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DOE OSTI2021

A new method for measuring the 3D turbulent velocity dispersion of molecular clouds

ABSTRACT The structure and star formation activity of a molecular cloud are fundamentally linked to its internal turbulence. However, accurately measuring the turbulent velocity dispersion is challenging due to projection effects and observational limitations, such as telescope resolution, particularly for clouds that include non-turbulent motions, such as large-scale rotation. Here, we develop a new method to recover the 3D turbulent velocity dispersion (σv,3D) from position–position–velocity (PPV) data. We simulate a rotating, turbulent, collapsing molecular cloud, and compare its intrinsic σv,3D with three different measures of the velocity dispersion accessible in PPV space: (1) the spatial mean of the 2nd-moment map, σi, (2) the standard deviation of the gradient/rotation-corrected 1st-moment map, σ(c − grad), and (3) a combination of (1) and (2), called the ‘gradient-corrected parent velocity dispersion’, $\sigma _{\mathrm{(p}-\mathrm{grad)}}=(\sigma _{\mathrm{i}}^2+\sigma _{(\mathrm{c}-\mathrm{grad)}}^2)^{1/2}$. We show that the gradient correction is crucial in order to recover purely turbulent motions of the cloud, independent of the orientation of the cloud with respect to the line of sight. We find that with a suitable correction factor and appropriate filters applied to the moment maps, all three statistics can be used to recover σv,3D, with method 3 being the most robust and reliable. We determine the correction factor as a function of the telescope beam size for different levels of cloud rotation, and find that for a beam full width at half-maximum f and cloud radius R, the 3D turbulent velocity dispersion can best be recovered from the gradient-corrected parent velocity dispersion via $\sigma _{v,\mathrm{3D}}= \left[(-0.29\pm 0.26)\, f/R + 1.93 \pm 0.15\right] \sigma _{\mathrm{(p}-\mathrm{grad)}}$ for f/R < 1, independent of the level of cloud rotation or LOS orientation.

Stewart, Madeleine↗

DOE OSTI2025

Shining a Light on the Nucleus: Photonuclear Measurements from Correlations to Charmonium

The atomic nucleus is comprised of a collection of nucleons (protons and neutrons), which are bound together by the nucleon-nucleon (NN) interaction that originates from Quantum Chromodynamics (QCD). While most nucleons experience the force from the rest of the nu- cleus as a single net “mean-field” interaction that binds them relatively weakly, a small but impactful fraction are in configurations called “Short-Range Correlations” (SRCs), in which they pair with another nucleon at very short distance to experience strong interactions, sig- nificant binding, and high momentum. Hard, high-energy scattering reactions in which an SRC pair is broken apart, knocking both nucleons out of the nucleus, provide the ability to probe the details of these SRC configurations in the nucleus. Previous measurements have had limited statistics and kinematic reach, and the theoretical tools available were in- sufficient to draw quantitative conclusions regarding the ground-state properties of SRCs. The studies described in this thesis represent the first global analysis of SRC breakup mea- surements in order to present a unified picture of SRCs within light- to medium-size nuclei. This includes the use of a novel theoretical framework, the Generalized Contact Formalism, which connects scattering cross-section measurements and the ground-state properties of the SRC pair, to quantitatively interpret a variety of electron-scattering measurements. This is brought to culmination by a report on the first measurement of SRC pairs via the use of hard meson photoproduction reactions, which, despite differing significantly from the me- chanics of electron-scattering, is well-described under a common framework, pointing to a consistent and universal picture of SRCs across reaction channels. I also report on the first measurement of J/¿ photoproduction in the near- and below-threshold kinematic region, giving the first insights to the gluonic structure of bound nucleons in the large-x “valence” region and providing constraints on a gluonic “EMC effect”. In addition to these studies, I provide details on the search for Primakoff production of axion-like particles using the pho- toproduction data taken for this experiment, and I conclude by describing studies of nucleon spin structure measurements that will be performed at the forthcoming U.S. Electron-Ion Collider.

Pybus, Jackson↗

DOE OSTI2021

Tunable Microwave Conductance of Nanodomains in Ferroelectric PbZr 0.2 Ti 0.8 O 3 Thin Film

Ferroelectric materials exhibit spontaneous polarization that can be switched by electric field. Beyond traditional applications as nonvolatile capacitive elements, the interplay between polarization and electronic transport in ferroelectric thin films has enabled a path to neuromorphic device applications involving resistive switching. A fundamental challenge, however, is that finite electronic conductivity may introduce considerable power dissipation and perhaps destabilize ferroelectricity itself. In this work, tunable microwave frequency electronic response of domain walls injected into ferroelectric lead zirconate titanate (PbZr 0.2 Ti 0.8 O 3 ) on the level of a single nanodomain is revealed. Tunable microwave response is detected through first-order reversal curve spectroscopy combined with scanning microwave impedance microscopy measurements taken near 3 GHz. Contributions of film interfaces to the measured AC conduction through subtractive milling, where the film exhibited improved conduction properties after removal of surface layers, are investigated. Using statistical analysis and finite element modeling, we inferred that the mechanism of tunable microwave conductance is the variable area of the domain wall in the switching volume. These observations open the possibilities for ferroelectric memristors or volatile resistive switches, localized to several tens of nanometers and operating according to well-defined dynamics under an applied field.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Estimating reaction parameters in mechanism-enabled population balance models of nanoparticle size distributions: A Bayesian inverse problem approach

In order to quantitatively predict nano- as well as other particle-size distributions, one needs to have both a mathematical model and estimates of the parameters that appear in these models. Here, we show how one can use Bayesian inversion to obtain statistical estimates for the parameters that appear in recently derived mechanism-enabled population balance models (ME-PBM) of nanoparticle growth. The Bayesian approach addresses the question of “how well do we know our parameters, along with their uncertainties?.” The results reveal that Bayesian inversion statistical analysis on an example, prototype $\mathrm{lr(0)_n}$ nanoparticle formation system allows one to estimate not just the most likely rate constants and other parameter values, but also their SDs, confidence intervals, and other statistical information. Moreover, knowing the reliability of the mechanistic model's parameters in turn helps inform one about the reliability of the proposed mechanism, as well as the reliability of its predictions. Importantly, the paper can also be seen as a tutorial with the additional goal of achieving a “Gold Standard” Bayesian inversion ME-PBM benchmark that others can use as a control to check their own use of this methodology for other systems of interest throughout nature. Overall, the results provide strong support for the hypothesis that there is substantial value in using a Bayesian inversion methodology for parameter estimation in particle formation systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Computational and Experimental Mechanistic Insights into the Ethanol-to-Butanol Upgrading Reaction over MgO

The mechanism of ethanol upgrading to higher products is still under debate, especially regarding intermediate species and hydrogenation and dehydrogenation steps. In this work, we conducted a combined theoretical and experimental approach to contribute to this discussion. For such, detailed electronic structure density functional theory calculations (aiming at probing density of states, infrared spectra, geometric parameters, charge densities, and reaction energetics) and diffuse reflectance infrared Fourier transform spectroscopy experiments were carried out revealing the relevance of an appropriate combination of reactive surface sites to support the formation of several intermediates that are formed in the C-C coupling over MgO. The roles of Mg and O sites were also studied under an electronic perspective and different geometrical arrangements. We found that a kink configuration was the most adequate for ethanol to 1-butanol upgrading. Our calculations also gave us arguments to propose distinct reaction routes, whose mutual predominance would depend upon reaction temperature. At temperatures up to 573 K, the so-called β-route, which goes through scission of a Cβ-H bond and formation of an oxametallacycle-like intermediate, would dominate the coupling, whereas at higher temperatures, up to 673 K, a more usual Guerbet mechanism, via an aldol coupling step and then consecutive hydrogenations, would be expected. Here, the theoretical conclusions were followed by a careful experimental strategy using sequential experimental planning techniques in order to estimate accurate parameters with the lowest possible experimental load. Information from these different sources were coupled to develop a mathematical model for the rate of the ethanol upgrading reaction, using a Langmuir-Hinshelwood-Hougen-Watson approach. The developed and statistically validated model adequately described the experimental data at 673 K and 1.1 bar total pressure for ethanol partial pressures in the range from 0 to 20 kPa.

09 BIOMASS FUELS↗

DOE OSTI2024

Expanding the access of wearable silicone wristbands in community-engaged research through best practices in data analysis and integration

Wearable silicone wristbands are a rapidly growing exposure assessment technology that offer researchers the ability to study previously inaccessible cohorts and have the potential to provide a more comprehensive picture of chemical exposure within diverse communities. However, there are no established best practices for analyzing the data within a study or across multiple studies, thereby limiting impact and access of these data for larger meta-analyses. We utilize data from three studies, from over 600 wristbands worn by participants in New York City and Eugene, Oregon, to present a first-of-its-kind manuscript detailing wristband data properties. We further discuss and provide concrete examples of key areas and considerations in common statistical modeling methods where best practices must be established to enable meta-analyses and integration of data from multiple studies. Finally, we detail important and challenging aspects of machine learning, meta-analysis, and data integration that researchers will face in order to extend beyond the limited scope of individual studies focused on specific populations.

Bramer, Lisa M.↗

DOE OSTI2022

Relationship Between the Marginal Probability of Failure for a CPP Test and the Recommended Corrosion Control Requirements for Hanford Double Shell Waste Tanks

The Hanford Site in Washington State currently stores millions of gallons of radioactive waste in underground, carbon steel, double shell tanks (DSTs) that were constructed between 1968 and 1986. A chemistry control and monitoring program has been established mitigate corrosion in order to extend the service life for the DSTs. The current waste temperatures in the DSTs are at historical lows (i.e., typically less than 50 °C). The previous chemistry control requirements were determined for conditions at temperatures significantly higher. SRNL undertook a statistically based investigation of the role of nitrate and halide ion (i.e., chloride and fluoride) induced pitting corrosion. The objective was to develop a comprehensive waste chemistry envelope for the simultaneous minimization of the pitting and SCC risks caused by halide and nitrate ions at the lower temperature conditions. On the basis of these tests, new chemistry control requirements were proposed and have since been implemented for pitting corrosion control.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2023

Data to Accompany: Expanding the access of wearable silicone wristbands in community-engaged research through best practices in data analysis and integration

Bramer, Lisa M↗

DOE OSTI2021

A Hybrid Energy System Workflow for Energy Portfolio Optimization

This manuscript develops a workflow, driven by data analytics algorithms, to support the optimization of the economic performance of an Integrated Energy System. The goal is to determine the optimum mix of capacities from a set of different energy producers (e.g., nuclear, gas, wind and solar). A stochastic-based optimizer is employed, based on Gaussian Process Modeling, which requires numerous samples for its training. Each sample represents a time series describing the demand, load, or other operational and economic profiles for various types of energy producers. These samples are synthetically generated using a reduced order modeling algorithm that reads a limited set of historical data, such as demand and load data from past years. Numerous data analysis methods are employed to construct the reduced order models, including, for example, the Auto Regressive Moving Average, Fourier series decomposition, and the peak detection algorithm. All these algorithms are designed to detrend the data and extract features that can be employed to generate synthetic time histories that preserve the statistical properties of the original limited historical data. The optimization cost function is based on an economic model that assesses the effective cost of energy based on two figures of merit: the specific cash flow stream for each energy producer and the total Net Present Value. An initial guess for the optimal capacities is obtained using the screening curve method. The results of the Gaussian Process model-based optimization are assessed using an exhaustive Monte Carlo search, with the results indicating reasonable optimization results. The workflow has been implemented inside the Idaho National Laboratory’s Risk Analysis and Virtual Environment (RAVEN) framework. The main contribution of this study addresses several challenges in the current optimization methods of the energy portfolios in IES: First, the feasibility of generating the synthetic time series of the periodic peak data; Second, the computational burden of the conventional stochastic optimization of the energy portfolio, associated with the need for repeated executions of system models; Third, the inadequacies of previous studies in terms of the comparisons of the impact of the economic parameters. The proposed workflow can provide a scientifically defendable strategy to support decision-making in the electricity market and to help energy distributors develop a better understanding of the performance of integrated energy systems.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2026

CoLoRe-2LPT: Lyman-$α$ mock catalogues for the validation of DESI cosmological analyses

The Lyman-$α$ (Ly$α$) forest has become a crucial probe for studying the large-scale structure of the universe at high redshift ($z > 2$), providing powerful constraints on Baryon Acoustic Oscillations (BAO) and the full-shape (FS) clustering of matter. As a key ingredient for upcoming BAO and FS analyses, we present a new generation of fast cosmological Ly$α$ mocks based on second-order Lagrangian perturbation theory (2LPT). These new mocks significantly improve upon previous log-normal approaches, both at accurately capturing small scale clustering and at recovering the non-linear broadening of the BAO peak. They are able to reproduce Ly$α$ statistics within $10\%$ of the latest DESI measurement; including the Ly$α$ bias and the redshift-space distortion $β$ parameter, mean transmitted flux, and 1D power spectrum. The corresponding quasar (QSO) clustering is also improved with respect to previous approaches, calibrated against high-resolution Abacus simulations, recovering the observational QSO linear bias to less than $5\%$ and improving redshift-space distortions via 2LPT velocities and the addition of Fingers-of-God effects. Furthermore, these mocks incorporate high column density systems and metal lines, allowing us to explore the effects and systematics induced by these astrophysical contaminants. This new set of mocks has been key for enhancing the modeling and validation of the DESI DR2 Ly$α$ full shape cosmological analysis. This work provides a physically motivated and computationally efficient tool for simulating current and next-generation Ly$α$ surveys and validating FS and BAO analysis.

Bernal, M.F. Ruiz-Herrera [Madrid, CIEMAT] (ORCID:↗

DOE OSTI2024

Search for Heavy Neutral Leptons at the MINER$\nu$A detector

Heavy Neutral Leptons (HNL) are particles hypothesised to provide a mass generation mechanism for the active (observed) neutrino species, which are known to have nonzero mass from the definitive observation of neutrino oscillations. HNL are eigenstates of mass of the order $\mathcal{O}(0.1 − 1\,\,\mathrm{GeV}/c^{2})$, which mix into the active flavour eigenstates through the extended leptonic mixing matrix. Apart from neutrino mass, they could provide a natural dark matter candidate and a mechanism for matter-antimatter asymmetry in the early Universe, giving rise to today’s matter-dominated cosmos. Searches for HNL typically attempt to either confirm the existence of HNL through an excess in data that is most compatible with an HNL hypothesis, or by setting limits on the HNL parameter space $\left(M_{N4}, \left|U_{\alpha 4}\right|^{2}\right)$ in the case of statistically insignificant excess. Such searches are intensifying as part of a global research programme at both colliders and accelerator / atmospheric neutrino experiments. One such setting is the MINER$\nu$A experiment, located in the NuMI beamline at Fermilab. MINER$\nu$A has collected a large amount of data over seven years of operation to measure the cross-sections of neutrino-nucleus interactions necessary to drive systematic uncertainties down, in order for neutrino oscillation experiments to achieve sensitivity to CP violation in the neutrino sector. With the high-energy, high-intensity NuMI beam, and with good timing, position, and angular resolution leading to sensitivity to HNL decays, MINER$\nu$A is fertile ground for an HNL search, which is performed in this thesis. Specifically, a novel, experiment-agnostic and general simulation of HNL production and decay is presented and deployed; this simulation has been incorporated in the ubiquitous GENIE neutrino event generator for use with neutrino experiments in the future. The event selection and background characterisation is discussed in detail, including the primary background coming from charged-current coherent and diffractive pion production from neutrino-nucleus interactions, and constraints on the background using control regions from MINER$\nu$A data are derived. Finally, by means of a fake-data study given a background of $\mathcal{O}(500)$ events, the discovery potential and limit-setting capacity of MINER$\nu$A is demonstrated, and ways to improve this capacity are expounded upon.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Suppressing the sample variance of DESI-like galaxy clustering with fast simulations

Ongoing and upcoming galaxy redshift surveys, such as the Dark Energy Spectroscopic Instrument (DESI) survey, will observe vast regions of sky and a wide range of redshifts. In order to model the observations and address various systematic uncertainties, N-body simulations are routinely adopted, however, the number of large simulations with sufficiently high mass resolution is usually limited by available computing time. Therefore, achieving a simulation volume with the effective statistical errors significantly smaller than those of the observations becomes prohibitively expensive. In this study, we apply the Convergence Acceleration by Regression and Pooling (CARPool) method to mitigate the sample variance of the DESI-like galaxy clustering in the AbacusSummit simulations, with the assistance of the quasi-N-body simulations FastPM. Based on the halo occupation distribution (HOD) models, we construct different FastPM galaxy catalogs, including the luminous red galaxies (LRGs), emission line galaxies (ELGs), and quasars, with their number densities and two-point clustering statistics well matched to those of AbacusSummit. We also employ the same initial conditions between AbacusSummit and FastPM to achieve high cross-correlation, as it is useful in effectively suppressing the variance. Our method of reducing noise in clustering is equivalent to performing a simulation with volume larger by a factor of 5 and 4 for LRGs and ELGs, respectively. We also mitigate the standard deviation of the LRG bispectrum with the triangular configurations k 2 = 2k 1 = 0.2 h Mpc -1 by a factor of 1.6. With smaller sample variance on galaxy clustering, we are able to constrain the baryon acoustic oscillations (BAO) scale parameters to higher precision. The CARPool method will be beneficial to better constrain the theoretical systematics of BAO, redshift space distortions (RSD) and primordial non-Gaussianity (NG).

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Fractional Quantum Hall Effect in Weyl Semimetals

Weyl semimetal may be thought of as a gapless topological phase protected by the chiral anomaly, where the symmetries involved in the anomaly are the U(1) charge conservation and the crystal translational symmetry. The absence of a band gap in a weakly interacting Weyl semimetal is mandated by the electronic structure topology and is guaranteed as long as the symmetries and the anomaly are intact. The nontrivial topology also manifests in the Fermi arc surface states and topological response, in particular taking the form of an anomalous Hall effect in magnetic Weyl semimetals, whose magnitude is only determined by the location of the Weyl nodes in the Brillouin zone. In this work, we consider the situation when the interactions are not weak and ask whether it is possible to open a gap in a magnetic Weyl semimetal while preserving its nontrivial electronic structure topology along with the translational and the charge conservation symmetries. Surprisingly, the answer turns out to be yes. The resulting topologically ordered state provides a nontrivial realization of the fractional quantum Hall effect in three spatial dimensions in the absence of an external magnetic field, which cannot be viewed as a stack of two dimensional states. Our state contains loop excitations with nontrivial braiding statistics when linked with lattice dislocations.

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↗

DOE OSTI2022

Small experiment, Big Data: the data production of the Muon $g-2$ Experiment

The Muon $g-2$ Experiment at Fermilab aims to measure the muon anomalous magnetic moment with the unprecedented precision of 140 parts per billion (ppb). In April 2021 the collaboration published the first measurement, based on the first year of data taking. The result confirmed the previous experiment at Brookhaven National Laboratory (BNL), and increased the long-standing tension with the Standard Model prediction to 4.2 $\sigma$. The experiment is now running the sixth year of data acquisition of positive muon data, having accumulated a total of $\sim$19 times the statistics of the BNL experiment. A collaboration-wide effort is now in place to help produce the multi-petabyte-sized data sets, a challenge typically faced by much bigger experiments. Having a quick production turnaround time is of critical importance in order to achieve a timely analysis and publication schedule. In this paper I will describe the production workflow, the former and current challenges, the resources, tools, and the future prospects of the Muon $g-2$ Experiment.

Girotti, Paolo↗

DOE OSTI2024

Strong Coupling of Hydrodynamics and Reactions in Nuclear Statistical Equilibrium for Modeling Convection in Massive Stars

We build on the simplified spectral deferred corrections (SDC) coupling of hydrodynamics and reactions to handle the case of nuclear statistical equilibrium (NSE) and electron/positron captures/decays in the cores of massive stars. Our approach blends a traditional reaction network on the grid with a tabulated NSE state from a very large, ${\mathcal O }(100)$ nuclei network. We demonstrate how to achieve second-order accuracy in the simplified-SDC framework when coupling NSE to hydrodynamics, with the ability to evolve the star on the hydrodynamics time step. We discuss the application of this method to convection in massive stars leading up to core collapse. We also show how to initialize the initial convective state from a 1D model in a self-consistent fashion. All of these developments are done in the publicly available Castro simulation code and the entire simulation methodology is fully GPU-accelerated.

Explosive nucleosynthesis↗

DOE OSTI2021

p +p - electroproduction off protons in deuterium: measurements of quasi-free cross sections and kinematic probing of final state interactions

In this study, the process of pi+pi- electroproduction off protons bound in deuterium nuclei is explored. The exploration is performed through the analysis of experimental data on electron scattering off the deuteron target, collected in Hall B at Jefferson Lab with the CLAS detector. As a main result, the set of integrated and single-differential cross sections of the reaction yvp(n) -> p'(n')pi+pi- is obtained. The cross sections are extracted in the quasi-free regime, which implies that only events not affected by final state interactions are subject to selection. The measurements are performed in the kinematic region of the invariant mass W from 1.3 GeV to 1.825 GeV and photon virtuality Q2 from 0.4 GeV2 to 1 GeV2. Sufficient experimental statistics allows narrow binning, i.e. 25 MeV in W and 0.05 GeV2 in Q2, while maintaining an adequate statistical uncertainty. The extraction of quasi-free cross sections is accompanied by the kinematic probing of FSI between the reaction final hadrons and the spectator neutron in the aforementioned exclusive channel. In this probing the distributions of missing quantities are used in order to investigate the relative spread of events with FSI along the reaction phase space, trace the difference of FSI manifestations in different reaction topologies, reveal details on alterations of the hadron momentum in FSI, and isolate FSI contributions of various final hadrons. The performed examination is also capable of retrieving information on some underlying FSI mechanisms, among which the process of resonance formation in the intermediate state of pion-neutron interactions is particularly remarkable.

Skorodumina, Iuliia↗

DOE OSTI2022

On analysis and stochastic modeling of the particle kinetic energy equation in particle-laden isotropic turbulent flows

In this study, we analyze three-dimensional particle-laden, isotropic turbulence to develop an understanding of inertial particle dynamics from a kinetic energy perspective. Data trends implying inhomogeneous sampling of the flow by particles are identified and used to support a proposed particle behavior: particles appear to accumulate in regions of low flow kinetic energy over time because they lose kinetic energy and slow down in such regions, ultimately causing them to spend more time there. To elucidate this behavior, we derive a particle kinetic energy equation from the particle momentum equation, which incorporates inertial effects through the Schiller–Naumann drag correlation. Upon extracting fundamental physics from this equation, hypotheses regarding the role of the Stokes number in the temporal change of particle kinetic energy and the previously proposed particle behavior are evaluated using simulation data considering three Stokes numbers. Finally, a Fokker–Planck equation is used to derive the steady-state probability density function of the particle kinetic energy. The model fits the simulation data well and provides a tool for further investigation into understanding preferential concentration, as well as a reduced order model for predicting particle kinetic energy in turbulent flows.

42 ENGINEERING↗