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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Quantum complexity of time evolution with chaotic Hamiltonians

We study the quantum complexity of time evolution in large-N chaotic systems, with the SYK model as our main example. This complexity is expected to increase linearly for exponential time prior to saturating at its maximum value, and is related to the length of minimal geodesics on the manifold of unitary operators that act on Hilbert space. Using the Euler-Arnold formalism, we demonstrate that there is always a geodesic between the identity and the time evolution operator e -iHt whose length grows linearly with time. This geodesic is minimal until there is an obstruction to its minimality, after which it can fail to be a minimum either locally or globally. We identify a criterion — the Eigenstate Complexity Hypothesis (ECH) — which bounds the overlap between offdiagonal energy eigenstate projectors and the k-local operators of the theory, and use it to argue that the linear geodesic will at least be a local minimum for exponential time. We show numerically that the large-N SYK model (which is chaotic) satisfies ECH and thus has no local obstructions to linear growth of complexity for exponential time, as expected from holographic duality. In contrast, we also study the case with N = 2 fermions (which is integrable) and find short-time linear complexity growth followed by oscillations. Our analysis relates complexity to familiar properties of physical theories like their spectra and the structure of energy eigenstates and has implications for the hypothesized computational complexity class separations PSPACE * BQP/poly and PSPACE * BQSUBEXP/subexp, and the “fast-forwarding” of quantum Hamiltonians.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Machine learning for the identification of phase transitions in interacting agent-based systems: A Desai-Zwanzig example

Deriving closed-form analytical expressions for reduced-order models, and judiciously choosing the closures leading to them, has long been the strategy of choice for studying phase- and noise-induced transitions for agent-based models (ABMs). In this paper, we propose a data-driven framework that pinpoints phase transitions for an ABM—the Desai-Zwanzig model—in its mean-field limit, using a smaller number of variables than traditional closed-form models. To this end, we use the manifold learning algorithm Diffusion Maps to identify a parsimonious set of data-driven latent variables, and we show that they are in one-to-one correspondence with the expected theoretical order parameter of the ABM. We then utilize a deep learning framework to obtain a conformal reparametrization of the data-driven coordinates that facilitates, in our example, the identification of a single parameter-dependent ordinary differential equation (ODE) in these coordinates. Additionally, we identify this ODE through a residual neural network inspired by a numerical integration scheme (forward Euler). We then use the identified ODE—enabled through an odd symmetry transformation—to construct the bifurcation diagram exhibiting the phase transition.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Explicit quantification of residence and flushing times in the Salish Sea using a sub-basin scale shoreline resolving model

The Salish Sea, located in the Pacific Northwest region of North America has complex currents and circulation features distributed over numerous interconnected deep basins with islands. Increased risk of exposure to oil spills and untreated wastewater from maritime emergencies and treatment plant failures have led to a need for quantifying residence and flushing characteristics at a sub-basin scale using a shoreline resolving hydrodynamic model. An unstructured grid model of the Salish Sea was developed using FVCOM with a ≈75-100m shoreline resolution. In addition to 7 tides and 23 salinity and temperature monitoring stations, an extensive currents data set from 135 stations collected over a span of three years was used for skill assessment and validation. Explicit forward computations were then conducted to define and quantify residence and flushing times in various sub-basins of interest using (a) Lagrangian particles and (b) Numerical/virtual dye experiments. The results in most basins show expected seasonal variability with longer flushing time associated with summer lower tides and lower freshwater inflows. However, contrary to expectation, flushing time is significantly longer in wintertime in large fjord-like basins such as Hood Canal (≈138 days), likely due to increased stratification and reduced mixing. The flushing time for the Puget Sound region of the Salish Sea is ≈115 days, while Georgia Basin is 240 days when analyzed as stand-alone basins with zero background concentrations. When examined as part of the flushing of the entire Puget Sound filled with virtual dye, the compounded flushing times for embedded sub-basins can be significantly longer in order of magnitudes and largely dictated by the flushing time of Puget Sound. The computed residence and flushing time scales tabulated over 36 sub-basins provide an improved understanding of water renewal in the system, informing pollution management actions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

A classical equation that accounts for observations of non-Arrhenius and cryogenic grain boundary migration

Observations of microstructural coarsening at cryogenic temperatures, as well as numerous simulations of grain boundary motion that show faster migration at low temperature than at high temperature, have been troubling because they do not follow the expected Arrhenius behavior. This work demonstrates that classical equations, that are not simplified, account for all these oddities and demonstrate that non-Arrhenius behavior can emerge from thermally activated processes. According to this classical model, this occurs when the intrinsic barrier energies of the processes become small, allowing activation at cryogenic temperatures. Additional thermal energy then allows the low energy process to proceed in reverse, so increasing temperature only serves to frustrate the forward motion. This classical form is shown to reconcile and describe a variety of diverse grain boundary migration observations.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Augmenting subspace optimization methods with linear bandits

In this work, we consider the framework of methods for unconstrained minimization that are, in each iteration, restricted to a model that is only a valid approximation to the objective function on some affine subspace containing an incumbent point. These methods are of practical interest in computational settings where derivative information is either expensive or impossible to obtain. Recent attention has been paid in the literature to employing randomized matrix sketching for generating the affine subspaces within this framework. We consider a relatively straightforward, deterministic augmentation of such a generic subspace optimization method. In particular, we consider a sequential optimization framework where actions consist of one-dimensional linear subspaces and rewards consist of (approximations to) the magnitudes of directional derivatives computed in the direction of the action subspace. Reward maximization in this context is consistent with maximizing lower bounds on descent guaranteed by first-order Taylor models. This sequential optimization problem can be analysed through the lens of dynamic regret. We modify an existing linear upper confidence bound (UCB) bandit method and prove sublinear dynamic regret in the subspace optimization setting. We demonstrate the efficacy of employing this linear UCB method in a setting where forward-mode algorithmic differentiation can provide directional derivatives in arbitrary directions and in a derivative-free setting. For the derivative-free setting, we propose SS-POUNDers, an extension of the derivative-free optimization method POUNDers that employs the linear UCB mechanism to identify promising subspaces. Our numerical experiments suggest a preference, in either computational setting, for employing a linear UCB mechanism within a subspace optimization method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Hot Springs and Geysers: Exploring Historical and Modern Impacts of Geothermal Energy Production on Associated Natural Surface Systems and Standardizing Management Practices

Surface thermal features, most notably hot springs and geysers are increasingly being recognized for their importance to ecosystems, indigenous cultures, and in some cases agriculture, recreation, and tourism. Geothermal project development poses a potential risk to these natural features but current regulatory requirements for assessing and managing these risks during exploration, permitting and monitoring are somewhat inconsistent and unpredictable across different geothermal fields. This has resulted in uncertainty and increases in exploration risk for geothermal energy developers that have led to costly project delays, cancellations, or hesitation to commit. Varying regulatory requirements may also influence public perception, fostering confusion, distrust and ultimately opposition to geothermal projects, further contributing to project delays or cancellations. At a time when there is an increasing urgency for reliable baseload clean energy, geothermal is a net-zero, renewable solution that additionally provides access to more equitable and environmentally just clean power. Continued integration of geothermal energy into the national energy roadmap can be facilitated through consistent and predictable permitting, providing regulators the framework they need, developers a clear path forward, and transparency that the public deserves. This project, currently in its beginning phases, seeks to address this important issue by providing a technical basis from which to build a preliminary protocol for assessing and managing potential impacts from new or existing geothermal energy projects to surface thermal features and their associated ecosystems. Development of this preliminary protocol will be informed by (1) a literature review of well-documented case studies in the western U.S. and New Zealand to understand the range of conditions that exemplify geothermal-surface thermal systems; (2) development of generic illustrative conceptual-numerical models to quantify, understand, and predict the first-order controls (e.g., pressure and permeability) on surface flows; and (3) additional independent and scientifically rigorous evaluations of geothermal-surface thermal system case studies from the Basin and Range Province that incorporate publicly available data as well as data provided by industry through data-sharing agreements. Learning from the successes of the process used to develop the Induced Seismicity Management Protocol (ISMP), we ultimately aim to use these initial efforts as a springboard for establishing a surface thermal feature management working group that will work collaboratively to finalize the protocol as well as co-create recommended best practices for implementation. We envision that the working group will primarily be composed of representatives from regulatory entities, government agencies, Tribes, academia, national laboratories, and industry, and will include early and regular engagement with community organizations and environmental groups. This will help ensure broad acceptance and implementation of the protocol, which will facilitate a more consistent, predictable, and standardized regulatory process, and help to ensure that geothermal energy continues to provide a reliable source of clean energy, and a pathway to achieving greater energy equity in the U.S.

Best Practices↗
DOE OSTI2024

Revealing the landscape of globally color-dual multi-loop integrands

Abstract We report on progress in understanding how to construct color-dual multi-loop amplitudes. First we identify a cubic theory, semi-abelian Yang-Mills, that unifies many of the color-dual theories studied in the literature, and provides a prescriptive approach for constructingD-dimensional color-dual numerators through one-loop directly from Feynman rules. By a simple weight counting argument, this approach does not further generalize to two-loops. As a first step in understanding the two-loop challenge, we use aD-dimensional color-dual bootstrap to successfully construct globally color-duallocaltwo-loop four-point nonlinear sigma model (NLSM) numerators. The double-copy of these NLSM numerators with themselves, pure Yang-Mills, and$$\mathcal{N}$$= 4 super-Yang-Mills correctly reproduce the known unitarity constructed integrands of special Galileons, Born-Infeld theory, and Dirac-Born-Infeld-Volkov-Akulov theory, respectively. Applying our bootstrap to two-loop four-point pure Yang-Mills, we exhaustively search the space of local numerators and find that it fails to satisfy global color-kinematics duality, completing a search previously initiated in the literature. We pinpoint the failure to the bowtie unitarity cut, and discuss a path forward towards non-local construction of color-dual integrands at generic loop order.

Physics↗
DOE OSTI2020

Southwest Wind Power R&D Test Site Development at the National Wind Technology Center (CRADA CRD-12-00472 Final Report)

Southwest Windpower, Inc. (SWWP) has been designing and distributing small wind turbines for more than 22 years and is the recognized global leader in the design, manufacturing and distribution of small wind systems (400-3000 watts). The company has been a pioneer in the development of wind technology and has built and shipped more than 170,000 wind turbines to over 120 countries worldwide. Headquartered in Flagstaff AZ, SWWP has sales representatives in over 88 countries. Applications for SWWP systems include residential homes, commercial properties, micro grids, remote cabins, telecom transmitters, offshore platforms, water pumping and sailboats. In addition, U.S. Department of Defense uses SWWP’s products in Forward Operating Bases (FOB’s), USGS uses them for remote monitoring of glacier movements and the CIA uses them to provide power seismic monitoring. Today, SWWP plans development of new technologies to address distributed energy market needs and become even more aggressive in international markets. This strategy includes extensive Research, Development, Demonstration & Deployment (RDD&D) activities to improve existing production line into more simple, reliable, and cost-effective wind turbine systems. Important part of such activities is the field testing of the new systems, which should provide: (i) validation of the reliable operation of hardware and software; (ii) validation of numerical models of the system and its components; (iii) field comparison of various control and optimization strategies; (iv) customized reliability testing; (v) customized monitoring and analysis testing; and (vi) IEC certification testing (vii) filed demonstration of system performance and reliability. Such field testing facility should encompass multiple towers and appropriate data acquisition systems. SWWP is exploring to move part of the engineering department to Colorado, and execute its RDD&D strategies in this new location. Partnership with NREL will provide great insights into SWWP’s RDD&D processes and more efficient commercialization by utilizing NWTC as the field testing site, and working close with NREL personnel. NWTC is ideally suited to strain the design. NREL is very experienced with customized and IEC testing. During this project, Southwest Windpower aims to improve the value proposition of distributed renewable energy, and make it a competitive choice in the energy markets. As of today, more then 170,000 small wind turbines, manufactured in the U.S., are installed in more then 180 countries. With the improved value proposition, Southwest Windpower wants to create and address new market needs, substantially increase its sales domestically and internationally, which should have positive impact on the creation of American jobs, competitiveness of U.S. economy, export or U.S. products, and the use of renewable energy.

17 WIND ENERGY↗
DOE OSTI2024

First observation of RMP ELM mitigation on MAST Upgrade

Abstract The first experimental attempts at controlling edge localised modes (ELMs) via the application of resonant magnetic perturbations on the MAST Upgrade tokamak are reported. Using the linear MHD model MARS-F, the phase shift between the upper and lower coil rows ΔΦ was optimised for toroidal mode number n = 1 and n = 2 fields, to provide forward guidance to experiments. In low β N discharges, the application of n = 1 3D fields caused the ELM frequency f E L M to increase by over a factor 20 relative to the reference, and also induced a locked mode, which did not cause a plasma termination nor an H-L back transition. However when β N was raised, this induced locked mode caused plasma termination which precluded mitigation access. Initially, applying a numerically optimised n = 2 field had no effect. However applying a rigid toroidal shift to this field caused a locked mode disruption, demonstrating the presence of a substantial n = 2 error field. Coil current ramps were conducted with ΔΦ set at 6 different values, resulting in either locked mode disruptions or no effect, but mitigation with n = 2 fields was not established.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

An adjoint-based optimization method for jointly inverting heterogeneous material properties and fault slip from earthquake surface deformation data

SUMMARY Analysis of tectonic and earthquake-cycle associated deformation of the crust can provide valuable insights into the underlying deformation processes including fault slip. How those processes are expressed at the surface depends on the lateral and depth variations of rock properties. The effect of such variations is often tested by forward models based on a priori geological or geophysical information. Here, we first develop a novel technique based on an open-source finite-element computational framework to invert geodetic constraints directly for heterogeneous media properties. We focus on the elastic, coseismic problem and seek to constrain variations in shear modulus and Poisson’s ratio, proxies for the effects of lithology and/or temperature and porous flow, respectively. The corresponding nonlinear inversion is implemented using adjoint-based optimization that efficiently reduces the cost function that includes the misfit between the calculated and observed displacements and a penalty term. We then extend our theoretical and numerical framework to simultaneously infer both heterogeneous Earth’s structure and fault slip from surface deformation. Based on a range of 2-D synthetic cases, we find that both model parameters can be satisfactorily estimated for the megathrust setting-inspired test problems considered. Within limits, this is the case even in the presence of noise and if the fault geometry is not perfectly known. Our method lays the foundation for a future reassessment of the information contained in increasingly data-rich settings, for example, geodetic GNSS constraints for large earthquakes such as the 2011 Tohoku-oki M9 event, or distributed deformation along plate boundaries as constrained from InSAR.

Geochemistry & Geophysics↗
DOE OSTI2025

Resummation for lattice QCD calculation of generalized parton distributions at nonzero skewness

Large-momentum effective theory (LaMET) provides an approach to directly calculate the x-dependence of generalized parton distributions (GPDs) on a Euclidean lattice through power expansion and a perturbative matching. When a parton’s momentum becomes soft, the corresponding logarithms in the matching kernel become non-negligible at higher orders of perturbation theory, which requires a resummation. But the resummation for the off-forward matrix elements at nonzero skewness ξ is difficult due to their multi-scale nature. In this work, we demonstrate that these logarithms are important only in the threshold limit, and derive the threshold factorization formula for the quasi-GPDs in LaMET. We then propose an approach to resum all the large logarithms based on the threshold factorization, which is implemented on a GPD model. We demonstrate that the LaMET prediction is reliable for [−1 + x 0 , −ξ − x 0 ] ∪ [−ξ + x 0 , ξ − x 0 ] ∪ [ξ + x 0 , 1 − x 0 ], where x 0 is a cutoff depending on hard parton momenta. Through our numerical tests with the GPD model, we demonstrate that our method is self-consistent and that the inverse matching does not spread the nonperturbative effects or power corrections to the perturbatively calculable regions.

hadronic spectroscopy↗
DOE OSTI2020

Deep Reinforcement Learning Based Volt-VAR Optimization in Smart Distribution Systems

This paper develops a model-free volt-VAR optimization (VVO) algorithm via multi-agent deep reinforcement learning (DRL) in unbalanced distribution systems. This method is novel since we cast the VVO problem in distribution networks to an intelligent deep Q-network (DQN) framework, which avoids solving a specific optimization model directly when facing time-varying operating conditions in the systems. We consider statuses/ratios of switchable capacitors, voltage regulators, and smart inverters installed at distributed generators as the action variables of the agents. A delicately designed reward function guides these agents to interact with the distribution system, in the direction of reinforcing voltage regulation and power loss reduction simultaneously. The forward-backward sweep method for radial three-phase distribution systems provides accurate power flow results within a few iterations to the DRL environment. The proposed method realizes the dual goals for VVO. We test this algorithm on the unbalanced IEEE 13-bus and 123-bus systems. Numerical simulations validate the excellent performance of this method in voltage regulation and power loss reduction.

41 EE - Solar Energy Technologies Office (EE-4S)↗
DOE OSTI2023

On the dual advantage of placing observations through forward sensitivity analysis

The four-dimensional variational data assimilation methodology for assimilating noisy observations into a deterministic model has been the workhorse in forecasting centres for over three decades. While this method provides a computationally efficient framework for dynamic data assimilation, it is largely silent on the important question concerning the minimum number and placement of observations. To answer this question, we demonstrate the dual advantage of placing the observations where the square of the sensitivity of the model solution with respect to the unknown control variables, called forward sensitivities, attains its maximum. By following this approach, we can force the observability Gramian to be of full rank, which in turn guarantees efficient recovery of the optimal values of the control variables, which is the first of the two advantages of this strategy. We further show that the proposed strategy of placing observations has another inherent optimality: the square of the sensitivity of the optimal estimates of the control with respect to the observations (used to obtain these estimates) attains its minimum value, a second advantage that is a direct consequence of the above strategy for placing observations. Our analytical framework and numerical experiments on linear and nonlinear systems confirm the effectiveness of our proposed strategy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Probabilistic estimation of depth-resolved profiles of soil thermal diffusivity from temperature time series: Supporting Data

This dataset consists of soil temperature time series that were used to estimate soil thermal diffusivity and its uncertainty trough the probabilistic modelling approach developed and presented in the article named "Probabilistic estimation of depth-resolved profiles of soil thermal diffusivity from temperature time series" and published in Earth Surface Dynamics. There are two compressed (.zip) files that contains synthetic (Synthetic_soiltemp_Teller.zip) and field (Field_soiltemp_Teller.zip) data. There is one MATLAB file that requires MATLAB to execute but any text editor can open it. The Synthetic_soiltemp_Teller.zip file includes 5 comma-delimited data files (.csv) each of which contains soil temperature time series generated through forward modeling (i.e., heat-conduction process in a heterogeneous medium using an explicit finite difference method) to mimic various types of temperature gradients, trend and fluctuations. These synthetic soil temperatures were used to investigate the impact of different environmental conditions on the uncertainty of thermal diffusivity estimates. The Field_soiltemp_Teller.zip file contains 28 comma-delimited data files (.csv) out of which (a) 27 files includes soil temperature time series recorded from 27 temperature probes located in a site along Teller Road about 40 km northwest of Nome, Alaska (64.72°N, 165.94°W), (b) one includes the name and coordinates of the 27 probes. These field soil temperatures were used to infer soil thermal diffusivity at numerous locations and depths in a discontinuous permafrost environment, and to evaluate the links between the estimated soil thermal diffusivity values and soil physical properties. The comma-delimited data files (.csv) of the synthetic and field soil temperature time series includes date and time (UTC) in the first column and soil temperature from 5 cm below the ground surface to 1.05 m depth (with 5 or 10 cm spacing between sensors) in the other columns. The measurements were acquired every 15 minutes. The Next-Generation Ecosystem Experiments: Arctic (NGEE Arctic), was a research effort to reduce uncertainty in Earth System Models by developing a predictive understanding of carbon-rich Arctic ecosystems and feedbacks to climate. NGEE Arctic was supported by the Department of Energy's Office of Biological and Environmental Research. The NGEE Arctic project had two field research sites: 1) located within the Arctic polygonal tundra coastal region on the Barrow Environmental Observatory (BEO) and the North Slope near Utqiagvik (Barrow), Alaska and 2) multiple areas on the discontinuous permafrost region of the Seward Peninsula north of Nome, Alaska. Through observations, experiments, and synthesis with existing datasets, NGEE Arctic provided an enhanced knowledge base for multi-scale modeling and contributed to improved process representation at global pan-Arctic scales within the Department of Energy's Earth system Model (the Energy Exascale Earth System Model, or E3SM), and specifically within the E3SM Land Model component (ELM).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks and Operators in Scientific Computing: Fluid and Solid Mechanics

Abstract Advancements in computing power have recently made it possible to utilize machine learning and deep learning to push scientific computing forward in a range of disciplines, such as fluid mechanics, solid mechanics, materials science, etc. The incorporation of neural networks is particularly crucial in this hybridization process. Due to their intrinsic architecture, conventional neural networks cannot be successfully trained and scoped when data are sparse, which is the case in many scientific and engineering domains. Nonetheless, neural networks provide a solid foundation to respect physics-driven or knowledge-based constraints during training. Generally speaking, there are three distinct neural network frameworks to enforce the underlying physics: (i) physics-guided neural networks (PgNNs), (ii) physics-informed neural networks (PiNNs), and (iii) physics-encoded neural networks (PeNNs). These methods provide distinct advantages for accelerating the numerical modeling of complex multiscale multiphysics phenomena. In addition, the recent developments in neural operators (NOs) add another dimension to these new simulation paradigms, especially when the real-time prediction of complex multiphysics systems is required. All these models also come with their own unique drawbacks and limitations that call for further fundamental research. This study aims to present a review of the four neural network frameworks (i.e., PgNNs, PiNNs, PeNNs, and NOs) used in scientific computing research. The state-of-the-art architectures and their applications are reviewed, limitations are discussed, and future research opportunities are presented in terms of improving algorithms, considering causalities, expanding applications, and coupling scientific and deep learning solvers.

Computer Science↗
DOE OSTI2022

DIAS: A Data-Informed Active Subspace Regularization Framework for Inverse Problems

This paper presents a regularization framework that aims to improve the fidelity of Tikhonov inverse solutions. At the heart of the framework is the data-informed regularization idea that only data-uninformed parameters need to be regularized, while the data-informed parameters, on which data and forward model are integrated, should remain untouched. We propose to employ the active subspace method to determine the data-informativeness of a parameter. The resulting framework is thus called a data-informed (DI) active subspace (DIAS) regularization. Four proposed DIAS variants are rigorously analyzed, shown to be robust with the regularization parameter and capable of avoiding polluting solution features informed by the data. They are thus well suited for problems with small or reasonably small noise corruptions in the data. Furthermore, the DIAS approaches can effectively reuse any Tikhonov regularization codes/libraries. Though they are readily applicable for nonlinear inverse problems, we focus on linear problems in this paper in order to gain insights into the framework. Various numerical results for linear inverse problems are presented to verify theoretical findings and to demonstrate advantages of the DIAS framework over the Tikhonov, truncated SVD, and the TSVD-based DI approaches.

Nguyen, Hai↗
DOE OSTI2023

Probability of Initiation in Neutron Transport

We discuss the numerical solution of the nonlinear integro-differential equation for the probability of a divergent neutron chain in a stationary system (i.e., the probability of initiation (POI)). We follow the development described in Bell’s classic paper on the stochastic theory of neutron transport. As noted by Bell, the linearized form of this equation resembles the linear adjoint neutron transport equation. A matrix formalism for the discretized steady state (or forward) neutron equation in slab geometry is first developed and is then used to derive the discrete adjoint equation. A main advantage of this discrete development is that the resulting discrete adjoint equation does not depend upon how the multigroup cross sections for the forward problem are obtained. That is, we derive the discrete adjoint directly from the discrete forward equations rather than discretizing directly the adjoint equation. This also guarantees that the discrete adjoint operator is consistent with the inner product used to define the adjoint operator. We discuss three approaches for the numerical solution of the POI equations, and present numerical results on several test problems. The three solution methods are a simple fixed-point iteration, a second approach that is akin to a nonlinear Power iteration, and a third approach which uses a Newton-Krylov nonlinear solver. We also give sufficient conditions to guarantee the existence and uniqueness of nontrivial solutions to our discrete POI equations when the discrete system is supercritical, and that only the trivial solution exists when the discrete system is subcritical. Our approach is modeled after the analysis presented for the continuous POI equations by Mokhtar-Kharroubi and Jarmouni-Idrissi, and by Pazy and Rabinowitz.

42 ENGINEERING↗
DOE OSTI2026

Signs of nonmonotonic finite-volume corrections to 𝑔 𝐴

We study finite-volume (FV) corrections to determinations of 𝑔 𝐴 via lattice quantum chromodynamics (QCD) using analytic results and numerical analysis. We observe that 𝑆⁢𝑈⁡(2) heavy Baryon chiral perturbation theory does not provide an unambiguous prediction for the sign of the FV correction, which is not surprising when one also considers large-𝑁 𝑐 constraints on the axial couplings. We further show that nonmonotonic FV corrections are naturally allowed when one considers either including explicit Δ-resonance degrees of freedom or one works to higher orders in the chiral expansion. We investigate the potential impact of these FV corrections with a precision study of 𝑔 𝐴 using models of FV corrections that are monotonic and nonmonotonic. Using lattice QCD data that is approximately at the 1% level of precision, we do not see significant evidence of nonmonotonic corrections. Looking forward to the next phase of lattice QCD calculations, we estimate that calculations that are between the 0.1% and 1% level of precision may be sensitive to these FV artifacts. Finally, we present an update of the CalLat prediction of 𝑔 𝐴 in the isospin limit with subpercent precision, 𝑔$^{QCD}_{𝐴}$ = 1.2674⁢(96).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗