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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Direct statistical simulation of the Lorenz96 system in model reduction approaches

Direct statistical simulation (DSS) of nonlinear dynamical systems bypasses the traditional route of accumulating statistics by lengthy direct numerical simulations by solving the equations that govern the statistics themselves. DSS suffers, however, from the curse of dimensionality as the statistics (such as correlations) generally have higher dimensions than the underlying dynamical variables. Here we investigate two approaches to reduce the dimensionality of DSS, illustrating each method with numerical experiments with the Lorenz96 dynamical system. The forms of DSS chosen here involve approximate closures at second and third order in the equal-time cumulants. We demonstrate significant reduction in computational effort that can be achieved without sacrificing the accuracy of DSS. The methods developed here can be applied to turbulent fluid and magnetohydrodynamical systems. Published by the American Physical Society 2025

Li, Kuan↗
DOE OSTI2023

On the convergence of statistics in simulations of stationary incompressible turbulent flows

When reporting statistics from simulations of statistically stationary chaotic phenomenon, it is important to verify that the simulations are time-converged. This condition is connected with the statistical error or number of digits with which statistics can be reliably reported. In this work we consider numerical experiments of low Reynolds number incompressible homogeneous and isotropic turbulence as a model problem to investigate statistical convergence over finite simulation times. Specifically, we investigate the time integration requirements that allow meaningful reporting of the statistical error associated with finiteness of the temporal domain. We address two key questions: (1) How long should a simulation be performed in terms of large eddy time, and (2) How should the simulation time be divided among temporal windows over which a quantity of interest is estimated so that its statistical error could be reliably reported? We find that reliable reporting of statistical errors requires simulations on the order of 10 4 large eddy times, which is orders of magnitude longer than typically performed. Additionally, data post-processing should employ windows of at least ten times the large eddy time scale, with the most robust computation of statistical error of the mean requiring window sizes of an additional factor of ten. For practical simulations, we demonstrate that it is possible to estimate the statistical error within a factor of two under a less stringent condition in which a minimum of four windows with size at least ten large eddy times are used. In conclusion, our observations for homogeneous isotropic turbulence are also shown to hold in turbulent channel flow.

42 ENGINEERING↗
DOE OSTI2024

Estimating Uncertainty in Simulated ENSO Statistics

Abstract Large ensembles of model simulations are frequently used to reduce the impact of internal variability when evaluating climate models and assessing climate change induced trends. However, the optimal number of ensemble members required to distinguish model biases and climate change signals from internal variability varies across models and metrics. Here we analyze the mean, variance and skewness of precipitation and sea surface temperature in the eastern equatorial Pacific region often used to describe the El Niño–Southern Oscillation (ENSO), obtained from large ensembles of Coupled model intercomparison project phase 6 climate simulations. Leveraging established statistical theory, we develop and assess equations to estimate, a priori, the ensemble size or simulation length required to limit sampling‐based uncertainties in ENSO statistics to within a desired tolerance. Our results confirm that the uncertainty of these statistics decreases with the square root of the time series length and/or ensemble size. Moreover, we demonstrate that uncertainties of these statistics are generally comparable when computed using either pre‐industrial control or historical runs. This suggests that pre‐industrial runs can sometimes be used to estimate the expected uncertainty of statistics computed from an existing historical member or ensemble, and the number of simulation years (run duration and/or ensemble size) required to adequately characterize the statistic. This advance allows us to use existing simulations (e.g., control runs that are performed during model development) to design ensembles that can sufficiently limit diagnostic uncertainties arising from simulated internal variability. These results may well be applicable to variables and regions beyond ENSO.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Testing the thermal Sunyaev-Zel’dovich power spectrum of a halo model using hydrodynamical simulations

Statistical properties of large-scale cosmological structures serve as powerful tools for constraining the cosmological properties of our Universe. Tracing the gas pressure, the thermal Sunyaev-Zel’dovich (tSZ) effect is a biased probe of mass distribution and, hence, can be used to test the physics of feedback or cosmological models. Therefore, it is crucial to develop robust modelling of hot gas pressure for applications to tSZ surveys. Since gas collapses into bound structures, it is expected that most of the tSZ signal is within halos produced by cosmic accretion shocks. Hence, simple empirical halo models can be used to predict the tSZ power spectra. In this study, we employed the HMx halo model to compare the tSZ power spectra with those of several hydrodynamical simulations: the Horizon suite and the Magneticum simulation. We examine various contributions to the tSZ power spectrum across different redshifts, including the one- and two-halo term decomposition, the amount of bound gas, the importance of different masses, and the electron pressure profiles. Our comparison of the tSZ power spectrum reveals discrepancies between the halo model and cosmological simulations that increase with redshift. We find a 20% to 50% difference between the measured and predicted tSZ angular power spectrum over the multipole range ℓ = 10 3 − 10 4 . Our analysis reveals that these differences are driven by the excess of power in the predicted two-halo term at low k and in the one-halo term at high k . At higher redshifts ( z ∼ 3), simulations indicate that more power comes from outside the virial radius than from inside, suggesting a limitation in the applicability of the halo model. We also observe differences in the pressure profiles, despite the fair level of agreement on the tSZ power spectrum at low redshift with the default calibration of the halo model. In conclusion, our study suggests that the properties of the halo model need to be carefully controlled against real or mock data to be proven useful for cosmological purposes.

Ayçoberry, Emma (ORCID:0000000292351195)↗
DOE OSTI2025

Stokes-dependent droplet collection efficiency on a NACA 0012 airfoil from droplet-informed simulations with statistical overloading

Accurate modelling of ice accretion on aircraft wings requires analysing droplet impingement on the surface to optimize the design of ice-protection systems. We perform Euler–Lagrange simulations of a droplet-laden flow impinging on a NACA 0012 airfoil. Our study includes water droplets with eight discrete sizes ranging from 1 to 160 microns. We vary the free-stream velocity of the incoming airflow in the range 60 ≤ U ≤ 240 m s −1 and the chord length of the airfoil in the range 0.5 ≤ c ≤ 2 m. Due to the dilute nature of supercooled clouds, one-way coupling is used in the simulations. The effects of droplet breakup and collision are also neglected. To reduce the computational cost, we employ statistical overloading of droplets, allowing us to simulate millions of impinging droplets in a time span on the order of milliseconds. Our results show that the droplet collection efficiency, which measures the likelihood of droplet impingement on the airfoil surface, increases with droplet size and free-stream velocity but decreases with airfoil size. We demonstrate that collection efficiency, impingement velocity and impingement angle are primarily dictated by a single non-dimensional parameter, the droplet Stokes number. We also identify a critical stagnation-streamline Stokes number below which impingements do not occur and use it to estimate the minimum droplet size for impingement. In addition, we observe droplet behaviour to become Stokes number independent at large values of the Stokes number. This article is part of the theme issue ‘Heat and mass transfer in frost and ice’.

Science & Technology - Other Topics↗
DOE OSTI2023

Λ Baryon Production in ν¯µ Interactions in the MicroBooNE Detector

The Cabibbo suppressed production of $\Lambda$ baryons in anti-neutrino interactions with nuclei is a rare process that is yet to be measured with a modern neutrino detector with automated reconstruction. The cross section for this process is sensitive to a number of unique nuclear effects, most notably the secondary interactions of the produced hyperon while attempting to escape from the nucleus. Other interactions within the nuclear remnant can impact the estimation of neutrino energy in oscillation measurements, and thus an accurate description of the nuclear environment is required. The strangeness violating hyperon production process is only available to anti-neutrinos. The model of this interaction is implemented into the NuWro neutrino interaction Monte Carlo simulation, and some predictions are presented, focusing on the role of nuclear effects. This model introduces a hyperon-nucleus potential, which calculations from hypernuclear theory permit to be strongly repulsive in th e case of $\Sigma$ baryons. The presence of this potential is found to sculpt the shape of the differential cross section in some variables. The MicroBooNE detector will be described, followed by a description of a measurement of the flux averaged, restricted phase space cross section of Cabibbo suppressed $\Lambda$ baryon production. A sophisticated event selection is employed, as a very large quantity of background neutrino interactions must be removed to perform the measurement with any sensitivity. This selection introduces some novel techniques such as the island finding method, and achieves a background reduction of $\sim 10^6$, with an efficiency of around 7\%. The calculation of the systematic uncertainties will be explained, including two procedures explored to handle sources of background with extremely poor simulation statistics: an in-situ constraint using data from sidebands, and a visual inspection of the data and simulation to remove the troublesome background events. The sensitivity to the $\Lambda$ baryon production cross section is calculated in the form of Bayesian posterior probability distributions, combining the systematic uncertainties with data and simulation statistical uncertainties. As a rare process, the statistical uncertainties are highly non-Gaussian, and the Bayesian approach is applied to include the full shapes of these uncertainties. Data corresponding to $2.2 \times 10^{20}$ protons on target of neutrino mode running and $4.9 \times 10^{20}$ protons on target of anti-neutrino running is analysed. When the data was unblinded, five $\Lambda$ production candidates were selected from the data, consistent with the MC simulation prediction of $5.3 \pm 1.1$ events. The final estimated cross section is $1.8^{+2.0}_{-1.6} \times 10^{-40}$cm$^2/$Ar when employing the sideband constraint procedure. A similar result of $2.0^{+2.2}_{-1.8} \times 10^{-40}$cm$^2/$Ar is obtained when performing the visual scan instead. The methods used in t his analysis are intended to be easily exported to other LArTPC detectors such as the Short Baseline Near Detector.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Analytical estimation of the signal to noise ratio efficiency in axion dark matter searches using a Savitzky-Golay filter

The signal to noise ratio efficiency ϵ SNR in axion dark matter searches has been estimated using large-statistic simulation data reflecting the background information and the expected axion signal power obtained from a real experiment. This usually requires a lot of computing time even with the assistance of powerful computing resources. Employing a Savitzky-Golay filter for background subtraction, in this work, we estimated a fully analytical ϵ SNR without relying on large-statistic simulation data, but only with an arbitrary axion mass and the relevant signal shape information. Hence, our work can provide ϵ SNR using minimal computing time and resources prior to the acquisition of experimental data, without the detailed information that has to be obtained from real experiments. Axion haloscope searches have been observing the coincidence that the frequency independent scale factor ξ is approximately consistent with the ϵ SNR . This was confirmed analytically in this work, when the window length of the Savitzky-Golay filter is reasonably wide enough, i.e., at least 5 times the signal window.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

A statistical and simulation-informed model for estimating permeability from pore size distribution in saturated geomaterials

Accurate permeability estimation is essential across subsurface engineering applications but remains challenging due to the complex pore structures of natural geomaterials. Traditional empirical methods and simplified theoretical models often inadequately capture the role of pore size distribution and connectivity. Here, this study develops a statistical and simulation-informed permeability model that collapses pore-scale complexity into a compact scaling of the form k = αϕμ d 2 , where ϕ is porosity, μ d is mean pore size, and α is a weakly varying coefficient. By combining pore network simulations with statistical analysis of unimodal and bimodal pore size distributions, we identify three key findings: (i) permeability is much more sensitive to mean pore size than to porosity; (ii) across extensive datasets, the ratio σ d /μ d (standard deviation to mean) clusters around a characteristic value ∼0.4, allowing the effects of the full pore size distribution to be represented by μ d and a narrowly varying α ≈ 0.05; and (iii) for bimodal systems, there exists a critical fraction of small pores ∼0.78 above which flow becomes small-pore dominated, enabling the definition of an effective flow-controlling pore population and facilitating simplified permeability estimation for such systems. The resulting model, which requires only porosity and a representative mean pore size as inputs, is validated against comprehensive experimental datasets (>1700 samples) spanning diverse soils and rocks and achieves good predictive accuracy. Overall, this work provides a physically grounded yet practically simple permeability estimator suitable for subsurface engineering, environmental protection, and resource management applications.

Permeability↗
DOE OSTI2026

A Framework for Parametric and Predictive Uncertainty Quantification in the E3SM Land Model: Assessing Site and Observable Generalizability

Quantifying parametric uncertainty using observations from individual sites provides a critical foundation for Earth system modeling, serving as a necessary first step before scaling up to regional or global applications. This study introduces a novel computational framework designed to enhance model predictability by reducing parametric uncertainty and assessing site and observable generalizability using various observational constraints. The framework integrates five components: Model Simulation, Statistical Emulation, Global Sensitivity Analysis (GSA), Model Calibration, and Model Prediction. Using the E3SM land model, we simulated site-level land-atmosphere carbon and energy fluxes from 2003 to 2007 across five evergreen needleleaf FLUXNET sites, perturbing 26 vegetation-related model parameters. Gaussian process emulators were employed to expedite GSA and model calibration. Four critical parameters that strongly influence selected land-atmosphere fluxes were identified by GSA. Bayesian approaches were used to infer parameter probability distributions leveraging synthetic data and FLUXNET observations. The results reveal that posterior parameter distributions vary significantly across different sites and observables within the same plant functional type. Probabilistic predictions indicate that parameters calibrated at one site can enhance predictive accuracy at other sites, although site heterogeneity may sometimes outweigh parametric uncertainty. Additionally, the probabilistic predictions demonstrate that calibration for one variable can also improve predictability for other variables, thereby maximizing predictive capabilities with limited observations. This framework provides a powerful approach for reducing parametric uncertainty in Earth system models and deepening our understanding of carbon dynamics and energy cycles. Its adaptability makes it a valuable tool for broader applications in Earth system modeling.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Using Host Galaxy Photometric Redshifts to Improve Cosmological Constraints with Type Ia Supernovae in the LSST Era

We perform a rigorous cosmology analysis on simulated Type Ia supernovae (SNe Ia) and evaluate the improvement from including photometric host galaxy redshifts compared to using only the "z spec " subset with spectroscopic redshifts from the host or SN. We use the Deep Drilling Fields (~50 deg 2 ) from the Photometric LSST Astronomical Time-Series Classification Challenge (PLAsTiCC) in combination with a low-z sample based on Data Challenge2. The analysis includes light-curve fitting to standardize the SN brightness, a high-statistics simulation to obtain a bias-corrected Hubble diagram, a statistical+systematics covariance matrix including calibration and photo-z uncertainties, and cosmology fitting with a prior from the cosmic microwave background. Compared to using the z spec subset, including events with SN+host photo-z results in (i) more precise distances for z > 0.5, (ii) a Hubble diagram that extends 0.3 further in redshift, and (iii) a 50% increase in the Dark Energy Task Force figure of merit (FoM) based on the w 0 w a CDM model. Analyzing 25 simulated data samples, the average bias on w 0 and w a is consistent with zero. The host photo-z systematic of 0.01 reduces FoM by only 2% because (i) most z < 0.5 events are in the z spec subset, (ii) the combined SN+host photo-z has ×2 smaller bias, and (iii) the anticorrelation between fitted redshift and color self-corrects distance errors. To prepare for analyzing real data, the next SN Ia cosmology analysis with photo-zs should include non–SN Ia contamination and host galaxy misassociations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

New Muon Campus Simulations for the Muon $g\textrm{-}2$ Experiment at Fermilab

The Muon $g\textrm{-}2$ Experiment (E989) at Fermilab conducted high-precision measurements of the muon anomalous magnetic moment $a_{\mu}$ using a storage ring from 2018 to 2023, achieving a remarkable precision of $200\:\mathrm{ppb}$ over Runs 1-3, with analyses for Runs 4-6 ongoing. A comprehensive understanding of the storage ring's beam dynamics and its accurate simulations are crucial for achieving the experiment's ambitious goals. One of the requirements for this effort is a very detailed knowledge of the phase space distribution of the beam. To address this requirement, we performed high-statistics simulations of the Muon $g\textrm{-}2$ Target Station (AP0) and the Muon Campus beamlines: M2 and M3, followed by the Delivery Ring, and then M4 and M5. The resulting muon distribution at the end of the M5 beamline from our previous $3\times10^{12}$ protons-on-target (PoT) simulation serves as an essential input for the storage ring simulations. In 2024, to facilitate the analyses of Runs 4-6, we have updated our Muon Campus models and re-optimised certain parameters to reflect the operational currents and wire chamber measurements of the beam. For these optimisations, we employed the heterogeneous island method, implemented in our evolutionary optimisation tool, glyfada. This key update addresses the need to use the best possible beam for the storage ring simulations and thus supports the experiment's overall precision. The Muon $g\textrm{-}2$ Experiment at Fermilab has successfully achieved its $70\:\mathrm{ppb}$ systematic uncertainty goal and collected 21 times more data than its predecessor at BNL. The updated and improved Muon Campus models and simulations not only facilitate the experiment's efforts to potentially resolve the current tension between experimental measurements and theoretical predictions of $a_{\mu}$, but also provide a basis for future simulations for the Mu2e Experiment (E-973), which utilises shared Muon Campus beamlines.

43 PARTICLE ACCELERATORS↗
DOE OSTI2025

169 Tm ( n , γ ) cross section and statistical decay properties from measurements at the DANCE facility

Background: Radiative neutron capture on thulium, which is a monoisotopic element, plays a role in different applications such as nuclear astrophysics or nuclear burning environments. Considerable discrepancies—reaching 20%—exist between evaluations in the unresolved-resonance region. Furthermore, experimental data on statistical 𝛾 decay in odd-odd rare-earth nuclei is scarce. There are still open questions about the systematics of the so-called scissors mode in the 𝑀⁢1 photon strength function, especially in odd-odd nuclei. Purpose: This work is focused on two main topics—deriving experimental 169 Tm ⁢(𝑛,𝛾) cross section and studying statistical 𝛾 decay of 170 Tm, in particular properties of the scissors mode. Methods: The capture experiments to obtain experimental cross section were performed at the Los Alamos Neutron Science Center using the time-of-flight technique and employing the Detector for Advanced Neutron Capture Experiments. Measured coincident 𝛾-ray spectra were also compared with statistical simulations using the dicebox code to test different models of level density and photon strength functions. Results: The capture cross section was determined from 1.8 eV to 0.97 MeV, the broadest neutron-energy range ever measured for this isotope. Several new resonances have been observed. The statistical 𝛾 decay of 170 Tm cannot be reproduced without a scissors mode resonance centered at ≈ 3.3MeV. Conclusions: The measured cross section in the unresolved-resonance region is generally lower than the latest evaluations. The derived 169 Tm 𝑠-process abundance is expected to increase by a factor of 1.26, while the changes of the abundances of elements heavier than 169 Tm are in the order of 0.2%. The scissors mode properties in 170 Tm are similar to those deduced in previous analyses of neighboring nuclei 168 Er and 166 Ho .

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Stochastic symplectic reduced-order modeling for model-form uncertainty quantification in molecular dynamics simulations in various statistical ensembles

Here, this work focuses on the representation of model-form uncertainties in molecular dynamics simulations in various statistical ensembles. In prior contributions, the modeling of such uncertainties was formalized and applied to quantify the impact of, and the error generated by, pair-potential selection in the microcanonical ensemble (NVE). In this work, we extend this formulation and present a linear-subspace reduced-order model for the canonical (NVT) and isobaric (NPT) ensembles. The symplectic reduced-order basis is randomized on the tangent space of the Stiefel manifold to provide topological relationships and capture model-form uncertainty. Using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS), we assess the relevance of these stochastic reduced-order atomistic models on canonical problems involving a Lennard-Jones fluid and an argon crystal melt.

42 ENGINEERING↗
DOE OSTI2024

Evidence of Directional Structural Superlubricity and Lévy Flights in a van der Waals Heterostructure

Abstract Structural superlubricity is a special frictionless contact in which two crystals are in incommensurate arrangement such that relative in‐plane translation is associated with vanishing energy barrier crossing. So far, it has been realized in multilayer graphene and other van der Waals (2D crystals with hexagonal or triangular crystalline symmetries, leading to isotropic frictionless contacts. Directional structural superlubricity, to date unrealized in 2D systems, is possible when the reciprocal lattices of the two crystals coincide in one direction only. Here, directional structural superlubricity a α‐bismuthene/graphite van der Waals system is evidenced, manifested by spontaneous hopping of the islands over hundreds of nanometers at room temperature, resolved by low‐energy electron microscopy and supported by registry simulations. Statistical analysis of individual and collective α‐bismuthene islands populations reveal a heavy‐tailed distribution of the hopping lengths and sticking times indicative of Lévy flight dynamics, largely unobserved in condensed‐matter systems.

Le Ster, Maxime↗
DOE OSTI2024

Probing nuclear structure of heavy ions at energies available at the CERN Large Hadron Collider

We perform high-statistics simulations to study the impacts of nuclear structure on the ratios of anisotropic flow observables in 208 Pb + 208 Pb and 129 Xe + 129 Xe collisions at the Large Hadron Collider. Even with 40% difference in atomic numbers between 208 Pb and 129 Xe nuclei, the ratios of anisotropic flow in the same centrality class between the two collision systems are strongly affected by the nuclear structure inputs in the initial state. The ratios of v 2 ⁡{4}/v 2 ⁡{2} in these collisions are sensitive to the nuclear skin thickness of the colliding nuclei, providing indirect constraints on the nuclei's neutron skin. In conclusion, our model predictions serve as a benchmark to compare with experimental measurements.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Probing fractional statistics in quantum simulators of spin liquid Hamiltonians

Recent advances in programmable quantum devices brought to the fore the intriguing possibility of using them to realise and investigate topological quantum spin liquid phases. This new and exciting direction brings about important research questions on how to probe and determine the presence of such exotic, highly entangled phases in a noisy quantum environment. One of the most promising tools is investigating the behaviour of the topological excitations, and in particular their fractional statistics. In this work we put forward a generic route to achieve this, and we illustrate it in the specific case of \mathbb{Z}_2 ℤ 2 topological spin liquids implemented with the aid of combinatorial gauge symmetry. We design a convenient architecture to study signatures of fractional statistics via quasiparticle interferometry, and we assess its robustness to diagonal and off-diagonal disorder, as well as to dephasing - effects that are generally pervasive in current quantum programmable devices. Interestingly, when turned on its head, our scheme provides a remarkably clear test of the “quantumness” of these devices, with robust signatures that crucially hinge on quantum coherence and quantum interference effects, and cannot be mimicked by classical stochastic processes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Tunable Nanostructures from Inverse Surfactants

Hierarchical materials in the natural world are often made through the self-assembly of amphiphilic molecules. Achieving similar structural complexity in synthetic materials requires understanding how various molecular parameters affect assembly behavior. In recent years, inverse surfactants─molecules with hydrophobic head groups and hydrophilic macromolecular tails─have been shown to self-assemble into supramolecular assemblies in aqueous solutions that show promise for a number of applications, including drug delivery. Here, we build an understanding of the morphological phase diagram of inverse surfactants using insights from scattering experiments, computer simulations, and statistical mechanics. The scattering and simulation results reveal that changing the headgroup size is an important molecular knob in controlling morphological transitions. The molecular size ratio of the hydrophobic group to the hydrophilic group emerges as a crucial dimensionless quantity in our theory and plays a determining role in setting the micelle structure and the transition from mesoscale to macroscale aggregates. Our minimal theory is able to qualitatively explain the key features of the morphological phase diagram, including the prevalence of fiber-like structures in comparison to spherical and planar micelles. Together, these findings provide a more complete picture of the molecular dependencies of assemblies of inverse surfactants, which we hope may aid in the de novo design of supramolecular structures.

Christakopoulos, Panagiotis [ORNL] (ORCID:00090004↗