Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “fitting”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Gemini Planet Imager Spectroscopy of the Dusty Substellar Companion HD 206893 B

We present new near-infrared Gemini Planet Imager (GPI) spectroscopy of HD 206893 B, a substellar companion orbiting within the debris disk of its F5V star. The J, H, K1, and K2 spectra from GPI demonstrate the extraordinarily red colors of the object, confirming it as the reddest substellar object observed to date. The significant flux increase throughout the infrared presents a challenging atmosphere to model with existing grids. Best-fit values vary from 1200 to 1800 K for effective temperature and from 3.0 to 5.0 for log(g), depending on which individual wavelength band is fit and which model suite is applied. The extreme redness of the companion can be partially reconciled by invoking a high-altitude layer of submicron dust particles, similar to dereddening approaches applied to the peculiar red field L dwarf population. However, reconciling the HD 206893 B spectra with even those of the reddest low-gravity L dwarf spectra still requires the contribution of additional atmospheric dust, potentially due to the debris disk environment in which the companion resides. Orbit fitting from 4 yr of astrometric monitoring is consistent with a ∼30 yr period, an orbital inclination of 147°, and a semimajor axis of 10 au, well within the estimated disk inner radius of ∼50 au. As one of a very few substellar companions imaged interior to a circumstellar disk, the properties of this system offer important dynamical constraints on companion–disk interaction and provide a benchmark for substellar and planetary atmospheric study.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

Polarimetric Geometric Modeling for mm-VLBI Observations of Black Holes

The Event Horizon Telescope (EHT) is a millimeter very long baseline interferometry (VLBI) array that has imaged the apparent shadows of the supermassive black holes M87* and Sagittarius A*. Polarimetric data from these observations contain a wealth of information on the black hole and accretion flow properties. In this work, we develop polarimetric geometric modeling methods for mm-VLBI data, focusing on approaches that fit data products with differing degrees of invariance to broad classes of calibration errors. We establish a fitting procedure using a polarimetric “m-ring” model to approximate the image structure near a black hole. By fitting this model to synthetic EHT data from general relativistic magnetohydrodynamic models, we show that the linear and circular polarization structure can be successfully approximated with relatively few model parameters. We then fit this model to EHT observations of M87* taken in 2017. In total intensity and linear polarization, the m-ring fits are consistent with previous results from imaging methods. In circular polarization, the m-ring fits indicate the presence of event-horizon-scale circular polarization structure, with a persistent dipolar asymmetry and orientation across several days. The same structure was recovered independently of observing band, used data products, and model assumptions. Despite this broad agreement, imaging methods do not produce similarly consistent results. Our circular polarization results, which imposed additional assumptions on the source structure, should thus be interpreted with some caution. Polarimetric geometric modeling provides a useful and powerful method to constrain the properties of horizon-scale polarized emission, particularly for sparse arrays like the EHT.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

COVID-19 global pandemic planning: Performance and electret charge of N95 respirators after recommended decontamination methods

Shortages of N95 respirators for use by medical personnel have driven consideration of novel conservation strategies, including decontamination for reuse and extended use. Decontamination methods listed as promising by the Centers for Disease Control and Prevention (CDC) (vaporous hydrogen peroxide (VHP), wet heat, ultraviolet irradiation (UVI)) and several methods considered for low resource environments (bleach, isopropyl alcohol and detergent/soap) were studied for two commonly used surgical N95 respirators (3M™ 1860 and 1870+ Aura™). Although N95 filtration performance depends on the electrostatically charged electret filtration layer, the impact of decontamination on this layer is largely unexplored. As such, respirator performance following decontamination was assessed based on the fit, filtration efficiency, and pressure drop, along with the relationship between (1) surface charge of the electret layer, and (2) elastic properties of the straps. Decontamination with VHP, wet heat, UVI, and bleach did not degrade fit and filtration performance or electret charge. Isopropyl alcohol and soap significantly degraded fit, filtration performance, and electret charge. Pressure drop across the respirators was unchanged. Modest degradation of N95 strap elasticity was observed in mechanical fatigue testing, a model for repeated donnings and doffings. CDC recommended decontamination methods including VHP, wet heat, and UV light did not degrade N95 respirator fit or filtration performance in these tests. Extended use of N95 respirators may degrade strap elasticity, but a loss of face seal integrity should be apparent during user seal checks. NIOSH recommends performing user seal checks after every donning to detect loss of appropriate fit. Decontamination methods which degrade electret charge such as alcohols or detergents should not be used on N95 respirators. The loss of N95 performance due to electret degradation would not be apparent to a respirator user or evident during a negative pressure user seal check.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Parameter inference from event ensembles and the top-quark mass

One of the key tasks of any particle collider is measurement. In practice, this is often done by fitting data to a simulation, which depends on many parameters. Sometimes, when the effects of varying different parameters are highly correlated, a large ensemble of data may be needed to resolve parameter-space degeneracies. An important example is measuring the top-quark mass, where other physical and unphysical parameters in the simulation must be profiled when fitting the top-quark mass parameter. We compare four different methodologies for top-quark mass measurement: a classical histogram fit similar to one commonly used in experiment augmented by soft-drop jet grooming; a 2D profile likelihood fit with a nuisance parameter; a machine-learning method called DCTR; and a linear regression approach, either using a least-squares fit or with a dense linearly-activated neural network. Despite the fact that individual events are totally uncorrelated, we find that the linear regression methods work most effectively when we input an ensemble of events sorted by mass, rather than training them on individual events. Although all methods provide robust extraction of the top-quark mass parameter, the linear network does marginally best and is remarkably simple. For the top study, we conclude that the Monte-Carlo-based uncertainty on current extractions of the top-quark mass from LHC data can be reduced significantly (by perhaps a factor of 2) using networks trained on sorted event ensembles. More generally, machine learning from ensembles for parameter estimation has broad potential for collider physics measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

SymbolFit: Automatic Parametric Modeling with Symbolic Regression

We introduce SymbolFit (API: https://github.com/hftsoi/symbolfit), a framework that automates parametric modeling by using symbolic regression to perform a machine-search for functions that fit the data while simultaneously providing uncertainty estimates in a single run. Traditionally, constructing a parametric model to accurately describe binned data has been a manual and iterative process, requiring an adequate functional form to be determined before the fit can be performed. The main challenge arises when the appropriate functional forms cannot be derived from first principles, especially when there is no underlying true closed-form function for the distribution. In this work, we develop a framework that automates and streamlines the process by utilizing symbolic regression, a machine learning technique that explores a vast space of candidate functions without requiring a predefined functional form because the functional form itself is treated as a trainable parameter, making the process far more efficient and effortless than traditional regression methods. We demonstrate the framework in high-energy physics experiments at the CERN Large Hadron Collider (LHC) using five real proton-proton collision datasets from new physics searches, including background modeling in resonance searches for high-mass dijet, trijet, paired-dijet, diphoton, and dimuon events. We show that our framework can flexibly and efficiently generate a wide range of candidate functions that fit a nontrivial distribution well using a simple fit configuration that varies only by random seed, and that the same fit configuration, which defines a vast function space, can also be applied to distributions of different shapes, whereas achieving a comparable result with traditional methods would have required extensive manual effort.

Tsoi, Ho Fung [Univ. of Pennsylvania, Philadelphia↗
DOE OSTI2021

Combined selection of the dynamic model and modeling error in nonlinear aeroelastic systems using Bayesian Inference

Here, we report a Bayesian framework for concurrent selection of physics-based models and (modeling) error models. We investigate the use of colored noise to capture the mismatch between the predictions of calibrated models and observational data that cannot be explained by measurement error alone within the context of Bayesian estimation for stochastic ordinary differential equations. Proposed models are characterized by the average data-fit, a measure of how well a model fits the measurements, and the model complexity measured using the Kullback–Leibler divergence. The use of a more complex error models increases the average data-fit but also increases the complexity of the combined model, possibly over-fitting the data. Bayesian model selection is used to find the optimal physical model as well as the optimal error model. The optimal model is defined using the evidence, where the average data-fit is balanced by the complexity of the model. The effect of colored noise process is illustrated using a nonlinear aeroelastic oscillator representing a rigid NACA0012 airfoil undergoing limit cycle oscillations due to complex fluid–structure interactions. Several quasi-steady and unsteady aerodynamic models are proposed with colored noise or white noise for the model error. The use of colored noise improves the predictive capabilities of simpler models.

42 ENGINEERING↗
DOE OSTI2024

Measurement of (anti)alpha production in central Pb–Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV

In this letter, measurements of (anti)alpha production in central (0–10%) Pb–Pb collisions at a center-of-mass energy per nucleon–nucleon pair of $\sqrt{s_{NN}} = 5.02$ TeV are presented, including the first measurement of an antialpha transverse-momentum spectrum. Owing to its large mass, the production of (anti)alpha is expected to be sensitive to different particle production models. The production yields and transverse-momentum spectra of nuclei are of particular interest because they provide a stringent test of these models. The averaged antialpha and alpha spectrum is compared to the spectra of lighter particles, by including it into a common blast-wave fit capturing the hydrodynamic-like flow of all particles. This fit is indicating that the (anti)alpha also participates in the collective expansion of the medium created in the collision. A blast-wave fit including only protons, (anti)alpha, and other light nuclei results in a similar flow velocity as the fit that includes all particles. A similar flow velocity, but a significantly larger kinetic freeze-out temperature is obtained when only protons and light nuclei are included in the fit. The coalescence parameter B 4 is well described by calculations from a statistical hadronization model but significantly underestimated by calculations assuming nucleus formation via coalescence of nucleons. Similarly, the (anti)alpha-to-proton ratio is well described by the statistical hadronization model. On the other hand, coalescence calculations including approaches with different implementations of the (anti)alpha substructure tend to underestimate the data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Overcoming significant challenges in extracting off-stoichiometric thermodynamics using the compound energy formalism through complementary use of experimental and first principles data: A case study of Ba 1-x Sr x FeO 3-δ

The compound energy formalism (CEF) is a powerful framework to describe the thermodynamics of metal oxides as a function of off-stoichiometry, temperature, and composition. The thermodynamic properties are crucial materials design attributes in metal oxide-based oxygen-exchange chemical processes. Despite the richness of information an accurate CEF model provides, a method to determine a unique and accurate fit for oxygen exchange materials remains elusive. This contribution details a method for fitting the CEF model that overcomes the current fitting challenges through three innovations: 1) the combination of density functional theory calculations with experimental data decorrelates excess terms and delineates the enthalpic/entropic contributions to the Gibbs free energy; 2) a systematic determination of the important CEF model terms, removing thermodynamic predetermining human intervention; 3) a self-consistent solution of the starting oxygen offstoichiometry (δ 0 ) of thermogravimetric measurements. Thus, our method enables the reliable extraction of off-stoichiometric metal oxide thermodynamic properties and facilitates rapid materials compositional screening, and reliable process design of systems dependent on off-stoichiometric redox-active metal oxides. We apply this method to a Ba x Sr 1-x FeO 3-δ test case. We find by systematically examining the performance of the CEF model fit with and without each innovation that all three innovations are necessary for an accurate fit. We determined that reduction enthalpy is higher and more sensitive to off-stoichiometry when the Sr fraction is large (139.5 and 185.3 kJ/mol O 2 for SrFeO 3 at δ = 0 and δ = 0.5, respectively vs. nearly constant 83 kJ/mol O 2 for BaFeO 3 ). However, the reduction entropy is mostly insensitive to Sr fraction, but highly dependent on δ suggesting larger contributions in the non-configurational entropy parameters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

A quantitative assessment of the model form error of friction models across different interface representations for jointed structures

Hysteretic models are widely used to model frictional interactions in joints to recreate experimental behavior. However, it is unclear which models are best suited for fitting or predicting the responses of structures. Here, the present study evaluates 26 friction model/interface representation combinations to quantify the model form error. A Quasi-Static Modal Analysis approach (termed Rayleigh Quotient Nonlinear Modal Analysis) is adopted to calculate the nonlinear system response, and a Multi-Objective Optimization is solved to fit experimental data of the first mode of the Brake-Reuß Beam. Optimized parameters from the first mode are applied to the second and third bending modes to quantify the predictive ability of the models. Formulations for both tracing full hysteresis loops and recreating hysteresis loops from a single loading curve (Masing assumptions) are considered. Smoothly varying models applied to a five patch representation showed the highest flexibility (for fitting mode 1) and good predictive potential (for modes 2 and 3). For a second formulation, which uses 152 frictional elements to represent the interface, the physically motivated spring in series with a Coulomb slip model (elastic dry friction) has high error for fitting mode 1 and performs near the middle for predicting higher modes. For both interface representation, the best fit models are not the most physical, but rather the ones with the most parameters (as expected); however, the more physical models perform somewhat better for predicting the higher modes.

42 ENGINEERING↗
DOE OSTI2025

Challenges of standard halo models in constraining galaxy properties from cosmic infrared background anisotropies

The halo model, combined with halo occupation distribution (HOD) prescriptions, is widely used to interpret cosmic infrared background (CIB) anisotropies and extract physical information about star-forming galaxies and their connection to large-scale structures. Recent CIB-specific implementations of the halo model have adopted more physical parameterizations. However, the extent to which these models can reliably recover meaningful physical parameters remains uncertain. We assessed whether the current parameterization of CIB halo models is sufficient to recover astrophysical quantities, such as star formation efficiency, η(M h , z), and halo mass at which the peak of star formation efficiency occurs, M max , when fit to mock data. We also assessed whether discrepancies arise from assumptions about galaxy emission (the HOD ingredients) or from more fundamental components in the halo model, such as bias and matter clustering. We fit the M21 CIB HOD model, implemented within the halo model framework, to mock CIB power spectra and star formation rate density (SFRD) data generated from the SIDES-Uchuu simulation, and compared the best-fit parameters to the known simulation inputs. We then repeated the analysis using a simplified version of the simulation (SSU), explicitly designed to match the HOD assumptions. A detailed comparison of model and simulation outputs was carried out to trace the origin of observed discrepancies. While the M21 HOD model provides a good fit to the mock data, it failed to recover the intrinsic parameters accurately, particularly the halo mass at which star formation efficiency peaks. This mismatch persists even when fitting data generated with the same model assumptions. We find strong agreement (within 5%) in the emission-related components (SFRD, emissivity), but observe a scale- and redshift-dependent offset exceeding 20% in the two-halo term of the CIB power spectrum. This likely arises from limitations in the treatment of halo bias and matter clustering within the linear approximation. Additionally, incorporating scatter in the SFR–halo mass relation and the spectral energy distribution (SED) templates significantly affects the shot noise (∼50%), but has only a modest impact (less than 10%) on the clustered component. These results suggest that recovering physical parameters from CIB clustering requires improvements to the cosmological ingredients of the halo model framework, such as adopting scale-dependent halo bias and nonlinear matter power spectra in addition to careful modeling of emission physics.

cosmic background radiation↗
DOE OSTI2021

Transport coefficients for magnetic-field evolution in inviscid magnetohydrodynamics

The magnetized resistivity and electrothermal tensors when substituted into the induction equation lead to electrothermal magnetic field generation, resistive magnetic diffusion, and magnetic field advection due to resistivity gradients, temperature gradients and currents. Here, the advection terms driven by temperature gradient and current have cross-field components (perpendicular to both the magnetic field and the driving term) that depend on significantly modified versions of Braginskii’s transport coefficients. The improved fits to Braginskii’s coefficients given by Epperlein and Haines and Ji and Held give physically incorrect results for cross-field advection at small Hall parameters (product of cyclotron frequency and collision time). The errors in Epperlein and Haines’ fits are particularly severe, giving increasing advection velocities below a Hall parameter of one when they should decrease linearly to zero. Epperlein and Haines’ fits can also give erroneous advection terms due to variations in effective atomic number. The only serious error in Braginskii’s fits is an overestimate in advection due to perpendicular resistivity. New fits for the cross-field advection terms are obtained from a direct numerical solution of the Fokker-Planck equation and Ji and Held’s higher order expansion approach that are continuous functions of the effective atomic number.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Quantifying electron temperature distributions from time-integrated x-ray emission spectra

K-shell x-ray emission spectroscopy is a standard tool used to diagnose the plasma conditions created in high-energy-density physics experiments. In the simplest approach, the emissivity-weighted average temperature of the plasma can be extracted by fitting an emission spectrum to a single temperature condition. It is known, however, that a range of plasma conditions can contribute to the measured spectra due to a combination of the evolution of the sample and spatial gradients. In this work, we define a parameterized model of the temperature distribution and use Markov Chain Monte Carlo sampling of the input parameters, yielding uncertainties in the fit parameters to assess the uniqueness of the inferred temperature distribution. Here we present the analysis of time-integrated S and Fe x-ray spectroscopic data from the Orion laser facility and demonstrate that while fitting each spectral region to a single temperature yields two different temperatures, both spectra can be fit simultaneously with a single temperature distribution. We find that fitting both spectral regions together requires a maximum temperature of $1310^{+90}_{-70}$ eV with significant contributions from temperatures down to 200 eV.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Did we hear the sound of the Universe boiling? Analysis using the full fluid velocity profiles and NANOGrav 15-year data

Abstract In this paper, we analyse sound waves arising from a cosmic phase transition where the full velocity profile is taken into account as an explanation for the gravitational wave spectrum observed by multiple pulsar timing array groups. Unlike the broken power law used in the literature, in this scenario the power law after the peak depends on the macroscopic properties of the phase transition, allowing for a better fit with pulsar timing array (PTA) data. We compare the best fit with that obtained using the usual broken power law and, unsurprisingly, find a better fit with the gravitational wave (GW) spectrum that utilizes the full velocity profile. Even more importantly, the thermal parameters that produce the best fit are quite different. We then discuss models that can produce the best-fit point and complementary probes using CMB experiments and searches for light particles in DUNE, IceCUBE-Gen2, neutrinoless doubleβ-decay, and forward physics facilities (FPF) at the LHC like FASERν, etc.

Astronomy & Astrophysics↗
DOE OSTI2024

3D radiated power analysis of JET SPI discharges using the Emis3D forward modeling tool

Abstract Precise values for radiated energy in tokamak disruption experiments are needed to validate disruption mitigation techniques for burning plasma tokamaks like ITER and SPARC. Control room analysis of radiated power ( P rad ) on JET assumes axisymmetry, since fitting 3D radiation structures with limited bolometry coverage is an under-determined problem. In mitigated disruptions, radiation is toroidally asymmetric and 3D, due to fast-growing 3D MHD modes and localized impurity sources. To address this problem, Emis3D adopts a physics motivated forward modeling (‘guess and check’) approach, comparing experimental bolometry data to synthetic data from user-defined radiation structures. Synthetic structures are observed with the Cherab modeling framework and a best fit chosen using a reduced χ 2 statistic. 2D tomographic inversion models are tested, as well as helical flux tubes and 3D MHD simulated structures from JOREK. Two nominally identical pure neon shattered pellet injection (SPI) mitigated discharges in JET are analyzed. 2D tomographic inversions with added toroidal freedom are the best fits in the thermal quench (TQ) and current quench (CQ). In the pre-TQ, 2D reconstructions are statistically the best fits, but are likely over-optimized and do not capture the 3D radiation structure seen in fast camera images. The next-best pre-TQ fits are helical structures that extend towards the high-field side, consistent with an impurity flow under the magnetic nozzle effect also observed in JOREK simulations. Whole-disruption radiated fractions of 0.98 + 0.03 / − 0.29 and 1.01 + 0.02 / − 0.17 are found, suggesting that the stored energy may have been fully mitigated by each SPI, although mitigation efficiencies well below ITER and SPARC requirements for high energy pulses are still within the large uncertainties. Emis3D is also used to validate JOREK SPI simulations, and confirms improvements in matching experiment from changes to impurity modeling. Time-dependent toroidal peaking factors are calculated and discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

SDSS-IV MaStar: [α/Fe] for the MaNGA Stellar Library from synthetic model spectra

ABSTRACT We calculate the α-enhancement ratio [α/Fe] for the Mapping Nearby Galaxies at APO (MaNGA) Stellar Library (MaStar) while also fitting for the fundamental atmospheric parameters effective temperature, surface gravity, and metallicity – Teff, log g, [Fe/H]. This approach builds upon a previous catalogue of stellar parameters, whereby only the fundamental atmospheric parameters are fit with solar-scaled models. Here, we use the same Markov Chain Monte Carlo method with the additional free parameter [α/Fe]. Using the full spectral fitting code pPXF, we are able to fit multiple lines sensitive to [α/Fe] for a more robust measurement. Quality flags based on the convergence of the sampler, errors in [α/Fe] and a cut in the χ2 of the model fit are used to clean the final catalogue, returning 17 214 spectra and values in the range of −0.25 < [α/Fe] < 0.48. Comparing our calculated [α/Fe] with literature values reveals a degeneracy in cool stars with log g ≥ ∼4; this comparison is then used to create an alternative and calibrated parameter set. We also plot the final catalogue in an [Fe/H] versus [α/Fe] diagram and recover the expected result of increasing [α/Fe] with decreasing [Fe/H] for Milky Way disc-halo stars. We apply our method to a subsample of spectra of uniform resolution and higher signal to noise that finds that our results are independent of this higher signal to noise. In the context of stellar population models, we are able to cover a parameter space for the creation of intermediate to old age models at solar-scaled [α/Fe], high [Fe/H] and enhanced [α/Fe], low [Fe/H].

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Phase space distribution functions and energy distributions of dark matter particles in haloes

ABSTRACT For a spherical dark matter halo with isotropic velocity distribution, the phase space distribution function (DF), the energy distribution, and the density profile form a set of self-consistent description of its equilibrium state, and knowing one is sufficient to determine the other two. The Navarro–Frenk–White density profile (NFW profile) is known to be a good approximation to the spherically averaged density distribution in simulated haloes. The DARKexp energy distribution is also known to compare well with the simulated energy distribution. We present a quantitative assessment of the NFW and DARKexp fits to the simulated DF and energy distribution for a wide range of haloes in a dark-matter-only simulation from the IllustrisTNG Project. As expected, we find that the NFW fits work well except at low energy when the density at small radii deviates from the NFW profile. Further, the NFW and DARKexp fits have comparable accuracy in the region where both fit well, but the DARKexp fits are better at low energy because they require matching of the central gravitational potential. We also find an approximate relation between the energy scale parametrizing the DARKexp energy distribution and that defined by the characteristic density and radius of the NFW profile. This relation may be linked to the relaxation process during halo formation.

Astronomy & Astrophysics↗
DOE OSTI2025

Constraining the phase shift of relativistic species in DESI BAOs

In the early Universe, neutrinos decouple quickly from the primordial plasma and propagate without further interactions. The impact of free-streaming neutrinos is to create a temporal shift in the gravitational potential that impacts the acoustic waves known as baryon acoustic oscillations (BAOs), resulting in a non-linear spatial shift in the Fourier-space BAO signal. In this work, we make use of and extend upon an existing methodology to measure the phase shift amplitude $\beta _{\phi }$ and apply it to the Dark Energy Spectroscopic Instrument (DESI) Data Release 1 (DR1) BAOs with an anisotropic BAO fitting pipeline. We validate the fitting methodology by testing the pipeline with two publicly available fitting codes applied to highly precise cubic box simulations and realistic simulations representative of the DESI DR1 data. We find further study towards the methods used in fitting the BAO signal will be necessary to ensure accurate constraints on $\beta _{\phi }$ in future DESI data releases. Using DESI DR1, we present individual measurements of the anisotropic BAO distortion parameters and the $\beta _{\phi }$ for the different tracers, and additionally a combined fit to $\beta _{\phi }$ resulting in $\beta _{\phi } = 2.7 \pm 1.7$. After including a prior on the distortion parameters from constraints using Planck we find $\beta _{\phi } = 2.7^{+0.60}_{-0.67}$ suggesting $\beta _{\phi } > 0$ at 4.3$\sigma$ significance. This result may hint at a phase shift that is not purely sourced from the standard model expectation for $N_{\rm {eff}}$ or could be a upwards statistical fluctuation in the measured $\beta _{\phi }$; this result relaxes in models with additional freedom beyond Lambda-cold dark matter.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Toward shell model interactions with credible uncertainties

Background: The nuclear shell model is a powerful framework for predicting nuclear structure observables, but relies on interaction matrix elements fit to experimental data as its inputs. Extending the shell model's applicability, particularly toward dripline nuclei, requires efficient fitting methods and credible uncertainty quantification. Traditional approaches face computational challenges and may underestimate uncertainties. Purpose: We develop and test a framework combining eigenvector continuation and Markov chain Monte Carlo to efficiently fit shell model interaction matrix elements and quantify their uncertainties. Methods: Eigenvector continuation is used to emulate shell model calculations, reducing computational costs. The emulator enables Markov chain Monte Carlo sampling to optimize interaction matrix elements and rigorously assess parametric uncertainties. Here, the framework is benchmarked using the USDB interaction in the 𝑠⁢𝑑 shell. Results: The emulator reproduces the USDB interaction with negligible error, validating its use in shell model fitting applications. However, we find that to obtain credible predictive intervals, the model defect of the shell model itself, rather than experimental or emulator error, must be taken into account in order to obtain credible uncertainties. Conclusions: The proposed framework provides an efficient and rigorous approach for fitting shell model interactions and quantifying uncertainties. Further, the normality assumption used in the past appears sufficient to describe the distribution of interaction matrix elements. However, it is crucial to account for model correlations to avoid underestimating uncertainties.

Nuclear forces↗