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At least 1,081 records · Page 60
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

What Is the Fractional Laplacian? A Comparative Review with New Results

The fractional Laplacian in $\mathbb{R}^{d}$, which we write as (–Δ) α/2 with, α ϵ (0, 2) has multiple equivalent characterizations. Furthermore, in bounded domains, boundary conditions must be incorporated in these characterizations in mathematically distinct ways, and there is currently no consensus in the literature as to which definition of the fractional Laplacian in bounded domains is most appropriate for a given application. The Riesz (or integral) definition, for example, admits a nonlocal boundary condition, where the value of a function must be prescribed on the entire exterior of the domain in order to compute its fractional Laplacian. Yet, the spectral definition requires only the standard local boundary condition. These differences, among others, lead us to ask the question: “What is the fractional Laplacian?” Beginning from first principles, we compare several commonly used definitions of the fractional Laplacian theoretically, through their stochastic interpretations as well as their analytical properties. Next, we present quantitative comparisons using a sample of state-of-the-art methods. We discuss recent advances on nonzero boundary conditions and present new methods to discretize such boundary value problems: radial basis function collocation (for the Riesz fractional Laplacian) and nonharmonic lifting (for the spectral fractional Laplacian). In our numerical studies, we aim to compare different definitions on bounded domains using a collection of benchmark problems. We consider the fractional Poisson equation with both zero and nonzero boundary conditions, where the fractional Laplacian is defined according to the Riesz definition, the spectral definition, the directional definition, and the horizon-based nonlocal definition. We verify the accuracy of the numerical methods used in the approximations for each operator, and we focus on identifying differences in the boundary behaviors of solutions to equations posed with these different definitions. Through our efforts, we aim to further engage the research community in open problems and assist practitioners in identifying the most appropriate definition and computational approach to use for their mathematical models in addressing anomalous transport in diverse applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Geostatistical interpolation of streambed hydrologic attributes with addition of left censored data and anisotropy

Spatial geostatistical interpolation of point measurements of streambed attributes in the hyporheic zone may be constrained by the streambed anisotropy, and data density and spatial distribution may significantly impact the results. Spatial clustering and low spatial data density can be caused by bedrock outcropping at the streambed limiting installation of in-stream piezometers. This study examines parameter error variability of the geostatistical interpolation using anisotropic interpolation methods and increasing the data density by adding left censored values (i.e., data below measurement limit) to locations where measurements were limited by exposed bedrock lining the streambed. The reduction in relative standard error of the interpolation was determined for the spatial distributions of streambed attributes including hydraulic conductivity, seepage flux, and mercury solute flux measured in two different years along a study reach in East Fork Poplar Creek, Tennessee, USA. Here, two methods to impute the left censored values were compared including the conventional half the detection limit substitution method, and the Stochastic Approximation of Expectation-Maximization (SAEM) algorithm, which both had comparable results. Imputing left censored data increased the data density to recommended ranges, reduced data clustering, increased the spatial dependence for some attributes, and reduced the standard error for each of the three attributes. For the reach considered herein, addition of the left censored values resulted in a larger error reduction than the consideration of anisotropy within the interpolation, which confirms the benefit of data addition to increase data density within data-limited river corridors.

58 GEOSCIENCES↗
DOE OSTI2012

The complex metal-rich boride Ti{sub 1+x}Rh{sub 2-x+y}Ir{sub 3-y}B{sub 3} (x=0.68, y=1.06) with a new structure type containing B{sub 4} zigzag fragments: Synthesis, crystal chemistry and theoretical calculations

Polycrystalline samples and single crystals of the new complex boride Ti{sub 1+x}Rh{sub 2-x+y}Ir{sub 3-y}B{sub 3} (x=0.68; y=1.06) were synthesized by arc-melting the elements in a water-cooled copper crucible under an argon atmosphere and characterized by X-Ray diffraction as well as EDX measurements. The crystal structure was refined on the basis of single crystal data. The new phase, which represents a new structure type containing trans zigzag B{sub 4} fragments as well as isolated boron atoms crystallizes in the orthorhombic space group Pbam (Nr. 55) with the lattice parameters a=8.620(1) A, b=14.995(2) A and c=3.234(1) A. First-principles density functional theory calculations using the Vienna ab-initio simulation package (VASP) were performed on an appropriate structural model (using a supercell approach) and the experimental crystallographic data could be reproduced accurately. Based on this model, the density of states and crystal orbital Hamilton population (for bonding analysis) were calculated, using the linear muffin-tin orbital atomic sphere approximation (LMTO-ASA) method. According to these calculations, this metal-rich compound should be metallic, as expected. Furthermore, very strong boron-boron interactions are observed in the trans zigzag B{sub 4} fragment, which induce a clear differentiation of two types of metal-boron contacts with different strength. The observed three-dimensional metal-metal interaction is in good agreement with the predicted metallic behavior. - graphical abstract: The structure of Ti{sub 1.68(2)}Rh{sub 2.38(6)}Ir{sub 1.94(4)} B{sub 3}, a new structure type containing planar trans zigzag B{sub 4} units, is another example which illustrates the tendency of metal-rich borides to form B-B bonds with increasing boron content. Beside the B{sub 4} fragment it exhibits one-dimensional chains of titanium atoms and hold one-dimensional strings of face-sharing empty tetrahedral and square pyramidal clusters (see figure). Highlights: Black-Right-Pointing-Pointer Synthesis of a new metal-rich complex boride. Black-Right-Pointing-Pointer New structure type containing isolated boron and trans zigzag B{sub 4} units. Black-Right-Pointing-Pointer Crystallographic parameters and bond length well reproduced by theory. Black-Right-Pointing-Pointer Strong boron-boron and metal-boron interactions responsible for structural stability. Black-Right-Pointing-Pointer Three-dimensional metallic network responsible for metallic behavior.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Thermoelectric, electronic, optical and chemical bonding properties of Ba{sub 2}PrRuO{sub 6}: At temperature 7 K and 150 K

Highlights: • DFT-FPLAPW method used for calculating the electronic structure. • The Fermi surface of BPRO (7 K and 150 K) is also calculated. • The complex dielectric function has been calculated. • Thermoelectric properties were also calculated using BoltzTraP code. • Power factor shows that both compounds are good thermoelectric materials at 600 K. - Abstract: We present first principles calculations of the band structure, density of states, electronic charge density, Fermi surface and optical properties of Ba{sub 2}PrRuO{sub 6} single crystals at two different temperatures. The atomic positions were optimized by minimizing the forces acting on the atoms. We have employed the full potential linear augmented plane wave method within local density approximation, generalized gradient approximation and Engel–Vosko generalized gradient approximation to treat the exchange correlation potential. The calculation shows that the compound is superconductor with strong hybridization near the Fermi energy level. Fermi surface is composed of two sheets. The calculated electronic specific heat capacities indicate, very close agreement with the experimental one. The bonding features of the compounds are analyzed using the electronic charge density in the (1 0 0) and (0–10) crystallographic planes. The dispersion of the optical constants was calculated and discussed. The thermoelectric properties are also calculated using the BoltzTrap code.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

Sensitivity analysis of high resolution gamma-ray detection for safeguards monitoring at natural uranium conversion facilities

Under the policies proposed by recent International Atomic Energy Agency (IAEA) circulars and policy papers, implementation of safeguards exists when any purified aqueous uranium solution or uranium oxides suitable for isotopic enrichment or fuel fabrication exists. Under IAEA Policy Paper 18, the starting point for nuclear material under safeguards was reinterpreted, suggesting that purified uranium compounds should be subject to safeguards procedures no later than the first point in the conversion process. In response to this technical need, a combination of simulation models and experimental measurements were employed in previous work to develop and validate gamma-ray nondestructive assay monitoring systems in a natural uranium conversion plant (NUCP). In particular, uranyl nitrate (UO 2 (NO 3 ) 2 ) solution exiting solvent extraction was identified as a key measurement point (KMP). Passive nondestructive assay techniques using high resolution gamma-ray spectroscopy were evaluated to determine their viability as a technical means for drawing safeguards conclusions at NUCPs, and if the IAEA detection requirements of 1 significant quantity (SQ) can be met in a timely manner. Building upon the aforementioned previous validation work on detector sensitivity to varying concentrations of uranyl nitrate via a series of dilution measurements, this work investigates detector response parameter sensitivities to gamma-ray signatures of uranyl nitrate. The full energy peak efficiency of a detection system is dependent upon the sample, geometry, absorption, and intrinsic efficiency parameters. Perturbation of these parameters translates into corresponding variations of the 185.7 keV peak area of the 235 U in uranyl nitrate. Such perturbations in the assayed signature impact the quality or versatility of the safeguards conclusions drawn. Given the potentially high throughput of uranyl nitrate in NUCPs, the ability to assay 1 SQ of material requires uncertainty «1%. Accounting for material self-shielding properties, pipe thickness, and source-detector orientation is instrumental in determining the robustness of gamma-ray detection in the process monitoring of uranyl nitrate in NUCPs. Monte Carlo models and ray-tracing models were employed to determine the sensitivity of the detected 185.7 keV photon to self-shielding properties, pipe thickness, and source-detector geometry. Considering the implementation of the detection of 1 SQ, diversion of 1 SQ becomes essentially undetectable given the systematic uncertainty, in addition to considerations such as propagating uncertainties due to pipe offset/position, as well as minor variations in pipe thickness. Consequently, pipe thickness was the most sensitive variable in affecting full energy efficiency of the 185.7 keV signature peak with up to 8% variation in efficiency for ±0.5 mm changes in Schedule 40 304L stainless steel piping. Furthermore, computation of the attenuation correction factor of the uranyl nitrate solution [CF(AT) (i.e. εsample)] using Parker's method using with the approximation for the geometrical factor κ≈π/4 was validated through experimental, Monte Carlo and ray-tracing calculations for a uranyl nitrate filled transfer pipe segment. Furthermore, quantifying sensitivity in detector position, as well as voiding effects due to bubbly flow or laminar flow with an air gap in the uranyl nitrate becomes increasingly important as considerations from (static) design-scale measurements translate into (dynamic) field operations tests.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2016

Quantifying Carbon-14 for Biology Using Cavity Ring-Down Spectroscopy

A cavity ring-down spectroscopy (CRDS) instrument was developed using mature, robust hardware for the measurement of carbon-14 in biological studies. The system was characterized using carbon-14 elevated glucose samples and returned a linear response up to 387 times contemporary carbon-14 concentrations. Carbon-14 free and contemporary carbon-14 samples with varying carbon-13 concentrations were used to assess the method detection limit of approximately one-third contemporary carbon-14 levels. Sources of inaccuracies are presented and discussed, and the capability to measure carbon-14 in biological samples is demonstrated by comparing pharmacokinetics from carbon-14 dosed guinea pigs analyzed by both CRDS and accelerator mass spectrometry. Here, the CRDS approach presented affords easy access to powerful carbon-14 tracer techniques that can characterize complex biochemical systems.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2019

Renormalized Singles Green’s Function for Quasi-Particle Calculations beyond the G 0 W 0 Approximation

Quasi-particle energies and band gaps in particular are critical for investigating novel materials. Commonly used density functional approximations (DFAs) systematically underestimate band gaps, and GW approximation is the established method of choice for good accuracy and reliability. However, G 0 W 0 has some undesired dependence on the DFA, while self-consistent GW (scGW) is expensive and not consistent in accuracy improvement. Here a simple and efficient G RS W 0 approach has been developed: a subspace diagonalization of the Hartree-Fock (HF) Hamiltonian with the DFA density matrix provides the new reference Green's function GRS that incorporates the effect of all single excitation contributions to the self-energy, thereby essentially eliminating the starting-point dependence. Calculations for molecules and large band gap solids demonstrate the significant improvement over G 0 W 0 and greatly reduced dependence on the initial DFA. GRS W0 approach also improve results for other bulks over G 0 W 0 but to a lesser extent, which could be due to the limitations in current implementation for bulks. The results demonstrate that to achieve good accuracy, it is not necessary to use hybrid DFA, which is expensive for bulks. Lastly, this work should be greatly significant in making GW a more robust approach.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

First-Principles Integrated Adsorption Modeling for Selective Capture of Uranium from Seawater by Polyamidoxime Sorbent Materials

Nuclear power is a relatively carbon-free energy source that has the capacity to be utilized today in an effort to stem the tides of global warming. The growing demand for nuclear energy, however, could put significant strain on our uranium ore resources, and the mining activities utilized to extract that ore can leave behind long-term environmental damage. A potential solution to enhance the supply of uranium fuel is to recover uranium from seawater using amidoximated adsorbent fibers. This technology has been studied for decades but is currently plagued by the material’s relatively poor selectivity of uranium over its main competitor vanadium. In this work, we investigate the binding schemes between uranium, vanadium, and the amidoxime functional groups on the adsorbent surface. Using quantum chemical methods, binding strengths are approximated for a set of complexation reactions between uranium and vanadium with amidoxime functionalities. Those approximations are then coupled with a comprehensive aqueous adsorption model developed in this work to simulate the adsorption of uranium and vanadium under laboratory conditions. Experimental adsorption studies with uranium and vanadium over a wide pH range are performed, and the data collected are compared against simulation results to validate the model. It was found that coupling ab initio calculations with process level adsorption modeling provides accurate predictions of the adsorption capacity and selectivity of the sorbent materials. Furthermore, this work demonstrates that this multiscale modeling paradigm could be utilized to aid in the selection of superior ligands or ligand compositions for the selective capture of metal ions. Furthermore, this first-principles integrated modeling approach opens the door to the in silico design of next-generation adsorbents with potentially superior efficiency and selectivity for uranium over vanadium in seawater.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Gaussian processes for autonomous data acquisition at large-scale synchrotron and neutron facilities

The execution and analysis of complex experiments are challenged by the vast dimensionality of the underlying parameter spaces. Although an increase in data-acquisition rates should allow broader querying of the parameter space, the complexity of experiments and the subtle dependence of the model function on input parameters remains daunting owing to the sheer number of variables. New strategies for autonomous data acquisition are being developed, with one promising direction being the use of Gaussian process regression (GPR). GPR is a quick, non-parametric and robust approximation and uncertainty quantification method that can be applied directly to autonomous data acquisition. We review GPR-driven autonomous experimentation and illustrate its functionality using real-world examples from large experimental facilities in the USA and France. We introduce the basics of a GPR-driven autonomous loop with a focus on Gaussian processes, and then shift the focus to the infrastructure that needs to be built around GPR to create a closed loop. Finally, the case studies we discuss show that Gaussian-process-based autonomous data acquisition is a widely applicable method that can facilitate the optimal use of instruments and facilities by enabling the efficient acquisition of high-value datasets.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Interaction energy and isosteric heat of adsorption between hydrogen and magnesium diboride

Hydrogen storage materials form a crucial research topic for future energy utilization employing hydrogen and among those of interest magnesium diboride (MgB 2 ) has shown its prevalence. In this study, a first-principles analytical adsorption model of one hydrogen molecule in the vicinity of various magnesium diboride crystal surfaces was developed in order to obtain surface thermodynamic properties as a function of molecular and lattice properties. Henry's law constant (K H ) and isosteric heat of adsorption (ΔH ads ) indicators of the affinity between a gaseous molecule and a solid surface are thus calculated. The results in this paper not only address questions pertaining to the first stage of hydrogen storage processes but also advance the understanding of physisorption thermodynamics of a neutral molecule (H 2 ) coming in contact with a layered metallic-like surface (MgB 2 ). Although the model is built from a framework of classical calculations, quantum effects are incorporated as the fractional charge of the ions on the free surfaces, which is essential for the calculation of analytic thermodynamic values that approximate calculations from other methods. To benchmark our theoretical models, periodic density functional calculations were performed to determine the interactions between H 2 and different MgB 2 surfaces from first-principles. By considering both the top and sublayers of MgB 2 in calculating interaction energy, we have analytically and computationally calculated the interaction energies of H 2 molecules and MgB 2 's terminated planes, and witnessed the strong dependence of interaction energies on surface charges. We have also observed a dipole flipping phenomenon which explains the discontinuity seen in the interaction energy graph of Mg(0001). Both analytical and computational results showed heat of adsorption at zero coverage varying at a very low range (<7 kJ mol -1 ).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Gas and dust dynamics in γ Cephei-type disks

Context. Giant planets are observed orbiting the primary stars of close binary systems. Such planets may have formed in compact circumprimary disks, which once surrounded these stars, under conditions much different than those encountered around single stars. Aims. In order to quantify the effects of the strong gravitational perturbations exerted on circumprimary disk material, the three-dimensional (3D) dynamics of gas and dust in orbit around the primary star of a compact and eccentric binary system was modeled by applying the stellar and orbital parameters of γ Cephei, a well-known system that can be representative of a class of close binaries. Methods. Circumprimary gas was approximated as an Eulerian viscous and compressible fluid and modeled by means of 3D hydrodynamical simulations, assuming locally isothermal conditions in the medium around the primary star. Dust grains were modeled as Lagrangean particles, subjected to gravity and aerodynamic drag forces. Models that include a giant planet were also considered. Results. Models indicate that spiral density waves excited around pericenter passage propagate toward the inner boundary of the disk, through at least a few pressure scale-heights from the mid-plane, inducing radial and vertical mixing in the gas. However, perturbations imparted to gas, both in terms of eccentricity and precession, are far weaker than previously estimated by two-dimensional (2D) simulations. Models predict small eccentricities, ≲0.03, and slow retrograde precession. The addition of a giant planet does not change the low eccentricity state of the disk. The parameters applied to the disk would lead to the formation of a massive planet, many times the mass of Jupiter, in agreement with some observations. Micron to mm-size dust grains are well coupled to the gas, resulting in similar dynamics and statistically similar distributions of orbital elements. The planet only affects the dust distributions locally. In agreement with outcomes of recent 2D models, the lifetime of an isolated circumprimary disk would be brief, ~10 5 years, because of its compact nature, requiring a long-term external supply of mass to allow for the in situ formation of a giant planet.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

The nonconforming Virtual Element Method for eigenvalue problems

In this work, we analyse the nonconforming Virtual Element Method (VEM) for the approximation of elliptic eigenvalue problems. The nonconforming VEM allows to treat in the same formulation the two- and three-dimensional case. We present two possible formulations of the discrete problem, derived respectively by the nonstabilized and stabilized approximation of the $L^2$-inner product, and we study the convergence properties of the corresponding discrete eigenvalue problem. The proposed schemes provide a correct approximation of the spectrum, in particular we prove optimal-order error estimates for the eigenfunctions and the usual double order of convergence of the eigenvalues. Finally we show a large set of numerical tests supporting the theoretical results, including a comparison with the conforming Virtual Element choice.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Modeling of Sandwich Sheets with Metallic Foam

World-wide vehicles safety experts agree that significant further reductions in fatalities and injuries can be achieved as a result of the use of new lightweight and energy absorbing materials. On this work, the authors present the development and evaluation of an innovative system able to perform reliable panels of sandwich sheets with metallic foam cores for industrial applications. The mathematical model used to describe the behavior of sandwich shells with metal cores foam is presented and some numerical examples are presented. In order to validate those results mechanical experiments are carried out. Using the crushable foam constitutive model, available on ABAQUS, a set of different mechanical tests were simulated. There are two variants of this model available on ABAQUS: the volumetric hardening model and the isotropic hardening model. As a first approximation we chose the isotropic hardening variant. The isotropic hardening model available uses a yield surface that is an ellipse centered at the origin in the p-q stress plane. Based on this constitutive model for the foam, numerical simulations of the tensile and bulge test will be conducted. The numerical results will be validated using the data obtained from the experimental results.

36 MATERIALS SCIENCE↗
DOE OSTI2011

Real-Valued Semigroups and (Causal) Diffusion

It can be shown that a process modeled by a strongly continuous real-valued semigroup (that has a space convolution operator as infinitesimal generator) cannot satisfy causality. By causality we mean that a characteristic feature of a process like an interface or a front must propagate with a finite speed. We present and discuss a causal model of diffusion that satisfies the semigroup property at a discrete set of time instants M:={l_brace}m{tau}|m is an element of N{sub 0}{r_brace} and that in contrast to the classical diffusion model is not smooth. More precisely, if v denotes the concentration of a substance diffusing with constant speed, then v is continuous but its time derivative is discontinuous at the discrete set M of time instants. It is this property of (causal) diffusion that forbids the classical limit procedure {tau}{yields}0 that leads to the noncausal diffusion model in Stochastics. Finally, we give two explanations why in some cases the discretization of the noncausal diffusion model can be considered as an approximation of the causal diffusion model. In particular, we present an inhomogeneous wave equation with a time dependent coefficient that is satisfied by causal diffusion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Electrons Emitted From Small Dust Grains: Comparison Of Sphere And Cube

Dust grains are exposed to high-energy electrons in different plasma environments. We have developed the numerical model that provides a description of the electron-solid (represented by grain surface) interaction. The model fits the experimental data from spherical samples of different materials rather well, however, dust grains in space are often edgy and coarse. Thus we extended grain geometry in the model to cubes as a first approximation of irregular surface.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2011

Self-Induced Oscillation for Electron-Hole Pair Confined in Quantum Dot

We study the time-dependent (TD) phenomena of the electron-hole or electron-electron pair confined in the square quantum dot (SQD) system by computationally solving TD Schroedinger equation under the unrestricted Hartree-Fock (UHF) approach. A typical vacillation is found both in the electron and hole when the charged pair is strongly confined in the SQD while the charged particles have initially the same orbital symmetry. The FFT analysis elucidates that the transition matrix element due to the coulomb interaction involves the eigen frequency {omega} being equal to the excitation energy when the resonative vacillation appears. Thus, Coulomb potential has a potential to cause the self-induced ''Rabi'' oscillation when the charged-particle pair is confined only in the QD.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗