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DOE OSTI2026

Challenges in Pulsed-Field Gradient Nuclear Magnetic Resonance on Magnetically Heterogeneous Interfaces: Sequence and Field-Dependent Apparent Diffusion Coefficients

It is well known that the internal gradient (gi) that exists within pores haunts the diffusion coefficient (D) as measured by the pulsed-field gradient (PFG) nuclear magnetic resonance (NMR). Several PFG-NMR methods developed to determine an accurate D were not successful. Then, the steady-state diffusion coefficient (Dapp,8) for the cation [C4mim]+ of [C4mim][Tf2N]; [1-butyl-3-methylimidazolium][bis(trifluoromethylsulfonyl)imde] ionic liquid confined in ordered mesoporous carbon (OMC) were determined by comparing Dapp,8 obtained from 1H PFG-NMR performed with three different stimulated echo sequences: STE, APFG, and MPFG under the two external magnetic field strength, B0 = 9.4 and 14.1 Tesla. The measured Dapp,8 which is an order of magnitude smaller than D of bulk [C4mim][Tf2N], is in good agreement between APFG and MPFG both in B0 = 9.4 and 14.1 Tesla. However, the strong gi artifact, which caused apparent diffusion coefficient (Dapp) depending strongly and weakly on B0 and temperature, respectively, in diffusion-time dependent Dapp, Dapp(?) obtained from a sequence with monopolar gradients (STE) was suppressed by using sequences employing bipolar gradients (APFG and MPFG) in the region of steady-state diffusion. But incompletely suppressed gi artifact resulting in the different behaviors of the early part of Dapp(?) between the sequences leads a ˜ 0.6 and 0.9 in MPFG and APFG, respectively, in the relationship between mean squared displacement and diffusion time: = 2Dta, where a = 0.5 and 1 for 1-dimensional single file diffusion and 3-dimensional bulk diffusion, respectively. The above observations clearly show that the diffusion behavior of ions/molecules within the pores and pore structure, such as the surface-to-volume ratio? (D?_app (?)=D_0 [1-4/(9vp) S/V v(D_0 ?)]) and tortuosity (T = D0/Dapp,8), are possible to be misunderstood, especially in the systems with a non-negligible gi. This work demonstrates that it may be necessary to test several PFG sequences under multiple external magnetic fields for the correct determination of the diffusion behavior of ions/molecules in the pores with a larger internal gradient, gi.

Han, Kee Sung↗

DOE OSTI2020

A Drift‐Kinetic Method for Obtaining Gradients in Plasma Properties From Single‐Point Distribution Function Data

Abstract In this paper, we derive a new drift‐kinetic method for estimating gradients in the plasma properties through a velocity space distribution at a single point. The gradients are intrinsically related to agyrotropic features of the distribution function. This method predicts the gradients in the magnetized distribution function and can predict gradients of arbitrary moments of the gyrotropic background distribution function. The method allows for estimates on density and pressure gradients on the scale of a Larmor radius, proving to resolve smaller scales than any method currently available to spacecraft. The model is verified with a set of fully kinetic VPIC particle‐in‐cell simulations.

Wetherton, B. A.↗

DOE OSTI2025

Soil moisture gradients strengthen mesoscale convective systems by increasing wind shear

Mesoscale convective systems are a class of storm linked to extensive flooding and other destructive hazards in many regions globally. In West Africa, soil moisture impacts provide a valuable source of predictability for mature storm hazards, but little is known about mature storm sensitivity to soil moisture in other climatic regions. Here we use a storm track dataset, satellite observations and reanalysis fields to investigate the response of mature storms to soil moisture in seven global storm hotspots—West Africa, India, South America, South Africa, Australia and the United States Great Plains. We demonstrate that mesoscale soil moisture gradients (~500 km) can enhance storms by driving increased vertical wind shear conditions, a crucial ingredient for storm organization, through the strengthening of atmospheric temperature gradients. This is evidenced by a 10–30% increase in precipitation feature size and rainfall for the largest storms on days with favourable soil moisture gradients compared with unfavourable gradients. Global simulations confirm that soil moisture gradients influence wind shear. The results demonstrate the importance of soil moisture feedbacks for accurate forecasting of mesoscale convective systems and future projections of extreme events under climate change.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Pantropical Indo-Atlantic temperature gradient modulates multi-decadal AMOC variability in models and observations

Abstract Interconnections between ocean basins are recognized as an important driver of climate variability. Recent modeling evidence suggests that the North Atlantic climate can respond to persistent warming of the tropical Indian Ocean sea surface temperature (SST) relative to the rest of the tropics (rTIO). Here, we use observational data to demonstrate that multi-decadal changes in pantropical ocean temperature gradients lead to variations of an SST-based proxy of the Atlantic Meridional Overturning Circulation (AMOC). The largest contribution to this temperature gradient-AMOCconnection comes from gradients between the Indian and Atlantic Oceans. TherTIOindex yields the strongest connection of this tropical temperature gradient to theAMOC. Focusing on the internally generated signal in three observational products reveals that an SST-basedAMOCproxy index has closely followed low-frequency changes ofrTIOtemperature with about 26-year lag since 1870. Analyzing the pre-industrial control simulations of 44 CMIP6 climate models shows that theAMOCproxy index lags simulated mid-latitudeAMOCvariations by 4 ± 4 years. These model simulations reveal the mechanism connectingAMOCvariations to pantropical ocean temperature gradients at a 27 ± 2 years lag, matching the observed time lag in 28 out of the 44 analyzed models. rTIO temperature changes affect the North Atlantic climate through atmospheric planetary waves, impacting temperature and salinity in the subpolar North Atlantic, which modifies deep convection and ultimately the AMOC. Through this mechanism, observed internalrTIOvariations can serve as a multi-decadal precursor ofAMOCchanges with important implications forAMOCdynamics and predictability.

Meteorology & Atmospheric Sciences↗

DOE OSTI2021

A diagrammatic approach for automatically deriving analytical gradients of tensor hyper-contracted electronic structure methods

In this work, we introduce a diagrammatic approach to facilitate the automatic derivation of analytical nuclear gradients for tensor hyper-contraction (THC) based electronic structure methods. The automatically derived gradients are guaranteed to have the same scaling in terms of both operation count and memory footprint as the underlying energy calculations, and the computation of a gradient is roughly three times as costly as the underlying energy. The new diagrammatic approach enables the first cubic scaling implementation of nuclear derivatives for THC tensors fitted in molecular orbital basis (MO-THC). Furthermore, application of this new approach to THC-MP2 analytical gradients leads to an implementation, which is at least four times faster than the previously reported, manually derived implementation. Finally, we apply the new approach to the 14 tensor contraction patterns appearing in the supporting subspace formulation of multireference perturbation theory, laying the foundation for developments of analytical nuclear gradients and nonadiabatic coupling vectors for multi-state CASPT2.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Near-cancellation of up- and down-gradient momentum transport in forced magnetized shear-flow turbulence

Visco-resistive magnetohydrodynamic turbulence, driven by a two-dimensional unstable shear layer that is maintained by an imposed body force, is examined by decomposing it into dissipationless linear eigenmodes of the initial profiles. The down-gradient momentum flux, as expected, originates from the large-scale instability. However, continual up-gradient momentum transport by large-scale linearly stable but nonlinearly excited eigenmodes is identified and found to nearly cancel the down-gradient transport by unstable modes. The stable modes effectuate this by depleting the large-scale turbulent fluctuations via energy transfer to the mean flow. This establishes a physical mechanism underlying the long-known observation that coherent vortices formed from nonlinear saturation of the instability reduce turbulent transport and fluctuations, as such vortices are composed of both the stable and unstable modes, which are nearly equal in their amplitudes. The impact of magnetic fields on the nonlinearly excited stable modes is then quantified. Furthermore, even when imposing a strong magnetic field that almost completely suppresses the instability, the up-gradient transport by the stable modes is at least two-thirds of the down-gradient transport by the unstable modes, whereas for weaker fields, this fraction reaches up to 98%. These effects are persistent with variations in magnetic Prandtl number and forcing strength. Finally, continuum modes are shown to be energetically less important, but essential for capturing the magnetic fluctuations and Maxwell stress. A simple analytical scaling law is derived for their saturated turbulent amplitudes. It predicts the falloff rate as the inverse of the Fourier wavenumber, a property which is confirmed in numerical simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Plasma gradient effect on direct laser acceleration

The transfer of a high-intensity laser pulse energy to a high-energy electron beam via the direct laser acceleration mechanism is shown to be significantly enhanced through control of the plasma density gradient. Experiments performed using the OMEGA EP facility's high-intensity beams altered the plasma density and gradients by changing the Mach number and the angle of the gas-jet nozzle to the laser axis. When a long density gradient at the rear of the target is used, the total high-energy electron number measured was enhanced by 4.5 times compared to a shorter rear gradient. Complementary two-dimensional simulations, which follow the laser field evolution and the corresponding electron dynamics, strongly support the key trends observed in the experiment. The effect is twofold, the long density gradient provides the longest acceleration distance while it minimizes the formation of the sheath field as the electron beam exits into the vacuum. This study shows the importance of tailoring the plasma density.

Laser plasma interactions↗

DOE OSTI2025

Al–W gradient density materials—Processing and dynamic ramp compression

Materials with high-density gradients are desired for controlling loading paths in dynamic compression, important for studying material properties in extreme conditions and inertial confinement fusion. The large density difference between Al and W makes them ideal choices for producing gradient density materials, but their extremely different melting temperatures make them challenging to fabricate simultaneously. We report a method for producing Al–W porosity-free materials with a fourfold increase in density (2.7–11 g/cm 3 ) across the composition range, from Al-rich to W-rich, without intermetallic phase formation. This was achieved by understanding the aluminum-dominated densification behavior and examining the influence of pressure and temperature on the densification of Al–W composites. Dynamic compression experiments conducted with the Al–W gradient density material produced shock ramp compressions as expected based on the designed composition, and the performed hydrodynamics simulations showed excellent agreement with experimental results. The results demonstrate that current activated pressure-assisted densification allows for the easy and rapid fabrication of gradient density materials with significant density gradients and tailored compositions, facilitating precise control of the loading paths. These materials have the potential to create customized pressure drives for advancing the fields of material science in extreme environments and dynamic compression.

Alloys↗

DOE OSTI2020

Galaxy properties as revealed by MaNGA – III. Kinematic profiles and stellar population gradients in S0s

ABSTRACT This is the third paper of a series where we study the stellar population gradients (SP; ages, metallicities, α-element abundance ratios, and stellar initial mass functions) of early-type galaxies (ETGs) at $z$ ≤ 0.08 from the Mapping Nearby Galaxies at APO Data Release 15 (MaNGA-DR15) survey. In this work, we focus on the S0 population and quantify how the SP varies across the population as well as with galactocentric distance. We do this by measuring Lick indices and comparing them to SP synthesis models. This requires spectra with high signal-to-noise ratio which we achieve by stacking in bins of luminosity (Lr) and central velocity dispersion (σ0). We find that: (1) there is a bimodality in the S0 population: S0s more massive than $3\times 10^{10}\, \mathrm{M}_\odot$ show stronger velocity dispersion and age gradients (age and σr decrease outwards) but little or no metallicity gradient, while the less massive ones present relatively flat age and velocity dispersion profiles, but a significant metallicity gradient (i.e. [M/H] decreases outwards). Above $2\times 10^{11}\, \mathrm{M}_\odot$, the number of S0s drops sharply. These two mass scales are also where global scaling relations of ETGs change slope. (2) S0s have steeper velocity dispersion profiles than fast-rotating elliptical galaxies (E-FRs) of the same luminosity and velocity dispersion. The kinematic profiles and SP gradients of E-FRs are both more similar to those of slow-rotating ellipticals (E-SRs) than to S0s, suggesting that E-FRs are not simply S0s viewed face-on. (3) At fixed σ0, more luminous S0s and E-FRs are younger, more metal rich and less α-enhanced. Evidently for these galaxies, the usual statement that ‘massive galaxies are older’ is not true if σ0 is held fixed.

Domínguez Sánchez, H.↗

DOE OSTI2026

Sub-Doppler Cooling of a Trapped Ion in a Phase-Stable Polarization Gradient

Trapped ions provide a highly controlled platform for quantum sensors, clocks, simulators, and computers, all of which depend on cooling ions close to their motional ground state. Existing methods like Doppler, resolved sideband, and dark resonance cooling balance trade-offs between the final temperature and cooling rate. A traveling polarization gradient has been shown to cool multiple modes quickly and in parallel, but utilizing a stable polarization gradient can achieve lower ion energies, while also allowing tailorable light-matter interactions in the sub-wavelength regime. In this Letter, we demonstrate cooling of a trapped ion below the Doppler limit using a phase-stable polarization gradient created using trap-integrated photonic devices. At an axial frequency of 2⁢𝜋×1.45 MHz we achieve ⟨𝑛⟩=1.56±0.07 in 150 μ⁢s and cooling rates of ∼0.3 quanta/μ⁢s. Here, we examine ion dynamics under different polarization gradient phases, detunings, and intensities, showing reasonable agreement between experimental results and a multilevel model. Cooling is fast and power efficient, with lower average motional Fock state occupation when compared to simulated operation under the corresponding running wave configuration. Our results demonstrate a well-controlled test bed for studying the dynamics of multilevel atomic systems in a phase-stable polarization gradient.

Atom & ion cooling↗

DOE OSTI2021

Simulation and experimental study of proton bunch self-modulation in plasma with linear density gradients

We present numerical simulations and experimental results of the self-modulation of a long proton bunch in a plasma with linear density gradients along the beam path. Simulation results agree with the experimental results reported [F. Braunmller, T. Nechaeva et al. (AWAKE Collaboration), Phys. Rev. Lett. 125, 264801 (2020)]: with negative gradients, the charge of the modulated bunch is lower than with positive gradients. In addition, the bunch modulation frequency varies with gradient. Simulation results show that dephasing of the wakefields with respect to the relativistic protons along the plasma is the main cause for the loss of charge. The study of the modulation frequency reveals details about the evolution of the self-modulation process along the plasma. In particular for negative gradients, the modulation frequency across time-resolved images of the bunch indicates the position along the plasma where protons leave the wakefields. Simulations and experimental results are in excellent agreement.

43 PARTICLE ACCELERATORS↗

DOE OSTI2024

Effect of the volume fraction gradient on the phase interaction force model for disperse two-phase flows

In this work, the effects of the particle volume fraction gradient on fluid-particle interactions are studied. The phase interaction force is decomposed into three terms. For the first term, namely the symmetrized force density, we present theoretical reasoning and numerical evidence to assume that it is independent of the particle volume fraction gradient. The second term is the particle volume fraction gradient times a newly introduced diffusion stress. The third term is the divergence of the particle-fluid-particle (PFP) stress. If this assumption of independence of the particle volume fraction gradient for the first term can be verified, to the first order of the ratio of the mean distance between particles to the macroscopic lengthscale, all three terms can be studied and modeled in flows with uniform particle distributions. Models thus obtained are applicable to statistically inhomogeneous flows, with the second and third terms accounting for statistical inhomogeneity. To verify this assumption, numerical simulations of flows passing fixed arrays of particles are performed. Both uniform and nonuniform particle volume fractions are studied and compared for disperse multiphase flows with the particle Reynolds numbers ranging from 1 to 100, and particle volume fraction ranging from 1% to 26% in statistically steady states. It is found that the symmetrized force (first) term can be well approximated by the drag force obtained from studies of uniform flows. The diffusion stress is positive along the flow direction and negative in the directions perpendicular to the flow. In the case of moving particles, this stress could potentially cause particle aggregation in the flow direction and dispersion in the directions perpendicular to the flow. Finally, the diffusion stress is only important when there is a volume fraction gradient, while the PFP stress can be important in inhomogeneous flows with either nonuniform particle concentrations or nonuniform average relative velocities between the phases.

42 ENGINEERING↗

DOE OSTI2024

Gradient Coding With Iterative Block Leverage Score Sampling

Gradient coding is a method for mitigating straggling servers in a centralized computing network that uses erasure-coding techniques to distributively carry out first-order optimization methods. Randomized numerical linear algebra uses randomization to develop improved algorithms for large-scale linear algebra computations. In this study, we propose a method for distributed optimization that combines gradient coding and randomized numerical linear algebra. The proposed method uses a randomized ℓ 2 -subspace embedding and a gradient coding technique to distribute blocks of data to the computational nodes of a centralized network, and at each iteration the central server only requires a small number of computations to obtain the steepest descent update. The novelty of our approach is that the data is replicated according to importance scores, called block leverage scores, in contrast to most gradient coding approaches that uniformly replicate the data blocks. Furthermore, we do not require a decoding step at each iteration, avoiding a bottleneck in previous gradient coding schemes. We show that our approach results in a valid ℓ 2 -subspace embedding, and that our resulting approximation converges to the optimal solution.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Electrochemical Modeling and Experimental Verification of Lithiation Gradients in Oxide Cathodes of Lithium-Ion Cells

Lithiated nickel-cobalt-manganese oxides, such as NCM523, are used in the positive electrode (cathode) of Li-ion cells. Using operando X-ray diffraction profilometry, lithiation gradients in the cathode matrix can be observed and quantified by expansion into Legendre polynomials with time-dependent weights. These weights (referred to as gradients) increase in magnitude when electric current flows through the cell, decrease during potentiostatic hold and finally relax to zero when the current is interrupted during open circuit rest. Both physics-based electrochemical models and operando X-ray experiments suggest that the time constants for gradient growth and abatement are primarily determined by ionic diffusion in the oxide particles, which in turn depends on their lithium content. In contrast, the magnitude of gradients depends mainly on the applied current. The X-ray profilometry provides a way of directly probing the formation and disappearance of Li gradients across the cathode during fast cycling, which can help to diagnose the effects of material degradation in the cells.

25 ENERGY STORAGE↗

DOE OSTI2022

High Performance Computing to Quantify the Evolution of Microscopic Concentration Gradients During Flash Processing

During the Flash process, the cross section of a plain-carbon or a low-alloy steel is austenitized through rapid heating and transformed on rapid cooling to a predominantly martensite + bainite structure with small amounts of retained austenite. Unlike conventional heat treating, homogeneity is intentionally avoided during Flash processing of steels. The Flash process assembly consists of a pair of rolls that transfer the steel sheets through the heating and cooling stage of the thermal cycle. The initial microstructure of the steel consists of ferrite (body-centered cubic iron) + carbide ((Fe,X)mCn) mixture. The heating rate through the peak temperature is a function of temperature and reaches a peak of about 300-400°C/s and the cooling rate has a maximum value of 3,000-4,000°C/s. The on-heating phase transformations include carbide dissolution, austenite (face-centered cubic iron) nucleation and growth, and diffusion of carbon and other substitutional elements in the steel. The on-cooling phase transformations include formation of martensite (body-centered tetragonal phase containing supersaturated solute) and bainite (ferrite plates with or without fine carbides). In this project, the focus is on Fe-C-Cr steels that are currently Flash processed for armor applications. The modeling effort proposed here will help optimize the Flash thermal cycle for these low alloy steels to achieve the target performance, which is an ongoing effort at SFP Works. A significant feature of Flash processed Fe-C-Cr steels is the presence of scatter in the through-thickness in the sheet. The variability in hardness results from a variability in the bainite + martensite microstructure that is sensitive to the local chemical concentration of C and Cr. Such a chemical inhomogeneity is intentionally obtained in the Flash process. Although such a microstructural gradient is presumably responsible for the exceptional properties of the Flash processed steel, it is very important to quantify the gradients as a function of Flash variabilities in processing parameters and the input microstructure. Understanding the mechanistic pathway that leads to microstructural gradients could be ground-breaking and instrumental for achieving better process control and optimized microstructural state to meet application-specific strength-ductility requirements. Since the final microstructure depends on setting up precise solute concentration gradients through a rapid heating process, and transforming these regions into various phases, it is important to understand how small changes in steel chemistry, input microstructure (carbide size and distribution), and process variables (Flash thermal cycle) will impact the solute concentration gradients.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

The Open Cluster Chemical Abundances and Mapping Survey. VI. Galactic Chemical Gradient Analysis from APOGEE DR17

The goal of the Open Cluster Chemical Abundances and Mapping (OCCAM) survey is to constrain key Galactic dynamic and chemical evolution parameters by the construction and analysis of a large, comprehensive, uniform data set of infrared spectra for stars in hundreds of open clusters. This sixth contribution from the OCCAM survey presents analysis of SDSS/APOGEE Data Release 17 (DR17) results for a sample of stars in 150 open clusters, 94 of which we designate to be "high-quality" based on the appearance of their color–magnitude diagram. We find the APOGEE DR17-derived [Fe/H] values to be in good agreement with those from previous high-resolution spectroscopic open cluster abundance studies. Using a subset of the high-quality sample, the Galactic abundance gradients were measured for 16 chemical elements, including [Fe/H], for both Galactocentric radius ($R$ GC ) and guiding center radius ($R$ guide ). We find an overall Galactic [Fe/H] versus RGC gradient of -0.073 ± 0.002 dex kpc -1 over the range of 6 > $R$ GC < 11.5 kpc, and a similar gradient is found for [Fe/H] versus $R$ guide . Significant Galactic abundance gradients are also noted for O, Mg, S, Ca, Mn, Na, Al, K, and Ce. Our large sample additionally allows us to explore the evolution of the gradients in four age bins for the remaining 15 elements.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Investigating profile stiffness and critical gradients in shaped TCV discharges using local gyrokinetic simulations of turbulent transport

The experimental observation made on the TCV tokamak of a significant confinement improvement in plasmas with negative triangularity ( δ < 0) compared to those with standard positive triangularity has been interpreted in terms of different degrees of profile stiffness (Sauter et al. Phys. Plasmas 21 055906, 2014) and/or different critical gradients. Employing the Eulerian gyrokinetic code GENE (Jenko et al. Phys. Plasmas 7 1904, 2000), profile stiffness and critical gradients are studied under TCV relevant conditions. For the considered experimental discharges, trapped electron modes (TEMs) and electron temperature gradient (ETG) modes are the dominant microinstabilities, with the latter providing a significant contribution to the non-linear electron heat fluxes near the plasma edge. Two series of simulations with different levels of realism are performed, addressing the question of profile stiffness at various radial locations. Retaining finite collisionality, impurities and electromagnetic effects, as well as the physical electron-to-ion mass ratio are all necessary in order to approach the experimental flux measurements. However, flux-tube simulations are unable to fully reproduce the TCV results, pointing towards the need to carry out radially nonlocal (global) simulations, i.e. retaining finite machine size effects, in a future study. Some conclusions about the effect of triangularity can nevertheless be drawn based on the flux-tube results. In particular, the importance of considering the sensitivity to both temperature and density gradient is shown. The flux tube results show an increase of the critical gradients towards the edge, further enhanced when δ < 0, and they also appear to indicate a reduction of profile stiffness towards plasma edge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1976

Temperature gradients and clear-air turbulence probabilities

In order to forecast clear-air turbulence (CAT) in jet aircraft flights, a study was conducted in which the data from a special-purpose instrument aboard a Boeing 747 jet airliner were compared with satellite-derived radiance gradients, conventional temperature gradients from analyzed maps, and temperature gradients obtained from a total air temperature sensor on the plane. The advantage of making use of satellite-derived data is that they are available worldwide without the need for radiosonde observations, which are scarce in many parts of the world. Major conclusions are that CAT probabilities are significantly higher over mountains than flat terrain, and that satellite radiance gradients appear to discriminate between CAT and no CAT better than conventional temperature gradients over flat lands, whereas the reverse is true over mountains, the differences between the two techniques being not large over mountains.

Bender, M. A.↗