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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.

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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

Adaptive Algebraic Multigrid for Finite Element Elliptic Equations with Random Coefficients

This thesis presents a two-grid algorithm based on Smoothed Aggregation Spectral Element Agglomeration Algebraic Multigrid (SA-ρAMGe) combined with adaptation. The aim is to build an efficient solver for the linear systems arising from discretization of second-order elliptic partial differential equations (PDEs) with stochastic coefficients. Examples include PDEs that model subsurface flow with random permeability field. During a Markov Chain Monte Carlo (MCMC) simulation process, that draws PDE coefficient samples from a certain distribution, the PDE coefficients change, hence the resulting linear systems to be solved change. At every such step the system (discretized PDE) needs to be solved and the computed solution used to evaluate some functional(s) of interest that then determine if the coefficient sample is acceptable or not. The MCMC process is hence computationally intensive and requires the solvers used to be efficient and fast. This fact that at every step of MCMC the resulting linear system changes, makes an already existing solver built for the old problem perhaps not as efficient for the problem corresponding to the new sampled coefficient. This motivates the main goal of our study, namely, to adapt an already existing solver to handle the problem (with changed coefficient) with the objective to achieve this goal to be faster and more efficient than building a completely new solver from scratch. Our approach utilizes the local element matrices (for the problem with changed coefficients) to build local problems associated with constructed by the method agglomerated elements (a set of subdomains that cover the given computational domain). We solve a generalized eigenproblem for each set in a subspace spanned by the previous local coarse space (used for the old solver) and a vector, component of the error, that the old solver cannot handle. A portion of the spectrum of these local eigen-problems (corresponding to eigenvalues close to zero) form the coarse basis used to define the new two-level method of our interest. We illustrate the performance of this adaptive two-level procedure with a large set of numerical experiments that demonstrate its efficiency over building the solvers from scratch.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

A method for eliminating Faraday rotation in cryostat windows in longitudinal magneto-optical Kerr effect measurements

A solution to the problem of disturbing effect of the background Faraday rotation in the cryostat windows on longitudinal magneto-optical Kerr effect (LMOKE) measured under vacuum conditions and/or at low temperatures is proposed. The method for eliminating the influence of Faraday rotation in cryostat windows is based on special arrangement of additional mirrors placed on sample holder. In this arrangement, the orientation of the cryostat window is perpendicular to the light beam direction and parallel to an external magnetic field generated by the H-frame electromagnet. The operation of the LMOKE magnetometer with the special sample holder based on polarization modulation technique with a photo-elastic modulator is theoretically analyzed with the use of Jones matrices, and formulas for evaluating of the actual Kerr rotation and ellipticity of the sample are derived. The feasibility of the method and good performance of the magnetometer is experimentally demonstrated for the LMOKE effect measured in Fe/Au multilayer structures. The influence of imperfect alignment of the magnetometer setup on the Kerr angles, as derived theoretically through the analytic model and verified experimentally, is examined and discussed.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2016

Local parametric instability near elliptic points in vortex flows under shear deformation

The dynamics of two point vortices embedded in an oscillatory external flow consisted of shear and rotational components is addressed. The region associated with steady-state elliptic points of the vortex motion is established to experience local parametric instability. The instability forces the point vortices with initial positions corresponding to the steady-state elliptic points to move in spiral-like divergent trajectories. This divergent motion continues until the nonlinear effects suppress their motion near the region associated with the steady-state separatrices. The local parametric instability is then demonstrated not to contribute considerably to enhancing the size of the chaotic motion regions. Instead, the size of the chaotic motion region mostly depends on overlaps of the nonlinear resonances emerging in the perturbed system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Reconstructing high-dimensional Hilbert-valued functions via compressed sensing

We present and analyze a novel sparse polynomial technique for approximating high-dimensional Hilbert-valued functions, with application to parameterized partial differential equations (PDEs) with deterministic and stochastic inputs. Our theoretical framework treats the function approximation problem as a joint sparse recovery problem, where the set of jointly sparse vectors is possibly infinite. To achieve the simultaneous reconstruction of Hilbert-valued functions in both parametric domain and Hilbert space, we propose a novel mixed-norm based `1 regularization method that exploits both energy and sparsity. Our approach requires extensions of concepts such as the restricted isometry and null space properties, allowing us to prove recovery guarantees for sparse Hilbert-valued function reconstruction. We complement the enclosed theory with an algorithm for Hilbert-valued recovery, based on standard forward-backward algorithm, meanwhile establishing its strong convergence in the considered infinite-dimensional setting. Finally, we demonstrate the minimal sample complexity requirements of our approach, relative to other popular methods, with numerical experiments approximating the solutions of high-dimensional parameterized elliptic PDEs.

Dexter, Nick↗
DOE OSTI2021

Hierarchical Inference with Bayesian Neural Networks: An Application to Strong Gravitational Lensing

In the past few years, approximate Bayesian Neural Networks (BNNs) have demonstrated the ability to produce statistically consistent posteriors on a wide range of inference problems at unprecedented speed and scale. However, any disconnect between training sets and the distribution of real-world objects can introduce bias when BNNs are applied to data. This is a common challenge in astrophysics and cosmology, where the unknown distribution of objects in our universe is often the science goal. In this work, we incorporate BNNs with flexible posterior parameterizations into a hierarchical inference framework that allows for the reconstruction of population hyperparameters and removes the bias introduced by the training distribution. We focus on the challenge of producing posterior PDFs for strong gravitational lens mass model parameters given Hubble Space Telescope–quality single-filter, lens-subtracted, synthetic imaging data. We show that the posterior PDFs are sufficiently accurate (statistically consistent with the truth) across a wide variety of power-law elliptical lens mass distributions. We then apply our approach to test data sets whose lens parameters are drawn from distributions that are drastically different from the training set. We show that our hierarchical inference framework mitigates the bias introduced by an unrepresentative training set's interim prior. Simultaneously, we can precisely reconstruct the population hyperparameters governing our test distributions. Our full pipeline, from training to hierarchical inference on thousands of lenses, can be run in a day. The framework presented here will allow us to efficiently exploit the full constraining power of future ground- and space-based surveys (https://github.com/swagnercarena/ovejero).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

An Improved Discrete Least-Squares/Reduced-Basis Method for Parameterized Elliptic PDEs

It is shown that the computational efficiency of the discrete least-squares (DLS) approximation of solutions of stochastic elliptic PDEs is improved by incorporating a reduced-basis method into the DLS framework. In particular, we consider stochastic elliptic PDEs with an affine dependence on the random variable. The goal is to recover the entire solution map from the parameter space to the finite element space. To this end, first, a reduced-basis solution using a weak greedy algorithm is constructed, then a DLS approximation is determined by evaluating the reduced-basis approximation instead of the full finite element approximation. The main advantage of the new approach is that one only need apply the DLS operator to the coefficients of the reduced-basis expansion, resulting in huge savings in both the storage of the DLS coefficients and the online cost of evaluating the DLS approximation. In addition, the recently developed quasi-optimal polynomial space is also adopted in the new approach, resulting in superior convergence rates for a wider class of problems than previous analyzed. Numerical experiments are provided that illustrate the theoretical results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Validation of general purpose mathematical efficiency modeling with ISOCS - 15579

Gamma spectroscopy is a commonly used method for radioactive waste characterization and activity determination in in-situ objects. The gamma rays emitted by radionuclides in the waste container matrix are highly penetrating and can be measured using one or more gamma ray detectors, thus allowing for a passive nondestructive assay. One problem is that a source based calibration of full energy peak efficiency can be difficult or impractical because of the large size and/or an unusual shape of the sample geometry. One attractive solution is to use mathematical efficiency modeling to calculate the full energy peak efficiency. The In-Situ Object Calibration Software (ISOCS) has successfully been used for more than a decade for mathematical efficiency modeling of template based geometries. Templates include the most common objects in waste characterization and D and D, including but not limited to: boxes, drums, and pipes with hotspots, beams, tanks and walls. Scenarios exist where these templates cannot model the desired measurement geometry. Canberra has developed a general purpose version of ISOCS where primitive objects can be combined into practically any geometry. The primitive objects are right circular cylinder, right elliptical cylinder, right circular cone, right elliptical cone, sphere, spheroid, ellipsoid, box (rectangular parallelepiped), torus, and beaker (any cylindrical symmetric object). Multiple primitive objects can be combined using the priority scheme and cut by planes into almost any desired shape. In addition, multiple objects can be defined in the same scene, for example cylinders next to each other or a pipe and a box. Collimators can be constructed as easily as in template based ISOCS. The ray tracing algorithm in ISOCS has been extended to support the new primitive objects for attenuation calculation between the radioactive source and the detector end cap. The new version uses the same vacuum efficiency response, or characterization, in the energy range 10 - 7000 keV of individual detectors to be able to calculate the efficiency as accurately as possible. MCNP has been shown to be able to calculate detection efficiencies for any geometry and the new version of ISOCS have been validated to MCNP. The vacuum efficiency is based on an MCNP model and this model was the base for constructing an identical model in MCNP as in ISOCS. The calculated efficiencies from the two codes have been compared and the agreement is within 3% except for the lowest energies for one geometry. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2012

(3 + 1)-dimensional cylindrical Korteweg-de Vries equation for nonextensive dust acoustic waves: Symbolic computation and exact solutions

By combining the effects of bounded cylindrical geometry, azimuthal and axial perturbations, the nonlinear dust acoustic waves (DAWs) in an unmagnetized plasma consisting of negatively charged dust grains, nonextensive ions, and nonextensive electrons are studied in this paper. Using the reductive perturbation method, a (3 + 1)-dimensional variable-coefficient cylindrical Korteweg-de Vries (KdV) equation describing the nonlinear propagation of DAWs is derived. Via the homogeneous balance principle, improved F-expansion technique and symbolic computation, the exact traveling and solitary wave solutions of the KdV equation are presented in terms of Jacobi elliptic functions. Moreover, the effects of the plasma parameters on the solitary wave structures are discussed in detail. The obtained results could help in providing a good fit between theoretical analysis and real applications in space physics and future laboratory plasma experiments where long-range interactions are present.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Towards Using Eshelby Calculations to Enhance Kinetic Model for Zirconium Hydride Precipitation

A C++ library (called Eshelby ) was implemented in fiscal year 2015 based upon the formulas documented in this report. The library implements a generalized version of Eshelby's inclusion problem. The library was written as a set of functions which can be called from another program; the principle intended use cases are kinetic models of precipitate formation in zirconium claddings where use of the Eshelby library provides needed elastic energy density calculations, as well as calculations of stress and strain in and around precipitates; it is intended that the library will be made open source. For isotropic inclusions in the form of oblate and prolate ellipsoids, the Eshelby library can be used for nearly any relevant/appropriate shape parameters to calculate strains, stresses and energy density at interior and exterior points. The Eshelby library uses a combination of analytical formulas and numerical routines making it very extensible. For example, the library can can easily be extended to include inclusions such as spheres since analytical expressions exist for the required elliptic integrals; similarly, general ellipsoids do not have analytical results for the required elliptic integrals but those integrals can be numerically evaluated and thus fit naturally into the Eshelby library. This report documents all formulas implemented in the Eshelby library and presents some demonstration calculations relevant to the intended application.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Large-scale assembly bias of dark matter halos

We present precise measurements of the assembly bias of dark matter halos, i.e. the dependence of halo bias on other properties than the mass, using curved 'separate universe' N-body simulations which effectively incorporate an infinite-wavelength matter overdensity into the background density. This method measures the LIMD (local-in-matter-density) bias parameters b {sub n} in the large-scale limit. We focus on the dependence of the first two Eulerian biases b {sup E} {sup {sub 1}} and b {sup E} {sup {sub 2}} on four halo properties: the concentration, spin, mass accretion rate, and ellipticity. We quantitatively compare our results with previous works in which assembly bias was measured on fairly small scales. Despite this difference, our findings are in good agreement with previous results. We also look at the joint dependence of bias on two halo properties in addition to the mass. Finally, using the excursion set peaks model, we attempt to shed new insights on how assembly bias arises in this analytical model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Comparison of multigrid algorithms for high‐order continuous finite element discretizations

Summary We present a comparison of different multigrid approaches for the solution of systems arising from high‐order continuous finite element discretizations of elliptic partial differential equations on complex geometries. We consider the pointwise Jacobi, the Chebyshev‐accelerated Jacobi, and the symmetric successive over‐relaxation smoothers, as well as elementwise block Jacobi smoothing. Three approaches for the multigrid hierarchy are compared: (1) high‐order h ‐multigrid, which uses high‐order interpolation and restriction between geometrically coarsened meshes; (2) p ‐multigrid, in which the polynomial order is reduced while the mesh remains unchanged, and the interpolation and restriction incorporate the different‐order basis functions; and (3) a first‐order approximation multigrid preconditioner constructed using the nodes of the high‐order discretization. This latter approach is often combined with algebraic multigrid for the low‐order operator and is attractive for high‐order discretizations on unstructured meshes, where geometric coarsening is difficult. Based on a simple performance model, we compare the computational cost of the different approaches. Using scalar test problems in two and three dimensions with constant and varying coefficients, we compare the performance of the different multigrid approaches for polynomial orders up to 16. Overall, both h ‐multigrid and p ‐multigrid work well; the first‐order approximation is less efficient. For constant coefficients, all smoothers work well. For variable coefficients, Chebyshev and symmetric successive over‐relaxation smoothing outperform Jacobi smoothing. While all of the tested methods converge in a mesh‐independent number of iterations, none of them behaves completely independent of the polynomial order. When multigrid is used as a preconditioner in a Krylov method, the iteration number decreases significantly compared with using multigrid as a solver. Copyright © 2015 John Wiley & Sons, Ltd.

Sundar, Hari↗
DOE OSTI2017

Optical properties of magnetic photonic crystals with an arbitrary magnetization orientation

We have studied the peculiarities of diffraction of light in magnetic photonic crystals at large values of magnetooptical activity parameter and modulation depth. We have considered the case of an arbitrary angle between the directions of the external static magnetic field and the normal to the layer. The problem has been solved by the modified Ambartsumyan layer summation method. It has been shown that the given system is nonreciprocal with respect to not only circular, but linear polarizations also. In this case, a new type of nonreciprocity is observed (namely, the relation R(α) ≠ R(–α) holds, where R is the reflection coefficient and α is the angle of incidence). It has been demonstrated that in the case of oblique incidence, there appears a new photonic forbidden band that is not selective relative to the polarization of incident light. We have detected strong dependences of reflectance, absorbance, transmittance nonreciprocity, and other characteristics on the angle between the direction of the external static magnetic field and the normal to the layer boundary. Such a system can be used as a controllable polarization filter and a mirror, as well as a source of circular (elliptic) polarization, a controllable optical diode, and so on.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Dynamical Friction and the Evolution of Supermassive Black Hole Binaries: The Final Hundred-parsec Problem

The supermassive black holes originally in the nuclei of two merging galaxies will form a binary in the remnant core. The early evolution of the massive binary is driven by dynamical friction before the binary becomes “hard” and eventually reaches coalescence through gravitational-wave emission. We consider the dynamical friction evolution of massive binaries consisting of a secondary hole orbiting inside a stellar cusp dominated by a more massive central black hole. In our treatment, we include the frictional force from stars moving faster than the inspiralling object, which is neglected in the standard Chandrasekhar treatment. We show that the binary eccentricity increases if the stellar cusp density profile rises less steeply than ρ∝r{sup −2}. In cusps shallower than ρ∝r{sup −1}, the frictional timescale can become very long due to the deficit of stars moving slower than the massive body. Although including fast stars increases the decay rate, low mass-ratio binaries (q≲10{sup −3}) in sufficiently massive galaxies have decay timescales longer than one Hubble time. During such minor mergers, the secondary hole stalls on an eccentric orbit at a distance of order one-tenth the influence radius of the primary hole (i.e., ≈10--100 pc for massive ellipticals). We calculate the expected number of stalled satellites as a function of the host galaxy mass and show that the brightest cluster galaxies should have ≳1 of such satellites orbiting within their cores. Our results could provide an explanation for a number of observations, which include multiple nuclei in core ellipticals, off-center AGNs, and eccentric nuclear disks.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Solving Critical Problems of the Muon Collider Higgs Factory: Optics, Magnets and their Protection, Detector Backgrounds

A low-energy medium-luminosity Muon Collider (MC) is being studied as a possible Higgs Factory (HF). Electrons from muon decays will deposit more than 300 kW in superconducting magnets of the HF collider ring. This imposes significant challenges to superconducting (SC) magnets used in the MC storage ring (SR) and interaction regions (IR). Magnet designs are proposed which provide high operating gradient and magnetic field in a large aperture to accommodate the large size of muon beams (due to low beta*), as well as a cooling system to intercept the large heat deposition from the showers induced by decay electrons. The distribution of heat deposition in the MC SR lattice elements requires large-aperture magnets in order to accommodate thick high-Z absorbers to protect the SC coils. Based on the developed MARS15 model and intensive simulations, a sophisticated radiation protection system was designed for the collider SR and IR to bring the peak power density in the superconducting coils below the quench limit and reduce the dynamic heat deposition in the cold mass by a factor of 100. The system consists of tight tungsten masks in the magnet interconnect regions and elliptical tungsten liners in the magnet aperture optimized individually for each magnet. These also reduce the background particle fluxes in the collider detector.

43 PARTICLE ACCELERATORS↗
DOE OSTI2017

Generation of circularly polarized XUV and soft-x-ray high-order harmonics by homonuclear and heteronuclear diatomic molecules subject to bichromatic counter-rotating circularly polarized intense laser fields

Recently, studies of bright circularly polarized high-harmonic beams from atoms in the soft-x-ray region as a source for x-ray magnetic circular dichroism measurement in a tabletop-scale setup have received considerable attention. In this paper, we address the problem with molecular targets and perform a detailed quantum study of H 2 +, CO, and N 2 molecules in bichromatic counter-rotating circularly polarized laser fields where we adopt wavelengths (1300 and 790 nm) and intensities (2 × 10 14 W/cm 2 ) reported in a recent experiment [Proc. Natl. Acad. Sci. USA 112, 14206 (2015)]. Our treatment of multiphoton processes in homonuclear and heteronuclear diatomic molecules is nonperturbative and based on the time-dependent density-functional theory for multielectron systems. The calculated radiation spectrum contains doublets of left and right circularly polarized harmonics with high-energy photons in the XUV and soft-x-ray ranges. Overall, our results reveal intriguing and substantially different nonlinear optical responses for homonuclear and heteronuclear diatomic molecules subject to circularly polarized intense laser fields. We study in detail the below- and above-threshold harmonic regions and analyze the ellipticity and phase of the generated harmonic peaks.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2018

A scalable geometric multigrid solver for nonsymmetric elliptic systems with application to variable-density flows

A geometric multigrid algorithm is introduced for solving nonsymmetric linear systems resulting from the discretization of the variable density Navier–Stokes equations on nonuniform structured rectilinear grids and high-Reynolds number flows. The restriction operation is defined such that the resulting system on the coarser grids is symmetric, thereby allowing for the use of efficient smoother algorithms. To achieve an optimal rate of convergence, the sequence of interpolation and restriction operations are determined through a dynamic procedure. A parallel partitioning strategy is introduced to minimize communication while maintaining the load balance between all processors. To test the proposed algorithm, we consider two cases: 1) homogeneous isotropic turbulence discretized on uniform grids and 2) turbulent duct flow discretized on stretched grids. Testing the algorithm on systems with up to a billion unknowns shows that the cost varies linearly with the number of unknowns. This O (N) behavior confirms the robustness of the proposed multigrid method regarding ill-conditioning of large systems characteristic of multiscale high-Reynolds number turbulent flows. The robustness of our method to density variations is established by considering cases where density varies sharply in space by a factor of up to 104, showing its applicability to two-phase flow problems. Strong and weak scalability studies are carried out, employing up to 30,000 processors, to examine the parallel performance of our implementation. Excellent scalability of our solver is shown for a granularity as low as 104 to 105 unknowns per processor. At its tested peak throughput, it solves approximately 4 billion unknowns per second employing over 16,000 processors with a parallel efficiency higher than 50%.

Computer Science↗
DOE OSTI2012

ORNL Biometric Eye Model for Iris Recognition

Iris recognition has been proven to be an accurate and reliable biometric. However, the recognition of non-ideal iris images such as off angle images is still an unsolved problem. We propose a new biometric targeted eye model and a method to reconstruct the off-axis eye to its frontal view allowing for recognition using existing methods and algorithms. This allows for existing enterprise level algorithms and approaches to be largely unmodified by using our work as a pre-processor to improve performance. In addition, we describe the `Limbus effect' and its importance for an accurate segmentation of off-axis irides. Our method uses an anatomically accurate human eye model and ray-tracing techniques to compute a transformation function, which reconstructs the iris to its frontal, non-refracted state. Then, the same eye model is used to render a frontal view of the reconstructed iris. The proposed method is fully described and results from synthetic data are shown to establish an upper limit on performance improvement and establish the importance of the proposed approach over traditional linear elliptical unwrapping methods. Our results with synthetic data demonstrate the ability to perform an accurate iris recognition with an image taken as much as 70 degrees off-axis.

Santos-Villalobos, Hector J↗