SEARCH · Search NASA

Results for “Tensor Approximation”

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.

SourceResearch connectionFrom yearThrough year

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

At least 181 records · Page 10

All sources NASA NTRS DOE OSTI

DOE OSTI2025

A novel transformation of the ice sheet Stokes equations and some of its properties and applications

We introduce a novel transformation of the Stokes equations into a form closely resembling the shallow Blatter–Pattyn equations. The two forms differ by only a few additional terms, while their variational formulations differ only by a single term in each horizontal direction. Specifically, the variational formulation of the Blatter–Pattyn model drops the vertical velocity in the second invariant of the strain rate tensor. Here we make use of the new transformation in two ways. First, we consider incorporating the transformed equations into a code that can be very easily converted from a Stokes to a Blatter–Pattyn model, and vice versa, by switching these terms on or off. This may be generalized so that the Stokes model is switched on adaptively only where the Blatter–Pattyn model loses accuracy. Second, the key role played by the vertical velocity in the Blatter–Pattyn approximation motivates new approximations. Two examples are presented. These require a mesh that enables the discrete continuity equation to be invertible for the vertical velocity in terms of the horizontal velocity components. Examples of such meshes, such as the first-order P1–E0 mesh and the second-order P2–E1 mesh, are given in both 2D and 3D. However, the transformed Stokes model has the same type of gravity forcing as the Blatter–Pattyn model, determined by the ice surface slope, thereby forgoing some of the mesh generality of the traditional formulation of the Stokes model.

58 GEOSCIENCES↗

NASA NTRS2014

Combined Uncertainty and A-Posteriori Error Bound Estimates for General CFD Calculations: Theory and Software Implementation

This workshop presentation discusses the design and implementation of numerical methods for the quantification of statistical uncertainty, including a-posteriori error bounds, for output quantities computed using CFD methods. Hydrodynamic realizations often contain numerical error arising from finite-dimensional approximation (e.g. numerical methods using grids, basis functions, particles) and statistical uncertainty arising from incomplete information and/or statistical characterization of model parameters and random fields. The first task at hand is to derive formal error bounds for statistics given realizations containing finite-dimensional numerical error [1]. The error in computed output statistics contains contributions from both realization error and the error resulting from the calculation of statistics integrals using a numerical method. A second task is to devise computable a-posteriori error bounds by numerically approximating all terms arising in the error bound estimates. For the same reason that CFD calculations including error bounds but omitting uncertainty modeling are only of limited value, CFD calculations including uncertainty modeling but omitting error bounds are only of limited value. To gain maximum value from CFD calculations, a general software package for uncertainty quantification with quantified error bounds has been developed at NASA. The package provides implementations for a suite of numerical methods used in uncertainty quantification: Dense tensorization basis methods [3] and a subscale recovery variant [1] for non-smooth data, Sparse tensorization methods[2] utilizing node-nested hierarchies, Sampling methods[4] for high-dimensional random variable spaces.

CFD↗

DOE OSTI2025

Crystal field splittings and magnetic ground state of the square-lattice antiferromagnets YbBi 2 ⁢ClO 4 and YbBi 2 ⁢IO 4 with J eff = $\frac{1}{2}$

Here, we report on the crystal field level splitting and magnetic ground state of the J eff = $\frac{1}{2}$ square lattice antiferromagnets YbBi 2 ⁢ClO 4 and YbBi 2 ⁢IO 4 using powder inelastic neutron scattering (INS) and neutron diffraction measurements. Both compounds exhibit a well-isolated Γ 7 doublet ground state under a tetragonal crystal field environment, confirming a robust J eff = $\frac{1}{2}$ picture with slight XY-type anisotropic character in the g-tensor. Notably, the ground state wave functions closely resemble the Γ 7 doublet expected in the perfect cubic limit, consistent with the nearly cubic ligand configuration of eight O 2- ions surrounding Yb 3+ . Below T N = 0.21 K, YbBi 2 ⁢IO 4 exhibits a stripe long-range magnetic order characterized by an ordering wave vector q m = (1/2, 0, 0) or its symmetry-equivalent (0, 1/2, 0), with magnetic moments aligned along q m . The ordered moment is approximately 79% of the classical prediction, significantly larger than expected from the isotropic J 1 -J 2 model, suggesting the possible involvement of exchange anisotropy in explaining this observation. We show that symmetry-allowed XXZ and bond-dependent anisotropic exchange terms in a square lattice can play a critical role in stabilizing the stripe order and suppressing the moment reduction as observed. These findings establish YbBi 2 ⁢ClO 4 and YbBi 2 ⁢IO 4 as unique platforms for exploring rich J eff = $\frac{1}{2}$ magnetism from two less investigated perspectives: (i) on a square lattice and (ii) within a (nearly) cubic ligand environment.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1991

Experimental investigation of turbulent flow through a circular-to-rectangular transition duct

Steady, incompressible, turbulent, swirl-free flow through a circular-to-rectangular transition duck was studied experimentally. The cross-sectional area remains the same at the exit as at the inlet, but varies through the transition section to a maximum value approximately 15 percent above the inlet value. The cross-sectional geometry everywhere along the duct is defined by the equation of a superellipse. Mean and turbulence data were accumulated utilizing pressure and hot-wire instrumentation at five stations along the test section. Data are presented for operating bulk Reynolds numbers of 88,000 and 390,000. Measured quantities include total and static pressure, the three components of the mean velocity vector, and the six components of the Reynolds stress tensor. In addition to the transition duct measurements, a hot-wire technique which relies on the sequential use of single rotatable normal and slant-wire probes was proposed. The technique is applicable for measurement of the total mean velocity vector and the complete Reynolds stress tensor when the primary flow is arbitrarily skewed relative to a plane which lies normal to the probe axis of rotation.

Davis, David O.↗

NASA NTRS2002

Co-Seismic Mass Dislocation and its Effect on Earth's Rotation and Gravity

Mantle processes often involve large-scale mass transport, ranging from mantle convection, tectonic motions, glacial isostatic adjustment, to tides, atmospheric and oceanic loadings, volcanism and seismicity. On very short time scale of less than an hour, co-seismic event, apart from the shaking that is the earthquake, leaves behind permanent (step-function-like) dislocations in the crust and mantle. This redistribution of mass changes the Earth's inertia tensor (and hence Earth's rotation in both length-of-day and polar motion), and the gravity field (in terms of spherical harmonic Stokes coefficients). The question is whether these effects are large enough to be of any significance. In this paper we report updated calculation results based on Chao & Gross (1987). The calculation uses the normal mode summation scheme, applied to nearly twenty thousand major earthquakes that occurred during 1976-2002, according to source mechanism solutions given by the Harvard Central Moment Tensor catalog. Compared to the truly large ones earlier in the century, the earthquakes we study are individually all too small to have left any discernible signature in geodetic records of Earth rotation or global gravity field. However, their collective effects continue to exhibit an extremely strong statistical tendencies. For example, earthquakes conspire to decrease J2 and J22 while shortening LOD, resulting in a rounder and more compact Earth. Strong tendency is also seen in the earthquakes trying to nudge the Earth rotation pole towards approximately 140 degrees E, roughly opposite to the observed polar drift direction. The geophysical significance and implications will be further studied.

Chao, B. F.↗

NASA NTRS1990

Theory of biaxial graded-index optical fiber

A biaxial graded-index fiber with a homogeneous cladding is studied. Two methods, wave equation and matrix differential equation, of formulating the problem and their respective solutions are discussed. For the wave equation formulation of the problem it is shown that for the case of a diagonal permittivity tensor the longitudinal electric and magnetic fields satisfy a pair of coupled second-order differential equations. Also, a generalized dispersion relation is derived in terms of the solutions for the longitudinal electric and magnetic fields. For the case of a step-index fiber, either isotropic or uniaxial, these differential equations can be solved exactly in terms of Bessel functions. For the cases of an istropic graded-index and a uniaxial graded-index fiber, a solution using the Wentzel, Krammers and Brillouin (WKB) approximation technique is shown. Results for some particular permittivity profiles are presented. Also the WKB solutions is compared with the vector solution found by Kurtz and Streifer. For the matrix formulation it is shown that the tangential components of the electric and magnetic fields satisfy a system of four first-order differential equations which can be conveniently written in matrix form. For the special case of meridional modes, the system of equations splits into two systems of two equations. A general iterative technique, asymptotic partitioning of systems of equations, for solving systems of differential equations is presented. As a simple example, Bessel's differential equation is written in matrix form and is solved using this asymptotic technique. Low order solutions for particular examples of a biaxial and uniaxial graded-index fiber are presented. Finally numerical results obtained using the asymptotic technique are presented for particular examples of isotropic and uniaxial step-index fibers and isotropic, uniaxial and biaxial graded-index fibers.

Kawalko, Stephen F.↗

DOE OSTI2025

A higher-order finite-element implementation of the nonlinear Fokker–Planck collision operator for charged particle collisions in a low density plasma

Collisions between particles in a low density plasma are described by the Fokker–Planck collision operator. In applications, this nonlinear integro-differential operator is often approximated by linearised or ad-hoc model operators due to computational cost and complexity. In this work, we present an implementation of the nonlinear Fokker–Planck collision operator written in terms of Rosenbluth potentials in the Rosenbluth–MacDonald–Judd (RMJ) form. The Rosenbluth potentials may be obtained either by direct integration or by solving partial differential equations (PDEs) similar to Poisson's equation: we optimise for performance and scalability by using sparse matrices to solve the relevant PDEs. We represent the distribution function using a tensor-product continuous-Galerkin finite-element representation and we derive and describe the implementation of the weak form of the collision operator. We present tests demonstrating a successful implementation using an explicit time integrator and we comment on the speed and accuracy of the operator. Finally, we speculate on the potential for applications in the current and next generation of kinetic plasma models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1994

Acoustics of laminar boundary layers breakdown

Boundary layer flow transition has long been suggested as a potential noise source in both marine (sonar-dome self noise) and aeronautical (aircraft cabin noise) applications, owing to the highly transient nature of process. The design of effective noise control strategies relies upon a clear understanding of the source mechanisms associated with the unsteady flow dynamics during transition. Due to formidable mathematical difficulties, theoretical predictions either are limited to early linear and weakly nonlinear stages of transition, or employ acoustic analogy theories based on approximate source field data, often in the form of empirical correlation. In the present work, an approach which combines direct numerical simulation of the source field with the Lighthill acoustic analogy is utilized. This approach takes advantage of the recent advancement in computational capabilities to obtain detailed information about the flow-induced acoustic sources. The transitional boundary layer flow is computed by solving the incompressible Navier-Stokes equations without model assumptions, thus allowing a direct evaluation of the pseudosound as well as source functions, including the Lighthill stress tensor and the wall shear stress. The latter are used for calculating the radiated pressure field based on the Curle-Powell solution of the Lighthill equation. This procedure allows a quantitative assessment of noise source mechanisms and the associated radiation characteristics during transition from primary instability up to the laminar breakdown stage. In particular, one is interested in comparing the roles played by the fluctuating volume Reynolds stress and the wall-shear-stresses, and in identifying specific flow processes and structures that are effective noise generators.

Wang, Meng↗

DOE OSTI2025

Quantitative Nonlinear Optical Polarimetry with High Spatial Resolution

Nonlinear optical microscopy such as in the optical second-harmonic generation (SHG) modality has become a popular tool today for probing materials in the physical and biological sciences. While imaging and spectroscopy are widely used in the microscopy mode, nonlinear polarimetry, which can shed light on materials’ symmetry and microstructure, is relatively underdeveloped. This is partly because quantitative analytical modeling of the optical SHG response for anisotropic crystals and films largely assumes low-numerical aperture (NA) focusing of light, where the plane-wave approximation is sufficient. Tight focusing provides unique benefits in revealing out-of-plane polarization responses, which cannot be detected by near-plane-wave illumination at normal incidence. Here, we outline a method for quantitatively analyzing SHG polarimetry measurements obtained under high-NA focusing within a microscope geometry. Experiments and simulations of a variety of standard samples, from single crystals to thin films, are in good agreement, including measured and simulated spatial SHG maps of ferroelectric domains. A solution to the inverse problem is demonstrated, where the spatial distribution of an SHG tensor with unknown tensor coefficient magnitudes is determined by experimentally measured polarimetry. The ability to extract the out-of-plane component of the nonlinear polarization in normal incidence is demonstrated, which can be valuable for high-resolution polarimetry of 2D materials, thin films, heterostructures, and uniaxial crystals with a strong out-of-plane response.

36 MATERIALS SCIENCE↗

NASA NTRS1998

Self-Consistent Simulation of the Magnetotail

Kinetic effects may be critically important at various stages of magnetotail evolution prior to and after the break up of substorms. The quasi-adiabaticity of ion dynamics results in the appearance of pronounced off diagonal terms in the pressure tensor (an effect that cannot be reproduced using the standard MHD (magnetohydrodynamic) approach). Only the appearance of these terms could support the formation of thin current sheets that recent experimental data have repeatedly indicated. We present in this paper the results of a self-consistent large-scale kinetic simulation of the Earth's magnetotail. We launch ions from the plasma mantle and self-consistently adjust the background magnetic field by computing the perturbations magnetic field from the particle current. We find that a thin current sheet with a half-thickness of approximately 0.3 R(sub E) quickly develops in the simulation. Also, the magnetotail evolves into a periodic state where the location of the X-line in the tail oscillates between x approximately 40 R(sub E) and x approximately 70 R(sub E) on a 5-minute time scale. Evidence of this periodic motion is also seen in the auroral precipitation profile of ions.

Peroomian, Vahe↗

NASA NTRS1994

The effects of gravity darkening on the ultraviolet continuum polarization produced by circumstellar disks

We investigate the effects of gravity darkening on the UV continuum polarization produced by an axisymmetric disk that surrounds a rapidly rotating star. Although the model is a single scattering approximation, we do include the effects of attenuation (electron scattering plus hydrogen bound-free absorption) by the disk, using an approach similar to that of Sobolev (1963). Because of the gravity darkening of the star and the attenuation within the disk, the radiation field is not axially symmetric about the radius vector. This implies that the polarization source functions are no longer provided by the finite disk depolarization factors of Cassinelli, Nordsieck, & Murison (1987), which are functions of the intensity moments in a spherically symmetric atmosphere. We reformulate the polarization source functions using generalized intensity moment tensors (J, H(sub i), K(sub ij)) that are valid for an arbitrary radiation field and envelope geometry. We find that the polarization source functions are simplest when using intensity moments in the observer's reference frame. On the other hand, the intensity moments are most easily evaluated in the stellar reference frame. Using the rotation transformation properties of the generalized intensity moments, we relate the observer's moments to those evaluated in the stellar reference frame. Our procedure for determining the polarization source functions thus merely involves choosing a set of Euler angles for the coordinate rotations, and then evaluating the associated rotation matrix. The geometrical complications of polarization transfer are thus reduced to obtaining a coordinate rotation matrix.

Bjorkman, J. E.↗

NASA NTRS1987

Altimetry data and the elastic stress tensor of subduction zones

The maximum shear stress (mss) field due to mass anomalies is estimated in the Apennines, the Kermadec-Tonga Trench, and the Rio Grande Rift areas and the results for each area are compared to observed seismicity. A maximum mss of 420 bar was calculated in the Kermadec-Tonga Trench region at a depth of 28 km. Two additional zones with more than 300 bar mss were also observed in the Kermadec-Tonga Trench study. Comparison of the calculated mss field with the observed seismicity in the Kermadec-Tonga showed two zones of well correlated activity. The Rio Grande Rift results showed a maximum mss of 700 bar occurring east of the rift and at a depth of 6 km. Recorded seismicity in the region was primarily constrained to a depth of approximately 5 km, correlating well to the results of the stress calculations. Two areas of high mss are found in the Apennine region: 120 bar at a depth of 55 km, and 149 bar at the surface. Seismic events observed in the Apennine area compare favorably with the mss field calculated, exhibiting two zones of activity. The case of loading by seamounts and icecaps are also simulated. Results for this study show that the mss reaches a maximum of about 1/3 that of the applied surface stress for both cases, and is located at a depth related to the diameter of the surface mass anomaly.

Caputo, Michele↗

DOE OSTI2026

IRMA

IRMA (In)elastic Representation of Materials As S(α,β) evaluations IRMA turns one phonon model into three outputs that usually require three separate tool chains: an evaluated nuclear-data file, predicted neutron-scattering spectra, and scattering kernels for Monte Carlo transport. The three outputs draw on a single, consistent description of the material, so the evaluation, the spectroscopy that can validate it, and the transport that uses it always agree about the physics. Nuclear data. IRMA writes ENDF-6 File 7 thermal scattering evaluations on automatically constructed (α, β) grids. This part reimplements and generalizes NJOY's LEAPR: the classic kernels reproduce freshly generated NJOY2016 tapes digit for digit and published reference tapes to about 1e-4, and the generalized paths add the exact coherent one-phonon term, anisotropic Debye-Waller tensors, coherent elastic for arbitrary crystals, and a per-species partition for polyatomic materials. The tapes feed NJOY, AMPX, FUDGE, and every transport code downstream of them. Neutron spectroscopy. The irma.spectra forward model projects the same physics onto an instrument's kinematics and resolution: INS spectra for VISION and generic indirect geometries, and 2-D S(Q,E) powder maps for direct-geometry spectrometers, from a phonopy model or straight from a phonon DOS. It can be used to predict a proposed measurement before beam time; in analysis, it supplies the calculated single-scattering counterpart of a measured spectrum, from the same material description the evaluation was built from. Monte Carlo transport. The irma.ncrystal exporter writes per-temperature scattering kernels for the companion NCrystal plugin, so McStas, OpenMC, and other NCrystal-aware codes sample the same physics. The exported kernels carry the per-site anisotropic Debye-Waller tensors, keeping directional coherent-elastic physics that NCrystal's standard scalar treatment does not represent. With the same physics inside a transport code, an entire beamline becomes a virtual experiment: IRMA's end-to-end validation ran a custom McStas implementation of the ARCS spectrometer, assembled from the existing McVine and McStas models, against measured data. From a bare crystal structure. The irma mlip front end builds the phonon model itself: a structure file and a choice of potential are enough. Nine pretrained machine-learned interatomic potentials are supported, on a laptop CPU, with no first-principles calculation; an approximate phonon model for a new material costs minutes, not a DFT campaign, and the build emits prefilled inputs for all three outputs. The result is a good starting point rather than a finished evaluation: survey-quality physics with every parameter exposed for review. A converged atomistic calculation enters the same way, as a phonopy model, when higher fidelity is needed.

Ramic, Kemal [Oak Ridge National Laboratory (ORNL)↗

DOE OSTI2024

A reduced-order model for nonlinear radiative transfer problems based on moment equations and POD-Petrov-Galerkin projection of the normalized Boltzmann transport equation

A data-driven projection-based reduced-order model (ROM) for nonlinear thermal radiative transfer (TRT) problems is presented. The TRT ROM is formulated by (i) a hierarchy of low-order quasidiffusion (aka variable Eddington factor) equations for moments of the radiation intensity and (ii) the normalized Boltzmann transport equation (BTE). The multilevel system of moment equations is derived by projection of the BTE onto a sequence of subspaces which represent elements of the phase space of the problem. Exact closure for the moment equations is provided by the Eddington tensor. A Petrov-Galerkin (PG) projection of the normalized BTE is formulated using a proper orthogonal decomposition (POD) basis representing the normalized radiation intensity over the whole phase space and time. The Eddington tensor linearly depends on the solution of the normalized BTE. By linear superposition of the POD basis functions, a low-rank expansion of the Eddington tensor is constructed with coefficients defined by the PG projected normalized BTE. The material energy balance (MEB) equation is coupled with the effective gray low-order equations which exist on the same dimensional scale as the MEB equation. The resulting TRT ROM is structure and asymptotic preserving. A detailed analysis of the ROM is performed on the classical Fleck-Cummings (F-C) TRT multigroup test problem in 2D geometry. Numerical results are presented to demonstrate the ROM's effectiveness in the simulation of radiation wave phenomena. Importantly, the ROM is shown to produce solutions with sufficiently high accuracy while using low-rank approximation of the normalized BTE solution. Essential physical characteristics of supersonic radiation wave are preserved in the ROM solutions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Aerodynamic Sensitivities over Separable Shape Tensors

Here, we present a comprehensive aerodynamic sensitivity analysis of airfoil parameterization informed by separable shape tensors. This parameterization approach uniquely benefits the design process by isolating various well-studied shape characteristics, such as airfoil thickness, and providing a well-regulated low-dimensional parameter domain for aerodynamic designs. Exploring the aerodynamic sensitivities of this novel parameterization can provide valuable insights for more robust designs and future manufacturing efforts. We construct a data-driven parameter space of airfoils using principal geodesic analysis of separable shape tensors informed by a curated database containing almost 20,000 suitable engineering airfoils. Analyzing the shape reconstruction error and the maximum mean discrepancy between joint distributions of aerodynamic quantities, we study the dimensionality of the learned parameter space. This simple numerical experiment demonstrates a dramatic dimension reduction that retains design effectiveness and promotes regularity of the shape representations. Finally, we generate new airfoils and use the HAM2D Reynolds-averaged Navier–Stokes solver to predict lift, drag, and moment coefficients. We compute multiple sensitivity metrics to quantify and assert the consistency of parameter influence on the aerodynamic quantities. We also explore low-dimensional polynomial ridge approximations to motivate physical intuitions and offer explanations of the approximated sensitivities.

17 WIND ENERGY↗

NASA NTRS1978

Linear and nonlinear interactions between the earth tide and a tectonically stressed earth

In the vincinity of earthquake focal regions, conditions may not be equal. Crustal rocks stressed to more than approximately 0.6 of their failure strength exhibit material properties over and above that of linear elasticity. Interactions between the earth tide and crustal rocks that are under high tectonic stress are discussed in terms of simple phenomenological models. In particular, the difference between a nonlinear elastic model of dilatancy and a dilatancy model that exhibits hysteresis is noted. It is concluded that the small changes in stress produced by the earth tide act as a probe of the properties of crustal rocks. Observations of earth tide tilts and strains in such high stress zones may, therefore, provide keys to the constitutive properties and the tectonic stress rate tensor of these zones.

Beaumont, C.↗

NASA NTRS1996

Seismic Excitation of the Polar Motion, 1977-1993

The mass redistribution in the earth as a result of an earthquake faulting changes the earth's inertia tensor, and hence its rotation. Using the complete formulae developed by CHAO and GROSS (1987) based on the normal mode theory, we calculated the earthquake-induced polar motion excitation for the largest 11,015 earthquakes that occurred during 1977.0-1993.6. The seismic excitations in this period are found to be two orders of magnitude below the detection threshold even with today's high precision earth rotation measurements. However, it was calculated that an earthquake of only one tenth the size of the great 1960 Chile event, if happened today, could be comfortably detected in polar motion observations. Furthermore, collectively these seismic excitations have a strong statistical tendency to nudge the pole towards approximately 140deg E, away from the actual observed polar drift direction. This non-random behavior, similarly found in other earthquake-induced changes in earth rotation and low-degree gravitational field by CHAO and GROSS (1987), manifests some geodynamic behavior yet to be explored.

Chao, Benjamin Fong↗

DOE OSTI2025

Constructing the infrared conformal generators on the fuzzy sphere

We investigate the conformal algebra on the fuzzy sphere, and in particular the generators of translations and special conformal transformations which are emergent symmetries in the infinite IR but are broken along the RG flow. We show how to extract these generators using the energy momentum tensor, which is complicated by the fact that one does not have a priori access to the energy momentum tensor of the CFT limit but rather must construct it numerically. We discuss and quantitatively analyze the main sources of corrections to the conformal generators due to the breaking of scale-invariance at finite energy, and develop efficient methods for removing these corrections. The resulting generators have matrix elements that match CFT predictions with accuracy varying from sub-percent level for the lowest-lying states up to several percent accuracy for states with dimension \sim 5 ∼ 5 with N=16 N = 16 fermions. We show that the generators can be used to accurately identify primary operators vs descendant operators in energy ranges where the spectrum is too dense to do the identification solely based on the approximate integer spacing within conformal multiplets.

Fardelli, Giulia (ORCID:0000000217998124)↗