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Elastic Stochastic Full Waveform Inversion (eSFWI)

This collaboration between Lawrence Livermore National Security, LLC (LLNS) as manager and operator of Lawrence Livermore National Laboratory (LLNL) and Chevron USA Inc., acting through its Chevron Technical Center division, aimed at developing next-generation computational methods for the Elastic Stochastic Full Waveform Inversion (eSFWI). Seismic imaging is heavily used in the oil and gas industry for identifying and operating subsurface reservoirs. Improved seismic imaging methods can improve productivity, lower costs, and improve operational and environmental safety. This CRADA demonstrated that new high-performance computing (HPC) architectures being rolled out over the next five years can enable unprecedented seismic imaging resolution when using eSFWI techniques to process active seismic data. An open-source computational mini-application was developed, capable of demonstrating near-peak performance for eSFWI algorithms on CPU and GPU enabled HPC platforms. Performance was demonstrated on LLNL HPC systems such as Lassen, as well as on Chevron systems. This project benefited Chevron USA Inc. by demonstrating the potential computational efficiency of their full waveform inversion capabilities used to characterize oil/gas reservoirs, which in turn benefits the public through potential increases in capabilities to perform analysis of leasing sites.

04 OIL SHALES AND TAR SANDS↗

Feasibility Assessment of Using Electrical Impedance Tomography for Damage Localization in Graphite Microreactor Components

Microreactors have great potential to decrease capital costs and construction timelines, reducing the barriers to implementing advanced nuclear reactor technologies. However, the lower power output of these microreactors introduces economic challenges if the operation and maintenance costs cannot be reduced sufficiently. Many microreactor concepts use graphite materials for in-core moderator and structural purposes, which will require periodic inspection or, ideally, in situ structural health monitoring. This work describes an initial evaluation of the feasibility of leveraging graphite’s semiconducting properties to perform electrical impedance tomography (EIT) for defect localization. First, a study was performed to identify the best methods for bonding electrical contacts to minimize the effects of contact resistance that interfere with impedance measurements of the graphite. After determining the best bonding approach, electrodes were attached to multiple graphite components with varying geometries (e.g., simple block and more representative microreactor hexagonal block). In parallel, finite element analysis approaches were developed and implemented to analyze the impact of defects and contact resistances and to inform an iterative inverse model for reconstructing the conductivity distribution. The results of this study show that defect localization in graphite components is possible using EIT if a sufficient number of electrodes (to improve spatial resolution) can be bonded using a technique with very low contact resistance and those contact resistances remain stable during reactor operation. If the reactor core and vessel design do not allow electrodes to be bonded during reactor operation, then it may be possible to detach/reattach electrodes between reactor operation and outages if a suitable mechanical connection that offers repeatable contact resistance can be identified. Alternatively, future work could focus on identifying contacts that can survive the harsh reactor operating environment so that contacts do not need to be removed.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Critical and Subcritical Californium Source Driven Noise Analysis Experiments with Fresh PWR Fuels Pins

These experiments were performed in 1983 between August 1 and September 16 and used 35 operational days of critical facility time at the Babcock & Wilcox critical facility in Lynchburg, Va. These measurements were to assess the capability of the Cf source driven noise analysis method to measure the subcriticality of light water reactor fresh fuel configurations. This report documents the experiments of 1983 that were not reported at that time. These measurement with 2.459 wt. % 235 U enriched uranium oxide fresh fuel pins started at the delayed critical configuration of the fully assembled pressurized water reactor (PWR) core configuration with 1511 parts per million (ppm) natural boron (19.8 wt. % 10 B) in the water. This was a cylindrical configuration of 4961 fuel pins. After the initial measurements at delayed criticality, subcritical measurements by the Cf source driven noise analysis method were performed in which the number of detectors and Cf source locations were varied. Additional boron was added to the water moderator and reflector to reduce the neutron multiplication factor, with resulting boron concentrations of 1561, 1613, 1765, 1880, 2104, 2384, 2975, 3606, and 4303 ppm. After the completion of these measurements the increased, the boron concentration was returned to that at delayed critical (1511 ppm) and the reactivity was decreased by reducing the number of fuel pins in steps to 3713, 2553, 1281, 749, and 333 fuel pins and then to that (289) of a s ingle square 17 x 17 pin array, corresponding to a single PW fuel element. For all measurement that started at delayed criticality and then reduced the neutron multiplication factor to various subcritical states, inverse kinetics rod drop measurements at the higher reactivities were also performed but not reported here. At all subcritical states the break frequency noise analysis data was fitted to obtain the prompt neutron decay constant. Some data presented in this report are from notes not in the logbook. The purpose of this report is to document the experimental information for the measurements performed so that a later date someone could perform the required uncertainty and calculational analyses and documentation to use these data for an International Nuclear Criticality Safety Benchmark Program (INCSBEP) or Nuclear Energy Agency (NEA) benchmark. The data from these measurements is available from the Laboratory Records Department of Oak Ridge National Laboratory and the logbook is available from INCSBEP at Idaho National Laboratory.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

The development of Gibbs's dyadic and implications for the gradient of a vector field

In this paper, we review the history of the dyadic as developed by Gibbs. This mathematical construct appeared in the second part of Gibbs's pamphlet on vector analysis (published in 1884), and it represented the first known development of a Cartesian theory of tensors. Gibbs made extensive use of the dyadic to express his theory of linear vector functions, that is, functions that acted on vectors and mapped them to new vectors. The dyadic proved to be a capable vehicle in Gibbs's hands, and his theory for dyadics (which we would now call second-order Cartesian tensors) was relatively advanced. The theory detailed notions such as the decomposition of vectors and conditions under which a tensor would have an inverse. While Gibbs's theory for linear operators expressed by dyadics was robust, it did not seem to garner the attention that the more conventional vector analysis (published in the first half of his pamphlet in 1881) did. Perhaps in part because of the general unfamiliarity with the dyadic, two distinct and conflicting definitions of the gradient of a vector field have arisen in the literature. The details of these differences in notation, possible reasons for the difference, and a potential resolution are proposed.

97 MATHEMATICS AND COMPUTING↗

Comparative Evaluation of Spectral Methods for Robust Reactor Noise Estimation

Reactor noise analysis provides a noninvasive means to determine neutron kinetic parameters from stochastic fluctuations in detector signals. However, standard cross-power spectral density (CPSD) analyses can be sensitive to numerical processing choices, which may introduce processing-dependent systematic shifts in estimates of the prompt neutron decay constant (α) and limit reproducibility. This study uses a hybrid multitaper–Welch spectral estimator to analyze subcritical noise measurements from a fast-spectrum critical assembly. The decay constant α was extracted using three frequency-domain methods: the CPSD, the magnitude-squared coherence (MSC), and the generalized magnitude-squared coherence (GMSC). These coherence-based estimators normalize detector auto-spectral structure and are expected to reduce the sensitivity of fitted α values to processing parameters. A Sobol global sensitivity analysis identified which numerical inputs most strongly influence the fitted values of α. All estimators produced a linear dependence of α on inverse count rate, with delayed-critical extrapolations near 1.7 × 10 4 s −1 , in agreement within 8% of MCNP6.3 KOPTS benchmark calculations. Sensitivity results show that while the CPSD depends on both time-bin width and taper selection, the MSC and GMSC are dominated by time-bin width alone, indicating reduced parameter coupling and greater robustness to processing variability. These findings demonstrate the feasibility and practical value of coherence-based spectral estimators for extracting α from reactor noise and support their broader application to multi-detector and irregular datasets in subcritical system characterization.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Enhanced resonant ultrasound spectroscopy for measurement of the elastic properties of multi-material systems

Understanding the elastic properties of materials is critical for their safe incorporation and predictable performance. Current methods of bulk elastic characterization often have notable limitations for in situ structural applications, with usage restricted to simple geometries and material distributions. To address these existing issues, this study sought to expand the capabilities of resonant ultrasound spectroscopy (RUS), an established nondestructive evaluation method, to include the characterization of isotropic multi-material samples. In this work, finite-element-based RUS analysis consisted of numerical simulations and experimental testing of composite samples comprised of material pairs with varying elasticity and density contrasts. Utilizing genetic algorithm inversion and mode matching, our results demonstrate that elastic properties of multi-material samples can be reliably identified within several percent of known or nominal values using a minimum number of identified resonance modes, given sample mass is held consistent. The accurate recovery of material properties for composite samples of varying material similarity and geometry expands the pool of viable samples for RUS and advances the method towards in situ inspection and evaluation.

36 MATERIALS SCIENCE↗

Establishing performance metrics for quantitative non-targeted analysis: a demonstration using per- and polyfluoroalkyl substances

Abstract Non-targeted analysis (NTA) is an increasingly popular technique for characterizing undefined chemical analytes. Generating quantitative NTA (qNTA) concentration estimates requires the use of training data from calibration “surrogates,” which can yield diminished predictive performance relative to targeted analysis. To evaluate performance differences between targeted and qNTA approaches, we defined new metrics that convey predictive accuracy, uncertainty (using 95% inverse confidence intervals), and reliability (the extent to which confidence intervals contain true values). We calculated and examined these newly defined metrics across five quantitative approaches applied to a mixture of 29 per- and polyfluoroalkyl substances (PFAS). The quantitative approaches spanned a traditional targeted design using chemical-specific calibration curves to a generalizable qNTA design using bootstrap-sampled calibration values from “global” chemical surrogates. As expected, the targeted approaches performed best, with major benefits realized from matched calibration curves and internal standard correction. In comparison to the benchmark targeted approach, the most generalizable qNTA approach (using “global” surrogates) showed a decrease in accuracy by a factor of ~4, an increase in uncertainty by a factor of ~1000, and a decrease in reliability by ~5%, on average. Using “expert-selected” surrogates ( n = 3) instead of “global” surrogates ( n = 25) for qNTA yielded improvements in predictive accuracy (by ~1.5×) and uncertainty (by ~70×) but at the cost of further-reduced reliability (by ~5%). Overall, our results illustrate the utility of qNTA approaches for a subclass of emerging contaminants and present a framework on which to develop new approaches for more complex use cases. Graphical Abstract

Pu, Shirley (ORCID:0000000201223797)↗

Local Inversion Symmetry Breaking and Thermodynamic Evidence for Ferrimagnetism in Fe 3 GaTe 2

The layered compound Fe 3 GaTe 2 is attracting attention due to its high Curie temperature, low dimensionality, and the presence of topological spin textures above room temperature, making Fe 3 GaTe 2 a good candidate for applications in spintronics. Here, in this study, we show, through transmission electron microscopy (TEM) techniques, that Fe 3 GaTe 2 single crystals break local inversion symmetry while maintaining global inversion symmetry according to X-ray diffraction. Coupled to the observation of Néel skyrmions via Lorentz-TEM, our structural analysis provides a convincing explanation for their presence in centrosymmetric materials. Magnetization measurements as a function of the temperature displays a sharp first-order thermodynamic phase-transition leading to a reduction in the magnetic moment. This implies that the ground state of Fe 3 GaTe 2 is globally ferrimagnetic and not a glassy magnetic state composed of ferrimagnetic, and ferromagnetic domains as previously claimed. Neutron diffraction studies indicate that the ferromagnetic to ferrimagnetic transition upon reducing the external magnetic field is associated with a change in the magnetic configuration/coupling between Fe1 and Fe2 moments. We observe a clear correlation between the hysteresis observed in both the skyrmion density and the magnetization of Fe 3 GaTe 2 . This indicates that its topological spin textures are affected by the development of ferrimagnetism upon cooling. Observation, via magnetic force microscopy, of magnetic bubbles at the magnetic phase boundary suggests skyrmions stabilized by the competition among magnetic phases and distinct exchange interactions. Our study provides an explanation for the observation of Néel skyrmions in centrosymmetric systems, while exposing a correlation between the distinct magnetic phases of Fe 3 GaTe 2 and topological spin textures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A new method for solving the linearized 1D Vlasov–Poisson system yielding a new class of solutions

We describe a new method for solving the linearized 1D Vlasov–Poisson system by using properties of Cauchy-type integrals. Our method remedies critical flaws of the two standard methods, reveals a previously unrecognized Gaussian-in-time-like decay, and can also account for an externally applied electric field. The Landau approximation involves deforming the Bromwich contour around the poles closest to the real axis due to the analytically continued dielectric function, finding the long-time behavior for a stable system: Landau damping. Jackson's generalization encircles all poles while sending the contour to infinity, assuming its contribution vanishes, which is not true in general. This gives incorrect solutions for physically reasonable configurations and can exhibit pathological behavior, of which we show examples. The van Kampen method expresses the solution for a stable equilibrium as a continuous superposition of waves, resulting in an opaque integral. Case's generalization includes unstable systems and predicts a decaying discrete mode for each growing discrete mode, an apparent contradiction to both the Jackson solution and ours. We show, without imposing additional constraints, that the decaying modes are never present in the time evolution due to an exact cancellation with part of the continuum. Our solution is free of integral expressions, is obtained using algebra and Laurent series expansions, does not rely on analytic continuations, and results in a correct asymptotically convergent form in the case of infinite sums. The analysis used can be readily applied in higher-dimensional, electromagnetic systems and also provides a new technique for evaluating certain inverse Laplace transforms.

Physics↗

Unusual characteristics of the carbon cycle during the 2015–2016 El Niño

The 2015–2016 El Niño was one of the strongest on record, but its influence on the carbon balance is less clear. Using Northern Hemisphere atmospheric CO 2 observations, we found both detrended atmospheric CO 2 growth rate (CGR) and CO 2 seasonal-cycle amplitude (SCA) of 2015–2016 were much higher than that of other El Niño events. The simultaneous high CGR and SCA were unusual, because our analysis of long-term CO 2 observations at Mauna Loa revealed a significantly negative correlation between CGR and SCA. Atmospheric inversions and terrestrial ecosystem models indicate strong northern land carbon uptake during spring but substantially reduced carbon uptake (or high emissions) during early autumn, which amplified SCA but also resulted in a small anomaly in annual carbon uptake of northern ecosystems in 2015–2016. This negative ecosystem carbon uptake anomaly in early autumn was primarily due to soil water deficits and more litter decomposition caused by enhanced spring productivity. Furthermore, our study demonstrates a decoupling between seasonality and annual carbon cycle balance in northern ecosystems over 2015–2016, which is unprecedented in the past five decades of El Niño events.

54 ENVIRONMENTAL SCIENCES↗

KKT Preconditioners for PDE-Constrained Optimization with the Helmholtz Equation

This paper considers preconditioners for the linear systems that arise from optimal control and inverse problems involving the Helmholtz equation. Specifically, we explore an all-at-once approach. The main contribution centers on the analysis of two block preconditioners. Variations of these preconditioners have been proposed and analyzed in prior works for optimal control problems where the underlying partial differential equation is a Laplace-like operator. In this paper, we extend some of the prior convergence results to Helmholtz-based optimization applications. Our analysis examines situations where control variables and observations are restricted to subregions of the computational domain. We prove that solver convergence rates do not deteriorate as the mesh is refined or as the wavenumber increases. More specifically, for one of the preconditioners we prove accelerated convergence as the wavenumber increases. Additionally, in situations where the control and observation subregions are disjoint, we observe that solver convergence rates have a weak dependence on the regularization parameter. We give a partial analysis of this behavior. We illustrate the performance of the preconditioners on control problems motivated by acoustic testing.

97 MATHEMATICS AND COMPUTING↗

Mechanical Activation and Cation Site Disorder in MgAl 2 O 4

The synthesis and crystallographic site occupancy were investigated for MgAl 2 O 4 with and without mechanical activation of the precursor powders. Heating to 1200 °C or higher resulted in the formation of a single spinel phase regardless of whether the powders were mechanically activated or not. Neutron diffraction analysis was used to determine cation site occupancy and revealed that mechanical activation resulted in a lower degree of cation site inversion compared to the nonactivated materials, which indicated that the powders were closer to thermodynamic equilibrium. This is the first study to characterize the effects of mechanical activation on crystallographic site occupancy in magnesium aluminate spinel using neutron diffraction.

36 MATERIALS SCIENCE↗

Upper limit on the chiral magnetic effect in isobar collisions at the Relativistic Heavy-Ion Collider

The chiral magnetic effect (CME) is a phenomenon that arises from the QCD anomaly in the presence of an external magnetic field. The experimental search for its evidence has been one of the key goals of the physics program of the Relativistic Heavy-Ion Collider. The STAR Collaboration has previously presented the results of a blind analysis of isobar collisions ( Ru 44 96 + Ru 44 96 , Zr 40 96 + Zr 40 96 ) in the search for the CME. The isobar ratio ( Y ) of CME-sensitive observable, charge separation scaled by elliptic anisotropy, is close to but systematically larger than the inverse multiplicity ratio, the naive background baseline. This indicates the potential existence of a CME signal and the presence of remaining nonflow background due to two- and three-particle correlations, which are different between the isobars. In this postblind analysis, we estimate the contributions from those nonflow correlations as a background baseline to Y , utilizing the isobar data as well as Heavy Ion Jet Interaction Generator simulations. This baseline is found consistent with the isobar ratio measurement, and an upper limit of 10% at 95% confidence level is extracted for the CME fraction in the charge separation measurement in isobar collisions at s NN = 200 GeV. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Diffusion kinetics of 3 He in pyroxene and plagioclase and applications to cosmogenic exposure dating and paleothermometry in mafic rocks

In this study, we investigate the diffusivity of cosmogenic 3 He in a variety of plagioclase and pyroxene compositions, and its application to paleothermometry and exposure dating in these minerals, through stepwise degassing experiments. While cosmogenic 3 He has been utilized for exposure dating in pyroxene for decades due to its retentivity, plagioclase, often found along with pyroxene in mafic rocks, is generally less retentive of cosmogenic noble gas. However, the diffusivity of 3 He in either plagioclase or pyroxene has not yet been measured quantitatively. A challenge in measuring diffusion kinetics by step-degassing experiments in poorly retentive minerals is the fact that significant amounts of He can be lost prior to the experiment. To address this issue, we apply a forward “multiple diffusion domain” (MDD) inversion model that includes model predictions of initial gas loss during irradiation and storage of the samples to account for this observation and add constraints to the diffusion parameters. We find that 3 He diffusivity in plagioclase appears to be highly variable. This variability can be explained by the MDD inversion models' inability to constrain the diffusion parameters when significant gas has been lost during irradiation and/or prolonged storage prior to experiment analysis, resulting in an overestimation of 3 He retentivity. Plagioclase samples that were kept frozen after irradiation, to limit this initial gas loss, yielded the most reliable estimate of diffusion kinetics. We find that 3 He in plagioclase is diffusively lost at Earth's surface temperatures on a timescale of 100 years and is therefore unsuitable for surface temperature paleothermometry. On the contrary, we find cosmogenic 3 He in pyroxene to be retentive at Earth's surface temperatures on a 1-million-year timescale.

Bergelin, Marie [Berkeley Geochronology Center (BG↗

Fermiology and transport properties of the candidate topological crystalline insulator SrAg 4 ⁢Sb 2

Compared to time-reversal symmetry-protected ℤ 2 topological insulators and Dirac/Weyl semimetals, there are significantly fewer candidates for topological crystalline insulators. SrAg 4 ⁢Sb 2 is predicted to exhibit topological crystalline insulator behavior when considering spin-orbit coupling. In this study, we systematically investigate single crystals of SrAg 4 ⁢Sb 2 using electrical transport and magnetic torque measurements, along with first-principles calculations. Our transport data reveals its compensated semimetal nature with a magnetoresistance up to around 700% at 2 K and 9 T. Analysis of de Haas–van Alphen oscillations uncovers a Fermi surface consisting of three distinct Fermi pockets with light effective masses. Comparison between the three-dimensional fermiology obtained from our oscillation data and the first-principles calculations demonstrates excellent agreement. This confirms the accuracy of the calculations, which indicate a band inversion centered at the 𝑇 point and identify the existence of nontrivial tube and needle hole Fermi pockets at Γ, alongside one trivial diamond electron pocket at the 𝐹 point in the Brillouin zone. Furthermore, symmetry and topology analysis results in two potential sets of topological invariants, suggesting the emergence of two-dimensional gapless Dirac surface states either on the 𝑎⁢𝑏 planes or on both the 𝑎⁢𝑏 planes and mirror planes, protected by crystal symmetries. Therefore, SrAg 4 ⁢Sb 2 emerges as a promising candidate topological crystalline insulator.

36 MATERIALS SCIENCE↗

Orphaned oil and gas well methane emission rates quantified using Gaussian plume inversions of ambient observations

Abstract. Annually, ∼ 3.6 million abandoned oil and gas wells in the US emit a combined ∼ 2.6 Tg methane (CH4), adversely affecting climate and regional air quality. However, these estimates depend on emission factors derived from measuring subpopulations of wells that vary by orders of magnitude due to very limited field sampling and poorly characterized distributions. Currently, US protocols to remediate orphaned wells lacks standardized quantification methods needed to both prioritize plugging and account for emission reductions. Therefore, sensitive, reliable, affordable, and scalable CH4 flux quantification methods are needed. We report the use of a simple Gaussian plume method where the dispersion parameters are constrained by in situ ground measurements of CH4 concentration at four locations 7.5–49 m downwind of the orphan well as well as local winds to estimate the leak rate from an orphan well. We derive a flux of 10.53 ± 1.16 kg CH4 h−1 during a venting procedure in April 2023 that agrees with the directly measured volumetric flow rate of 9.00 ± 0.25 kg CH4 h−1. This is 71 % greater than the 5.3 kg CH4 h−1 flux measured 7 months prior. Additionally, we discovered a secondary leak through the surface casing inferred as 0.43–0.67 kg CH4 h−1 both by our ground Gaussian analysis and by transecting the plume with an uncrewed aerial system (UAS). We show that in situ determination of the dispersion parameters used in our Gaussian inversions allows us to measure methane emissions to 15 % accuracy, significantly reducing errors when compared to the standard practice of assuming stability class. Our results help develop simpler methods and protocols for robust orphan well emission quantification that can be used for reporting.

Follansbee, Emily↗

Large-momentum effective theory’s asymptotic extrapolation vs the inverse problem

Large-momentum effective theory is a physics-guided systematic expansion to calculate light-cone parton distributions, including collinear (PDFs) and transverse-momentum-dependent ones, at any fixed momentum fraction 𝑥 within a range of [𝑥 min , 𝑥 max ]. It theoretically solves the ill-posed inverse problem that afflicts other theoretical approaches to collinear PDFs, such as short-distance factorizations. Recently, Dutrieux et al. raised practical concerns about whether current or even future lattice data will have sufficient precision in the subasymptotic correlation region to support an error-controlled extrapolation—and if not, whether it becomes an inverse problem where the relevant uncertainties cannot be properly quantified. While we agree that not all current lattice data have the desired precision to qualify for an asymptotic extrapolation, some calculations do, and more are expected in the future. We comment on the analysis and results in Dutrieux et al. and argue that a physics-based systematic extrapolation still provides the most reliable error estimates, even when the data quality is not ideal. In contrast, reframing the long-distance asymptotic extrapolation as a data-driven-only inverse problem with ad hoc mathematical conditioning could lead to unnecessarily conservative errors.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

The influence of protein electrostatics on potential inversion in flavoproteins

Biology uses relatively few electron-transfer cofactors, tuning their potentials, electronic couplings, and reorganization energies to carry out the required chemistry. It is remarkable that the potential ordering of two-electron transfer active flavins can be normal (first oxidation at low potential and second oxidation at high potential) or inverted, and the gap between the potentials can be as large as one volt. Analysis based on structural bioinformatics and electrostatics indicates that the ordering of the flavin redox potential is influenced by protein electrostatics. In all 36 flavoproteins examined, the introduction of a negative charge near the flavin in silico increases the extent of potential inversion (by lowering the electrochemical potential of the second electron-transfer step); the introduction of a positive charge near the flavin favors normally ordered potentials. We also find that the addition of positive charges increases the electrochemical potential for the naturally occurring one-electron transition in flavodoxins (between deprotonated hydroquinone and neutral semiquinone) and also increases the second one-electron transition in bifurcating flavins (between anionic semiquinone and fully oxidized flavin). Finally, we find that proximity of a proton acceptor, notably conserved arginine, supports proton-coupled electron transfer because it may act as a proton acceptor, promoting potential inversion. This key arginine residue may enable two-electron transfer chemistry by promoting the proton-coupled electron transfer process over the pure electron transfer process, suggesting how a protein's flavin environment may influence one- or two-electron chemistry in flavoproteins.

Singh, Niven [Duke Univ., Durham, NC (United State↗