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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Multilevel Parareal Algorithm with Averaging for Oscillatory Problems

The present study is an extension of the work done by Peddle, Haut, and Wingate and Haut and Wingate, where a two-level Parareal method with mapping and averaging is examined. The method proposed in this paper is a multilevel Parareal method with arbitrarily many levels, which is not restricted to the two-level case. We give an asymptotic error estimate which reduces to the two-level estimate for the case when only two levels are considered. Introducing more than two levels has important consequences for the averaging procedure, as we choose separate averaging windows for each of the different levels, which is an additional new feature of the present study. The different averaging windows make the proposed method especially appropriate for nonlinear multiscale problems, because we can introduce a level for each intrinsic scale of the problem and adapt the averaging procedure such that we reproduce the behavior of the model on the particular scale resolved by the level. The method is applied to nonlinear differential equations. The nonlinearities can generate a range of frequencies in the problem. The computational cost of the new method is investigated and studied on several examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Average and Marginal Capacity Credit Values of Renewable Energy and Battery Storage in the United States Power System

As deployment of renewable resources and storage continue to significantly grow in the coming decades, these technologies will play increasingly important roles in maintaining power systems' resource adequacy. Few analyses so far offer comprehensive comparisons of forward-looking average and marginal capacity credits of variable renewable energy and storage in the U.S. interconnections across a wide range of possible futures. To fill this research gap, we quantify the average and marginal capacity credits of solar PV, onshore and offshore wind, and batteries between 2026 and 2050 across the U.S power systems to examine the temporal trends, spatial patterns, and trade-offs between these two capacity accreditation approaches. Across technologies, capacity credits of solar PV most clearly follow downward trends over time, reflecting the significant rise in solar PV generation share as the grid decarbonizes. While battery storages' generation shares also rise significantly over time, their capacity credits always remain stably high due to their capabilities to be dispatched strategically during critical periods to maintain reliability. On the other hand, capacity credits of wind technologies in general follow slight upward trends as their generation shares level off. There are strong spatial variabilities of both average and marginal capacity credits across technologies, but capacity credits of solar PV displaying the most obvious spatial patterns with high capacity credits concentrating in wind-rich, solar-poor regions in SPP, PJM, and MISO, suggesting potential reliability benefits of interconnection-wide planning for renewable energy deployments. Additionally, except for offshore wind, average capacity credits of all other renewable technologies tend to be higher than their marginal capacity credits, indicating that existing renewable resources tend to be accredited higher than new resources at almost any time.

25 ENERGY STORAGE↗
DOE OSTI2025

Bounce-averaged theory in arbitrary multi-well plasmas: solution domains and the graph structure of their connections

Bounce-averaged theories provide a framework for simulating relatively slow processes, such as collisional transport and quasilinear diffusion, by averaging these processes over the fast periodic motions of a particle on a closed orbit. This procedure dramatically increases the characteristic time scale and reduces the dimensionality of the modelled system. The natural coordinates for such calculations are the constants of motion (COM) of the fast particle motion, which by definition do not change during an orbit. However, for sufficiently complicated fields – particularly in the presence of local maxima of the electric potential and magnetic field – the COM are not sufficient to specify the particle trajectory. In such cases, multiple domains in COM space must be used to solve the problem, with boundary conditions enforced between the domains to ensure continuity and particle conservation. Previously, these domains have been imposed by hand, or by recognising local maxima in the fields, limiting the flexibility of bounce-averaged simulations. Here, we present a general set of conditions for identifying consistent domains and the boundary condition connections between the domains, allowing the application of bounce-averaged theories in arbitrarily complicated and dynamically evolving electromagnetic field geometries. We also show how the connections between the domains can be represented by a directed graph, which can help to succinctly represent the trajectory bifurcation structure.

fusion plasma↗
DOE OSTI2026

Averages of 𝑏-hadron, 𝑐-hadron, and 𝜏-lepton properties as of 2023

This paper reports world averages of measurements of 𝑏-hadron, 𝑐-hadron, and 𝜏-lepton properties obtained by the Heavy Flavor Averaging Group using results available before October 2023. In rare cases, significant results obtained several months later are also used. For the averaging, common input parameters used in the various analyses are adjusted (rescaled) to common values, and known correlations are taken into account. The averages include branching fractions, lifetimes, neutral meson mixing parameters, 𝐶⁢𝑃 violation parameters, parameters of semileptonic decays, and Cabibbo-Kobayashi-Maskawa matrix elements.

Bottom quark production↗
DOE OSTI2025

Significant acceleration of solid-state NMR simulations via three-angle powder averaging

The anisotropic frequency shifts imparted onto the NMR resonance frequency depend on the spherical angular coordinates that describe the orientations of the NMR interaction tensors with respect to the applied magnetic field direction. Experiments performed using magic-angle spinning, however, gain a dependence on a third angle: the rotor phase γ. Traditionally, a carousel average is performed to integrate over γ, which leads to a slow convergence of intensities without contributing to the underlying powder patterns. Herein, we show an order of magnitude acceleration in computation time may be obtained by including the γ-averaging into the main powder average to eliminate redundant calculation of resonance frequencies.

magic-angle spinning↗
DOE OSTI2024

The lion, the witch, and the wormhole: ensemble averaging the symmetric product orbifold

Abstract We consider the ensemble average of two dimensional symmetric product orbifold CFTs Sym N (𝕋 D ) over the Narain moduli space. We argue for a bulk dual given byNcopies of an abelian Chern-Simons theory coupled to topological gravity, endowed with a discrete gauge symmetry exchanging theNcopies. As a check of this proposal, we calculate the ensemble average of various partition and correlation functions of the symmetric product orbifold theory and compare the resulting expressions to gauge theory quantities in the bulk. We comment on the ensemble average of the tensionless string partition function on AdS 3 × S 3 × 𝕋 4 by considering the specific case ofD= 4 with the addition of supersymmetry.

Physics↗
DOE OSTI2026

Average hydrodynamic radius analysis reveals critical solvation thresholds in high-concentration lithium electrolytes

Understanding the solvation structures of lithium salts in carbonate- and ether-based electrolytes is central to explaining the exceptional stability of high-concentration electrolytes (HCEs) and localized high-concentration electrolytes (LHCEs). Conventional techniques such as vibrational spectroscopy and one-dimensional NMR provide only limited information, typically restricted to coordination ratios and ion-pair distributions, without revealing the actual size and mass of solution complexes. Here, in this study, we introduce an average hydrodynamic radius (AHR) analysis based on internally referenced DOSY NMR, which enables direct estimation of the average volume and molecular weight of lithium–solvent complexes in solution. Using LiFSI–EMC and LiFSI–EMC–TTE electrolytes, we demonstrate that the onset of effective lithium metal stabilization and aluminum corrosion suppression coincides with the formation of very large complexes, whose average volume exceeds 300 times that of free EMC molecules. This finding supports a new “blocking mechanism,” wherein bulky solvated complexes impede direct solvent access to reactive surfaces. The AHR analysis thus not only clarifies the fundamental origin of HCE and LHCE effectiveness, but also provides a broadly applicable experimental framework for probing complex solvation structures and guiding rational electrolyte design.

Concentrated electrolytes↗
DOE OSTI2025

Tailoring coherent beam combined laser pulse trains for high peak and average power applications

Laser systems based on coherent beam combination (CBC) that rely on tiled pupil architecture intrinsically carry digital capabilities independently applicable to all three essential characteristics of a laser pulse: amplitude, phase and polarization. Those capabilities allow the far-field energy distribution to be flexibly tailored in real time. Operation in the femtosecond regime at high repetition rates gives access to a wide range of applications requiring both high peak and average powers. We address the task of independent peak versus average power adjustment needed for applications seeking to decouple nonlinear phenomena associated with GW peak power from the thermal load inherent to kW average power operation. The technical solutions proposed are presented in the framework of the Ecole Polytechnique XCAN CBC laser platform (61 independent channels) with an emphasis on thermal management measures implemented to ensure its nominal operation.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Areal-Averaged Surface Albedo (ArealAveAlb) Value-Added Product

The surface albedo plays an important role in the Earth's radiation balance. This report provides information on how to estimate areal-averaged surface albedo from ground-based measurements of solar radiation at five wavelengths (415,500,615,675, and 870 nm). The report first explains why this estimation is important and challenging. Then the report defines both the required and complimentary inputs for the corresponding Areal-Averaged Surface Albedo (ArealAveAlb) Value-Added Product (VAP) and highlights the major outputs of this VAP. The following section explains how estimation of the areal-averaged surface albedo at four wavelengths (500,615,675, and 870 nm) can be performed for different surface types, including those partly covered by snow. The final section provides three examples that illustrate the VAP’s performance and emphasizes the benefits of complementary inputs, such as distinct cloud types and precipitation.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

The rigorous upscaling of advection-dominated transport in heterogeneous porous media via the Method of Finite Averages

Systems involving advection-dominated transport through heterogeneous porous and fractured media are ubiquitous in subsurface engineering applications. However, upscaling such systems continues to challenge rigorous modeling efforts, particularly when advection is stronger than diffusion at fine spatial scales (i.e., when the Péclet number is greater than one at length scales that characterize a system’s unit-cells, representative elementary volumes, or averaging regions). Here, in this work, we propose and validate a strategy for extending the Method of Finite Averages (MoFA), a rigorous upscaling methodology for heterogeneous porous media, to upscale transport systems experiencing stronger advection than diffusion at fine scales (i.e., fine-scale Péclet numbers greater than one). We detail the strategy, the physical conditions under which it can be applied while retaining a priori modeling error guarantees, and implement the strategy to obtain a MoFA model for advective-diffusive transport that accommodates advective physics at fine spatial scales. We then perform two numerical experiments considering systems with system-scale Péclet numbers of 300 and 1000 — which correspond to fine-scale Péclet numbers of 30 and 100, respectively — to verify that the error guarantees are met under the strategy. After, we conduct a numerical study to demonstrate the strategy’s advantages over the original MoFA methodology. The results suggest that rigorously-upscaled transport models for heterogeneous porous media experiencing advective physics at finer spatial scales can be derived through MoFA and resolved orders of magnitude faster than their pore-scale counterparts. The results also suggest that the presented strategy is limited to modeling shallow concentration gradients when there are large differences between the time scales related to advection and a system’s temporally-varying boundary conditions. This limitation hinders the strategy’s practicality in modeling more advective systems, and as such, opportunity exists for developing additional strategies that accommodate rapidly-varying boundary conditions — and consequentially, steeper concentration gradients — while modeling advective systems with MoFA.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Wormholes without averaging

After averaging over fermion couplings, SYK has a collective field description that sometimes has “wormhole” solutions. We study the fate of these wormholes when the couplings are fixed. Working mainly in a simple model, we find that the wormhole saddles persist, but that new saddles also appear elsewhere in the integration space — “half-wormholes.” The wormhole contributions depend only weakly on the specific choice of couplings, while the half-wormhole contributions are strongly sensitive. The half-wormholes are crucial for factorization of decoupled systems with fixed couplings, but they vanish after averaging, leaving the non-factorizing wormhole behind.

1/N Expansion↗
DOE OSTI2024

Non-averaged single-molecule tertiary structures reveal RNA self-folding through individual-particle cryo-electron tomography

Large-scale and continuous conformational changes in the RNA self-folding process present significant challenges for structural studies, often requiring trade-offs between resolution and observational scope. Here, we utilize individual-particle cryo-electron tomography (IPET) to examine the post-transcriptional self-folding process of designed RNA origami 6-helix bundle with a clasp helix (6HBC). By avoiding selection, classification, averaging, or chemical fixation and optimizing cryo-ET data acquisition parameters, we reconstruct 120 three-dimensional (3D) density maps from 120 individual particles at an electron dose of no more than 168 e - Å -2 , achieving averaged resolutions ranging from 23 to 35 Å, as estimated by Fourier shell correlation (FSC) at 0.5. Each map allows us to identify distinct RNA helices and determine a unique tertiary structure. Statistical analysis of these 120 structures confirms two reported conformations and reveals a range of kinetically trapped, intermediate, and highly compacted states, demonstrating a maturation folding landscape likely driven by helix-helix compaction interactions.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Self-similar Reynolds-averaged mechanical–scalar turbulence models for Rayleigh–Taylor mixing induced by power-law accelerations in the small Atwood number limit

Analytical self-similar solutions to two-, three-, and four-equation Reynolds-averaged mechanical–scalar turbulence models describing turbulent Rayleigh–Taylor mixing driven by a temporal power-law acceleration are derived in the small Atwood number (Boussinesq) limit. The solutions generalize those previously derived for constant acceleration Rayleigh–Taylor mixing for models based on the turbulent kinetic energy K and its dissipation rate ε, together with the scalar variance S and its dissipation rate χ [O. Schilling, “Self-similar Reynolds-averaged mechanical–scalar turbulence models for Rayleigh–Taylor, Richtmyer–Meshkov, and Kelvin–Helmholtz instability-induced mixing in the small Atwood number limit,” Phys. Fluids 33, 085129 (2021)]. The turbulent fields are expressed in terms of the model coefficients and power-law exponent, with their temporal power-law scalings obtained by requiring that the self-similar equations are explicitly time-independent. Mixing layer growth parameters and other physical observables are obtained explicitly as functions of the model coefficients and parameterized by the exponent of the power-law acceleration. Values for physical observables in the constant acceleration case are used to calibrate the two-, three-, and four-equation models, such that the self-similar solutions are consistent with experimental and numerical simulation data corresponding to a canonical (i.e., constant acceleration) Rayleigh–Taylor turbulent flow. The calibrated four-equation model is then used to numerically reconstruct the mean and turbulent fields, and turbulent equation budgets across the mixing layer for several values of the power-law exponent. Finally, the reference solutions derived here can be used to understand the model predictions for strongly accelerated or decelerated Rayleigh–Taylor mixing in the large Reynolds number limit.

42 ENGINEERING↗
DOE OSTI2025

Average Rényi entanglement entropy in Gaussian boson sampling

Recently, many experiments have been conducted with the goal of demonstrating a quantum advantage over classical computation. One popular framework for these experiments is Gaussian boson sampling, where quadratic photonic input states are interfered via a linear optical unitary and subsequently measured in the Fock basis. In this paper, we study the modal entanglement of the output states in this framework just before the measurement stage. Specifically, we compute Page curves as measured by various Rényi- α entropies, where the Page curve describes the entanglement between two partitioned groups of output modes averaged over all linear optical unitaries. We derive these formulas for α = 1 (i.e., the von Neumann entropy) and, more generally, for all positive integer α , in the asymptotic limit of infinite number of modes and for input states that are composed of single-mode-squeezed-vacuum state with equal squeezing strength. We then analyze the limiting behaviors when the squeezing is small and large. Having determined the averages, we then explicitly calculate the Rényi- α variance for integers α > 1 and are able to show that these entropies are weakly typical. Published by the American Physical Society 2025

Youm, Jason (ORCID:0009000057597782)↗
DOE OSTI2026

Quantifying uncertainty in physics-based predictions of rare-isotope production cross sections via Bayesian-inspired model averaging across nuclear mass tables

Accurate prediction of fragmentation cross sections is essential for rare-isotope beam production, planning new-isotope searches, and designing experiments to study the most exotic regions of the nuclear chart. However, existing reaction models and phenomenological cross-section parametrizations often exhibit significant deviations over broad regions of mass and charge. In this work, a Bayesian-inspired model-averaging framework is developed to combine abrasion-ablation (AA) calculations based on multiple nuclear mass tables into a single statistically weighted estimate. For the calibrated systems, the model weights are assigned empirically according to the relative quality of fit to measured cross sections, thereby reducing systematic model bias while preserving the underlying physics content of the AA description. The weights are constrained using proton-rich fragmentation data for the 78 Kr and 124 Xe projectiles. The resulting parameter trends are then propagated to the 92 Mo and 144 Sm systems through a controlled scaling procedure. In the present implementation, the excitation-energy prescription is fixed, while the averaging is performed across nuclear-mass inputs; the framework provides both weighted cross sections and associated uncertainty estimates. Applied to proton-rich fragmentation, the present approach provides a practical basis for interpolation and limited extrapolation in regions relevant to rare-isotope production. The resulting predictions are used to assess the production of very proton-rich nuclei, and candidate new isotopes are discussed.

Bayesian methods↗
DOE OSTI2025

Shifting and tilting towards enhanced piezoelectricity in high-temperature ceramics: an average structure study of (1 − x )BiFe 2/8 Ti 3/8 Mg 3/8 O 3 – x PbTiO 3 through X-ray and neutron diffraction

A comprehensive report is provided of the average structure of a high Curie temperature ferroelectric ceramic, (1 − x)BiFe 2/8 Ti 3/8 Mg 3/8 O 3 –xPbTiO 3 (BFTM–xPT) when x = 0.25–0.375 at room temperature. Both neutron and synchrotron X-ray powder diffraction data were collected and combined Rietveld refinements were completed. These data revealed that, of the compositions studied, BFTM–xPT crystallizes as mixed phase material. At x = 0.25–0.275, the average structure of each phase is best described by space groups R3c and Cc. At 0.30 ≥ x ≥ 0.35, a morphotropic phase boundary is present and is best modelled by space groups P4mm and Cc, where space group Cc is the dominant phase. As the concentration of PbTiO 3 increases, the amount of octahedral tilting decreases and x = 0.375 exhibits a loss of octahedral tilting and crystallizes in space groups P4mm and Cm. In conclusion, an updated phase diagram at room temperature of this novel system is given and structural intricacies responsible for its piezoelectric properties are revealed.

high Curie temperature↗
DOE OSTI2024

Privacy-preserving Average Consensus Algorithm with Beaver Triple

A privacy-preserving average consensus algorithm is designed based on the Beaver triple technique against passive adversaries. The Beaver triple technique is integrated into a restructure of the discrete-time average consensus algorithm to preserve the privacy of initial values of agents in a multiagent system. The performance of the algorithm is theoretically analyzed.

Wang, Peng [Shanghai Jiao Tong University, China]↗
DOE OSTI2025

Privacy-Preserving Average Consensus With Beaver Triple and Communication Obfuscation

A privacy-preserving average consensus algorithm is proposed that synergizes the Beaver triple in secret sharing theory and noise obfuscation. The algorithm safeguards the initial values of agents against passive adversaries in a multiagent system. It is proved that the proposed algorithm can concurrently ensure average consensus and privacy, while also reducing the online computation and communication overhead compared to encryption-based ones. In addition, it imposes a less stringent condition for privacy preservation compared to certain noise-obfuscation techniques.

Beaver triple↗