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DOE OSTI2021

Constructing angular distributions of neutrinos in core-collapse supernovae from zeroth and first moments calibrated by full Boltzmann neutrino transport

Two-moment neutrino transport methods have been widely used for developing theoretical models of core-collapse supernovae (CCSN), since they substantially reduce the computational burden inherent in the multidimensional neutrino-radiation hydrodynamical simulations. The approximation, however, comes at a price; the detailed structure of angular distribution of neutrinos is sacrificed, that is the main drawback of this approach. In this paper, we develop a novel method by which to construct angular distributions of neutrinos from the zeroth and first angular moments. In our method, the angular distribution is expressed with two quadratic functions of the neutrino angle in a piecewise fashion. We determine the best parameters in the fitting function by comparing to the neutrino data in a spherically symmetric CCSN model with full Boltzmann neutrino transport. We demonstrate the capability of our method by using our recent 2D CCSN model. In this work, we find that the essential features of the angular distributions can be well reconstructed, whereas the angular distributions of incoming neutrinos tend to have large errors that increase with flux factor ($\textit{κ}$). This issue originates from the insensitiveness of incoming neutrinos to $\textit{κ}$, that is an intrinsic limitation in moment methods. Based on the results of the demonstration, we assess the reliability of electron- neutrinos lepton number (ELN)-crossing searches with the two-moment neutrino transport. This analysis is complementary to our [L. Johns and H. Nagakura arXiv:2104.04106] that scrutinizes the limitation of crossing searches with a few moments. We find that the systematic errors of angular distributions for incoming neutrinos lead to misjudgements of the crossing at $\textit{κ}$ ≳ 0.5. This casts doubt on the results of ELN-crossing searches based on two-moment methods in some previous studies.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Uncertainty estimation of bifurcated solutions in the Rayleigh–Bénard problem for advanced nuclear reactors applications

Multiphysics models of nuclear reactors frequently comprise nonlinear systems of equations. The nonlinear nature of these models could lead to solution bifurcations, where a small change in a certain parameter, e.g., the thermophysical properties of the coolant, can lead to a sudden change in the system’s behavior. At the point in parameter space where this happens, called a critical point, the Jacobian matrix of the model’s nonlinear operator becomes singular potentially permitting multiple solutions to coexist. In this paper, we perform uncertainty estimation (UE) in a parameter range that includes bifurcated solutions within the context of Rayleigh–Bénard problem. We perform this analysis assuming uncertain temperature difference, and tilt angle for the iterative solution algorithm with a unit Prandtl number (Pr = 1). Also, we perform this analysis under uncertain thermophysical properties for both FLiBe molten salt and liquid sodium as working fluid. We deploy two approaches to compute statistical moments for the resulting distributions of selected flow-field variables. The first approach is the blind computation of the mean and the standard deviation without any consideration of solution bifurcation, while the second approach utilizes k-means clustering to cluster each branch’s solutions together and compute separate statistical moments for each branch. The statistical distributions are obtained by perturbing the selected parameters about nominal values that correspond to a solution on one of the valid branches, and that solution is used as initial guess for the iterative solution algorithm. We found that perturbation of any parameter when its nominal value is close to its critical point always leads to branch jumping, i.e., the iterations converge to a solution on a branch different from the branch of the initial guess. This produces a statistical ensemble comprised of fundamentally different solutions leading to wrong mean values and uncertainty estimates, whereas clustering provides an efficient way to deal with this type of computation. This work is important for developing Gen IV nuclear systems because many of these systems rely on natural convection for cooling especially in accident conditions.

97 - MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Deriving cloud droplet number concentration from surface-based remote sensors with an emphasis on lidar measurements

Abstract. Given the importance of constraining cloud droplet number concentrations (Nd) in low-level clouds, we explore two methods for retrieving Nd from surface-based remote sensing that emphasize the information content in lidar measurements. Because Nd is the zeroth moment of the droplet size distribution (DSD), and all remote sensing approaches respond to DSD moments that are at least 2 orders of magnitude greater than the zeroth moment, deriving Nd from remote sensing measurements has significant uncertainty. At minimum, such algorithms require the extrapolation of information from two other measurements that respond to different moments of the DSD. Lidar, for instance, is sensitive to the second moment (cross-sectional area) of the DSD, while other measures from microwave sensors respond to higher-order moments. We develop methods using a simple lidar forward model that demonstrates that the depth to the maximum in lidar-attenuated backscatter (Rmax⁡) is strongly sensitive to Nd when some measure of the liquid water content vertical profile is given or assumed. Knowledge of Rmax⁡ to within 5 m can constrain Nd to within several tens of percent. However, operational lidar networks provide vertical resolutions of > 15 m, making a direct calculation of Nd from Rmax⁡ very uncertain. Therefore, we develop a Bayesian optimal estimation algorithm that brings additional information to the inversion such as lidar-derived extinction and radar reflectivity near the cloud top. This statistical approach provides reasonable characterizations of Nd and effective radius (re) to within approximately a factor of 2 and 30 %, respectively. By comparing surface-derived cloud properties with MODIS satellite and aircraft data collected during the MARCUS and CAPRICORN II campaigns, we demonstrate the utility of the methodology.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

A Triple-Moment Representation of Ice in the Predicted Particle Properties (P3) Microphysics Scheme

In the original Predicted Particle Properties (P3) bulk microphysics scheme, all ice-phase hydrometeors are represented by one or more “free” ice categories, where the physical properties evolve smoothly through changes to the four prognostic variables (per category), and with a two-moment representation of the particle size distribution. As such, the spectral dispersion cannot evolve independently, which thus results in limitations in representation of ice—in particular, hail—due to necessary constraints in the scheme to prevent excessive gravitational size sorting. To overcome this, P3 has been modified to include a three-moment representation of the size distribution of each ice category through the addition of a fifth prognostic variable, the sixth moment of the size distribution. The details of the three-moment ice parameterization in P3 are provided. The behavior of the modified scheme, with the single-ice-category configuration, is illustrated through simulations in a simple 1D kinematic model framework as well as with near large-eddy-resolving (250-m grid spacing) 3D simulations of a hail-producing supercell. It is shown that the three-moment ice configuration controls size sorting in a physically based way and leads to an improved capacity to simulate large, heavily rimed ice (hail), including mean and maximum sizes and reflectivity, and thus an overall improvement in the representation of ice-phase particles in the P3 scheme.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

String-based axial and helicity-flip GPDs: A comparison to lattice QCD

We construct an analytic, string-based representation of the nucleon’s axial and helicity-flip conformal moments of generalized parton distributions (GPDs) that holds for skewness and for both the quark and gluon channels. The starting point is the Mellin-Barnes resummation of the conformal partial-wave expansion, where the moments are parametrized by open- (Reggeon) and closed-string (Pomeron) trajectories with slopes determined by experimental form factors and meson/glueball spectroscopy. The forward limits are fixed by the empirical unpolarized and polarized parton distributions. Polynomiality, crossing symmetry, and support are satisfied by construction. After next-to-leading order Dokshitzer-Gribov-Lipatov-Altarelli-Parisi/Efremov-Radyushkin-Brodsky-Lepage evolution to μ = 2 GeV our analytic framework (i) reproduces some of the currently available lattice moments of E and H˜ in the nonsinglet sector, (ii) predicts sea-quark and gluon polarized moments that will be testable by forthcoming simulations and experiments at Jefferson Lab and the future Electron-Ion Collider, and (iii) yields axial and helicity-flip GPDs in x-space in reasonable agreement with lattice QCD.

Gauge-gravity dualities↗

DOE OSTI2023

Moment-Fourier approach to ion parallel fluid closures and transport for a toroidally confined plasma

A general method of solving the drift kinetic equation is developed for an axisymmetric magnetic field. Expanding a distribution function in general moments, a set of ordinary differential equations is obtained. Successively expanding the moments and magnetic-field involved quantities in Fourier series, a set of linear algebraic equations is obtained. The set of full (Maxwellian and non-Maxwellian) moment equations is solved to express the first-order density, temperature, and flow velocity in terms of radial gradients of the zeroth-order pressure and temperature. Closure relations that connect parallel heat flux density and viscosity to the radial gradients and parallel gradients of temperature and flow velocity are also obtained by solving the non-Maxwellian moment equations. The closure relations combined with the linearized fluid equations reproduce the same solution obtained directly from the full moment equations. Furthermore, the method can be generalized to derive closures and transport for an electron-ion plasma and a multi-ion plasma in a general magnetic field.

neoclassical transport↗

DOE OSTI2024

Orbital angular momentum at small $x$ revisited

We revisit the problem of the small Bjorken-x asymptotics of the quark and gluon orbital angular momentum (OAM) distributions in the proton utilizing the revised small-x helicity evolution derived recently in [1]. We relate the quark and gluon OAM distributions at small x to the polarized dipole amplitudes and their (first) impact-parameter moments. To obtain the OAM distributions, we derive novel small-x evolution equations for the impact-parameter moments of the polarized dipole amplitudes in the double-logarithmic approximation (summing powers of α s ln 2 (1/x) with α s the strong coupling constant). We solve these evolution equations numerically and extract the leading large-N c , small-x asymptotics of the quark and gluon OAM distributions, which we determine to be ${L}_{q+\overline{q}}\left(x,{Q}^2\right)\sim {L}_G\left(x,{Q}^2\right)\sim \Delta \Sigma \left(x,{Q}^2\right)\sim \Delta G\left(x,{Q}^2\right)\sim {\left(\frac{1}{2}\right)}^{3.66\sqrt{\frac{\alpha_s{N}_c}{2_π}}}$in agreement with [2] within the precision of our numerical evaluation. (Here N c is the number of quark colors.) We also investigate the ratios of the quark and gluon OAM distributions to their helicity distribution counterparts in the small-x region.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Neutrino fast flavor oscillations with moments: Linear stability analysis and application to neutron star mergers

Providing an accurate modeling of neutrino physics in dense astrophysical environments such as binary neutron star mergers presents a challenge for hydrodynamic simulations. Nevertheless, understanding how flavor transformation can occur and affect the dynamics, the mass ejection, and the nucleosynthesis will need to be achieved in the future. Computationally expensive, large-scale simulations frequently evolve the first classical angular moments of the neutrino distributions. By promoting these quantities to matrices in flavor space, we develop a linear stability analysis of fast flavor oscillations using only the first two “quantum” moments, which notably requires generalizing the classical closure relations that appropriately truncate the hierarchy of moment equations in order to treat quantum flavor coherence. After showing the efficiency of this method on a well-understood test situation, we perform a systematic search of the occurrence of fast flavor instabilities in a neutron star merger simulation. Here, we discuss the successes and shortcomings of moment linear stability analysis, as this framework provides a time-efficient way to design and study better closure prescriptions in the future.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Propagation Pattern for Moment Representation of the Lattice Boltzmann Method

A propagation pattern for the moment representation of the regularized lattice Boltzmann method (LBM) in three dimensions is presented. Using effectively lossless compression, the simulation state is stored as a set of moments of the lattice Boltzmann distribution function, instead of the distribution function itself. An efficient cache-aware propagation pattern for this moment representation has the effect of substantially reducing both the storage and memory bandwidth required for LBM simulations. This article extends recent work with the moment representation by expanding the performance analysis on central processing unit (CPU) architectures, considering how boundary conditions are implemented, and demonstrating the effectiveness of the moment representation on a graphics processing unit (GPU) architecture.

42 ENGINEERING↗

DOE OSTI2025

Bayesian Inference for the Seismic Moment Tensor Using Regional Waveforms and Teleseismic- P Polarities with a Data-Derived Distribution of Velocity Models and Source Locations

The largest source of uncertainty in any source inversion is the velocity model used in the transfer function that relates observed ground motion to the seismic moment tensor. However, standard inverse procedure often does not quantify uncertainty in the seismic moment tensor due to error in the Green’s functions from uncertain event location and Earth structure. Here, we incorporate this uncertainty into an estimation of the seismic moment tensor using a data-derived distribution of velocity models based on complementary geophysical data sets, including thickness constraints, velocity profiles, gravity data, surface-wave group velocities, and regional body-wave travel times. The data-derived distribution of velocity models is then used as a prior distribution of Green’s functions for use in Bayesian inference of an unknown seismic moment tensor using regional and teleseismic-P waveforms. The use of multiple data sets is important for gaining resolution to different components of the moment tensor. The combined likelihood is estimated using data-specific error models and the posterior of the seismic moment tensor is estimated and interpreted in terms of the most probable source type.

58 GEOSCIENCES↗

DOE OSTI2022

Nucleon isovector momentum fraction, helicity and transversity moment using Lattice QCD

We present our recent high precision calculations (Phys. Rev. D102 (2020) no.5, 054512 and JHEP 04 (2021) 044, JHEP 21 (2020) 004) of the first moment of nucleon isovector polarized, unpolarized and transversity distributions, i.e., momentum fraction, helicity and transversity moment, respectively. We use the standard method for the calculation of these moments (via matrix elements of twist two operators), and carry out a detailed analysis of the sources of systematic uncertainty, in particular of excited state contributions. Our calculations have been performed using two different lattice setups (Clover-on-HISQ and Clover-on-Clover), each with several ensembles. They give consistent results that are in agreement with global fit analyses.

Mondal, Santanu↗

DOE OSTI2024

Transverse momentum moments

We establish robust relations between Transverse Momentum Dependent distributions (TMDs) and collinear distributions. We define weighted integrals of TMDs that we call Transverse Momentum Moments (TMMs) and prove that TMMs are equal to collinear distributions evaluated in some minimal subtraction scheme. The conversion to the modified minimal subtraction ( MS ¯ ) scheme can be done by a calculable factor, which we derive up to three loops for some cases. We discuss in detail the zeroth, the first, and the second TMMs and provide phenomenological results for them based on the current extractions of TMDs. The results of this paper open new avenues for theoretical and phenomenological investigation of the three-dimensional and collinear hadron structures. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Microscopic characterization of the magnetic properties of the itinerant antiferromagnet La 2 Ni 7 by La 139 NMR/NQR measurements

In this study, 139 La nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) measurements have been performed to investigate the magnetic properties of the itinerant magnet La 2 Ni 7 , which shows a series of antiferromagnetic (AFM) phase transitions at T N1 = 61 K, T N2 = 56 K, and T N3 = 42 K under zero magnetic field. Two distinct La NMR signals were observed due to the two crystallographically inequivalent La sites in La 2 Ni 7 (La1 and La2 in the La 2 Ni 4 and the LaNi 5 subunits of the La 2 Ni 7 unit cell, respectively). From the 139 La NQR spectrum in the AFM state below T N3 , the AFM state was revealed to be a commensurate state where Ni-ordered moments align along the crystalline c axis. Owing to the two different La sites, we were able to estimate the average values of the Ni-ordered moments (0.09 – 0.10 μB / Ni and 0.17 μB / Ni around La1 and La2, respectively) from 139 La NMR spectrum measurements in the AFM state below T N3 , suggesting a nonuniform distribution of the Ni-ordered moments in the AFM state. In contrast, a more uniform distribution of the Ni-ordered moments in the saturated paramagnetic state induced by the application of high magnetic fields is observed. The temperature dependence of the sublattice magnetization measured by the internal magnetic induction at the La2 site in the AFM state was reproduced by a local-moment model better than the self-consistent renormalization (SCR) theory for weak itinerant antiferromagnets. Given the small Ni-ordered moments in the magnetically ordered state, our results suggest that La 2 Ni 7 has characteristics of both itinerant nature and localized nature in its magnetism. With this in mind, it is noteworthy that the temperature dependence of nuclear spin-relaxation rates (1/T 1 ) in the paramagnetic state above T N1 measured at zero magnetic field can be explained qualitatively by both the SCR theory and the local-moment model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Precision e + e − hemisphere masses in the dijet region with power corrections

We derive high-precision results for the e + e − heavy jet mass (HJM) dσ/dρ and dihemisphere mass (DHM) d 2 σ/(ds 1 ds 2 ) distributions, for s 1 ~ s 2 , in the dijet region. New results include: i) the N 3 LL resummation for HJM of large logarithms ln n (ρ) at small ρ including the exact two-loop non-global hemisphere soft function, the 4-loop cusp anomalous dimension and the 3-loop hard and jet functions, ii) N 3 LL results for DHM with resummation of logarithms ln(s 1,2 /Q 2 ) when there is no large separation between s 1 and s 2 , iii) profile functions for HJM to give results simultaneously valid in the peak and tail regions, iv) a complete two-dimensional basis of non-perturbative functions which can be used for double differential observables, that are needed for both HJM and DHM in the peak region, and v) an implementation of renormalon subtractions for large-angle soft radiation to $\mathcal{O}$ (α$^{3}_{s}$) together with a resummation of the additional large ln(Qρ/Λ QCD ) logarithms. Here Q is the e + e − center-of-mass energy. Our resummation results are combined with known fixed-order $\mathcal{O}$ (α$^{3}_{s}$) results and we discuss the convergence and remaining perturbative uncertainty in the cross section. We also prove that, at order 1/Q, the first moment of the HJM distribution involves an additional non-perturbative parameter compared to the power correction that shifts the tail of the spectrum (where 1 ≫ ρ ≫ Λ QCD /Q). This differs from thrust where a single non-perturbative parameter at order 1/Q describes both the first moment and the tail, and it disfavors models of power corrections employing a single non-perturbative parameter, such as the low-scale effective coupling model. In this paper we focus only on the dijet region, not the far-tail distribution for ρ ≳ 0.2 beyond which the trijet factorization and resummation become important.

Factorization↗

DOE OSTI2021

Using solenoid as multipurpose tool for measuring beam parameters

Solenoids are frequently used for focusing low-energy beams. In this paper, we show how they can serve as multipurpose diagnostics tools to measure various beam parameters, including energy, emittance, the second moments of the transverse distribution, and the beam position and angle with respect to the solenoid’s axis. The energy measurement is based on rotation of the plane of the transverse motion, as opposed to generating dispersion with a dipole. Measurement of the beam trajectory with respect to the solenoid axis is done by analyzing the beam orbit downstream of the solenoid while varying its current. The second moments are calculated by analyzing the beam image on a profile monitor while accounting for the beam rotation caused by the solenoid. We describe in detail the corresponding procedures and the experimental results of these measurements.

43 PARTICLE ACCELERATORS↗

DOE OSTI2021

Measurement of charged particle multiplicity distributions in DIS at HERA and its implication to entanglement entropy of partons

Charged particle multiplicity distributions in positron-proton deep inelastic scattering at a centre-of-mass energy √s = 319 GeV are measured. The data are collected with the H1 detector at HERA corresponding to an integrated luminosity of 136 pb -1 . Charged particle multiplicities are measured as a function of photon virtuality Q 2 , inelasticity y and pseudorapidity η in the laboratory and the hadronic centre-of-mass frames. Predictions from different Monte Carlo models are compared to the data. The first and second moments of the multiplicity distributions are determined and the KNO scaling behaviour is investigated. The multiplicity distributions as a function of Q 2 and the Bjorken variable x bj are converted to the hadron entropy S hadron , and predictions from a quantum entanglement model are tested.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Beyond magnons in Nd 2 ScNbO 7 : An Ising pyrochlore antiferromagnet with all-in–all-out order and random fields

We report the low-temperature magnetic properties of Nd 3+ pyrochlore Nd 2 ScNbO 7 . Susceptibility and magnetization show an easy-axis moment, and heat capacity reveals a phase transition to long-range order at T N =371(2) mK with a fully recovered ΔS=Rln(2), 53% of it recovered for T>T N . Elastic neutron scattering shows a long-range all-in all-out magnetic order with low-Q diffuse elastic scattering. Inelastic neutron scattering shows a low-energy flat band, indicating a magnetic Hamiltonian similar to Nd 2 Zr 2 O 7 . Nuclear hyperfine excitations measured by ultra-high-resolution neutron backscattering indicate a distribution of static electronic moments below T N , which may be due to B-site disorder influencing Nd crystal electric fields. Analysis of heat-capacity data shows an unexpected T-linear or T 3/2 term which is inconsistent with conventional magnon quasiparticles, but is consistent with fractionalized spinons or gapless local spin excitations. We use legacy data to show similar behavior in Nd 2 Zr 2 O 7 . Comparing local static moments also reveals a suppression of the nuclear Schottky anomaly in temperature, evidencing a fraction of Nd sites with nearly zero static moment, consistent with exchange-disorder-induced random singlet formation. Finally, taken together, these measurements suggest an unusual fluctuating magnetic ground state which mimics a spin liquid, but may not actually be one.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Spatial and Temporal Variability of Vertical Velocity under Shallow Cumulus

Vertical velocity distribution below cloud is one of the key determinants of cloud life cycle, but observations of this variable are extremely sparse in space. Doppler lidar retrievals and large-eddy simulations at the U.S. Department of Energy’s Atmospheric Radiation Measurement User Facility Southern Great Plains site are used to determine whether vertical velocity statistics from temporally dense profiles at a single location can be substituted for spatial vertical velocity statistics. We show that even a small number (five) of widely distributed [ O (1°) latitude/longitude spacing] lidars is sufficient sampling to reconstruct domainwide spatial vertical velocity variance, but not higher moments of the vertical velocity distribution. Spatial and temporal vertical velocity variances in the Doppler lidar observations are nearly interchangeable as long as the spatial variance is temporally averaged and the temporal variance is averaged across lidars. This is true even though the dominant spatial scales of vertical velocity variability are ≲ 3 km, more than an order of magnitude smaller than the spacing between the lidars. Further, in the limit where the temporal variance does not vary across a spatial domain (e.g., if the meteorological and surface forcing of the atmospheric turbulence is homogeneous across the domain) and the domain-mean vertical velocity is zero, the commonly available retrieval of temporal vertical velocity variance at one site is equivalent to the spatial variance over the domain. We use an updraft parcel model to show that substituting temporal for spatial vertical velocity statistics will have a relatively minor effect on cloud droplet number concentrations.

54 ENVIRONMENTAL SCIENCES↗