Search NASA⌕ Search

SEARCH · Search NASA

Results for “Approximate inverses”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 379 records · Page 21

Evidence for Two Separate but Interlaced Components of the Chromospheric Magnetic Field

Chromospheric fibrils are generally thought to trace out low-lying, mainly horizontal magnetic elds that fan out from flux concentrations in the photosphere. A high-resolution (approximately 0.1" per pixel) image, taken in the core of the Ca II 854.2 nm line and covering an unusually large area, shows the dark brils within an active region remnant as fine, looplike features that are aligned parallel to each other and have lengths comparable to a supergranular diameter. Comparison with simultaneous line-of-sight magnetograms confirms that the fibrils are centered above intranetwork areas (supergranular cell interiors), with one end rooted just inside the neighboring plage or strong unipolar network but the other endpoint less clearly defined. Focusing on a particular arcade-like structure lying entirely on one side of a lament channel (large-scale polarity inversion), we find that the total amount of positive-polarity flux underlying this "fibril arcade" is approximately 50 times greater than the total amount of negative-polarity flux. Thus, if the brils represent closed loops, they must consist of very weak fields (in terms of total magnetic flux), which are interpenetrated by a more vertical field that contains most of the flux. This surprising result suggests that the fibrils in unipolar regions connect the network to the nearby intranetwork flux, while the bulk of the network flux links to remote regions of the opposite polarity, forming a second, higher canopy above the fibril canopy. The chromospheric field near the edge of the network thus has an interlaced structure resembling that in sunspot penumbrae.

Reardom, K. P.↗

A mixed, unified forward/inverse framework for earthquake problems: fault implementation and coseismic slip estimate

SUMMARY We introduce a new finite-element (FE) based computational framework to solve forward and inverse elastic deformation problems for earthquake faulting via the adjoint method. Based on two advanced computational libraries, FEniCS and hIPPYlib for the forward and inverse problems, respectively, this framework is flexible, transparent and easily extensible. We represent a fault discontinuity through a mixed FE elasticity formulation, which approximates the stress with higher order accuracy and exposes the prescribed slip explicitly in the variational form without using conventional split node and decomposition discrete approaches. This also allows the first order optimality condition, that is the vanishing of the gradient, to be expressed in continuous form, which leads to consistent discretizations of all field variables, including the slip. We show comparisons with the standard, pure displacement formulation and a model containing an in-plane mode II crack, whose slip is prescribed via the split node technique. We demonstrate the potential of this new computational framework by performing a linear coseismic slip inversion through adjoint-based optimization methods, without requiring computation of elastic Green’s functions. Specifically, we consider a penalized least squares formulation, which in a Bayesian setting—under the assumption of Gaussian noise and prior—reflects the negative log of the posterior distribution. The comparison of the inversion results with a standard, linear inverse theory approach based on Okada’s solutions shows analogous results. Preliminary uncertainties are estimated via eigenvalue analysis of the Hessian of the penalized least squares objective function. Our implementation is fully open-source and Jupyter notebooks to reproduce our results are provided. The extension to a fully Bayesian framework for detailed uncertainty quantification and non-linear inversions, including for heterogeneous media earthquake problems, will be analysed in a forthcoming paper.

58 GEOSCIENCES↗

The Relaxation Matrix for Symmetric Tops with Inversion Symmetry. I. Effects of Line Coupling on Self-Broadened v (sub 1) and Pure Rotational Bands of NH3

The Robert-Bonamy formalism has been commonly used to calculate half-widths and shifts of spectral lines for decades. This formalism is based on several approximations. Among them, two have not been fully addressed: the isolated line approximation and the neglect of coupling between the translational and internal motions. Recently, we have shown that the isolated line approximation is not necessary in developing semi-classical line shape theories. Based on this progress, we have been able to develop a new formalism that enables not only to reduce uncertainties on calculated half-widths and shifts, but also to model line mixing effects on spectra starting from the knowledge of the intermolecular potential. In our previous studies, the new formalism had been applied to linear and asymmetric-top molecules. In the present study, the method has been extended to symmetric-top molecules with inversion symmetry. As expected, the inversion splitting induces a complete failure of the isolated line approximation. We have calculated the complex relaxation matrices of selfbroadened NH3. The half-widths and shifts in the ν1 and the pure rotational bands are reported in the present paper. When compared with measurements, the calculated half-widths match the experimental data very well, since the inapplicable isolated line approximation has been removed. With respect to the shifts, only qualitative results are obtained and discussed. Calculated off-diagonal elements of the relaxation matrix and a comparison with the observed line mixing effects are reported in the companion paper (Paper II).

Trajectory models↗

Deployment of a double scatter system for directional detection of background neutron radiation

The detection of special nuclear materials (SNM) requires the understanding of nuclear signatures that allow the discrimination against background. In particular, understanding neutron background characteristics such as count rates and energies and their correlations with environmental conditions and surroundings of measurement locations is important in enhancing SNM detection capabilities. The Mobile Imager of Neutrons for Emergency Responders (MINER) was deployed for 8 weeks in downtown San Francisco (CA) to study such neutron background characteristics in an urban environment. Of specific interest was the investigation of the impact of surrounding buildings on the neutron background count rates and to answer the question whether buildings act as absorber of neutrons or as sources via the so-called ship effect. MINER consists of 16 liquid scintillator detector elements and can be operated as a neutron spectrometer, as a neutron imager, or simply as a counter of fast neutrons. As expected, the neutron background rate was found to be inversely proportional to the atmospheric pressure. In the energy range where MINER is most sensitive, approximately 1–10 MeV, it was found that the shape of the detected background spectrum is similar to that of a detected fission spectrum, indicating the limited discrimination power of the neutron energy. The similarities between the detected background neutron spectrum and fission sources makes it difficult to discriminate SNM from background based solely on the energies observed. The images produced using maximum likelihood expectation maximization revealed that neutrons preferentially are coming from areas in the environment that have open sky, indicating that the surrounding buildings act as absorbers of neutrons rather than sources as expected by the ship effect. Here, the inherent properties of a neutron scatter camera limit the achievable image quality and the effective deployment to systematically map neutron background signatures due to the low count rate.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

A Comparison of Exact and Model Exchange–Correlation Potentials for Molecules

Accurate exchange–correlation (XC) potentials for three-dimensional systems–via solution of the inverse density functional theory (DFT) problem–are now available to test the quality of DFT approximations. Herein, the exact XC potential for seven molecules–dihydrogen at four different bond-lengths, lithium hydride, water, and ortho-benzyne–are computed from full configuration interaction reference densities. These are compared to model XC potentials from nonlocal (B3LYP, HSE06, SCAN0, and M08-HX) and semilocal/local (SCAN, PBE, and PW92) XC functionals. Whereas for most systems, relative errors in the ground-state densities are O(10 –3 –10 –2 ) , the model XC potentials have much higher errors of O(10 –1 –10 0 ) . Among the model XC functionals, SCAN0 offers the best agreement with the exact XC potential, underlining the significance of satisfying exact conditions as well as including nonlocal effects in XC functionals. This work indicates that tests against the exact XC potential will provide a promising new direction for building more accurate XC functionals for DFT.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Inverse kinematics study of the energy levels of 21 Ne populated with the 20 Ne +𝑑 reaction

In recent years there has been significant experimental effort aimed at studying the impact of 16 O neutron poisoning on the weak 𝑠 process in rotating massive stars. Improving the understanding of energy levels in 21 Ne is crucial to reducing uncertainties in the rates of the 𝛼-induced reactions on 17 O that determine the overall efficiency of the weak 𝑠 process. This paper reports on one such experiment: a study of the 20 Ne (𝑑,𝑝)⁢ 21 Ne reaction in inverse kinematics. Deduced spin-parity assignments were made based on adiabatic distorted-wave approximation analysis and neutron partial widths were estimated by comparison with a previous experiment. Of particular significance for nuclear astrophysics is the resulting neutron partial width for the 7820-keV energy level, estimated to be 12 200 ⁢(2900)⁢ eV, and an upper limit of ≤ 9300 eV for that of the 7749-keV energy level. These results are in tension with previous studies and therefore this paper also discusses the current state of the research into the astrophysically relevant energy levels and highlights both areas of agreement and areas of disagreement between this and various other studies that have investigated this nucleus.

direct reactions↗

Enhancing ACPF Analysis: Integrating Newton-Raphson Method with Gradient Descent and Computational Graphs

This paper presents a new method for enhancing Alternating Current Power Flow (ACPF) analysis. The method integrates the Newton-Raphson (NR) method with Enhanced-Gradient Descent (GD) and computational graphs. The integration of renewable energy sources in power systems introduces variability and unpredictability, and this method addresses these challenges. It leverages the robustness of NR for accurate approximations and the flexibility of GD for handling variable conditions, all without requiring Jacobian matrix inversion. Furthermore, computational graphs provide a structured and visual framework that simplifies and systematizes the application of these methods. The goal of this fusion is to overcome the limitations of traditional ACPF methods and improve the resilience, adaptability, and efficiency of modern power grid analyses. We validate the effectiveness of our advanced algorithm through comprehensive testing on established IEEE benchmark systems. Furthermore, our findings demonstrate that our approach not only speeds up the convergence process but also ensures consistent performance across diverse system states, representing a significant advancement in power flow computation.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Inverse Compton Cooling in the Coronae of Simulated Black Hole Accretion Flows

Here we present a formulation for a local cooling function to be employed in the diffuse, hot corona region of 3D GRMHD simulations of accreting black holes. This new cooling function calculates the cooling rate due to inverse Compton scattering by considering the relevant microphysics in each cell in the corona and approximating the radiation energy density and Compton temperature thereby integrating over the thermal seed photon flux from the disk surface. The method either assumes the ion and electron temperatures are equal (1T) or calculates them separately (2T) using an instantaneous equilibrium approach predicated on the actual relevant rate equations (Coulomb and Compton). The method is shown to be consistent with a more detailed ray-tracing calculation where the bulk of the cooling occurs, but is substantially less costly to perform. As an example, we apply these methods to a harm3d simulation of a 10M⊙, non-spinning black hole, accreting at nominally 1% the Eddington value. This new approach leads to radiative efficiency values sime65% above Novikov–Thorne, with a larger fraction of total cooling in the corona as compared to simulations performed using the original target-temperature cooling function. Time-averaged post-processing reveals that the continuum spectral observations predicted from these simulations are qualitatively similar to actual X-ray binary data, especially so for the 1T approach, which yields a harder power-law component (Γ = 2.25) compared to the 2T version (Γ = 2.53).

79 ASTRONOMY AND ASTROPHYSICS↗

Structure of the atmosphere of Jupiter from Pioneer 10 and 11 radio occultation measurements

A technique for incorporating effects of the oblateness of Jupiter's atmosphere into the data analysis procedure for radio-occultation measurements is described which makes use of a spherical harmonic representation of the gravity field to compute the shape of the planet. With this technique, the center of refraction is located by the radius of curvature and the normal direction at the closest approach point of the ray. The present technique, a subsequent approximation involving the use of a constant center of refraction, and the Abel integral transform inversion method for spherical planets are applied to Pioneer 10 and 11 data. All the intermediate results obtained show a temperature inversion between 10 and 100 mb, with temperatures from 130 to 170 K at 10 mb and from 80 to 120 K at 100 mb. Comparison of the radio-occultation profiles with radiative-convective equilibrium models and the temperature profile based on Pioneer 10 IR radiometer data indicates good agreement between the models and the occultation results.

Kliore, A. J.↗

Two-dimensional electrostatic turbulence with variable density and pressure

Large-scale turbulence transverse to a uniform dc magnetic field is considered from the point of view of a two-fluid model of an electrostatic plasma of variable density. An approximation motivated by 'geostrophic' techniques of dynamic meteorology is introduced. It is argued that the inverse cascade phenomenon should persist in the presence of variable pressure and density.

Montgomery, D.↗

Far-infrared rotational emission by carbon monoxide

Accurate theoretical collisional excitation rates are used to determine the emissivities of CO rotational lines for an H2 molecule content of at least 10,000/cu cm, temperature in the range 100-3000 K, and J not more than 60 under the assumption that the lines are optically thin. An approximate analytic expression for the emissivities which is valid in this region is obtained. Population inversions in the lower rotational levels occur for densities of molecular H2 around 1000-100,000/cu cm and temperatures T not more than about 50 K provided photon trapping is unimportant. Interstellar shocks observed edge-on are a potential source of weak millimeter-wave CO maser emission.

Mckee, C. F.↗

Recursive inverse kinematics for robot arms via Kalman filtering and Bryson-Frazier smoothing

This paper applies linear filtering and smoothing theory to solve recursively the inverse kinematics problem for serial multilink manipulators. This problem is to find a set of joint angles that achieve a prescribed tip position and/or orientation. A widely applicable numerical search solution is presented. The approach finds the minimum of a generalized distance between the desired and the actual manipulator tip position and/or orientation. Both a first-order steepest-descent gradient search and a second-order Newton-Raphson search are developed. The optimal relaxation factor required for the steepest descent method is computed recursively using an outward/inward procedure similar to those used typically for recursive inverse dynamics calculations. The second-order search requires evaluation of a gradient and an approximate Hessian. A Gauss-Markov approach is used to approximate the Hessian matrix in terms of products of first-order derivatives. This matrix is inverted recursively using a two-stage process of inward Kalman filtering followed by outward smoothing. This two-stage process is analogous to that recently developed by the author to solve by means of spatial filtering and smoothing the forward dynamics problem for serial manipulators.

Rodriguez, G.↗

Photon number amplification/duplication through parametric conversion

The performance of parametric conversion in achieving number amplification and duplication is analyzed. It is shown that the effective maximum gains G(sub *) remain well below their integer ideal values, even for large signals. Correspondingly, one has output Fano factors F(sub *) which are increasing functions of the input photon number. On the other hand, in the inverse (deamplifier/recombiner) operating mode quasi-ideal gains G(sub *) and small factors F(sub *) approximately equal to 10 percent are obtained. Output noise and non-ideal gains are ascribed to spontaneous parametric emission.

Dariano, G. M.↗

Rotating-Pump Design Code

Pump Design (PUMPDES) is a computer program for designing a rotating pump for liquid hydrogen, liquid oxygen, liquid nitrogen, water, methane, or ethane. Using realistic properties of these fluids provided by another program called GASPAK, this code performs a station-by-station, mean-line analysis along the pump flow path, obtaining thermodynamic properties of the pumped fluid at each station and evaluating hydraulic losses along the flow path. The variables at each station are obtained under constraints that are consistent with the underlying physical principles. The code evaluates the performance of each stage and the overall pump. In addition, by judiciously choosing the givens and the unknowns, the code can perform a geometric inverse design function: that is, it can compute a pump geometry that yields a closest approximation of given design point. The code contains two major parts: one for an axial-rotor/inducer and one for a multistage centrifugal pump. The inducer and the centrifugal pump are functionally integrated. The code can be used in designing and/or evaluating the inducer/centrifugal-pump combination or the centrifugal pump alone. The code is written in standard Fortran 77.

Walker, James F.↗

Inverse Compton Cooling in the Coronae of Simulated Black Hole Accretion Flows

We present a formulation for a local cooling function to be employed in the diffuse, hot corona region of 3D GRMHD simulations of accreting black holes. This new cooling function calculates the cooling rate due to inverse Compton scattering by considering the relevant microphysics in each cell in the corona and approximating the radiation energy density and Compton temperature there by integrating over the thermal seed photon flux from the disk surface. The method either assumes ion and electron tem- peratures are equal (1T), or calculates them separately (2T) using an instantaneous equilibrium approach predicated on the actual relevant rate equations (Coulomb and Compton). The method is shown to be consistent with a more detailed ray-tracing calculation where the bulk of the cooling occurs, but is substantially less costly to per- form. As an example, we apply these methods to a harm3d simulation of a 10M⊙, non-spinning black hole, accreting at nominally 1% the Eddington value. Both 1T and 2T approaches lead to increased radiative efficiency and a larger fraction of total cooling in the corona as compared to the original target-temperature cooling function used by harm3d, especially in the 1T case. Time-averaged post-processing reveals that the continuum spectral observations predicted from these simulations are qualitatively similar to actual X-ray binary data, especially so for the 1T approach which yields a harder power-law component (Γ = 2.25) compared to the 2T version (Γ = 2.53).

Brooks E. Kinch↗

From the Great Wave of Translation to the Force between Quarks

Here, the chance observation of a novel traveling wave in a canal led over time to the formulation of a nonlinear wave equation—the Korteweg–de Vries equation—that describes strikingly robust disturbances now called solitons. The figure of an isolated soliton corresponds to a reflectionless potential that supports a single bound state in the one-dimensional Schrödinger equation. An appropriate combination of individual solitons yields a symmetric reflectionless potential that supports multiple bound states. Thus, the KdV equation opens the path to solving the inverse scattering problem for a collection of bound states. Applied to the quarkonium spectra, this formalism allows the construction of reflectionless approximations to the confining potentials that account for the force between quarks, and to tests of the flavor-independence of the interquark interaction.

Inverse Scattering↗

Airborne Sunphotometer Measurements of Aerosol Optical Depth and Columnar Water Vapor During the Puerto Rico Dust Experiment, and Comparison with Land, Aircraft, and Satellite Measurements

Analyses of aerosol optical depth (AOD) and columnar water vapor (CWV) measurements obtained with the six-channel NASA Ames Airborne Tracking Sunphotometer (AATS-6) mounted on a twin-engine aircraft during the summer 2000 Puerto Rico Dust Experiment are presented. In general, aerosol extinction values calculated from AATS-6 AOD measurements acquired during aircraft profiles up to 5 km ASL reproduce the vertical structure measured by coincident aircraft in-situ measurements of total aerosol number and surface area concentration. Calculations show that the spectral dependence of AOD was small (mean Angstrom wavelength exponents of approximately 0.20) within three atmospheric layers defined as the total column beneath the top of each aircraft profile, the region beneath the trade wind inversion, and the region within the Saharan Air Layer (SAL) above the trade inversion. This spectral behavior is consistent with attenuation of incoming solar radiation by large dust particles or by dust plus sea salt. Values of CWV calculated from profile measurements by AATS-6 at 941.9 nm and from aircraft in-situ measurements by a chilled mirror dewpoint hygrometer agree to within approximately 4% (0.13 g/sq cm). AATS-6 AOD values measured on the ground at Roosevelt Roads Naval Air Station and during low altitude aircraft runs over the adjacent Cabras Island aerosol/radiation ground site agree to within 0.004 to 0.030 with coincident data obtained with an AERONET Sun/sky Cimel radiometer located at Cabras Island. For the same observation times, AERONET retrievals of CWV exceed AATS-6 values by a mean of 0.74 g/sq cm (approximately 21 %) for the 2.9-3.9 g/sq cm measured by AATS-6. Comparison of AATS-6 aerosol extinction values obtained during four aircraft ascents over Cabras Island with corresponding values calculated from coincident aerosol backscatter measurements by a ground-based micro-pulse lidar (MPL-Net) located at Cabras yields a similar vertical structure above the trade inversion. Finally, AATS-6 AOD values measured during low altitude aircraft traverses over the ocean are compared with corresponding AOD values retrieved over water from upwelling radiance measurements by the MODIS, TOMS, and GOES-8 Imager satellite sensors, with mixed results. These exercises highlight the need for continued satellite sensor comparison/validation studies to improve satellite AOD retrieval algorithms, and the usefulness of airborne sunphotometer measurements in the validation process.

Livingston, John M.↗

The usefulness of Klett's inversion algorthms to simulated satellite Lidar returns

The lidar equation is a special form of the radiative transport equation in single scattering approximation and describes the return signal of a lidar. Klett's algorithm for retrieving the total extinction coefficient profile was developed for application to ground-based lidar returns by a backward integration from the far end to the near end, the range where the incident and backscattered pulse overlap totally. The applicability of Klett's algorithm to satellite backscatter lidar returns was assessed. The simulated data of a 1 J Alexandrite laser operated at about 0.7 micron and at a satellite flight level of 840 km.

Kastner, M.↗