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DOE OSTI2026

Nonequilibrium universality of the nonreciprocally coupled 𝑂⁡(𝑛 1 ) × 𝑂⁡(𝑛 2 ) model

Nonequilibrium dynamics play an important role in all contexts of physics, both classical and quantum as well as living and nonliving, so it is crucial to develop a foundational understanding of nonequilibrium phase transitions. In this work we investigate an important class of nonequilibrium dynamics in the form of nonreciprocal interactions. In particular we study how nonreciprocal coupling between two 𝑂⁡(𝑛𝑖) order parameters (with 𝑖 = 1,2) affects the universality at a multicritical point, extending the analysis of J. T. Young et al. [Phys. Rev. X 10, 011039 (2020)], which considered the case 𝑛 1 = 𝑛 2 = 1, i.e., a ℤ 2 × ℤ 2 model. We show that nonequilibrium fixed points (NEFPs) emerge for a broad range of 𝑛 1 ,𝑛 2 and exhibit intrinsically nonequilibrium critical phenomena, namely a violation of fluctuation-dissipation relations at all scales and underdamped oscillations near criticality in contrast to the overdamped relaxational dynamics of the corresponding equilibrium models. Furthermore, the NEFPs exhibit an emergent discrete scale invariance in certain physically relevant regimes of 𝑛 1 ,𝑛 2 , but not others, depending on whether the critical exponent 𝜈 is real or complex. The boundary between these two regions is described by an exceptional point in the renormalization group (RG) flow, leading to distinctive features in correlation functions and the phase diagram. Another contrast with the previous work is the number and stability of the NEFPs as well as the underlying topology of the RG flow. Lastly, we investigate an extreme form of nonreciprocity where one order parameter is independent of the other order parameter but not vice versa. Unlike the ℤ 2 × ℤ 2 model, which becomes nonperturbative in this case, we identify a distinct nonequilibrium universality class whose dependent field similarly violates fluctuation-dissipation relations but does not exhibit discrete scale invariance or underdamped oscillations near criticality.

Critical phenomena↗

DOE OSTI2023

Scaling and Complexity of Stress Fluctuations Associated with Smooth and Jerky Flow in FeCoNiTiAl High-Entropy Alloy

Recent observations of jerky flow in high-entropy alloys (HEA) revealed a high role of self-organization of dislocations in their plasticity. The present work reports the first results of the investigation of stress fluctuations during plastic deformation of an FeCoNiTiAl alloy, examined in a wide temperature range covering both smooth and jerky flow. These fluctuations, which accompany the overall deformation behavior representing an essentially slower stress evolution controlled by the work hardening, were processed using complementary approaches comprising Fourier spectral analysis, refined composite multiscale entropy, and multifractal formalisms. The joint analysis at distinct scales testified that even a macroscopically smooth plastic flow is accompanied by nonrandom fluctuations, disclosing the self-organized dynamics of dislocations. Qualitative changes in such a fine-scale “noise” were found with varying temperature. The observed diversity is significant for understanding the relationships between different scales of plasticity of HEAs and crystal materials in general.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Supernova neutrino signals based on long-term axisymmetric simulations

ABSTRACT We study theoretical neutrino signals from core-collapse supernova (CCSN) computed using axisymmetric CCSN simulations that cover the post-bounce phase up to ∼4 s. We provide basic quantities of the neutrino signals such as event rates, energy spectra, and cumulative number of events at some terrestrial neutrino detectors, and then discuss some new features in the late phase that emerge in our models. Contrary to popular belief, neutrino emissions in the late phase are not always steady, but rather have temporal fluctuations, the vigour of which hinges on the CCSN model and neutrino flavour. We find that such temporal variations are not primarily driven by proto-neutron star convection, but by fallback accretion in exploding models. We assess the detectability of these temporal variations, and find that IceCube is the most promising detector with which to resolve them. We also update fitting formulae first proposed in our previous paper for which the total neutrino energy emitted at the CCSN source is estimated from the cumulative number of events in each detector. This will be a powerful technique with which to analyse real observations, particularly for low-statistics data.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Studying Rate of Fire Spread Using Landscape Statistics and FIRETEC

Wildfires are multi-system and multi-scale processes that are influenced by the land and atmosphere. Here, we study the influence of land, in terms of topography and vegetation, on uphill and downhill fire spread using data of the state of California as a testbed. The California landscape is first quantified by reclassifying its dominant vegetation types into grass, trees, and shrubs. Next, statistics of slope, vegetation height, and live fuel moisture percentage for each dominant vegetation type are gathered to create ensembles of idealized computational fluid dynamics (CFD) model simulations representative of the landscape. Rate of spread values for each CFD simulation are recorded to observe the differences in perturbing slope and fuel moisture for each vegetation type. We have found that all vegetation types prefer slopes of less than 30 degrees. Trees in the California data are 10 to 40 meters high, whereas shrub heights are less than 3 meters and grass heights are less than 1 meter. The live fuel moisture percentage of both trees and shrubs fluctuates around approximately 100% over one year (2019-2020). Using these parameters as inputs into the CFD model, fire spread rate is found to be fastest in the grass ensemble (maximum 12 m s -1 ), followed by shrubs (maximum 10 m s -1 ) and lastly by trees (maximum 7 m s -1 ). Increasing slope increases the spread rate of the uphill fire but the downhill spread decreases for slopes greater than 15 degrees. Increasing fuel moisture decreases the spread rate both up and down the hill. This study highlights the impacts that topography and vegetation have on fire spread.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Explainable tokamak-agnostic forecasting of fusion plasma instability via megahertz turbulent fluctuations

Scientific applications of artificial intelligence (AI) often remain limited by device-specific training and unexplained “black-box” approaches, creating fundamental barriers to cross-system generalization. This challenge is critical for nuclear fusion, where future reactors will have limited operational data for AI training. Here, we demonstrate that our neural network, trained solely on megahertz-scale turbulence measurements from one machine (DIII-D), forecasts Type-I edge localized mode (ELM) onsets in a different tokamak (KSTAR) through zero-shot weight transfer following physics-consistent preprocessing without device-specific retraining. Through an explainable AI framework combining gradient-weighted class activation mapping with physics validation, we reveal that our network can internalize physics relationships governing the ELM instabilities rather than memorizing device-specific patterns. The network perceives spatiotemporal features that correlate consistently with independently calculated instability growth rates, magnetohydrodynamic stability limits, and pedestal structure dynamics. Statistical analyses of dimensionally-reduced saliency features reveal the identical triangular features between the saliency representations, instability growth rates, and prediction probability across tokamaks, providing evidence that our forecasting system can show tokamak-agnostic generalization. This work contributes to a foundation for explainable scientific AI systems, where cross-system developments are essential for transcending traditional domain-specific constraints.

AI↗

NASA NTRS1990

A statistical study of the differential very long baseline interferometry delay rate error budget

The delta differential one-way Doppler (delta-DOD) error budget is assessed by analyzing 12 years of dual-frequency Deep Space Network very long baseline interferometry data. A typical delta-DOD observation is outlined, and the Magellan error budget along with tropospheric effects are considered. Formation of quasar-quasar observables, RMS delta-DOD residual, angular source separation and time separation between observations are discussed, along with elevation angle and atmospheric pathlength dependence, solar-plasma and ionospheric effects. It is concluded that the weak dependence of the delta-DOD error on angular source separation can mean that quasars with larger angular separation from a spacecraft may be used as navigation reference with little increase in the delta-DOD error. It is also indicated that the delta-DOD errors are dominated by wet troposphere fluctuations, and the results of numerical integrations for the single-station RMS delay rate at different elevation angles are presented.

Edwards, Charles D.↗

DOE OSTI2026

Unified and Consistent Structure Growth Measurements from Joint ACT, SPT, and Planck CMB Lensing

We present the tightest cosmic microwave background (CMB) lensing constraints to date on the growth of structure by combining CMB lensing measurements from the Atacama Cosmology Telescope (ACT), the South Pole Telescope (SPT), and Planck. Each of these surveys individually provides lensing measurements with similarly high statistical power, achieving signal-to-noise ratios of approximately 40. The combined lensing band powers represent the most precise CMB lensing power spectrum measurement to date with a signal-to-noise ratio of 61 and an amplitude of A lens recon = 1.025 ± 0.017 with respect to the theory prediction from the best-fit CMB Planck-ACT cosmology. The band powers from all three lensing datasets, analyzed jointly, yield a 1.6% measurement of the parameter combination S 8 CMBL ≡ σ 8 ( Ω m / 0.3 ) 0.25 = 0.82 5 - 0.013 + 0.015 . Including dark energy spectroscopic instrument baryon acoustic oscillation (BAO) data improves the constraint on the amplitude of matter fluctuations to σ 8 = 0.829 ± 0.009 (a 1.1% determination). When combining with uncalibrated supernovae from Pantheon+, we present a 4% sound-horizon-independent estimate of H 0 = 66.4 ± 2.5 km s - 1 Mpc - 1 . The joint lensing constraints on structure growth and present-day Hubble rate are fully consistent with a Λ CDM model fit to the primary CMB data from Planck and ACT. While the precise upper limit is sensitive to the choice of data and underlying model assumptions, when varying the neutrino mass sum within the Λ CDM cosmological model, the combination of primary CMB, BAO, and CMB lensing drives the probable upper limit for the mass sum towards lower values, comparable to the minimum mass prior required by neutrino oscillation experiments.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

An Energy-Integrated Analysis for Measuring the Anomalous Precession Frequenzc for the Muon g - 2 Experiment at Fermilab

In the search for physics beyond the Standard Model, the Muon g - 2 Experiment at Fermilab (E989) will make the most precise measurement of the anomalous magnetic moment of the muon, a μ . Improvements in precision come from both increased statistics and new techniques to significantly reduce previous systematic uncertainties. The muon a μ is determined by extracting both the anomalous spin precession frequency, ω a , and the average magnetic field sampled by the muons, B. Traditionally an energy threshold analysis method which requires reconstruction of decay positrons from the muon decay, μ + → e + ν e ν μ has been used to extract ω a . This thesis will describe a novel, energy-integrated analysis method for ωa extraction that does not require full reconstruction of positron hits and lowers the energy threshold therefore sampling more of the stored muons. This new technique has different sensitivities to effects like gain fluctuations and positron pulse pile-up. The analysis results will focus on data taken in 2019, the second year of running the experiment.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1995

Analysis of the two-point velocity correlations in turbulent boundary layer flows

The general objective of the present work is to explore the use of Rapid Distortion Theory (RDT) in analysis of the two-point statistics of the log-layer. RDT is applicable only to unsteady flows where the non-linear turbulence-turbulence interaction can be neglected in comparison to linear turbulence-mean interactions. Here we propose to use RDT to examine the structure of the large energy-containing scales and their interaction with the mean flow in the log-region. The contents of the work are twofold: First, two-point analysis methods will be used to derive the law-of-the-wall for the special case of zero mean pressure gradient. The basic assumptions needed are one-dimensionality in the mean flow and homogeneity of the fluctuations. It will be shown that a formal solution of the two-point correlation equation can be obtained as a power series in the von Karman constant, known to be on the order of 0.4. In the second part, a detailed analysis of the two-point correlation function in the log-layer will be given. The fundamental set of equations and a functional relation for the two-point correlation function will be derived. An asymptotic expansion procedure will be used in the log-layer to match Kolmogorov's universal range and the one-point correlations to the inviscid outer region valid for large correlation distances.

Oberlack, M.↗

DOE OSTI2025

Unified and consistent structure growth measurements from joint ACT, SPT and \textit{Planck} CMB lensing

We present the tightest cosmic microwave background (CMB) lensing constraints to date on the growth of structure by combining CMB lensing measurements from the Atacama Cosmology Telescope (ACT), the South Pole Telescope (SPT) and \textit{Planck}. Each of these surveys individually provides lensing measurements with similarly high statistical power, achieving signal-to-noise ratios of approximately 40. The combined lensing bandpowers represent the most precise CMB lensing power spectrum measurement to date with a signal-to-noise ratio of 61 and an amplitude of $A_\mathrm{lens}^\mathrm{recon} = 1.025 \pm 0.017$ with respect to the theory prediction from the best-fit CMB \textit{Planck}-ACT cosmology. The bandpowers from all three lensing datasets, analyzed jointly, yield a $1.6\%$ measurement of the parameter combination $S_8^\mathrm{CMBL} \equiv σ_8\,(Ω_m/0.3)^{0.25} = 0.825^{+0.015}_{-0.013}$. Including Dark Energy Spectroscopic Instrument (DESI) Baryon Acoustic Oscillation (BAO) data improves the constraint on the amplitude of matter fluctuations to $σ_8 = 0.829 \pm 0.009$ (a $1.1\%$ determination). When combining with uncalibrated supernovae from \texttt{Pantheon+}, we present a $4\%$ sound-horizon-independent estimate of $H_0=66.4\pm2.5\,\mathrm{km\,s^{-1}\,Mpc^{-1}} $. The joint lensing constraints on structure growth and present-day Hubble rate are fully consistent with a $Λ$CDM model fit to the primary CMB data from \textit{Planck} and ACT. While the precise upper limit is sensitive to the choice of data and underlying model assumptions, when varying the neutrino mass sum within the $Λ\mathrm{CDM}$ cosmological model, the combination of primary CMB, BAO and CMB lensing drives the probable upper limit for the mass sum towards lower values, comparable to the minimum mass prior required by neutrino oscillation experiments.

Cosmology and Nongalactic Astrophysics (astro-ph.C↗

NASA NTRS1990

Testing the Sun-climate Connection with Paleoclimate Data

If there is a significant sun-climate connection, it should be detectable in high-resolution paleoclimate records. Of particular interest is the last few thousand years, where we have both indices of solar variability (C-14 and Be-10) and climate variations (alpine glaciers, tree rings, ice cores, corals, etc.). Although there are a few exceptions, statistical analyses of solar and climate records generally indicates a flickering relationship between the two -- sometimes it seems to be present, sometimes not. The most repeatable solar climate periods occur at approx. 120 and approx. 56 yrs, although there is also evidence for approx. 420 and approx. 200 yrs. power in some records. However, coherence between solar and climate spectra is usually low, and occurrence of solar spectra in climate records is sometimes dependent on choice of analysis program. These results suggest in general a relatively weak sun-climate link on time scales of decades to centuries. This conclusion is consistent with previous studies and with the observation that inferred climate fluctuations of 1.0 to 1.5 C on this time scale would require solar constant variations of approximately 0.5 to 1.0 percent. This change in forcing is almost an order of magnitude greater than observed changes over the last solar cycle and appears to be on the far-outer limit of acceptable changes for a Maunder Minimum-type event.

Crowley, Thomas J.↗

NASA NTRS1988

Statistical properties of solar granulation from the SOUP instrument on Spacelab 2

The Solar Optical Universal Polarimeter (SOUP) on Spacelab 2 collected movies of solar granulation completely free from atmospheric blurring, and are not degraded by pointint jitter (the pointing stability was 0.003 sec root mean square). The movies illustrate that the solar five minute oscillation has a major role in the appearance of solar granulation and that exploding granules are a common feature of the granule evolution. Using 3-D Fourier filtering techniques the oscillations were removed and it was demonstrated that the autocorrelation lifetime of granulation is a factor of two greater in magnetic field regions than in field-free quiet sun. Horizontal velocities were measured and flow patterns were observed on the scale of meso- and super granulation. In quiet regions the mean flow velocity is 370 m/s while in the magnetic regions it is about 125 m/s. It was also found that the root mean square (RMS) fluctuating horizonal velocity field is substantially greater in quiet sun than in strong magnetic field regions. By superimposing the location of exploding granules on the average flow maps it was found that they appear almost exclusively in the center of mesogranulation size flow cells. Because of the nonuniformity of the distribution of exploding granules, the evolution of the granulation pattern in mesogranule cell centers and boundaries differs fundamentally. It is clear from this study there is neither a typical granule nor a typical granule evolution.

Topka, K.↗

NASA NTRS2021

The Temporal and Spatial Development of dB/dt for Substorms

Ground induced currents (GICs) due to space weather are a threat to high voltage power transmission systems. However, knowledge of ground conductivity is the largest source of errors in the determination of GICs. A good proxy for GICs is dB/dt obtained from the Bx and By components of the magnetic field fluctuations. It is known that dB/dt values associated with magnetic storms can reach dangerous levels for power transmission systems. On the other hand, it is not uncommon for dB/dt values associated with substorms to exceed prior Pulkkinen and Molinski critical thresholds of 1.5 nT/s and 5 nT/s, respectively, and the temporal and spatial changes of the dB/dt associated with substorms, unlike storms, are not well understood. Using two dimensional maps of dB/dt over North America and Greenland derived from the spherical elementary currents, we investigate the temporal and spatial change of dB/dt for both a single substorm event and a two dimensional superposed epoch analysis of many substorms. Both the single event and the statistical analysis shows a sudden increase of dB/dt at substorm onset followed by an expansion poleward, westward, and eastward after the onset during the expansion phase. The area of dB/dt values exceeding the two critical thresholds from the initial onset dB/dt values showed little to no expansion equatorward. The temporal and spatial development of the dB/dt resembles the temporal and spatial change of the auroral emissions. Substorm values of dB/dt peak shortly after the auroral onset time and in at least one event exceeded 35 nT/s for a non-storm time substorm. In many of our 81 cases the area that exceeds the threshold of 1.5 nT/s is over several million square kilometers and after about 30 minutes the dB/dt values fall below the threshold level. These results address one of goals of the Space Weather Action Plan, which are to establish benchmarks for space weather events and improve modeling and prediction of their impacts on infrastructure. Plain language: The change in the ground magnetic field with respect to time (dB/dt) associated with magnetic storms (a large disturbance of the magnetic field of the earth) can reach dangerous levels for power transmission systems. On the other hand, substorms, which are a smaller more localized disturbance of the Earth’s magnetic field, are more common. It is not uncommon for substorm dB/dt values to also exceed dangerous levels and the temporal and spatial changes of the dB/dt associated with substorms, unlike storms, are not well understood. Our analysis shows a sudden increase of dB/dt at substorm onset, which peaks shortly after the start of the substorm, followed shortly after by an expansion northward, westward, and eastward after the onset.

ionospheric currents↗

DOE OSTI2023

A statistical mechanics framework for polymer chain scission, based on the concepts of distorted bond potential and asymptotic matching

To design increasingly tough, resilient, and fatigue-resistant elastomers and hydrogels, the relationship between controllable network parameters at the molecular level (bond type, non-uniform chain length, entanglement density, etc.) to macroscopic quantities that govern damage and failure must be established. Many of the most successful constitutive models for elastomers have been rooted in statistical mechanical treatments of polymer chains. Typically, such constitutive models have used variants of the freely jointed chain model with rigid links. However, since the free energy state of a polymer chain is dominated by enthalpic bond distortion effects as the chain approaches its rupture point, bond extensibility ought to be accounted for if the model is intended to capture chain rupture. To that end, a new bond potential is supplemented to the freely jointed chain model (as derived in the u FJC framework of Buche and Silberstein (2021) and Buche et al. (2022)), which we have extended to yield a tractable, closed-form model of single chain behavior that should be amenable to continuum-level constitutive model development. Inspired by the asymptotically matched u FJC model response in both the low/intermediate chain force and high chain force regimes, a simple, quasi-polynomial bond potential energy function is derived. This bond potential exhibits harmonic behavior near the equilibrium state and anharmonic behavior for large bond stretches tending to a characteristic energy plateau (akin to the Lennard-Jones and Morse bond potentials). Using this bond potential, approximate yet highly-accurate analytical functions for bond stretch and chain force dependent upon chain stretch are established. Then, using this polymer chain model, a stochastic thermal fluctuation-driven chain rupture framework is developed. This framework is based upon a force-modified tilted bond potential that accounts for distortional bond potential energy, allowing for the derivation and subsequent calculation of the dissipated chain scission energy. Here, the cases of rate-dependent and rate-independent scission are accounted for throughout the rupture framework. The impact of Kuhn segment number on chain rupture behavior is also investigated. The model is fit to single chain mechanical response data collected from atomic force microscopy tensile tests for validation and to glean deeper insight into the molecular physics taking place. Due to their analytical nature, this polymer chain model and the associated rupture framework can in the future be implemented in finite element models accounting for fracture and fatigue in polydisperse elastomer networks.

36 MATERIALS SCIENCE↗

NASA NTRS1978

Period variations in pulsating X-ray sources. II - Torque variations and stellar response

A statistical description of variations in the torque acting on a rotating neutron star is developed in terms of stationary random processes and is used to calculate the torque power spectrum, stellar response power spectrum, and the total mean square variation in the crustal angular velocity of the star. The response of a star with a finite frequency internal mode is calculated with the aid of phenomenological equations which correspond to a generalized two-component model of the star. The form of the stellar response functions is examined in a number of limiting cases of physical interest, and the dependence of the response power on both the period of observation and the time over which fluctuating torques have been acting is discussed.

Lamb, F. K.↗

NASA NTRS1990

Development of a two-dimensional zonally averaged statistical-dynamical model. III - The parameterization of the eddy fluxes of heat and moisture

A number of perpetual January simulations are carried out with a two-dimensional zonally averaged model employing various parameterizations of the eddy fluxes of heat (potential temperature) and moisture. The parameterizations are evaluated by comparing these results with the eddy fluxes calculated in a parallel simulation using a three-dimensional general circulation model with zonally symmetric forcing. The three-dimensional model's performance in turn is evaluated by comparing its results using realistic (nonsymmetric) boundary conditions with observations. Branscome's parameterization of the meridional eddy flux of heat and Leovy's parameterization of the meridional eddy flux of moisture simulate the seasonal and latitudinal variations of these fluxes reasonably well, while somewhat underestimating their magnitudes. New parameterizations of the vertical eddy fluxes are developed that take into account the enhancement of the eddy mixing slope in a growing baroclinic wave due to condensation, and also the effect of eddy fluctuations in relative humidity. The new parameterizations, when tested in the two-dimensional model, simulate the seasonal, latitudinal, and vertical variations of the vertical eddy fluxes quite well, when compared with the three-dimensional model, and only underestimate the magnitude of the fluxes by 10 to 20 percent.

Stone, Peter H.↗

DOE OSTI2023

BEYONDPLANCK VI. Noise characterization and modeling

We present a Bayesian method for estimating instrumental noise parameters and propagating noise uncertainties within the global BeyondPlanck Gibbs sampling framework, and apply this to Planck Low Frequency Instrument (LFI) time-ordered data. Following previous literature, we initially adopt a 1/ f model for the noise power spectral density (PSD), but find the need for an additional lognormal component in the noise model for the 30 and 44 GHz bands. We implement an optimal Wiener-filter (or constrained realization) gap-filling procedure to account for masked data. We then use this procedure to both estimate the gapless correlated noise in the time-domain, n corr , and to sample the noise PSD parameters, ξ n = {σ 0 , f knee , α, A p }. In contrast to previous Planck analyses, we assume piecewise stationary noise only within each pointing period (PID), not throughout the full mission, but we adopt the LFI Data Processing Center (DPC) results as priors on α and f knee . On average, we find best-fit correlated noise parameters that are mostly consistent with previous results, with a few notable exceptions. However, a detailed inspection of the time-dependent results reveals many important findings. First and foremost, we find strong evidence for statistically significant temporal variations in all noise PSD parameters, many of which are directly correlated with satellite housekeeping data. Second, while the simple 1/ f model appears to be an excellent fit for the LFI 70 GHz channel, there is evidence for additional correlated noise not described by a 1/ f model in the 30 and 44 GHz channels, including within the primary science frequency range of 0.1–1 Hz. In general, most 30 and 44 GHz channels exhibit deviations from 1/ f at the 2–3σ level in each one hour pointing period, motivating the addition of the lognormal noise component for these bands. For some periods of time, we also find evidence of strong common mode noise fluctuations across the entire focal plane. Overall, we conclude that a simple 1/ f profile is not adequate to fully characterize the Planck LFI noise, even when fitted hour-by-hour, and a more general model is required. These findings have important implications for large-scale CMB polarization reconstruction with the Planck LFI data, and the current work is a first attempt at understanding and mitigating these issues.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Lagrangian and Eulerian drag models that are consistent between Euler-Lagrange and Euler-Euler (two-fluid) approaches for homogeneous systems

The undisturbed flow of a particle is of fundamental importance since it controls both the undisturbed flow force and the perturbation force (which includes quasisteady, added-mass, and history forces). Here we use the pairwise interaction extended point particle framework to evaluate the undisturbed flow of each particle through superposition of the perturbation flow induced by all its neighbors. This approach allows calculation of various statistics related to undisturbed fluid velocity under conditions of both stationary and nonstationary particles. In a random distribution of stationary particles, while the macroscale undisturbed flow is slowly varying, the microscale undisturbed flow that arises due to the perturbation flow of neighbors varies substantially from one particle to another and this in turn leads to large variation in the hydrodynamic force exerted on the particles. The effect of particle motion is generally to increase the particle-to-particle variation in the undisturbed fluid velocity of the particles. We observe that this increase is greater for the transverse component than for the streamwise component. As a result, with increasing random particle motion, the distribution of undisturbed fluid-velocity fluctuation becomes isotropic. Three different normalized forces are defined: $Φ^L$ is the Lagrangian normalized force on an individual particle suitable for application in a microscale-informed Euler-Lagrange simulation, $Φ^E$ is the Eulerian normalized average force suitable for application in an Euler-Euler simulation, and $Φ^{LE}$ is the Lagrangian normalized force on an individual particle suitable for application in the standard Euler-Lagrange simulation. In this work, we establish precise relations between these different definitions. The drag laws developed based on particle-resolved direct numerical simulation results and experiments are appropriate for application only as the Eulerian normalized average force. We introduce the force consistency relation and use it to obtain an expression for $Φ^L$, which when applied to each particle and averaged over all the particles equals $Φ^E$. The results are first obtained in the limit of stationary particles and then extended to the general case of nonstationary particles.

42 ENGINEERING↗