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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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Long-run growth rate in a random multiplicative model

We consider the long-run growth rate of the average value of a random multiplicative process x{sub i+1} = a{sub i}x{sub i} where the multipliers a{sub i}=1+ρexp(σW{sub i}₋1/2 σ²t{sub i}) have Markovian dependence given by the exponential of a standard Brownian motion W{sub i}. The average value (x{sub n}) is given by the grand partition function of a one-dimensional lattice gas with two-body linear attractive interactions placed in a uniform field. We study the Lyapunov exponent λ=lim{sub n→∞}1/n log(x{sub n}), at fixed β=1/2 σ²t{sub n}n, and show that it is given by the equation of state of the lattice gas in thermodynamical equilibrium. The Lyapunov exponent has discontinuous partial derivatives along a curve in the (ρ, β) plane ending at a critical point (ρ{sub C}, β{sub C}) which is related to a phase transition in the equivalent lattice gas. Using the equivalence of the lattice gas with a bosonic system, we obtain the exact solution for the equation of state in the thermodynamical limit n → ∞.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Computational stochastic model of ions implantation

Implantation flux ions into crystal leads to phase transition /PT/ 1-st kind. Damaging lattice is associated with processes clustering vacancies and gaseous bubbles as well their brownian motion. System of stochastic differential equations /SDEs/ Ito for evolution stochastic dynamical variables corresponds to the superposition Wiener processes. The kinetic equations in partial derivatives /KE/, Kolmogorov-Feller and Einstein-Smolukhovskii, were formulated for nucleation into lattice of weakly soluble gases. According theory, coefficients of stochastic and kinetic equations uniquely related. Radiation stimulated phase transition are characterized by kinetic distribution functions /DFs/ of implanted clusters versus their sizes and depth of gas penetration into lattice. Macroscopic parameters of kinetics such as the porosity and stress calculated in thin layers metal/dielectric due to Xe{sup ++} irradiation are attracted as example. Predictions of porosity, important for validation accumulation stresses in surfaces, can be applied at restoring of objects the cultural heritage.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Local and linear chemical reactivity response functions at finite temperature in density functional theory

We explore the local and nonlocal response functions of the grand canonical potential density functional at nonzero temperature. In analogy to the zero-temperature treatment, local (e.g., the average electron density and the local softness) and nonlocal (e.g., the softness kernel) intrinsic response functions are defined as partial derivatives of the grand canonical potential with respect to its thermodynamic variables (i.e., the chemical potential of the electron reservoir and the external potential generated by the atomic nuclei). To define the local and nonlocal response functions of the electron density (e.g., the Fukui function, the linear density response function, and the dual descriptor), we differentiate with respect to the average electron number and the external potential. The well-known mathematical relationships between the intrinsic response functions and the electron-density responses are generalized to nonzero temperature, and we prove that in the zero-temperature limit, our results recover well-known identities from the density functional theory of chemical reactivity. Specific working equations and numerical results are provided for the 3-state ensemble model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Full-dimensional global potential energy surfaces describing abstraction and exchange for the H + H{sub 2}S reaction

For the H + H{sub 2}S system, ∼34 000 data points are sampled over a large configuration space including both abstraction and exchange channels, and calculated at the level of explicitly correlated unrestricted coupled cluster method with singles, doubles, and perturbative triples excitations with the augmented correlation-consistent polarized triple zeta basis set (UCCSD(T)-F12a/aug-cc-pVTZ). The data set was fit using the newly proposed permutation invariant polynomial-neural network (PIP-NN) method with three different vectors as the input: two redundant sets of PIPs, one with the maximum order four (PES-I) and one with the maximum order three (PES-II), and nine non-redundant PIPs (PES-III). All these PESs show small fitting errors and essentially the same performance in representing the title system. Various kinetics and dynamical properties are calculated using the tunneling corrected transition state theory and quasi-classical trajectory, and compared with available experimental results. At a collision energy of 10 kcal/mol, both the H{sub 2} and SH products are found to be internally cold, with ∼20% of H{sub 2} at its first vibrational excited state, while SH is essentially a spectator. The angular distributions of the products are mainly in backward with considerable contributions from sideway direction. In addition, analytical partial derivatives of any PIP-NN PES with respect to the coordinates of atoms are derived by making use of the monomial symmetrization algorithm [Z. Xie and J. M. Bowman, J. Chem. Theory Comput. 6, 26–34 (2010)]. It can not only accelerate the evaluation of the derivatives, but also improve the energy convergence significantly.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Features in simulation of crystal growth using the hyperbolic PFC equation and the dependence of the numerical solution on the parameters of the computational grid

We investigate the three-dimensional mathematical model of crystal growth called PFC (Phase Field Crystal) in a hyperbolic modification. This model is also called the modified model PFC (originally PFC model is formulated in parabolic form) and allows to describe both slow and rapid crystallization processes on atomic length scales and on diffusive time scales. Modified PFC model is described by the differential equation in partial derivatives of the sixth order in space and second order in time. The solution of this equation is possible only by numerical methods. Previously, authors created the software package for the solution of the Phase Field Crystal problem, based on the method of isogeometric analysis (IGA) and PetIGA program library. During further investigation it was found that the quality of the solution can strongly depends on the discretization parameters of a numerical method. In this report, we show the features that should be taken into account during constructing the computational grid for the numerical simulation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

On the mechanism of ionization oscillations in Hall thrusters

Low-frequency ionization oscillations involving plasma and neutral density (breathing modes) are the most violent perturbations in Hall thrusters for electric propulsion. Because of its simplicity, the zero-dimensional (0D) predator–prey model of two nonlinearly coupled ordinary differential equations for plasma and neutral density has often been used for the characterization of such oscillations and scaling estimates. In this work, we investigate the properties of its continuum analog, the one-dimensional (1D) system of two nonlinearly coupled equations in partial derivatives (PDEs) for plasma and neutral density. This is a more general model, of which the standard 0D predator–prey model is a special limit case. We show that the 1D model is stable and does not show any oscillations for the boundary conditions relevant to Hall thrusters and the uniform ion velocity. We then propose a reduced 1D model based on two coupled PDEs for plasma and neutral densities that is unstable and exhibit oscillations if the ion velocity profile with the near-the-anode back-flow (toward the anode) region is used. Comparisons of the reduced model with the predictions of the full model that takes into account the self-consistent plasma response show that the main properties of the breathing mode are well captured. In particular, it is shown that the frequency of the breathing mode oscillations is weakly dependent on the final ion velocity but shows a strong correlation with the width of the ion back-flow region.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Anomalous temperature dependence of the experimental x-ray structure factor of supercooled water

The structural changes of water upon deep supercooling were studied through wide-angle x-ray scattering at SwissFEL. The experimental setup had a momentum transfer range of 4.5 Å-1, which covered the principal doublet of the x-ray structure factor of water. The oxygen–oxygen structure factor was obtained for temperatures down to 228.5 ± 0.6 K. Similar to previous studies, the second diffraction peak increased strongly in amplitude as the structural change accelerated toward a local tetrahedral structure upon deep supercooling. We also observed an anomalous trend for the second peak position of the oxygen–oxygen structure factor (q 2 ). We found that q 2 exhibits an unprecedented positive partial derivative with respect to temperature for temperatures below 236 K. Based on Fourier inversion of our experimental data combined with reference data, we propose that the anomalous q 2 shift originates from that a repeat spacing in the tetrahedral network, associated with all peaks in the oxygen–oxygen pair-correlation function, gives rise to a less dense local ordering that resembles that of low-density amorphous ice. The findings are consistent with that liquid water consists of a pentamer-based hydrogen-bonded network with low density upon deep supercooling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Approximating accelerator impedances with resonator networks

It is common in the accelerator community to use the impedance of accelerator components to describe wake interactions in the frequency domain. However, it is often desirable to understand such wake interactions in the time domain in a general manner for excitations that are not necessarily Gaussian in nature. Here, the conventional method for doing this involves taking the inverse Fourier Transform of the component impedance, obtaining the Green's Function, and then convolving it with the desired excitation distribution. This method can prove numerically cumbersome, for a convolution integral must be evaluated for each individual point in time when the wake function is desired. An alternative to this method would be to compute the wake function analytically, which would sidestep the need for repetitive integration. Only a handful of cases, however, are simple enough for this method to be tenable. One of these cases is the case where the component in question is an RLC resonator, which has a closed-form analytical wake function solution. This means that a component which can be represented in terms of resonators can leverage this solution. As it happens, common network synthesis techniques may be used to map arbitrary impedance profiles to RLC resonator networks in a manner the accelerator community has yet to take advantage of. In this work, we will use Foster Canonical Resonator Networks and partial derivative descent optimization to develop a technique for synthesizing resonator networks that well approximate the impedances of real-world accelerator components. We will link this synthesis to the closed-form resonator wake function solution, giving rise to a powerful workflow that may be used to streamline beam dynamics simulations.

43 PARTICLE ACCELERATORS↗
DOE OSTI2017

Global seismic attenuation imaging using full-waveform inversion: a comparative assessment of different choices of misfit functionals

We present the results of synthetic tests that aim at evaluating the relative performance of three different definitions of misfit functionals in the context of 3-D imaging of shear wave attenuation in the earth’s upper mantle at the global scale, using long-period full-waveform data. The synthetic tests are conducted with simple hypothetical upper-mantle models that contain Q μ anomalies centred at different depths and locations, with or without additional seismic velocity anomalies. To build synthetic waveform data sets, we performed simulations of 50 events in the hypothetical (target) models, using the spectral element method, filtered in the period range 60–400 s. The selected events are chosen among 273 events used in the development of radially anisotropic model SEMUCB-WM1 and recorded at 495 stations worldwide. The synthetic Z-component waveforms correspond to paths and time intervals (fundamental mode and overtone Rayleigh waves) that exist in the real waveform data set. The inversions for shear attenuation structure are carried out using a Gauss–Newton optimization scheme in which the gradient and Hessian are computed using normal mode perturbation theory. The three different misfit functionals considered are based on time domain waveform (WF) and waveform envelope (E-WF) differences, as well as spectral amplitude ratios (SA), between observed and predicted waveforms. We evaluate the performance of the three misfit functional definitions in the presence of seismic noise and unresolved S-wave velocity heterogeneity and discuss the relative importance of physical dispersion effects due to 3-D Q μ structure. We observed that the performance of WF is poorer than the other two misfit functionals in recovering attenuation structure, unless anelastic dispersion effects are taken into account in the calculation of partial derivatives. WF also turns out to be more sensitive to seismic noise than E-WF and SA. Overall, SA performs best for attenuation imaging. Our tests show that it is important to account for 3-D elastic effects (focusing) before inverting for Q μ . Additionally, we show that including high signal-to-noise ratio overtone wave packets is necessary to resolve Q μ structure at depths greater than 250 km.

58 GEOSCIENCES↗
DOE OSTI2019

Eruptive Activity on the Western Flank of Piton de la Fournaise (La Réunion Island, Indian Ocean): Insights on Magma Transfer, Storage and Evolution at an Oceanic Volcanic Island

Abstract Petrological and geochemical (major element, trace element, Sr–Nd isotope) data for recent (<5 kyr old) basalts that sporadically erupt on the western flank of Piton de la Fournaise (PdF), one of the most active volcanoes on Earth, allow the tracking of magma transfer and evolution from mantle to crustal depths. In the western peripheral area of PdF we document the broadly synchronous eruptions of (1) primitive olivine and olivine–clinopyroxene transitional basalts with tholeiitic affinity that are closely associated in space with (2) transitional olivine basalts with alkaline affinity, and (3) hybrid lavas, intermediate between the ‘alkaline’ and the ‘tholeiitic’ end-members. The composition of the latter overlaps with that of the lavas frequently erupted from the conduit system feeding the main summit cone. AlphaMELTS modelling, and fluid inclusion and clinopyroxene barometry, constrain the conditions of magma storage at 10–30 km, and the ascent of magma from the upper mantle to the shallow crustal plumbing system. Variable degrees of mantle melting, together with minor source heterogeneity and contamination with cumulate-derived partial melts, contribute to the diversity of PdF magmas. However, all these processes do not represent the dominant factors that produce the large variability we found in major element composition. Indeed, the composition of basalts erupted from PdF peripheral centers is strongly controlled by polybaric olivine–clinopyroxene fractionation at pressures higher than 3 kbar. Crystal textures and geochemical modelling suggest that fast magma ascent is critical to prevent clinopyroxene dissolution. Conversely, long-lasting magma stagnation promotes pyroxene resorption and magma differentiation. ‘Central’ eruptions occurring close to the PdF summit cone emit variably more evolved melts, which result from olivine–clinopyroxene–plagioclase differentiation at intermediate–shallow pressure (<3 kbar and in most cases <1 kbar). Deep and extensive magma mixing before injection into the crustal magma conduit system, located below the summit region, results in the apparent homogeneity of basalts erupted from the central area. As regards ‘peripheral’ eruptions, deep-seated stagnation of basaltic melts and differentiation at the mantle–crust transition zone (c. 4 kbar) produces a range of magma compositions. We demonstrate that rapid magma ascent from deep-seated reservoirs can bypass the central plumbing system. The eruptions of these magmas both in the central area and on the densely populated flanks have major consequences in terms of volcanic hazard at PdF.

Boudoire, G.↗
DOE OSTI2024

Random coordinate descent: A simple alternative for optimizing parameterized quantum circuits

Variational quantum algorithms rely on the optimization of parameterized quantum circuits in noisy settings. The commonly used back-propagation procedure in classical machine learning is not directly applicable in this setting due to the collapse of quantum states after measurements. Thus, gradient estimations constitute a significant overhead in a gradient-based optimization of such quantum circuits. This paper introduces a random coordinate descent algorithm as a practical and easy-to-implement alternative to the full gradient descent algorithm. This algorithm only requires one partial derivative at each iteration. Motivated by the behavior of measurement noise in the practical optimization of parameterized quantum circuits, this paper presents an optimization problem setting that is amenable to analysis. Under this setting, the random coordinate descent algorithm exhibits the same level of stochastic stability as the full gradient approach, making it as resilient to noise. The complexity of the random coordinate descent method is generally no worse than that of the gradient descent and can be much better for various quantum optimization problems with anisotropic Lipschitz constants. Theoretical analysis and extensive numerical experiments validate our findings. Published by the American Physical Society 2024

Ding, Zhiyan (ORCID:000000018863403X)↗
DOE OSTI2024

A simple solution to the Rietveld refinement recipe problem

Rietveld refinements are widely used for many purposes in the physical sciences. Conducting a Rietveld refinement typically requires expert input because correct results may require that parameters be added to the fit in the proper order. This order will depend on the nature of the data and the initial parameter values. A mechanism for computing the next parameter to add to the refinement is shown. The fitting function is evaluated with the current parameter value set and each parameter incremented and decremented by a small offset. This provides the partial derivatives with respect to each parameter, along with information to discriminate meaningful values from numerical computational errors. The implementation of this mechanism in the open-source GSAS-II program is discussed. This new method is discussed as an important step towards the development of automated Rietveld refinement technology.

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

Temperature-dependent spectral mismatch corrections

This study develops the mathematical foundation for a translation of solar cell short-circuit current from one thermal and spectral irradiance operating condition to another without the use of ill-defined and error-prone temperature coefficients typically employed in solar cell metrology. Using the partial derivative of quantum efficiency with respect to temperature, the conventional isothermal expression for spectral mismatch corrections is modified to account for changes of current due to temperature; this modification completely eliminates the need for short-circuit-current temperature coefficients. An example calculation is provided to demonstrate use of the new translation.

14 SOLAR ENERGY↗
DOE OSTI2019

Topology Inference of Unknown Networks Based on Robust Virtual Coordinate Systems

Learning and exploring the connectivity of unknown networks represent an important problem in practical applications of communication networks and social-media networks. Modeling large-scale networks as connected graphs is highly desirable to extract their connectivity information among nodes to visualize network topology, disseminate data, and improve routing efficiency. This paper investigates a simple measurement model in which a small subset of source nodes collect hop distance information from networked nodes in order to generate a virtual coordinate system (VCS) for networks of unknown topology. We establish the VCS to define logical distance among nodes based on principal component analysis and to determine connectivity relationship and effective routing methods. More importantly, we present a robust analytical algorithm to derive the VCS against practical issues of missing and corrupted measurements. We also develop a connectivity inference method which classifies nodes into layers based on the hop distances and derives partial information on network connectivity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Analytic error analysis of cross section interpolation methods in nodal diffusion codes - II: Numerical results

This paper is the second part of a two-part paper that documents the numerical results for the partial derivatives model presented in part I. In this paper, we derive the error bounds for the analytical point-wise error expression and verify our bounds with numerical experiments. The point-wise error expressions make available, and bound, the sources that contribute to the total error of the interpolated cross section in terms of the Lagrange interpolation errors and the model form error. MPACT is used to generate two-group homogenized cross sections for Westinghouse's AP1000 Region 4 lattice to evaluate the accuracy of the bounds. Error bounds calculated over a grid are compared to numerical data for uni-variate and multi-variate interpolation. The point-wise error bounds of a typical case matrix - two branches in each state variable - are displayed for bi-variate interpolation in the state variables: moderator density, fuel temperature, and boron concentration. The error bounds are shown to be highly accurate compared to numerical results, and in accordance with the underlying physics. We then discuss and show how the sources of error contribute to the total error, and consider the improvement of each error source. Finally, we mention future work such as propagating our cross section error bounds through a reactivity calculation. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2019

Application of symmetries to differential equations: symmetry reduction and solution transformation examples

In the following lecture notes, we provide an outline of what we mean by symmetries of differential equations and illustrate their utility in simplification of differential equations which may lead to solutions. Loosely, a symmetry of a differential equation is a local group of transformations acting on the space of independent and dependent variables that transform solutions of a differential equation to new solutions, i.e., if Δ(x,u,p)=0 denotes a differential equation with a solution prescribed by [x,u,p], then knowlege of a symmetry facilitates the attainment of a new solution, [$\tilde{x}$, $\tilde{u}$, $\tilde{p}$], such that Δ(x,u,p)=Δ($\tilde{x}$, $\tilde{u}$, $\tilde{p}$)=0. In Equations (1) and (2), x, u and p denote the independent variables, dependent variables and partial derivatives, respectively and the tildes denote the transformations. Equation (2) will subsequently be referred to as the symmetry criterion. We can apply the knowlede of the existence of a symmetry in two ways: 1) If not solution is known apriori, the symmetry can be applied to simplify the differential equation through the method of symmetry reduction. Often, the resultant simplification may enable a solution to be determined; 2) If we already possess a solution to a different equation, knowledge of an admissible symmetry enables us to generate new solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

An Adaptive Optimizer for Measurement-Frugal Variational Algorithms

Variational hybrid quantum-classical algorithms (VHQCAs) have the potential to be useful in the era of near-term quantum computing. However, recently there has been concern regarding the number of measurements needed for convergence of VHQCAs. Here, we address this concern by investigating the classical optimizer in VHQCAs. We introduce a novel optimizer called individual Coupled Adaptive Number of Shots (iCANS). This adaptive optimizer frugally selects the number of measurements (i.e., number of shots) both for a given iteration and for a given partial derivative in a stochastic gradient descent. We numerically simulate the performance of iCANS for the variational quantum eigensolver and for variational quantum compiling, with and without noise. In all cases, and especially in the noisy case, iCANS tends to out-perform state-of-the-art optimizers for VHQCAs. We therefore believe this adaptive optimizer will be useful for realistic VHQCA implementations, where the number of measurements is limited.

97 MATHEMATICS AND COMPUTING↗