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DOE OSTI2023

Capturing the Coverage Dependence of Aromatics’ Adsorption through Mean-Field Models

To capture the dominant interactions (surface-mediated and through-space steric) in catalytic hydrodeoxygenation systems, coverage-dependent mean-field models of aromatic adsorption are developed on Pt(111) and Ru(0001). We derive three key insights from this work: (1) we can universally apply mean-field models to capture the coverage-dependent behavior of oxygenated aromatics on transition metal surfaces, (2) we can deconvolute surface-mediated and throughspace steric interactions from the mean-field model, and (3) we can develop relatively accurate models that predict the adsorption energy of aromatics on transition metal surfaces for the full coverage range using the work function at lowest modeled coverage. In conclusion, our approach enables the rapid prediction of coverage-dependent behavior of oxygenated aromatics on transition metal surfaces, reducing the computational cost associated with these studies by an order of magnitude.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

AMOC Variability in Climate Models and Its Dependence on the Mean State

Abstract Understanding internal variability of the climate system is critical when isolating internal and anthropogenically forced signals. Here, we investigate the modes of Atlantic Meridional Overturning Circulation ( AMOC ) variability using perturbation experiments with the Institut Pierre‐Simon Laplace's (IPSL) coupled model and compare them to Coupled Model Intercomparison Project Phase 6 (CMIP6) pre‐industrial control simulations. We identify two characteristic modes of variability—decadal‐to‐multidecadal ( DMD var ) and centennial ( CEN var ). The former is driven largely by temperature anomalies in the subpolar North Atlantic, while the latter is driven by salinity in the western subpolar North Atlantic. The amplitude of each mode scales linearly with the mean AMOC strength in the IPSL experiments. The DMD var amplitude correlates well with the AMOC mean strength across CMIP6 models, while the CEN var mode does not. These findings suggest that the strength of DMD var depends robustly on the North Atlantic mean state, while the CEN var mode may be model‐dependent.

Ferster, Brady S. [LOCEAN‐IPSL Sorbonne Université↗

DOE OSTI2022

Deep learning potential of mean force between polymer grafted nanoparticles

Grafting polymer chains on the surfaces of nanoparticles is a well-known route to control their self-assembly and distribution in a polymer matrix. A wide variety of self-assembled structures are achieved by changing the grafting patterns on the surface of an individual nanoparticle. However, an accurate estimation of the effective potential of mean force between a pair of grafted nanoparticles that determines their assembly and distribution in a polymer matrix is an outstanding challenge in nanoscience. We address this problem via deep learning. As a proof of concept, here we report a deep learning framework that learns the interaction between a pair of single-chain grafted spherical nanoparticles from their molecular dynamics trajectory. Subsequently, we carry out the deep learning potential of mean force-based molecular simulation that predicts the self-assembly of a large number of single-chain grafted nanoparticles into various anisotropic superstructures, including percolating networks and bilayers depending on the nanoparticle concentration in three-dimensions. The deep learning potential of mean force-predicted self-assembled superstructures are consistent with the actual superstructures of single-chain polymer grafted spherical nanoparticles. This deep learning framework is very generic and extensible to more complex systems including multiple-chain grafted nanoparticles. Finally, we expect that this deep learning approach will accelerate the characterization and prediction of the self-assembly and phase behaviour of polymer-grafted and unfunctionalized nanoparticles in free space or a polymer matrix.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Gaunt and Breit two-electron contributions to mean-field transformations and fine structure splitting

Materials utilized by novel energy systems are often studied using weakly correlated mean-field theories. However, if these systems incorporate heavy elements, relativistic effects must be included. Therefore, a Kramers unrestricted coupled cluster with singles and doubles excitation formalism within a molecular mean-field exact two-component framework (X2C mmf ) using a four-component Dirac–Hartree–Fock (DHF) reference state is presented. The exact X2C mmf transformed normal-order Hamiltonian incorporates all one-electron and two-electron (2e) contributions from the Coulomb, Gaunt, and Breit operators and is used with the equation of motion method to calculate the excitation energies of the alkali group of elements. Using this framework, the effects of 2e Gaunt and Breit integrals are studied. Results demonstrate growing contributions from these integrals to the generated X2C mmf mean-fields and electronic fine structure calculations with increasing atomic number. Overall, this paper outlines the method, its effect within the X2C mmf approach, and lays the foundation for future theoretical development of relativistic calculations within this framework.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Rapid subsurface analysis of frequency-domain thermoreflectance images with K-means clustering

K-means clustering analysis is applied to frequency-domain thermoreflectance (FDTR) hyperspectral image data to rapidly screen the spatial distribution of thermophysical properties at material interfaces. Performing FDTR while raster scanning a sample consisting of 8.6 μm of doped-silicon (Si) bonded to a doped-Si substrate identifies spatial variation in the subsurface bond quality. Routine thermal analysis at select pixels quantifies this variation in bond quality and allows assignment of bonded, partially bonded, and unbonded regions. Performing this same routine thermal analysis across the entire map, however, becomes too computationally demanding for rapid screening of bond quality. To address this, K-means clustering was used to reduce the dimensionality of the dataset from more than 20 000 pixel spectra to just K = 3 component spectra. The three component spectra were then used to express every pixel in the image through a least-squares minimized linear combination providing continuous interpolation between the components across spatially varying features, e.g., bonded to unbonded transition regions. Fitting the component spectra to the thermal model, thermal properties for each K cluster are extracted and then distributed according to the weighting established by the regressed linear combination. Thermophysical property maps are then constructed and capture significant variation in bond quality over 25 μm length scales. The use of K-means clustering to achieve these thermal property maps results in a 74-fold speed improvement over explicit fitting of every pixel.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Mean force emission theory for classical bremsstrahlung in strongly coupled plasmas

This work presents mean force emission theory, which extends the classical theory of bremsstrahlung emission to strongly coupled plasmas. In the high-frequency limit, the theory reduces to solving for the electron trajectory during a binary collision, but where the electron–ion interactions occur through the potential of mean force. In the low-frequency limit, it uses an autocorrelation formalism that captures effects of multiple collisions and strongly correlated motion. The predictions are benchmarked by comparison with first-principles classical molecular dynamics simulations of a fully ionized hydrogen plasma in which all interactions are repulsive. The comparison shows good agreement up to Coulomb coupling strengths of Γ∼30. The theory improves upon traditional models by including strong coupling effects and systematically including the effect of multiple collisions. Furthermore, mean force emission theory provides evidence that the Drude correction factor commonly used in quantum calculations of optical quantities may not be adequate at strong coupling.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Bootstrap embedding for interacting electrons in phonon coherent-state mean field

Here, we develop a Fermi–Bose bootstrap embedding framework for the ground state of interacting electrons coupled to a phonon mean field. The method combines bootstrap embedding for correlated electrons with a self-consistent coherent-state mean-field treatment for phonons. This method models the interacting electron–phonon problem as a system of correlated electrons traveling in a self-consistently specified potential landscape, allowing for efficient treatment of large lattice systems. Convergence of the methods for fragment size and total system size is demonstrated for the one-dimensional Hubbard–Holstein model for up to 350 sites. Finite-size scaling is performed to extrapolate to the infinite system size. Benchmarking against the density matrix renormalization group for a small 8-site system at half- and quarter-filling shows an orders-of-magnitude runtime advantage. The comparison further reveals that the method performs best in regimes dominated by localization, such as the Mott insulating phase and the strong-coupling tiny polaron regime, where the local embedding ansatz is still valid. However, due to the mean-field treatment for phonons, we find limitations of our methods in the weakly coupled delocalized region and at the Peierls transition, where quantum phonon fluctuations and long-range kinetic correlations become substantial.

Islam, Shariful [North Carolina State University, ↗

DOE OSTI2024

Determination of the mean energy of fast electron losses and anisotropies through thick-target emission on WEST

Abstract A new method to obtain the mean energy of fast electron losses in fusion plasmas using a versatile multi-energy hard x-ray (HXR) detector is presented. The method is based on measuring the thick-target emission of tungsten in the divertor region produced by fast electron losses interacting with the target and modeling the tungsten spectra by a Monte Carlo code which simulates the interaction between a beam of electrons and a solid target. The mean energy of the fast electron losses is determined through the comparison between the experimental and synthetic emission. The results show that fast electron losses during lower hybrid current drive discharges at WEST have a mean energy of 90–140 keV and represent only 2% of the total heat flux at the target. Additionally, anisotropic HXR emission has been detected for the first time at the WEST core and edge plasma, with opposite directions. It is due to the forward-peak emission of two distinctive populations of fast electrons: co-current fast electrons in the core and counter-current fast electron losses at the inner strike point. In view of future experiments like ITER where electron cyclotron current drive will generate a fast electron population, this technique could serve as a real-time monitor of fast electron losses and eventually feed an actuator on the current drive generation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Influence of inhomogeneous stochasticity on the falsifiability of mean-field theories and examples from accretion disc modelling

ABSTRACT Despite spatial and temporal fluctuations in turbulent astrophysical systems, mean-field theories can be used to describe their secular evolution. However, observations taken over time scales much shorter than dynamical time scales capture a system in a single state of its turbulence ensemble. Comparing with mean-field theory can falsify the latter only if the theory is additionally supplied with a quantified precision. The central limit theorem provides appropriate estimates to the precision only when fluctuations contribute linearly to an observable and with constant coherent scales. Here, we introduce an error propagation formula that relaxes both limitations, allowing for non-linear functional forms of observables and inhomogeneous coherent scales and amplitudes of fluctuations. The method is exemplified in the context of accretion disc theories, where inhomogeneous fluctuations in the surface temperature are propagated to the disc emission spectrum – the latter being a non-linear and non-local function of the former. The derived precision depends non-monotonically on emission frequency. Using the same method, we investigate how binned spectral fluctuations in telescope data change with the spectral resolving power. We discuss the broader implications for falsifiability of a mean-field theory.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Residual mean field model of valence quarks in the nucleon

Abstract We develop a non-perturbative model for valence parton distribution functions (PDFs) based on the mean field interactions of valence quarks in the nucleonic interior. The main motivation for the model is to obtain a mean field description of the valence quarks as a baseline to study the short range quark–quark interactions that generate the high x tail of PDFs. The model is based on the separation of the valence three-quark cluster and residual system in the nucleon. Then the nucleon structure function is calculated within the effective light-front diagrammatic approach introducing nonperturbative light-front valence quark and residual wave functions. Within the model a new relation is obtained between the position, $$x_p$$ x p , of the peak of $$xq_V(x)$$ x q V ( x ) distribution of the valence quark and the effective mass of the residual system, $$m_R$$ m R , in the form: $$x_{p} \approx {1\over 4} (1-{m_R\over m_N})$$ x p ≈ 1 4 ( 1 - m R m N ) at starting $$Q^2$$ Q 2 . This relation explains the difference in the peak positions for d- and u-quarks through the expected difference of residual masses for valence d- and u-quark distributions. The parameters of the model are fixed by fitting the calculated valence quark distributions to the phenomenological PDFs. This allowed us to estimate the overall mean field contribution in baryonic and momentum sum rules for valence d- and u-quarks. Finally, the evaluated parameters of the non-perturbative wave functions of valence 3q-cluster and residual system can be used in calculation of other quantities such as nucleon form factors, generalized partonic and transverse momentum distributions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Subpolar North Atlantic Mean State Affects the Response of the Atlantic Meridional Overturning Circulation to the North Atlantic Oscillation in CMIP6 Models

Abstract The Atlantic meridional overturning circulation (AMOC) plays an important role in climate, transporting heat and salt to the subpolar North Atlantic. The AMOC’s variability is sensitive to atmospheric forcing, especially the North Atlantic Oscillation (NAO). Because AMOC observations are short, climate models are a valuable tool to study the AMOC’s variability. Yet, there are known issues with climate models, like uncertainties and systematic biases. To investigate this, preindustrial control experiments from models participating in the phase 6 of Coupled Model Intercomparison Project (CMIP6) are evaluated. There is a large, but correlated, spread in the models’ subpolar gyre mean surface temperature and salinity. By splitting models into groups of either a warm–salty or cold–fresh subpolar gyre, it is shown that warm–salty models have a lower sea ice cover in the Labrador Sea and, hence, enable a larger heat loss during a positive NAO. Stratification in the Labrador Sea is also weaker in warm–salty models, such that the larger NAO-related heat loss can also affect greater depths. As a result, subsurface density anomalies are much stronger in the warm–salty models than in those that tend to be cold and fresh. As these anomalies propagate southward along the western boundary, they establish a zonal density gradient anomaly that promotes a stronger delayed AMOC response to the NAO in the warm–salty models. These findings demonstrate how model mean state errors are linked across variables and affect variability, emphasizing the need for improvement of the subpolar North Atlantic mean states in models.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

E3SMv3 ‘Nephele’ Perturbed Parameter Ensemble Value-Added Product for ENA, SGP, NSA, and Global Means

Processed output from the E3SMv3 Nephele perturbed parameter ensemble (PPE). This product contains global means of present-day (using 2010 aerosol forcings) and preindustrial (using 1850 aerosol forcings) monthly and daily global-mean quantities, as well as hourly mean quantities at the E3SMv3 model grid cell closest to the ENA, SGP, and NSA ARM sites. In this PPE, the E3SMv3 model was run for 27 months in an atmosphere-only configuration with free tropospheric winds nudged to reanalysis. Each ensemble member represents a unique combination of 25 model parameter values (in the microphysics, convective microphysics, and aerosol schemes) that were perturbed randomly and simultaneously. The E3SMv3 default configuration is included as member 0. See https://doi.org/10.22541/essoar.174907165.57104591/v1 (in review) for more information on the Nephele PPE and the perturbed parameters.

Model atmospheric temperature↗

DOE OSTI2025

Replication Data for: Measurement of the mean number of muons with energies above 500 GeV in air showers detected with the IceCube Neutrino Observatory

Measurement of the mean number of muons with energies above 500 GeV in air showers detected with the IceCube Neutrino Observatory This data release accompanies results submitted to Physical Review D describing the measurement of the average multiplicity of TeV muons with IceCube. It contains the data necessary to reproduce the main plots from the paper (Figs. 7 and 9), i.e. the numerical results for the average number of muons with energies above 500 GeV as a function of primary cosmic ray energy. For any questions about this data release, please write to analysis@icecube.wisc.edu. Files included in this release: <ul> <li>A README file <li>Files including data to reproduce the results plots from the paper (see below for details) <li>An example python script showing how to read and plot the data </ul> What is in the files icecube_Nmu500_X_Y.txt: Y indicates wether the file contains values obtained from experimental data (Y="data") or air-shower simulations (Y="MC"). X indicates the hadronic interaction model for which the plot is made. If Y="data", this means that the experimental data was interpreted using this model. If Y="MC", it means that the simulations were performed with this model. The three models included are Sibyll 2.1, QGSJet-II.04, and EPOS-LHC (see paper for references). The file with X="modelaverage" gives the average over the three individual results with the deviations from the average included in the systematic uncertainties. Please see the README file for details on how the data is structured in the files.

Astroparticle Physics↗

DOE OSTI2021

Balanced k -means clustering on an adiabatic quantum computer

Adiabatic quantum computers are a promising platform for efficiently solving challenging optimization problems. Therefore, many are interested in using these computers to train computationally expensive machine learning models. We present a quantum approach to solving the balanced k-means clustering training problem on the D-Wave 2000Q adiabatic quantum computer. In order to do this, we formulate the training problem as a quadratic unconstrained binary optimization (QUBO) problem. Unlike existing classical algorithms, our QUBO formulation targets the global solution to the balanced k-means model. We test our approach on a number of small problems and observe that despite the theoretical benefits of the QUBO formulation, the clustering solution obtained by a modern quantum computer is usually inferior to the solution obtained by the best classical clustering algorithms. Nevertheless, the solutions provided by the quantum computer do exhibit some promising characteristics. We also perform a scalability study to estimate the run time of our approach on large problems using future quantum hardware. Finally, as a final proof of concept, we used the quantum approach to cluster random subsets of the Iris benchmark data set.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Multiple redox mechanisms for water-gas shift reaction on Fe 3 O 4 (1 1 1) surface: A density functional theory and mean-field microkinetic modeling study

In this work, we investigated redox mechanisms for the high temperature (HT) water–gas shift reaction (WGSR) on the Fe 3 O 4 (1 1 1) surface using density functional theory (DFT) calculations and mean-field microkinetic modeling (MKM). The redox pathways branched into three Langmuir-Hinshelwood processes (LH1, LH2 and LH3) and one Mars-van-Krevelen (MVK) process (in the presence of oxygen vacancy) from multidentate binding of CO and CO 2 over four available reactive sites (Fe oct2 , Fe tet1 , Fe bridge, and O1). We found that the LH1 and LH2 processes have CO adsorption at a single iron site (Fe oct2 or Fe tet1 ), while the LH3 and MVK processes have stronger chemisorption of CO or CO 2 by both the Fe oct2 site and the O 1 site. From the mechanistic study of these reaction path, we recognized that availability of O 1 sites was key to proceed to either CO oxidation by the single site (LH1, LH2) or by the dual site (LH3, MVK). We observed that the reaction energetics were significantly different in the CO oxidation steps, where the single or dual site results in markedly different apparent activation energy (73–281 kJ/mol) and reaction rates (10 -3 –10 -10 mol∙m -2 ∙s -1 ) among the four reaction mechanisms. The utilization of mean field MKM with DFT reaction energetics helps explain the experimental debates for the catalytic reaction details as well as providing a possible direction to engineer the catalyst with higher activity.

42 ENGINEERING↗

DOE OSTI2024

Mean-Field Ring Polymer Rates Using a Population Dividing Surface

Mean-field Ring Polymer Molecular Dynamics (MF-RPMD) offers a computationally efficient method for the simulation of reaction rates in multi-level systems. Previous work has established that, to model a nonadiabatic state-to-state reaction accurately, the dividing surface must be chosen to explicitly sample kinked ring polymer configurations where at least one bead is in a different electronic state than the others. Building on this, we introduce a population difference coordinate and a kink-constrained dividing surface, and we test the accuracy of the resulting mean-field rate theory on a series of bilinear coupling model systems. Here, we demonstrate that this new MF-RPMD rate approach is efficient to implement and quantitatively accurate for models over a wide range of driving forces, coupling strengths, and temperatures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Cycle equivalence classes, orthogonal Weingarten calculus, and the mean field theory of memristive systems

Abstract It has been recently noted that for a class of dynamical systems with explicit conservation laws represented via projector operators, the dynamics can be understood in terms of lower dimensional equations. This is the case, for instance, of memristive circuits. Memristive systems are important classes of devices with wide-ranging applications in electronic circuits, artificial neural networks, and memory storage. We show that such mean-field theories can emerge from averages over the group of orthogonal matrices, interpreted as cycle-preserving transformations applied to the projector operator describing Kirchhoff’s laws. Our results provide insights into the fundamental principles underlying the behavior of resistive and memristive circuits and highlight the importance of conservation laws for their mean-field theories. In addition, we argue that our results shed light on the nature of the critical avalanches observed in quasi-two-dimensional nanowires as boundary phenomena.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Production of neutron-rich heavy nuclei in deep-inelastic 208 Pb + 208 Pb collisions within the stochastic mean-field theory

In deep-inelastic collisions of heavy nuclei, reaction products with a wide range of mass and charge are produced. Such collisions been considered as a possible way to produce superheavy nuclei, as an alternative to fusion reactions. To provide reliable theoretical predictions, it is desired to develop microscopic approaches that correctly and accurately describe nucleon transfer processes in dissipative collisions of heavy nuclei. The purpose of the present work is (1) to investigate the mechanism of nucleon transfers in dissipative collisions of two heavy nuclei, and (2) to explore possible pathways to produce neutron-rich heavy nuclei, through detailed theoretical analyses of fluctuations and correlations in nucleon transfers in 208 Pb + 208 Pb reactions. Three-dimensional time-dependent Hartree-Fock (TDHF) calculations are performed for the collisions of 208 Pb + 208 Pb at 𝐸 c.m. = 832, 936, and 1040 MeV, using the Skyrme SLy4d energy density functional. To calculate fluctuations and correlations in nucleon transfers, we employ the stochastic mean-field (SMF) theory, and the results are compared with another theoretical framework currently available, the time-dependent random phase approximation (TDRPA). Primary and secondary production cross sections are calculated with the SMF theory combined with a statistical model, GEMINI ++ . Using information of nucleon flow across a neck of colliding nuclei in TDHF calculations, we solve quantal diffusion equations for fluctuations and correlations in nucleon transfers based on the SMF theory. From the SMF calculations, we obtain the time evolution of diffusion coefficients as well as fluctuations and correlations in nucleon transfers for a range of initial orbital angular momenta. We compare the results of the SMF calculations with those of TDRPA, showing that TDRPA tends to predict substantially larger fluctuations and correlations in strongly damped collisions of heavy nuclei, which exhibit complex initial angular momentum dependence, while the SMF results provide almost constant (stable) values. Using the obtained fluctuations and correlations, we calculate primary and secondary production cross sections for the 208 Pb + 208 Pb collisions. From the results, we find that both lighter and heavier reaction products as compared to 208 Pb are produced for a wide region in the 𝑁−𝑍 plane as primary products, thanks to the quantal diffusion mechanism in the dissipative collisions. However, we show that cross sections for production of heavy nuclei with 𝑍 ≳ 90 or 𝑁 ≳ 135 are washed out due to secondary particle evaporation and/or fission processes. On the other hand, we find that there remain sizable cross sections for production of neutron-rich nuclei along 𝑁 = 126 with 𝑍< 82, even after secondary disintegration processes. We demonstrate that the secondary production cross sections depend weakly on incident energies, but lower (higher) energy is slightly preferred for production of nuclei with smaller (larger) atomic numbers as compared to 𝑍 = 82. Here, based on the microscopic SMF calculations, it has been shown that deep-inelastic collisions of heavy nuclei, such as 208 Pb + 208 Pb examined in this study, can be a promising means to produce neutron-rich heavy nuclei along 𝑁=126. Discrepancies between the SMF and TDRPA approaches are left unsolved for future investigations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗