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DOE OSTI2022

Augmented Adam-Gibbs model for glass melt viscosity and configuration entropy as functions of temperature and composition

As the temperature of glass melt increases, its structure approaches the state of a simple liquid while the configuration entropy approaches a maximum value. We describe this gradual change using a power law function of inverse temperature. The Adam-Gibbs model for glass viscosity as a function of temperature and glass composition augmented in this way is greatly simplified when applied to common glass families occupying moderate composition regions, such as float glass or nuclear waste glasses, on which properties can be approximated as linear functions of composition. The parsimonious model thus obtained is preferable for use in optimizing glass formulation and mathematical modeling of glass melting and forming. For multicomponent glasses with N viscosity-affecting components, the augmented Adam-Gibbs model requires 2N + 3 adjustable parameters. The model efficacy is demonstrated by fitting the model to a viscosity-temperature-composition dataset for low-activity nuclear waste glasses.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1999

Improving the Accuracy of Quadrature Method Solutions of Fredholm Integral Equations that Arise from Nonlinear Two-Point Boundary Value Problems

In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + integral(0 to 1) g(x,t) F(t, y(t)) dt, 0 less than or equal to x less than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integrals equations arise, e.g., when one applies Green's function techniques to nonlinear two-point boundary value problems of the form U''(x) = f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and g(l) = y(sub 1), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trapezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.

Sidi, Avram↗

DOE OSTI2024

Extracting Higher Central Charge from a Single Wave Function

A (2+1)D topologically ordered phase may or may not have a gappable edge, even if its chiral central charge c_ is vanishing. Recently, it was discovered that a quantity regarded as a "higher" version of chiral central charge gives a further obstruction beyond c_ to gapping out the edge. Here, in this Letter, we show that the higher central charges can be characterized by the expectation value of the partial rotation operator acting on the wave function of the topologically ordered state. This allows us to extract the higher central charge from a single wave function, which can be evaluated on a quantum computer. Our characterization of the higher central charge is analytically derived from the modular properties of edge conformal field theory, as well as the numerical results with the ν = 1/2 bosonic Laughlin state and the non-Abelian gapped phase of the Kitaev honeycomb model, which corresponds to U(1) 2 and Ising topological order, respectively. The Letter establishes a numerical method to obtain a set of obstructions to the gappable edge of (2+1)D bosonic topological order beyond c_, which enables us to completely determine if a (2+1)D bosonic Abelian topological order has a gappable edge or not. We also point out that the expectation values of the partial rotation on a single wave function put a constraint on the low-energy spectrum of the bulk-boundary system of (2+1)D bosonic topological order, reminiscent of the Lieb-Schultz-Mattis-type theorems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Density functional modeling of the binding energies between aluminosilicate oligomers and different metal cations

Interactions between negatively charged aluminosilicate species and positively charged metal cations are critical to many important engineering processes and applications, including sustainable cements and aluminosilicate glasses. In an effort to probe these interactions, here we have calculated the pair-wise interaction energies (i.e., binding energies) between aluminosilicate dimer/trimer and 17 different metal cations M n+ (M n+ = Li + , Na + , K + , Cu + , Cu 2+ , Co 2+ , Zn 2+ , Ni 2+ , Mg 2+ , Ca 2+ , Ti 2+ , Fe 2+ , Fe 3+ , Co 3+ , Cr 3+ , Ti 4+ and Cr 6+ ) using a density functional theory (DFT) approach. Analysis of the DFT-optimized structural representations for the clusters (dimer/trimer + M n+ ) shows that their structural attributes (e.g., interatomic distances) are generally consistent with literature observations on aluminosilicate glasses. The DFT-derived binding energies are seen to vary considerably depending on the type of cations (i.e., charge and ionic radii) and aluminosilicate species (i.e., dimer or trimer). A survey of the literature reveals that the difference in the calculated binding energies between different M n+ can be used to explain many literature observations associated with the impact of metal cations on materials properties (e.g., glass corrosion, mineral dissolution, and ionic transport). Analysis of all the DFT-derived binding energies reveals that the correlation between these energy values and the ionic potential and field strength of the metal cations are well captured by 2nd order polynomial functions ( R 2 values of 0.99–1.00 are achieved for regressions). Given that the ionic potential and field strength of a given metal cation can be readily estimated using well-tabulated ionic radii available in the literature, these simple polynomial functions would enable rapid estimation of the binding energies of a much wider range of cations with the aluminosilicate dimer/trimer, providing guidance on the design and optimization of sustainable cements and aluminosilicate glasses and their associated applications. Finally, the limitations associated with using these simple model systems to model complex interactions are also discussed.

Gong, Kai↗

DOE OSTI2020

Investigation into the event-activity dependence of $\Upsilon$(nS) relative production in proton-proton collisions at $ \sqrt{s} $ = 7 TeV

The ratios of the production cross sections between the excited ϒ(2S) and ϒ(3S) mesons and the ϒ(1S) ground state, detected via their decay into two muons, are studied as a function of the number of charged particles in the event. The data are from proton-proton collisions at $ \sqrt{s} $ = 7 TeV, corresponding to an integrated luminosity of 4.8 fb$^{−1}$, collected with the CMS detector at the LHC. Evidence of a decrease in these ratios as a function of the particle multiplicity is observed, more pronounced at low transverse momentum $ {p}_{\mathrm{T}}^{\upmu \upmu} $. For ϒ(nS) mesons with $ {p}_{\mathrm{T}}^{\upmu \upmu} $> 7 GeV, where most of the data were collected, the correlation with multiplicity is studied as a function of the underlying event transverse sphericity and the number of particles in a cone around the ϒ(nS) direction. The ratios are found to be multiplicity independent for jet-like events. The mean $ {p}_{\mathrm{T}}^{\upmu \upmu} $ values for the ϒ(nS) states as a function of particle multiplicity are also measured and found to grow more steeply as their mass increases.[graphic not available: see fulltext]

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1999

Generalized Functions for the Fractional Calculus

Previous papers have used two important functions for the solution of fractional order differential equations, the Mittag-Leffler functionE(sub q)[at(exp q)](1903a, 1903b, 1905), and the F-function F(sub q)[a,t] of Hartley & Lorenzo (1998). These functions provided direct solution and important understanding for the fundamental linear fractional order differential equation and for the related initial value problem (Hartley and Lorenzo, 1999). This paper examines related functions and their Laplace transforms. Presented for consideration are two generalized functions, the R-function and the G-function, useful in analysis and as a basis for computation in the fractional calculus. The R-function is unique in that it contains all of the derivatives and integrals of the F-function. The R-function also returns itself on qth order differ-integration. An example application of the R-function is provided. A further generalization of the R-function, called the G-function brings in the effects of repeated and partially repeated fractional poles.

Lorenzo, Carl F.↗

NASA NTRS1997

Interactions between integrin receptors and fibronectin are required for calvarial osteoblast differentiation in vitro

We previously showed that anti-fibronectin antibodies or soluble fibronectin fragments containing the central cell-binding domain inhibit formation of mineralized nodules by fetal calvarial osteoblasts in vitro. These findings suggest a critical role for fibronectin in osteoblast differentiation and morphogenesis. In this study we tested the hypothesis that fibronectin's effects on osteogenesis are mediated via direct interactions with integrin receptors for fibronectin on osteoblasts. Immunocytochemical analysis identified the integrin fibronectin receptor alpha5ss1 in fetal rat calvarial tissue and in cultured osteoblasts at all stages of differentiation. Three other integrins, alpha3ss1, alpha8ss1 and alphavss3, which can bind fibronectin, as well as other matrix components, were also identified in tissue and at all stages of cell culture. Immunoprecipitation data showed that alpha5ss1 levels are constant throughout osteoblast differentiation whereas levels of alpha3ss1 and alpha8ss1 decline in mature mineralized cultures. To determine whether integrin fibronectin receptors are required for osteoblast formation of mineralized nodules, we examined the extent of nodule formation in the presence and absence of function-perturbing anti-integrin antibodies. The antibodies were present continuously in cultures beginning at confluence (day 3), and nodule formation was measured at days 10 and 20. An anti-alpha5 integrin subunit antibody reduced nodule formation to less than 5% of control values at both time points. Inhibition of nodule formation was reversible and did not affect cell attachment and viability. Function-perturbing antibodies against alpha3ss1 and alpha8ss1 also reduced nodule formation, to less than 20% of control values. In contrast, function-perturbing antibodies to alphavss3 and alphavss5 did not affect nodule formation, indicating that the inhibitions noted were indeed specific. To determine the effect of antibody treatment on gene expression, steady-state mRNA expression was examined and found to be suppressed for osteoblast markers alkaline phosphatase and osteocalcin. Together, these results indicate that direct osteoblast interactions with the extracellular matrix are mediated by a select group of integrin receptors that includes alpha5ss1, alpha3ss1 and alpha8ss1. We further conclude that the specific alpha5ss1 fibronectin receptor mediates critical interactions between osteoblasts and fibronectin required for both bone morphogenesis and osteoblast differentiation.

NASA Center ARC↗

DOE OSTI2019

FATES Parameters and Output for Parameter Sensitivity at the Panama Barro Colorado Island Testbed

This data package contains a set of Functionally Assembled Terrestrial Ecosystem Simulator (FATES) history files and parameter values for the set of model simulations used in Koven et al. Manuscript "Benchmarking and Parameter Sensitivity of Physiological and Vegetation Dynamics using the Functionally Assembled Terrestrial Ecosystem Simulator (FATES) at Barro Colorado Island, Panama." It includes several ensembles of FATES runs, where each ensemble is comprised of a set of 576 runs that have different values of PFT traits. The ensembles include 1 PFT, 2 PFT, 3 PFT, and 10 PFT simulations. Different ensembles also have different values of disturbance and height sorting parameters, and structural differences including running FATES within different LSMs.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1999

Improving the Accuracy of Quadrature Method Solutions of Fredholm Integral Equations That Arise from Nonlinear Two-Point Boundary Value Problems

In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + definite integral of g(x, t)F(t,y(t))dt with limits between 0 and 1,0 less than or equal to x les than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integral equations arise, e.g., when one applied Green's function techniques to nonlinear two-point boundary value problems of the form y "(x) =f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and y(l) = y(sub l), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trepezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal rule, thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.

Sidi, Avram↗

NASA NTRS1972

On optimizing the treatment of exchange perturbations.

Most theories of exchange perturbations would give the exact energy and wave function if carried out to an infinite order. However, the different methods give different values for the second-order energy, and different values for E(1), the expectation value of the Hamiltonian corresponding to the zeroth- plus first-order wave function. In the presented paper, it is shown that the zeroth- plus first-order wave function obtained by optimizing the basic equation which is used in most exchange perturbation treatments is the exact wave function for the perturbation system and E(1) is the exact energy.

Hirschfelder, J. O.↗

NASA NTRS1995

Uncertainties for two-dimensional models of solar rotation from helioseismic eigenfrequency splitting

Observed solar p-mode frequency splittings can be used to estimate angular velocity as a function of position in the solar interior. Formal uncertainties of such estimates depend on the method of estimation (e.g., least-squares), the distribution of errors in the observations, and the parameterization imposed on the angular velocity. We obtain lower bounds on the uncertainties that do not depend on the method of estimation; the bounds depend on an assumed parameterization, but the fact that they are lower bounds for the 'true' uncertainty does not. Ninety-five percent confidence intervals for estimates of the angular velocity from 1986 Big Bear Solar Observatory (BBSO) data, based on a 3659 element tensor-product cubic-spline parameterization, are everywhere wider than 120 nHz, and exceed 60,000 nHz near the core. When compared with estimates of the solar rotation, these bounds reveal that useful inferences based on pointwise estimates of the angular velocity using 1986 BBSO splitting data are not feasible over most of the Sun's volume. The discouraging size of the uncertainties is due principally to the fact that helioseismic measurements are insensitive to changes in the angular velocity at individual points, so estimates of point values based on splittings are extremely uncertain. Functionals that measure distributed 'smooth' properties are, in general, better constrained than estimates of the rotation at a point. For example, the uncertainties in estimated differences of average rotation between adjacent blocks of about 0.001 solar volumes across the base of the convective zone are much smaller, and one of several estimated differences we compute appears significant at the 95% level.

Genovese, Christopher R.↗

NASA NTRS1993

FNAS computational modeling

Numerical calculations of the electronic properties of liquid II-VI semiconductors, particularly CdTe and ZnTe were performed. The measured conductivity of these liquid alloys were modeled by assuming that the dominant temperature effect is the increase in the number of dangling bonds with increasing temperature. For low to moderate values of electron correlation, the calculated conductivity as a function of dangling bond concentration closely follows the measured conductivity as a function of temperature. Both the temperature dependence of the chemical potential and the thermal smearing in region of the Fermi surface have a large effect on calculated values of conductivity.

Franz, J. R.↗

DOE OSTI2020

Kinetic Modeling and Experimental Studies of Capacitively Coupled Macro- and Microplasmas at Microwave Frequencies

The effect of driving frequency in the range of 13.56 MHz to 73 MHz on electron energy distribution and electron heating modes in a 50 mTorr capacitively coupled argon plasma discharge is studied using 1D-3V particle-in-cell simulations. Calculated electron energy probability functions exhibit three distinct temperatures for low-, mid-, and high-energy electrons at all the studied driving frequencies. When compared to published experimental data, the calculated probability functions show a reasonable agreement for the energy range resolved in the measurements (about 2 eV to 10 eV). Discrepancies due to limitations in experimental energy resolution outside this range lead to differences between computational and experimental values of the electron number density determined from the distribution functions, and the predicted effective electron temperature is within 25 % of experimental values. The impedance of the discharge is interpreted in terms of a homogeneous equivalent circuit model and the driving frequency dependence of the inferred combined sheath thickness is found to obey a known, theoretically-derived, power law. The average power transferred from the field to the electrons (electron heating) is computed, and a region of negative heating near the sheath edge, particularly at higher driving frequencies, is identified. Analysis of the electron momentum equation shows that electron inertia, which on temporal averaging would be zero in a linear regime, is responsible for negative values of power deposition near the sheath edge at high driving frequencies due to the highly nonlinear behavior of the discharge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2015

Development and Characterization of a Rate-Dependent Three-Dimensional Macroscopic Plasticity Model Suitable for Use in Composite Impact Problems

Several key capabilities have been identified by the aerospace community as lacking in the material/models for composite materials currently available within commercial transient dynamic finite element codes such as LS-DYNA. Some of the specific desired features that have been identified include the incorporation of both plasticity and damage within the material model, the capability of using the material model to analyze the response of both three-dimensional solid elements and two dimensional shell elements, and the ability to simulate the response of composites composed with a variety of composite architectures, including laminates, weaves and braids. In addition, a need has been expressed to have a material model that utilizes tabulated experimentally based input to define the evolution of plasticity and damage as opposed to utilizing discrete input parameters (such as modulus and strength) and analytical functions based on curve fitting. To begin to address these needs, an orthotropic macroscopic plasticity based model suitable for implementation within LS-DYNA has been developed. Specifically, the Tsai-Wu composite failure model has been generalized and extended to a strain-hardening based orthotropic plasticity model with a non-associative flow rule. The coefficients in the yield function are determined based on tabulated stress-strain curves in the various normal and shear directions, along with selected off-axis curves. Incorporating rate dependence into the yield function is achieved by using a series of tabluated input curves, each at a different constant strain rate. The non-associative flow-rule is used to compute the evolution of the effective plastic strain. Systematic procedures have been developed to determine the values of the various coefficients in the yield function and the flow rule based on the tabulated input data. An algorithm based on the radial return method has been developed to facilitate the numerical implementation of the material model. The presented paper will present in detail the development of the orthotropic plasticity model and the procedures used to obtain the required material parameters. Methods in which a combination of actual testing and selective numerical testing can be combined to yield the appropriate input data for the model will be described. A specific laminated polymer matrix composite will be examined to demonstrate the application of the model.

Impact↗

DOE OSTI2020

Accurate determination of production data of the non-standard positron emitter 86 Y via the 86 Sr(p,n)-reaction

In view of several significant discrepancies in the excitation function of the 86 Sr(p,n) 86g+xm Y reaction which is the method of choice for the production of the non-standard positron emitter 86 Y for theranostic application, we carried out a careful measurement of the cross sections of this reaction from its threshold up to 16.2 MeV at Forschungszentrum Jülich (FZJ) and from 14.3 to 24.5 MeV at LBNL. Thin samples of 96.4% enriched 86 SrCO 3 were prepared by sedimentation and, after irradiation with protons in a stacked-form, the induced radioactivity was measured by high-resolution γ -ray spectrometry. The projectile flux was determined by using the monitor reactions nat Cu(p,xn) 62,63,65 Zn and nat Ti(p,x) 48 V, and the calculated proton energy for each sample was verified by considering the ratios of two reaction products of different thresholds. Additionally, the experimental cross section data obtained agreed well with the results of a nuclear model calculation based on the code TALYS. From the cross section data, the integral yield of 86 Y was calculated. Over the optimum production energy range E p = 14 → 7 MeV the yield of 86 Y amounts to 291 MBq/μA for 1 h irradiation time. This value is appreciably lower than the previous literature values calculated from measured and evaluated excitation functions. It is, however, more compatible with the experimental yields of 86 Y obtained in clinical scale production runs. The levels of the isotopic impurities 87m Y, 87g Y, and 88 Y were also estimated and found to be <2% in sum.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

NASA NTRS2003

Theory of Collective Intelligence

In this chapter an analysis of the behavior of an arbitrary (perhaps massive) collective of computational processes in terms of an associated "world" utility function is presented We concentrate on the situation where each process in the collective can be viewed as though it were striving to maximize its own private utility function. For such situations the central design issue is how to initialize/update the collective's structure, and in particular the private utility functions, so as to induce the overall collective to behave in a way that has large values of the world utility. Traditional "team game" approaches to this problem simply set each private utility function equal to the world utility function. The "Collective Intelligence" (COIN) framework is a semi-formal set of heuristics that recently have been used to construct private utility. functions that in many experiments have resulted in world utility values up to orders of magnitude superior to that ensuing from use of the team game utility. In this paper we introduce a formal mathematics for analyzing and designing collectives. We also use this mathematics to suggest new private utilities that should outperform the COIN heuristics in certain kinds of domains. In accompanying work we use that mathematics to explain previous experimental results concerning the superiority of COIN heuristics. In that accompanying work we also use the mathematics to make numerical predictions, some of which we then test. In this way these two papers establish the study of collectives as a proper science, involving theory, explanation of old experiments, prediction concerning new experiments, and engineering insights.

Nash equilibrium↗

NASA NTRS1978

TNT equivalency of M10 propellant

Peak, side-on blast overpressure and scaled, positive impulse have been measured for M10 single-perforated propellant, web size 0.018 inches, using configurations that simulate the handling of bulk material during processing and shipment. Quantities of 11.34, 22.7, 45.4, and 65.8 kg were tested in orthorhombic shipping containers and fiberboard boxes. High explosive equivalency values for each test series were obtained as a function of scaled distance by comparison to known pressure, arrival time and impulse characteristics for hemispherical TNT surface bursts. The equivalencies were found to depend significantly on scaled distance, with higher values of 150-100 percent (pressure) and 350-125 percent (positive impulse) for the extremes within the range from 1.19 to 3.57 m/cube root of kg. Equivalencies as low as 60-140 percent (pressure) and 30-75 percent (positive impulse) were obtained in the range of 7.14 to 15.8 m/cube root of kg. Within experimental error, both peak pressure and positive impulse scaled as a function of charge weight for all quantities tested in the orthorhombic configuration.

Mcintyre, F. L.↗

DOE OSTI2020

Computational Evaluation of Carriers in Facilitated Transport Membranes for Postcombustion Carbon Capture

Incorporating molecular amines as mobile carriers in facilitated transport membranes (FTMs) has been demonstrated to significantly enhance the CO 2 permeance and CO 2 /N 2 selectivity of the membrane for CO 2 capture from flue gas. In this study, by employing computational techniques including density functional theory calculations and molecular simulations, the role of mobile carriers has been systematically studied at a molecular level from the perspectives of the amine–CO 2 reaction chemistry, diffusivities of carriers and gases, and N 2 solubility. The latter two properties were also investigated as a function of water uptake. The water uptake values of FTMs were experimentally quantified too. The introduction of mobile carriers was shown to substantially enhance the diffusivities of CO 2 reaction products compared to FTMs without mobile carriers. The choice of mobile carriers was also demonstrated to influence the separation performance. Computationally, 2-(1-piperazinyl)ethylamine sarcosinate (PZEA-Sar) exhibited a faster reaction kinetics and slightly higher CO 2 absorption capacity as compared to piperazine glycinate (PZ-Gly). Experimentally, the FTM incorporating PZEA-Sar mobile carriers also showed a higher CO 2 permeance. The good agreement validated the computational models employed and insights generated in this study. In conclusion, the outcomes of this work shed light on the future design and selection of carrier structures, and the adopted computational approaches can be employed to discover promising mobile carrier candidates.

20 FOSSIL-FUELED POWER PLANTS↗