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DOE OSTI2025

Analytical gradient-based optimization of CALPHAD model parameters

The calibration of CALPHAD (CALculation of PHAse Diagrams) models involves the solution of a very challenging high-dimensional multiobjective optimization problem. Traditional approaches to parameter fitting predominantly rely on gradient-free methods, which while robust, are computationally inefficient and often scale poorly with model complexity. In this work, we introduce and demonstrate a generalizable framework for analytic gradient-based optimization of the parameters of the CALPHAD model enabled by the recently formalized Jansson derivative technique. This method allows for efficient evaluation of gradients of thermodynamic properties at equilibrium with respect to model parameters, even in the presence of arbitrarily complex internal degrees of freedom. Leveraging these semi-analytic gradients, we employ the conjugate gradient (CG) method to optimize thermodynamic model parameters for four binary alloy systems: Cu-Mg, Fe-Ni, Cr-Ni, and Cr-Fe. Across all systems, CG achieves comparable or superior optimality relative to Bayesian ensemble Markov Chain Monte Carlo (MCMC) with improvements in computational efficiency ranging from one to three orders of magnitude. Furthermore, our results establish a new paradigm for CALPHAD assessments in which high fidelity data-rich model calibration becomes tractable using deterministic gradient-informed algorithms.

CALPHAD↗

DOE OSTI2023

A universal velocity transformation for boundary layers with pressure gradients

The logarithmic law of the wall does not capture the mean flow when a boundary layer is subjected to a strong pressure gradient. In such a boundary layer, the mean flow is affected by the spatio-temporal history of the imposed pressure gradient; and accounting for history effects remains a challenge. This work aims to develop a universal mean flow scaling for boundary layers subjected to arbitrary adverse or/and favourable pressure gradients. Here, we derive from the Navier–Stokes equation a velocity transformation that accounts for the history effects and maps the mean flow to the canonical law of the wall. The transformation is tested against channel flows with a suddenly imposed adverse or favourable pressure gradient, boundary layer flows subjected to an adverse pressure gradient, and Couette–Poiseuille flows with a streamwise pressure gradient. It is found that the transformed velocity profiles follow closely the equilibrium law of the wall.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Impact of the electron density and temperature gradient on drift-wave turbulence in the Large Plasma Device

In this paper we present an experimental study of edge turbulence in the Large Plasma Device at UCLA. We utilize a scan of discharge power and prefill pressure (neutral density) to show experimentally that turbulent density fluctuations decrease with decreasing density gradient, as predicted for resistive drift-wave turbulence (RDWT). As expected for RDWT, we observe that the cross-phase between the density and potential fluctuations is close to 0. Moreover, the addition of an electron temperature gradient leads to a reduction in the amplitude of the density fluctuations, as expected for RDWT. However, counter to theoretical expectations, we find that the potential fluctuations do not follow the same trends as the density fluctuations for changes either in density gradients or the addition of a temperature gradient. The disconnect between the density and potential fluctuations is connected to changes in the parallel flows as a result of differences in the prefill pressure, i.e. neutral density. Further analysis of the density and potential fluctuation spectra show that the electron temperature gradient reduces the low frequency fluctuations up to $10 \,{\rm kHz}$ and the introduction of a temperature gradient leads to an unexpected ${\sim }{\rm \pi}$ shift of the density–potential cross-phase at ${\sim }10\,{\rm kHz}$ , while maintaining the typical resistive drift-wave cross-phase at lower frequencies. These experiments partly confirm existing knowledge on resistive drift-wave turbulence, but also introduce new observations that indicate a need for dedicated nonlinear three-dimensional turbulence simulations that include neutrals.

Physics↗

DOE OSTI2026

Integrated-photonics-based systems for polarization-gradient cooling of trapped ions

Trapped ions are a promising modality for quantum systems, with demonstrated utility as the basis for quantum processors and optical clocks. However, traditional trapped-ion systems are implemented using complex free-space optical configurations, whose large size and susceptibility to vibrations and drift inhibit scaling to large numbers of qubits. In recent years, integrated-photonics-based systems have been demonstrated as an avenue to address the challenge of scaling trapped-ion systems while maintaining high fidelities. While these previous demonstrations have implemented both Doppler and resolved-sideband cooling of trapped ions, these cooling techniques are fundamentally limited in efficiency. In contrast, polarization-gradient cooling can enable faster and more power-efficient cooling and, therefore, improved computational efficiencies in trapped-ion systems. While free-space implementations of polarization-gradient cooling have demonstrated advantages over other cooling mechanisms, polarization-gradient cooling has never previously been implemented using integrated photonics. In this paper, we design and experimentally demonstrate key polarization-diverse integrated-photonics devices and utilize them to implement a variety of integrated-photonics-based polarization-gradient-cooling systems, culminating in the first experimental demonstration of polarization-gradient cooling of a trapped ion by an integrated-photonics-based system. By demonstrating polarization-gradient cooling using an integrated-photonics-based system and, in general, opening up the field of polarization-diverse integrated-photonics-based devices and systems for trapped ions, this work facilitates new capabilities for integrated-photonics-based trapped-ion platforms.

atom optics↗

DOE OSTI2023

Stochastic gradient descent for optimization for nuclear systems

The use of gradient descent methods for optimizing k-eigenvalue nuclear systems has been shown to be useful in the past, but the use of k-eigenvalue gradients have proved computationally challenging due to their stochastic nature. ADAM is a gradient descent method that accounts for gradients with a stochastic nature. This analysis uses challenge problems constructed to verify if ADAM is a suitable tool to optimize k-eigenvalue nuclear systems. ADAM is able to successfully optimize nuclear systems using the gradients of k-eigenvalue problems despite their stochastic nature and uncertainty. Furthermore, it is clearly demonstrated that low-compute time, high-variance estimates of the gradient lead to better performance in the optimization challenge problems tested here.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Analytical gradients for molecular-orbital-based machine learning

We report molecular-orbital-based machine learning (MOB-ML) enables the prediction of accurate correlation energies at the cost of obtaining molecular orbitals. Here, we present the derivation, implementation, and numerical demonstration of MOB-ML analytical nuclear gradients, which are formulated in a general Lagrangian framework to enforce orthogonality, localization, and Brillouin constraints on the molecular orbitals. The MOB-ML gradient framework is general with respect to the regression technique (e.g., Gaussian process regression or neural networks) and the MOB feature design. We show that MOB-ML gradients are highly accurate compared to other ML methods on the ISO17 dataset while only being trained on energies for hundreds of molecules compared to energies and gradients for hundreds of thousands of molecules for the other ML methods. The MOB-ML gradients are also shown to yield accurate optimized structures at a computational cost for the gradient evaluation that is comparable to a density-corrected density functional theory calculation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Ab-initio Cu alloy design for high-gradient accelerating structures

Operation of normal conducting accelerator structures at high accelerating gradients is beneficial for many accelerator applications in basic science, industry, medicine, and National Security. RF breakdown is the major factor that limits the achievable accelerating gradients. Previous experiments on copper (Cu) have demonstrated that RF breakdown probability can be significantly decreased by hardening the material and alloying Cu with solutes such as silver (Ag). In this paper, we propose a figure-of-merit (FOM) that characterizes the ability of Cu alloys to withstand high-gradients. The FOM represents a trade-off between hardening through solid solution strengthening and the additional thermal stress induced by incremental RF pulse heating resulting from changes in electronic properties induced by alloying. We performed high-throughput ab initio calculations and computed the FOM for a large number of binary Cu alloys. Several promising candidate alloys for high-gradient accelerating structures were identified, such as CuAg, CuCd, CuHg, CuAu, CuIn, and CuMg. CuAg alloys have previously exhibited low RF breakdown rates in experiments. The results provide guidance for selecting alloys for the future high-gradient normal conducting accelerating structures operating at very high gradients.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Constraining the shape of Milky Way satellites with distance gradients

We combine the Dark Energy Camera Legacy Survey DR8 photometry with Gaia photometry to study the 3D structure of Bootes I, Draco, Ursa Minor, Sextans, and Sculptor dwarf galaxies using blue horizontal branch (BHB) stars as distance indicators. We construct a new colour–absolute magnitude of BHB stars that we use to measure the distance gradients within the body of the dwarf galaxies. We detect a statistically significant non-zero gradient only in Sextans and Sculptor. Through modelling of the gradient and 2D density of the systems by triaxial Plummer models, we find that the distance gradients in both dwarf galaxies are inconsistent with prolate shape, but compatible with oblate or triaxial shapes. In order to explain the observed gradients, oblate models of Sextans and Sculptor need to have a significant intrinsic ellipticity larger than 0.47 for Sextans and 0.46 for Sculptor. Furthermore, the flattened oblate shape may imply a significant anisotropy in velocity distribution in order to be consistent with the lack of significant velocity gradients in these systems.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Measuring a Low Horizontal Hydraulic Gradient in a High Transmissivity Aquifer

Abstract High transmissivity aquifers typically have low hydraulic gradients (i.e., a flat water table). Measuring low gradients using water levels can be problematic because measurement error may be greater than the true difference in water levels (i.e., a low signal‐to‐noise ratio). In this study, the feasibility of measuring a hydraulic gradient in the range of 10 −6 to 10 −5 m/m was demonstrated. The study was performed at a site where the depth to water from land surface ranged from 40.1 to 94.2 m and the aquifer transmissivity was estimated at 41,300 m 2 /d (hydraulic conductivity of 18,800 m/d). The goals of the study were to reduce measurement error as much as practicable and assess the importance of factors affecting water level measurement accuracy. Well verticality was the largest source of error (0.000 to 0.168 m; median of 0.014 m), and geodetic survey of casing elevations was the next most important source of error (0.002 to 0.013 m; median of 0.005 m). Variability due to barometric pressure fluctuations was not an important factor at the site. Hydraulic heads were measured to an accuracy of ±0.0065 m, and the average hydraulic gradient was estimated to be 8.0 × 10 −6 (±0.9 × 10 −6 ) m/m. The improvement in accuracy allowed for two reversals in the groundwater flow direction to be identified, after which the gradient averaged 2.5 × 10 −5 (±0.4 × 10 −5 ) m/m. This study showed it is possible to sufficiently control sources of error to measure hydraulic gradients in the 10 −6 to 10 −5 m/m range.

McDonald, John P.↗

DOE OSTI2025

Vertical canopy gradients of respiration drive plant carbon budgets and leaf area index

Despite its importance for determining global carbon fluxes, leaf respiration remains poorly constrained in land surface models (LSMs). We tested the sensitivity of the Energy Exascale Earth System Model Land Model – Functionally Assembled Terrestrial Ecosystem Simulator (ELM-FATES) to variation in the canopy gradients of leaf maintenance respiration (R dark ). We ran global and point simulations varying the canopy gradient of R dark to explore the impacts on forest structure, composition, and carbon cycling. In global simulations, steeper canopy gradients of R dark lead to increased understory survival and leaf biomass. Leaf area index (LAI) increased up to 77% in tropical regions compared with the default parameterization, improving alignment with remotely sensed benchmarks. Global vegetation carbon varied from 308 Pg C to 449 Pg C across the ensemble. In tropical forest simulations, steeper gradients of R dark had a large impact on successional dynamics. Results show the importance of canopy gradients in leaf traits and fluxes for determining plant carbon budgets and emergent ecosystem properties such as competitive dynamics, LAI, and vegetation carbon. The high-model sensitivity to canopy gradients in R dark highlights the need for more observations of how leaf traits and fluxes vary along light micro-environments to inform critical dynamics in LSMs.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

Time-Resolved X-ray Operando Observations of Lithiation Gradients across the Cathode Matrix and Individual Oxide Particles during Fast Cycling of a Li-Ion Cell

Lithiated transition metal oxides serve as active materials in the positive electrode (cathode) of lithium-ion cells. During electrochemical cycling, lithium ions intercalate and deintercalate into these oxide particles. This behavior causes two types of lithiation gradients to emerge: (i) a bulk gradient across the depth of the cathode matrix (averaged over individual oxide particles) and (ii) a microscopic gradient across the particles themselves, which also depends on their location in the electrode. Here we show how both gradients can be studied using operando X-ray diffraction during 4C charge and 4C discharge. The oxide (de)lithiation is estimated from the unit cell parameters by indexing the X-ray diffraction spectra. By fitting the lithiation profiles with orthogonal polynomials, the bulk gradients across the electrode thickness are quantified. These gradients develop as the current flows through the cell and dissipate during open-circuit and potentiostatic-hold periods. Further details of lithiation dynamics can be obtained through shape analysis of the Bragg peaks. In particular, from electrochemical model simulations, we show that the width and skewness of the (003) peak track (de)lithiation fronts moving across the individual oxide particles.

(003) peak↗

DOE OSTI2022

Statistical Modeling of Peak Accelerating Gradients in LCLS-II and LCLS-II-HE

In this report, we study the vertical test gradient performance and the gradient degradation between vertical test and cryomodule test for the 1.3 GHz LCLS-II cavities. We develop a model of peak gradient statistics, and use our understanding of the LCLS-II results and the changes implemented for LCLS-II-HE to estimate the expected gradient statistics for the new machine. Finally, we lay out a plan to ensure that the LCLS-II-HE cryomodule gradient specifications are met while minimizing cavity disqualification by introducing a variable acceptance threshold for the accelerating gradient.

43 PARTICLE ACCELERATORS↗

NASA NTRS1975

Cosmic ray intensity gradients in the solar system

Recent progress in the determination of cosmic-ray intensity gradients is reviewed. Direct satellite measurements of the integral gradient are described together with various types of indirect measurements, including measurements of the Ar-37/Ar-39 ratio in samples from the Lost City meteorite, studies of anisotropies in neutron-monitor counting rates, and analysis of the sidereal diurnal anisotropy observed at a single point on earth. Nucleonic radial gradients and electron gradients measured by satellites in differential energy windows are discussed, and theoretical studies of the physical processes involved in these gradients are summarized. Observations of intensity gradients in heliographic latitude are reported.

Mckibben, R. B.↗

NASA NTRS1976

Coronal temperatures and temperature gradients from OSO-7 spectroheliograms

Temperatures and temperature gradients for the outer corona are obtained from brightness gradients of EUV lines that were measured with the spectroheliograph on OSO-7. Brightness gradients show considerable deviations from isothermal model calculations that include collisional excitation and photoexcitation. A negative temperature gradient that gives both positive and negative ion-abundance gradients appears to be able to account for the discrepancy. For the 284-A of Fe XV, perhaps the strongest line from the outer corona, measurements during 1972 appear to be consistent with a temperature near 2.3 million K near the equator at about 1.3 solar radii from the solar center and with temperature-gradient values near -0.7 that extend from as low as 1.2 to about 1.8 solar radii. Temperatures from strong lines of Fe XIV and Fe XVI indicate that variations of about 200,000 K exist along lines of sight where emission is appreciable. There appears to be some agreement between these results and temperature measurements from ion abundances in the solar wind and the Doppler width of the 5303-A line.

Nakada, M. P.↗

NASA NTRS1978

Theoretical study of the effect of wind velocity gradients on longitudinal stability and control in climbing and level flight

A change in the wind vector over a short distance along the flight path (wind gradient) has caused several severe airplane accidents during take-off and landing. Results of a previous study showed that, in descending flight, a positive wind gradient (decreasing head wind) caused severe divergent motion and a negative wind gradient (decreasing tail wind) caused oscillatory motion which should not create a control problem. The results obtained when the same method of analysis was applied to climbing and to straight and level flight are reported. In straight and level flight, a wind gradient was found to cause effects similar to those found in descending flight. In climbing flight, it was found that a negative wind gradient caused a slightly divergent oscillation that presented no control problems and a positive wind gradient caused oscillatory divergence. Results of motion studies indicated that adequate control of the airplane motions can be provided by automatic control systems.

Sherman, W. L.↗

NASA NTRS1983

Latitudinal and field-aligned cosmic ray gradients 2 to 5 AU Voyagers 1 and 2 and IMP 8

Results are presented showing that the contemporary picture of a relatively small heliocentric radial gradient is generally correct. They emphasize that such a gradient should really be thought of in terms of field-aligned structures since the cosmic ray populations tend to 'corotate' locally with the interplanetary field structure. Nonuniform latitudinal gradients of approximately 2 to 5 percent/deg in structures lasting 10 to 30 days are identified unambiguously. Additional evidence is seen for somewhat smaller latitudinal gradients often north to south and probably mixed with small field-aligned gradients of less than 1 percent/AU that persist for several solar rotations. It is suggested that these smallest ephemeral latitudinal gradients manifest themselves by affecting the degree of irregularity in diurnal variations of high latitude neutron monitors.

Roelof, E. C.↗

NASA NTRS1989

Numerical optimization in Hilbert space using inexact function and gradient evaluations

Trust region algorithms provide a robust iterative technique for solving non-convex unstrained optimization problems, but in many instances it is prohibitively expensive to compute high accuracy function and gradient values for the method. Of particular interest are inverse and parameter estimation problems, since function and gradient evaluations involve numerically solving large systems of differential equations. A global convergence theory is presented for trust region algorithms in which neither function nor gradient values are known exactly. The theory is formulated in a Hilbert space setting so that it can be applied to variational problems as well as the finite dimensional problems normally seen in trust region literature. The conditions concerning allowable error are remarkably relaxed: relative errors in the gradient error condition is automatically satisfied if the error is orthogonal to the gradient approximation. A technique for estimating gradient error and improving the approximation is also presented.

Carter, Richard G.↗

NASA NTRS1993

A displacement gradient BEM for accurate stress computation near boundaries in 2-D anisotropic problems

A displacement gradient method for 2D anisotropic elasticity problems is presented, which effectively minimizes the boundary layer effect through a two-step procedure. First, the boundary integral equations are solved for the unknown boundary displacements and tractions. Second, a direct integral equation for displacement gradients is developed in terms of boundary tractions. Three methods based on different evaluation procedures and locations for determining the displacement gradients are proposed. In the first method the displacement gradients are averaged at nodes common to adjacent elements. The second method stores the gradients element-wise. In the third method, the gradients are evaluated at the nodes of discontinuous elements. The three methods are applied to near-isotropic plates with circular and elliptic cutouts. It is concluded that all three methods can yield accurate stress distributions.

Sistla, R.↗