American plate. The simplest geometry consistent with the trench slip vectors is a geometry in which the North American plate extends south to 41 deg N, and possibly includes northern Honshu and southern Hokkaido. Although these results imply that the diffuse seismicity that connects the Lena River delta to Sakhalin Island and the eastern Sea of Japan records motion between Eurasia and North America, onshore geologic and seismic data define an additional belt of seismicity in Siberia that cannot be explained with this geometry. Assuming that these two seismic belts constitute evidence for an Okhotsk block, two published kinematic models for motion of the Okhotsk block are tested. The first model, which predicts motion of up to 15 mm/yr relative to North America, is rejected because Kuril and Japan trench slip vectors are fit more poorly than for the simpler geometry described above. The second model gives a good fit to the trench slip vectors, but only if Okhotsk-North America motion is slower than 5 mm/yr.

Demets, Charles↗
NASA NTRS1987

The derivation of vector magnetic fields from Stokes profiles - Integral versus least squares fitting techniques

The results of two methods for deriving photospheric vector magnetic fields from the Zeeman effect, as observed in the Fe I line at 6302.5 A at high spectral resolution (45 mA), are compared. The first method does not take magnetooptical effects into account, but determines the vector magnetic field from the integral properties of the Stokes profiles. The second method is an iterative least-squares fitting technique which fits the observed Stokes profiles to the profiles predicted by the Unno-Rachkovsky solution to the radiative transfer equation. For sunspot fields above about 1500 gauss, the two methods are found to agree in derived azimuthal and inclination angles to within about + or - 20 deg.

Ronan, R. S.↗
NASA NTRS1971

Analysis of ATS photographs using a specially designed electronic console

Measurements of cloud motion, cloud size, and growth rate were made on four days in the vicinity of rawin stations in the BOMEX network. These measurements were compared with the rawins and levels of best fit ranging from 980 to 250 mb were found. No correlation was found between cloud size and level of best fit. The magnitude of the vector difference between the cloud motion and wind at the level of best fit was as high as 15 knots for clouds with levels of best fit below the 500-mb level and 8 knots for clouds with levels of best fit above the 500-mb level. When cloud motion vectors with levels of best fit at or above the 500-mb level were compared with winds at the 300-mb level, the vector difference increased to as much as 16 knots or double the greatest minimum vector difference. A comparison between cloud motions and winds at the level of best fit showed that the clouds tended to move slightly faster than the observed winds and to move slightly to the left of the wind direction. Rate of growth appeared to influence whether clouds moved faster or slower than the wind. No relationship between cloud size and amount of deviation from the wind direction was observed.

Blackmer, R. H., Jr.↗
NASA NTRS1980

Initial geomagnetic field model from MAGSAT

Magsat data from magnetically quiet days were used to derive a thirteenth degree and order spherical harmonic geomagnetic field model, MGST(3/80). The model utilized both scalar and vector data and fit that data with standard deviations of 8, 52, 55 and 97 nT for the scalar magnitude, B sub r, B sub theta and B sub phi respectively. When compared with earlier models, the Earth's dipole moment continues to decrease at a rate of about 26 nT/year. Evaluation of earlier models with Magsat data shows that the scalar field at the Magsat epoch is best predicted by the POGO(2/72) model but that the AWC/75 and IGS/75 are better for predicting vector fields.

Langel, R. A.↗
NASA NTRS1980

Initial geomagnetic field model from Magsat vector data

Magsat data from the magnetically quiet days of November 5-6, 1979, were used to derive a thirteenth degree and order spherical harmonic geomagnetic field model, MGST(6/80). The model utilized both scalar and high-accuracy vector data and fit that data with root-mean-square deviations of 8.2, 6.9, 7.6 and 7.4 nT for the scalar magnitude, B(r), B(theta), and B(phi), respectively. The model includes the three first-order coefficients of the external field. Comparison with averaged Dst indicates that zero Dst corresponds with 25 nT of horizontal field from external sources. When compared with earlier models, the earth's dipole moment continues to decrease at a rate of about 26 nT/yr. Evaluation of earlier models with Magsat data shows that the scalar field at the Magsat epoch is best predicted by the POGO(2/72) model but that the WC80, AWC/75 and IGS/75 are better for predicting vector fields.

Langel, R. A.↗
DOE OSTI2021

Water dynamics in C–S–H and M-S-H cement pastes: A revised jump-diffusion and rotation-diffusion model

The Quasi-Elastic Neutron Scattering (QENS) spectra from four cement pastes are re-analyzed by a new revised jump-diffusion and rotation-diffusion model (rJRM). From the QENS fit, it can be seen that the rJRM is an improved model to fit QENS spectra within the whole detected neutron energy transfer and scattering vector. By the rJRM fitting, the structure parameters extracted from QENS spectra show that both the additives aluminum-silicate nanotubes (ASN) and carboxyl group functionalized ASN (ASN-COOH) can improve magnesium-silicate-hydrate (M-S-H) toward calcium-silicate-hydrate (C–S–H) direction in mechanical properties, but the improvement is weakened with decreasing temperatures. The extracted dynamical parameters show that there is a dynamic anomaly near 230 K in not only translational but also rotational diffusion of water confined in all the investigated samples. In conclusion, the anomaly in rotational diffusion is new compared with those results obtained by the QENS fit using other models.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Probing gravity with the DES-CMASS sample and BOSS spectroscopy

ABSTRACT The DES-CMASS sample (DMASS) is designed to optimally combine the weak lensing measurements from the Dark Energy Survey (DES) and redshift-space distortions (RSD) probed by the CMASS galaxy sample from the Baryonic Oscillation Spectroscopic Survey. In this paper, we demonstrate the feasibility of adopting DMASS as the equivalent of CMASS for a joint analysis of DES and BOSS in the framework of modified gravity. We utilize the angular clustering of the DMASS galaxies, cosmic shear of the DES metacalibration sources, and cross-correlation of the two as data vectors. By jointly fitting the combination of the data with the RSD measurements from the CMASS sample and Planck data, we obtain the constraints on modified gravity parameters $\mu _0=-0.37^{+0.47}_{-0.45}$ and $\Sigma _0=0.078^{+0.078}_{-0.082}$. Our constraints of modified gravity with DMASS are tighter than those with the DES Year 1 redMaGiC sample with the same external data sets by 29 per cent for μ0 and 21 per cent for Σ0, and comparable to the published results of the DES Year 1 modified gravity analysis despite this work using fewer external data sets. This improvement is mainly because the galaxy bias parameter is shared and more tightly constrained by both CMASS and DMASS, effectively breaking the degeneracy between the galaxy bias and other cosmological parameters. Such an approach to optimally combine photometric and spectroscopic surveys using a photometric sample equivalent to a spectroscopic sample can be applied to combining future surveys having a limited overlap such as DESI and LSST.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1977

Present-day plate motions

A data set comprising 110 spreading rates, 78 transform fault azimuths and 142 earthquake slip vectors was inverted to yield a new instantaneous plate motion model, designated RM2. The mean averaging interval for the relative motion data was reduced to less than 3 My. A detailed comparison of RM2 with angular velocity vectors which best fit the data along individual plate boundaries indicates that RM2 performs close to optimally in most regions, with several notable exceptions. On the other hand, a previous estimate (RM1) failed to satisfy an extensive set of new data collected in the South Atlantic Ocean. It is shown that RM1 incorrectly predicts the plate kinematics in the South Atlantic because the presently available data are inconsistent with the plate geometry assumed in deriving RM1. It is demonstrated that this inconsistency can be remedied by postulating the existence of internal deformation with the Indian plate, although alternate explanations are possible.

Minster, J. B.↗
NASA NTRS1978

Present-day plate motions

An instantaneous plate-motion model, Relative Motion 2 (RM2), is obtained by inverting a data set comprising 110 spreading rates, 78 transform fault azimuths, and 142 earthquake slip vectors. RM2 is compared with angular velocity vectors which best fit the data along individual plate boundaries and, while the model performs close to optimally in most regions, attention is directed to those regions which are not suitably described by the model. Reasons for the discrepancies between RM2 and observations for the India-Antarctica plate boundary, the Pacific-India plate boundary, and the east-west trending transform fault azimuths observed in the French-American Mid-Ocean Undersea Study area are discussed.

Minster, J. B.↗