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 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Forward and inverse modeling of fault transmissibility in subsurface flows

Characterizing physical properties of faults, such as their transmissibility, is crucial for performing predictive numerical simulation of subsurface flows, such as those encountered in petroleum engineering and remediation of subsurface contamination. Here, this paper provides a complete investigation of the inverse problem for fault transmissibility in subsurface flow models, under appropriate assumptions on fault structure. In particular, the following aspects are considered: 1) fault modeling and well-posedness of the forward problem; 2) finite element (FEM) discretizations of the forward problem and their rigorous a priori convergence analysis; 3) Well-posedness of the Bayesian inverse problem, FEM discretization of the infinite dimensional Bayesian inverse formulation, and its rigorous a priori analysis. Moreover, computation of the maximum a posteriori (MAP) point via fast inexact Newton-conjugate gradient optimization and a Laplace approximation of the Bayesian posterior are also presented. Numerical results illustrate the use of the proposed fault model in forward and inverse problems for subsurface flows in two dimensional domains with multiple faults.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Characterization of core neutrals using passive measurements of the D α spectrum near the X -point in the DIII-D tokamak

New spectroscopic measurements of deuterium Balmer-α emission are used to infer the spatial distribution of neutral particles near the X-point in a diverted high confinement mode plasma. The charge exchange neutral spectroscopy (CENS) diagnostic—recently installed on the DIII-D tokamak—uses 15 lines of sight extending from the edge of the confined region (ρ ≈ 0.7) to the X-point in lower single-null plasmas. Each CENS line of sight is spectrally resolved around the deuterium Balmer-α wavelength (6561 Å) to measure the Doppler shift, line broadening, and intensity of Dα emission. Thermal line broadening is used to identify emission from neutrals undergoing charge-exchange (CX) with high temperature ions in the confined plasma. This spectral information allows a more accurate determination of the neutral density deeper inside the confined plasma compared to traditional filter-based diagnostics. We present two methods of analyzing CENS measurements: (1) fitting the spectrum from each view-chord separately, and (2) a tomographic method for inverting the neutral density over a 2D region of space using all CENS views collectively. The neutral density profile is found to decay exponentially in the radial direction with two scale-lengths. In the pedestal region the neutral density decays at a rate approximately equal to the local mean-free-path for CX collisions, $L_{n_\mathrm{D0}}\approx \lambda_\text{CX}$. Further inside the plasma the neutral density decays at a rate equal to the mean-free-path for ionization, $L_{n_\mathrm{D0}}\approx \lambda_\text{inz.}$. The separatrix $n_\mathrm{D0}$ value is found to be approximately $2\times10^{15}$ m−3. Based on results from the 2D inversion, the density of neutrals is found to increase along the separatrix approaching the X-point by a factor of $\approx 5\times$ over the region covered by the CENS diagnostic.

X-point neutrals↗
DOE OSTI2022

Narrow Slot Gasket Grooves And Step Changes In Width

We provide corrections to the slot capacitance and inverse inductance per unit length for slot gasket groove geometries using an approximate conformal mapping approach. We also provide corrections for abrupt step changes in slot width along with boundary discontinuity conditions for implementation in the various slot models.

42 ENGINEERING↗
DOE OSTI2025

Hydraulic Testing of the Lost Lake Aquifer Near Recovery Well RWM001R

An aquifer pumping test was conducted on the Lost Lake Aquifer Zone (LLAZ) at the recently installed recovery well RWM001R in accordance with the approved test plan (Dixon, 2024). The objective of the testing was to determine baseline well performance parameters and aquifer hydraulic conductivity. This testing consisted of two step-drawdown tests to determine well performance properties and two constant pumping rate aquifer tests with recovery periods to determine aquifer hydraulic properties. Well performance parameters determined included specific capacity, well efficiency, and head loss coefficients. The results of the step-drawdown testing are presented in Tables ES1 and ES2 whereas the results of the constant pumping rate testing are presented in Table ES3. The average specific capacity of RWM001R operating at pump capacity (~54 gpm) was 2.2 gpm/ft using data from the final step of both tests. The average well efficiency determined from both step-drawdown tests was 56% using data from the final step of both tests. For both step-drawdown tests, well efficiency was inversely related to the pumping rate with the average efficiency decreasing from approximately 79% to 56%. Aquifer head loss coefficients from both tests were comparable (Table ES2).

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1975

Some procedures for computerized electronic data processing of absorption measurements from artificial earth satellites

The processing of data obtained from solar absorption radiation measurements is discussed. The position of the satellite was obtained by numerical integration of the differential equations of motion using initial conditions. The position of the sun was calculated as a function of time, and the tangential elevation was determined approximately from the positions of the satellite and the sun. The coefficients of an approximation formula and of a data smoothing process were determined, and the inversion of an Abel integral equation is solved analytically.

Trinkkeller, B.↗
NASA NTRS1994

Gamma-ray observations of NGC 253 and M82 with OSSE

Gamma-ray observations of the nearby starburst galaxies NGC 253 and M82 over the energy range (0.05-10) MeV have been obtained with the Oriented Scintillation Spectrometer Experiment (OSSE) spectrometer on the Compton Gamma-Ray Observatory (CGRO). The priority of these galaxies as OSSE targets had been established on the grounds that the average supernova rate may be high in starbursts as indicated by infrared and radio observations, and at distances of approximately 3 Mpc a significant chance of supernova gamm-ray line detection exists. NGC 253 was detected in continuum emission up to 165 keV with a total significance of 4.4 sigma and an estimated luminosity of 3 x 10(exp 40) ergs/s. The spectrum is best fit by a power law of photon index approximately 2.5. We consider the possible contribution of different emission mechanisms, including inverse Compton scattering, bremsstrahlung, discrete sources, and Type Ia/Ib supernova continuum to the measured flux. No significant continuum flux was observed from M82. A search for the gamma-ray line from the decay of the most abundant radioactive element produced in supernovae (Ni-56 yields Co-56 yields Fe-56) yielded no significant detection: the 3 sigma upper limits to the line fluxes at 0.158, 0.812, 0.847, and 1.238 MeV for both galaxies are obtained.

Bhattacharya, D.↗
NASA NTRS1996

Some Experiences with Nonoverlapping Schur Complement Parallel Preconditioning for CFD Calculations

In this work we consider solving matrices which arise from the discretization of advection-diffusion field equations on arbitrary triangulated domains using stabilized numerical methods. The talk will discuss several candidate matrix preconditioning algorithms based on the 2 x 2 block factorization induced by an apriori partitioning of the triangulated domain. Application of the 2 x 2 block preconditioner requires the formation and inversion of the Schur complement submatrix. We consider several strategies for simplifying this task: incomplete Schur complement factorizations, drop tolerance element filling, Schur complement probing, and localized Schur complement inversion. Numerical results will be shown comparing performance and efficiency of these approximations. The matrix preconditioner has also been embedded into a Newton algorithm for solving the nonlinear Euler and Navier-Stokes equations governing compressible flow. The remainder of the talk will show numerous examples in CFD to demonstrate the efficiency and robustness of the techniques.

Barth, Timothy J.↗
NASA NTRS1997

Combined Numerical/Analytical Perturbation Solutions of the Navier-Stokes Equations for Aerodynamic (Ejector Nozzle) Flows

In spite of the rapid advances in both scalar and parallel computational tools, the large number and breadth of variables involved in aerodynamic systems make the use of parabolized or even boundary layer fluid flow models impractical for both preliminary design and inverse design problems. Given this restriction, we have concluded that reduced or approximate models are an important family of tools for design purposes. This study of a combined perturbation/numerical modeling methodology with an application to ejector-mixer nozzles (shown schematically in the following figure) is nearing completion. The work is being funded by a grant from the NASA Lewis Research Center to Texas A&M University. These ejector-mixer nozzle models are designed to be of use to the High Speed Civil Transport Program and may be adopted by both NASA and industry. A computer code incorporating the ejector-mixer models is under development. This code, the Differential Reduced Ejector/Mixer Analysis (DREA), can be run fast enough to be used as a subroutine or to be called by a design optimization routine. Simplified conservation equations--x-momentum, energy, and mass conservation--are used to define the model. Unlike other preliminary design models, DREA requires minimal empirical input and includes vortical mixing and a fully compressible formulation among other features. DREA is being validated by comparing it with results obtained from open literature and proprietary industry data. Preliminary results for a subsonic ejector and a supersonic ejector are shown. In addition, dedicated experiments have been performed at Texas A&M. These experiments use a hydraulic/gas flow analog to provide information about the inviscid mixing interface structure. Final validation and documentation of this work is expected by May of 1997. However, preliminary versions of DREA can be expected in early 1997. In summary, DREA provides a sufficiently detailed and realistic ejector-mixer nozzle model at a computational cost compatible with preliminary design applications.

DeChant, Lawrence J.↗
NASA NTRS2012

Iterative Atmospheric Correction Scheme and the Polarization Color of Alpine Snow

Characterization of the Earth's surface is crucial to remote sensing, both to map geomorphological features and because subtracting this signal is essential during retrievals of the atmospheric constituents located between the surface and the sensor. Current operational algorithms model the surface total reflectance through a weighted linear combination of a few geometry-dependent kernels, each devised to describe a particular scattering mechanism. The information content of these measurements is overwhelmed by that of instruments with polarization capabilities: proposed models in this case are based on the Fresnel reflectance of an isotropic distribution of facets. Because of its remarkable lack of spectral contrast, the polarized reflectance of land surfaces in the shortwave infrared spectral region, where atmospheric scattering is minimal, can be used to model the surface also at shorter wavelengths, where aerosol retrievals are attempted based on well-established scattering theories. In radiative transfer simulations, straightforward separation of the surface and atmospheric contributions is not possible without approximations because of the coupling introduced by multiple reflections. Within a general inversion framework, the problem can be eliminated by linearizing the radiative transfer calculation, and making the Jacobian (i.e., the derivative expressing the sensitivity of the reflectance with respect to model parameters) available at output. We present a general methodology based on a Gauss-Newton iterative search, which automates this procedure and eliminates de facto the need of an ad hoc atmospheric correction. In this case study we analyze the color variations in the polarized reflectance measured by the NASA Goddard Institute of Space Studies Research Scanning Polarimeter during a survey of late-season snowfields in the High Sierra. This insofar unique dataset presents challenges linked to the rugged topography associated with the alpine environment and a likely high water content due to melting. The analysis benefits from ancillary information provided by the NASA Langley High Spectral Resolution Lidar deployed on the same aircraft. The results obtained from the iterative scheme are contrasted against the surface polarized reflectance obtained ignoring multiple reflections, via the simplistic subtraction of the atmospheric scattering contribution. Finally, the retrieved reflectance is modeled after the scattering properties of a dense collection of ice crystals at the surface. Confirming that the polarized reflectance of snow is spectrally flat would allow to extend the techniques already in use for polarimetric retrievals of aerosol properties over land to the large portion of snow-covered pixels plaguing orbital and suborbital observations.

Polarized BRDF↗
DOE OSTI2023

Ab initio calculations of low-energy quasiparticle lifetimes in bilayer graphene

Motivated by recent experimental results we calculate from first-principles the lifetime of low-energy quasiparticles in bilayer graphene (BLG). Here, we take into account the scattering rate arising from electron-electron interactions within the GW approximation for the electron self-energy and consider several p-type doping levels ranging from 0 to ρ ≈ 2.4 × 10 12 holes/cm 2 . In the undoped case we find that the average inverse lifetime scales linearly with energy away from the charge neutrality point, with values in good agreement with experiments. The decay rate is approximately three times larger than in monolayer graphene, a consequence of the enhanced screening in BLG. In the doped case, the dependence of the inverse lifetime on quasiparticle energy acquires a non-linear component due to the opening of an additional decay channel mediated by acoustic plasmons.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Microcanonical rates from ring-polymer molecular dynamics: Direct-shooting, stationary-phase, and maximum-entropy approaches

We address the calculation of microcanonical reaction rates for processes involving significant nuclear quantum effects using ring-polymer molecular dynamics (RPMD), both with and without electronically non-adiabatic transitions. After illustrating the shortcomings of the naive free-particle direct-shooting method, in which the temperature of the internal ring-polymer modes is set to the translational energy scale, we investigate alternative strategies based on the expression for the microcanonical rate in terms of the inverse Laplace transform of the thermal reaction rate. It is shown that simple application of the stationary-phase approximation (SPA) dramatically improves the performance of the microcanonical rates using RPMD, particularly in the low-energy region where tunneling dominates. Using the SPA as a Bayesian prior, numerically exact RPMD microcanonical rates are then obtained using maximum entropy inversion of the thermal reaction rates for both electronically adiabatic and non-adiabatic model systems. Finally, the direct-shooting method is revisited using the SPA-determined temperature for the internal ring-polymer modes, leading to a simple, direct-simulation method with improved accuracy in the tunneling regime. This work suggests a general strategy for the extraction of microcanonical dynamical quantities from RPMD (or other approximate thermal) simulations.

Tao, Xuecheng↗
NASA NTRS1993

Mathmatical modeling for diffractive optics

We consider a 'diffractive optic' to be a biperiodic surface separating two half-spaces, each having constant constitutive parameters; within a unit cell of the periodic surface and across the transition zone between the two half-spaces, the constitutive parameters can be a continuous, complex-valued function. Mathematical models for diffractive optics have been developed, and implemented as numerical codes, both for the 'direct' problem and for the 'inverse' problem. In problems of the 'direct' class, the diffractive optic is specified, and the full set of Maxwell's equations is cast in a variational form and solved numerically by a finite element approach. This approach is well-posed in the sense that existence and uniqueness of the solution can be proved and specific convergence conditions can be derived. An example of a metallic grating at a Wood anomaly is presented as a case where other approaches are known to have convergence problems. In problems of the 'inverse' class, some information about the diffracted field (e.g., the far-field intensity) is given, and the problem is to find the periodic structure in some optimal sense. Two approaches are described: phase reconstruction in the far-field approximation; and relaxed optimal design based on the Helmholtz equation. Practical examples are discussed for each approach to the inverse problem, including array generators in the far-field case and antireflective structures for the relaxed optimal design.

Dobson, David↗
DOE OSTI2024

Prime VI

SAND2025-03757O Prime VI is a distribution-of-disease outbreak model calibration code based on variational inference. It accompanies a publication for submission to Statistics in Medicine journal, and the code will be maintained for open-source use on Sandia's GitLab. The software provides methods for calibrating an epidemiological model to measured case-count data for a multitude of correlated spatial regions. The code solves a Bayesian inverse problem for model calibration where the posterior over-model parameters are approximated through a custom implementation of variational inference. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Safta, Cosmin↗
NASA NTRS1974

Preliminary measurements of aircraft aerodynamic noise

Flight measurements of aerodynamic noise were made on an AeroCommander airplane with engines off and a JetStar airplane with engines at both idle power and completely shut off. The overall sound level for these airplanes in the landing configuration varied as the sixth power of the aircraft velocity. For the JetStar airplane, the overall sound level decreased as the inverse square of the distance in the lateral direction. The aerodynamic noise was approximately 11 decibels below the FAR Part 36 noise level for the JetStar airplane. The landing gear were a significant contributor to aerodynamic noise for both aircraft.

Lasagna, P. L.↗
NASA NTRS1976

Time dispersion of energetic solar particles, unexpected velocity and species dependence

The intensity-time behavior for protons and helium, as well as for carbon, oxygen and iron ions was measured following the 1974 September 19 solar flare for energies between 0.5 and approximately 5 MeV per nucleon. The profiles displayed a time dispersion which is inversely proportional to velocity for each individual species. In addition, at a given velocity the time dispersion also depended on the charge to mass ratio of the ion. Based on this latter dependence, it was concluded that while carbon and oxygen are essentially fully stripped, iron nuclei are not, having an effective charge Q = 10 + or - 5. The observed dispersion cannot be explained by purely rigidity dependent diffusive propagation.

Gallagher, J. J.↗
NASA NTRS1981

Venus. I - Carbon monoxide distribution and molecular-line searches

An observational program to study variations of the vertical distribution of CO in the Venus atmosphere is presented. Measurements of the J = 0 - 1 absorption line at 2.6 mm wavelength are reported for two phase angles in 1977, one near eastern elongation (February) and the other near inferior conjunction (April). The two spectra are significantly different, with the April absorption line being narrower and deeper. The results of numerical inversion calculations show that the CO mixing ratio increases by a factor of approximately 100 between 78 and 100 km and that the CO abundance above approximately 100 km is greatest on the night-side hemisphere. These conclusions are in qualitative agreement with theoretical models. In addition to the CO observations, a search for other molecules was made to provide further information on the composition of the Venus middle atmosphere. The J = 0 - 1 transition of (C-13)O was detected and upper limits were derived for nine other molecules.

Wilson, W. J.↗
NASA NTRS1986

Solution of the symmetric eigenproblem AX=lambda BX by delayed division

Delayed division is an iterative method for solving the linear eigenvalue problem AX = lambda BX for a limited number of small eigenvalues and their corresponding eigenvectors. The distinctive feature of the method is the reduction of the problem to an approximate triangular form by systematically dropping quadratic terms in the eigenvalue lambda. The report describes the pivoting strategy in the reduction and the method for preserving symmetry in submatrices at each reduction step. Along with the approximate triangular reduction, the report extends some techniques used in the method of inverse subspace iteration. Examples are included for problems of varying complexity.

Thurston, G. A.↗