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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.

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DOE OSTI2024

Development of a multiphase PIC model for slurry flow modeling

MFIX-Exa is a recently released multiphase CFD code originally developed for the simulation of particle-laden gas-solid flows. Due to its high-performance computing capabilities, MFIX-Exa is an ideal candidate for scale-up studies of slurry reactors, specifically the coarse-grained particle-in-cell (PIC) model with its statistical treatment of the particle phase. Unfortunately, several physical models that were neglected during original development because they are not relevant for high-density ratio gas-solid flows are important in slurry flows where the particle-to-fluid density ratio is near unity. In this preliminary work we focus on the effective (suspension) viscosity. The models of Brinkman (1952), Krieger and Dougherty (1956), and Cheng and Law (2003) are considered. The impact of the effective viscosity model is studied on horizontal pipe flow. The experimental data of Gillies et al. (2002) is used to assess the pressure drop predictions.

Fullmer, William D.↗
DOE OSTI2020

Three-Dimensional Imaging Lidar for Characterizing Particle Fields and Organisms in the Mesopelagic Zone

The ocean’s mesopelagic zone is largely uncharacterized despite its vital role in sustaining ocean ecosystems. The composition, cycling, and fate of particle fields in the mesopelagic lacks an integrative multi-scale understanding of organism migration patterns, distribution, and diversity. This problem is addressed by combining complementary technologies with overlapping size spectra, including profiler mounted optical scattering sensors, profiler, and ship mounted acoustic devices, and a custom Unobtrusive Multi-Static Lidar Imager (UMSLI). This unique sensor suite can observe distributions of particles including organisms over a six order of magnitude dynamic size range, from microns to meters. Overlapping size ranges between different methods allows for cross-validation. This work focuses on the lidar imaging measurements and optical backscattering and attenuation, covering a combined particle size range of 0.1 mm to several cm. Particles at the small end of this range are sized using an existing backscattering time series inversion method after Briggs et al. (2013). Larger particles are resolved with UMSLI over an expanding volume using three-dimensional photo-realistic laser serial imaging. UMSLI’s image rectifying ability over time allows for derivation of particle concentration, size, and spatial distribution. Technical details on the development and post-processing methods for the novel UMSLI system are provided. Image resolved particle size distributions (PSDs) revealed a size shift from smaller to larger particles (>0.5 mm) as indicated by flatter slopes from dawn (slope = 2.6) to dusk (slope = 3.0). PSD trends are supported by an optical backscatter and transmissometer time series inversion analysis. Size shifts in the particle field are largely attributed to aggregation effects. Images support evidence of temporal variation between dusk and dawn stations through statistical analysis of particle concentrations for particle sizes 0.50–5.41 mm. Spatial analysis of the particle field revealed a dominantly uniform distributed marine snow background. The importance and potential of integrated approaches to studying particle and organism dynamics in ocean environments are discussed.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Spectro-Microscopy Studies of Atmospheric Particles

Our project investigated composition and physical properties of individual atmospheric particles collected in field campaigns organized by the DOE Atmospheric Systems Research and Atmospheric Radiation Measurement (ASR/ARM) programs, such as the Green Ocean Amazon (GoAmazon, 2014/5), the Holistic Interactions of Shallow Clouds, Aerosols, and Land-Ecosystems (HI-SCALE, 2016/7), the Aerosol and Cloud Experiment in the Eastern North Atlantic (ACE-ENA, 2017/8), the Aerosol–Ice Formation Closure Pilot Study (AEROICESTUDY, 2019) and in additional small-scale supporting field experiments focused on the investigation of the light-absorbing (aka brown carbon) atmospheric particles. In these studies, we investigated the contribution of natural and anthropogenic sources to populations of atmospheric particles during representative atmospheric conditions; characterized particle composition and evaluated their hygroscopic properties and propensity to act as cloud condensation nuclei (CCN) and ice nuclei (IN); correlated typical particle-type and mixing state characteristics with real-time measurements in the areas of studies. We used multi-modal spectro-microscopy techniques to examine elemental and molecular composition, mixing state, size, and higher order morphology for individual particles. Specifically, we used computer-controlled scanning electron microscopy and X-ray microanalysis for quantitative analysis of particle elemental composition, and we used transmission electron microscopy to provide additional information on the distribution of different components within individual particles (particle heterogeneity). We used synchrotron-based scanning transmission X-ray microscopy for quantitative description of the mixing state and molecular bonding of carbon in particles. The particle composition, mixing state, and morphology from analyzed periods was then combined with the real-time ARM measurements of aerosol size distribution, CCN concentration, hygroscopicity, and aerosol bulk composition. Combined together, results of our studies allowed us to assess the major particle sources (biogenic vs. anthropogenic, primary vs secondary) and gain insight into the atmospheric processing of aerosol particles resulting from condensation, coagulation, oxidative aging, and cloud processing. In collaboration with other scientists involved in field campaigns, we carried out statistical analysis of particle properties and their source-specific contributions to regional aerosol loading under representative air mass, meteorological, and cloud conditions.

scanning transmission X-ray microscopy↗
DOE OSTI2025

Generating multi-scale Li-ion battery cathode particles with radial grain architectures using stereological generative adversarial networks

Abstract Understanding structure-property relationships of Li-ion battery cathodes is crucial for optimizing rate-performance and cycle-life resilience. However, correlating the morphology of cathode particles, such as in LiNi0.8Mn0.1Co0.1O2 (NMC811), and their inner grain architecture with electrode performance is challenging, particularly, due to the significant length-scale difference between grain and particle sizes. Experimentally, it is not feasible to image such a high number of particles with full granular detail. A second challenge is that sufficiently high-resolution 3D imaging techniques remain expensive and are sparsely available at research institutions. Here, we present a stereological generative adversarial network-based model fitting approach to tackle this, that generates representative 3D information from 2D data, enabling characterization of materials in 3D using cost-effective 2D data. Once calibrated, this multi-scale model can rapidly generate virtual cathode particles that are statistically similar to experimental data, and thus is suitable for virtual characterization and materials testing through numerical simulations. A large dataset of simulated particles with inner grain architecture has been made publicly available.

25 ENERGY STORAGE↗
DOE OSTI2021

Deterministic Calibration of MFiX-PIC, Part 1: Settling Bed

The Particle-in-cell (PIC) numerical approach for modeling granular solids in fluid flow has gained significant interest in recent years. Valued for its often shorter time-to-solution, the PIC formulation relies on modeling statistical groupings of particles called parcels in cooperation with a solids stress model to affect local solids velocity. This is in contrast to the discrete element model (DEM) where every particle in a system is modelled individually and directly coupled to local solids velocity through Newtonian mechanics. The U.S. Department of Energy (DOE), National Energy Technology Laboratory (NETL) develops and maintains Multiphase Flow with Interphase eXchanges (MFiX), a collection of open-source computational fluid dynamics (CFD) solvers. Included in the MFiX suite are traditional two-fluid model (TFM) and DEM solvers, and a recently added PIC solver (NETL, 2021). In general, PIC methodologies offer an accuracy trade-off in lieu of computational speed; and therefore, it is important to assess the credibility of MFiX-PIC simulations. For this purpose, a systematic verification, validation and uncertainty quantification (VVUQ) effort was initiated at NETL to assess the new PIC solver

42 ENGINEERING↗
DOE OSTI2023

Lagrangian large eddy simulations via physics-informed machine learning

High-Reynolds number homogeneous isotropic turbulence (HIT) is fully described within the Navier–Stokes (NS) equations, which are notoriously difficult to solve numerically. Engineers, interested primarily in describing turbulence at a reduced range of resolved scales, have designed heuristics, known as large eddy simulation (LES). LES is described in terms of the temporally evolving Eulerian velocity field defined over a spatial grid with the mean-spacing correspondent to the resolved scale. This classic Eulerian LES depends on assumptions about effects of subgrid scales on the resolved scales. Here, we take an alternative approach and design LES heuristics stated in terms of Lagrangian particles moving with the flow. Our Lagrangian LES, thus L-LES, is described by equations generalizing the weakly compressible smoothed particle hydrodynamics formulation with extended parametric and functional freedom, which is then resolved via Machine Learning training on Lagrangian data from direct numerical simulations of the NS equations. The L-LES model includes physics-informed parameterization and functional form, by combining physics-based parameters and physics-inspired Neural Networks to describe the evolution of turbulence within the resolved range of scales. The subgrid-scale contributions are modeled separately with physical constraints to account for the effects from unresolved scales. We build the resulting model under the differentiable programming framework to facilitate efficient training. We experiment with loss functions of different types, including physics-informed ones accounting for statistics of Lagrangian particles. We show that our L-LES model is capable of reproducing Eulerian and unique Lagrangian turbulence structures and statistics over a range of turbulent Mach numbers.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

RU Net for Automatic Characterization of TRISO Fuel Cross Sections

TRistructural ISOtropic (TRISO) particle fuel is a type of nuclear fuel known for its high-temperature and high-burnup performance. Each sub-millimeter diameter TRISO particle consists of uranium-oxycarbide (UCO) or UO2 fuel kernel, coated with buffer, inner pyrolytic carbon (IPyC), silicon carbide (SiC), and outer pyrolytic carbon (OPyC) layers. The SiC layer acts as the main containment barrier for the TRISO particle to retain the fission products, while the IPyC and OPyC layers provide additional barriers to the release of fission products, especially fission gases. During irradiation, phenomena like kernel swelling, buffer densification, and IPyC fracture may impact fuel performance. Post-irradiation microscopy on entire compact cross sections or samples of individual particles deconsolidated from compacts is often used to identify these irradiation-induced changes in morphology. However, each fuel compact generally contains thousands of TRISO particles. To get statistical information on these phenomena, it is cumbersome work if done manually. For example, to get information about swelling/densification behaviors of different layers or kernels after irradiation, researchers previously manually measured the perimeter of each TRISO layer in hundreds of particles after four rounds of iterative grinding and polishing encompassing more than 2000 cross-section images for a total of four fuel compacts. To attempt to reduce the subjectivity inherent in that process and accelerate data analysis, we conducted a study on the automatic TRISO layer segmentation on cross-sectional microscopic images using Convolutional Neural Networks (CNNs). CNNs are a class of machine learning algorithms specifically designed for processing structured grid data that have gained popularity in recent years due to their remarkable performance in various computer vision tasks, including image classification, object detection, and image segmentation. In this research, we have generated the large irradiated TRISO layer dataset with more than 2000 cross-section TRISO microscopic images and the corresponding annotated images. Based on these annotated images, we have employed different CNNs for automatic segmentation of different TRISO layers. These include RU-Net (developed in this study), as well as three existing architectures: U-Net, Residual Network (ResNet), and Attention U-Net. The preliminary results show that the model based on RU-Net has the best performance in terms of intersection-over-union (IoU). Through the aid of these CNN models, we can expedite the analysis of TRISO particle cross-sections, significantly reducing the manual labor involved and improving the objectivity of the segmentation results.

Convolutional Neural Networks↗
DOE OSTI2023

Code for the manuscript "Lagrangian Large Eddy Simulations vis Physics-informed Machine Learning"

We would like to disclose a code based on Python/Pytorch, in which we implement the data-driven physics-informed machine learning of Lagrangian large eddy simulation that is described in the manuscript "Lagrangian Large Eddy Simulations via Physics-Informed Machine Learning ". High-Reynolds number Homogeneous Isotropic Turbulence is fully described within the Navier-Stokes (NS) equations, which are notoriously difficult to solve numerically. Engineers, interested primarily in describing turbulence at a reduced range of resolved scales, have designed heuristics, known as Large Eddy Simulation (LES). LES is described in terms of the temporally evolving Eulerian velocity field defined over a spatial grid with the mean-spacing correspondent to the resolved scale. This classic Eulerian LES depends on assumptions about the effects of sub-grid scales on the resolved scales. Here, we take an alternative approach and design novel LES heuristics stated in terms of Lagrangian particles moving with the flow. Our \emph{Lagrangian LES}, thus L-LES, is described by equations generalizing the weakly compressible Smoothed Particle Hydrodynamics formulation with extended parametric and functional freedom, which is then resolved via Machine Learning training on Lagrangian data from Direct Numerical Simulations of the NS equations. The L-LES model includes physics-informed parameterization and functional form, by combining physics-based parameters and physics-inspired Neural Networks to describe the evolution of turbulence within the resolved range of scales. The sub-grid scale contributions are modeled separately with physical constraints to account for the effects from un-resolved scales. We build the resulting model under the Differentiable Programming framework to facilitate efficient training. We experiment with loss functions of different types, including physics-informed ones accounting for statistics of Lagrangian particles. We show that our Lagrangian LES model is capable of reproducing Eulerian and unique Lagrangian turbulence structures and statistics over a range of turbulent Mach numbers.

Tian, Yifeng↗
DOE OSTI2020

The discrete Green's function paradigm for two-way coupled Euler-Lagrange simulation

We outline a methodology for the simulation of particle-laden flows whereby the dispersed and fluid phases are two-way coupled. The drag force which couples fluid and particle momentum depends on the undisturbed fluid velocity at the particle location, and this latter quantity requires modelling. We demonstrate that the undisturbed fluid velocity, in the low particle Reynolds number limit, can be related exactly to the discrete Green's function of the discrete Stokes equations. The method is general in that it can be extended to other partial differential equations which may be associated with particle-laden flows, such as the thermal energy equation or Maxwell's equations. In this work, we demonstrate the method of discrete Green's functions by obtaining these functions for the Navier-Stokes equations at low particle Reynolds number in a two-plane channel geometry. We perform verification at low and finite particle Reynolds number for the case of a point-particle settling under gravity parallel to a plane wall, for different wall normal separations. In comparing to other point-particle schemes the discrete Green's function approach is the most robust at low particle Reynolds number, accurate at all wall-normal separations and is the most accurate in the near wall region at finite Reynolds number. We discuss how the accuracy away from the wall at finite Reynolds number could be improved by appealing to Oseen-like discrete Green's functions. Finally we demonstrate that the discrete Green's function approach can have important implications on statistics of particle-laden turbulent channel flow.

42 ENGINEERING↗
DOE OSTI2026

Slow Quasiparticle Dynamics and Anyonic Statistics in a Fractional Quantum Hall Fabry-Pérot Interferometer

Anyons are two-dimensional particles with fractional exchange statistics that emerge as elementary excitations of fractional quantum Hall phases. Experimentally, their exchange statistics can be measured in the edge-state Fabry-Pérot interferometer, wherein the presence of 𝑁 𝑞⁢𝑝 localized anyons contributes a phase 𝑁 𝑞⁢𝑝⁢ 𝜃 𝑎 to the interference pattern where 𝜃 𝑎 is twice the exchange phase. Here we report the observation of large, hysteretic phase jumps in a monolayer graphene Fabry-Pérot interferometer at 𝜈 = 1/3. When the filling factor is increased from 𝜈 < 1/3 toward the center of the plateau, we observe phase slips with magnitude Δ⁢𝜃 ≈ 2⁢𝜋/3, consistent with the addition of individual quasiparticles to the interferometer bulk. These phase slips occur as instantaneous jumps in the interference signal, with intervals between the jumps indicating quasiparticle equilibration times exceeding 20 min. We use this long timescale to investigate the effect of changes in interferometer area 𝐴 𝐼 and 𝑁 𝑞⁢𝑝 independently at fixed magnetic field, revealing a striking memory effect in the phase slip magnitude. In particular, as the 𝜈 =1/3 plateau is approached from higher filling, we observed phase slips with Δ⁢𝜃 significantly larger than 2⁢𝜋/3 over the same range of gate voltage where quantized jumps are seen for increasing 𝜈. We discuss this asymmetry in terms of bulk-edge coupling of quasiparticles localized near the edge or in the bulk, and argue that this effect can be qualitatively reconciled with theoretical expectations for strongly interacting quasiparticles in the presence of weak disorder and strongly nonequilibrium charge dynamics. Besides providing a replication of interferometric measurements sensitive to 𝜃 𝑎 , our results highlight the key role played by charge dynamics on signatures of the anyon phase, and demonstrate that fractional quasiparticles can be indefinitely localized in nonequilibrium configurations.

anyons↗
DOE OSTI2022

Automated processing of environmental transmission electron microscopy images for quantification of thin film dewetting and carbon nanotube nucleation dynamics

We report scalable production of carbon nanotubes (CNTs) requires catalysts and reaction conditions that provide high nucleation efficiency. In situ characterization methods such as environmental transmission electron microscopy (ETEM) can reveal fundamental mechanisms of synthesis, but to date have primarily provided qualitative observations on small sample sizes. Here, quantitative analysis is performed using high-resolution, high-rate video capture of ETEM experimentation coupled with automated image processing, involving computer vision algorithms and convolutional neural networks. By this approach, we detect distinct nanoparticle formation from an alumina-supported iron thin film and subsequent CNT nucleation from the nanoparticles. The statistical summary of particles in each video shows that, compared to a H 2 -only atmosphere, pretreatment of the catalyst with carbon added to the H 2 atmosphere results in a smaller average particle diameter, a 2-fold increase in particle density (to 5300 particles/μm 2 ), a 3-fold increase in CNT nucleation efficiency (to 92%), and more than a 5-fold increase in CNT density (to 4800/μm 2 ). Addition of carbon during exposure to H 2 is also more effective than NH 3 at dewetting the catalyst film and increasing the CNT nucleation efficiency, in spite of NH 3 being a stronger reducing agent for iron. Insights from this study are applicable to improving CNT yield and productivity in both batch-style and continuous processes.

25 ENERGY STORAGE↗
DOE OSTI2026

Third integer resonant extraction transit time simulation studies

In this work, we present the investigation of transit time of particles in the non-linear third-integer resonant extraction process. Transit time is defined as the number of turns a particle takes to get extracted once it is in the unstable region in the phase space, i.e., outside the triangular separatrix in case of third-integer resonance. The study of transit time is important because transit time directly contributes to the beam response time during resonant extraction and thus knowing it apriori would be practically useful in designing of the extraction system. In this work, we shall investigate the analytical derivation of the transit time of particles (to the first order Kobayashi Hamiltonian) in different parts of the phase space distribution and compare against the analytical results. We also compare the simulation result of the transit time of particles (with higher statistics) for the static as well as dynamic extraction conditions cases, particularly in the context of resonant extraction parameters for Mu2e experiment at Fermilab.

Narayanan, Aakaash [Fermilab]↗
DOE OSTI2025

Third Integer Resonant Extraction Transit Time Simulation Studies

In this work, we present the investigation of transit time of particles in the non-linear third-integer resonant extraction process. Transit time is defined as the number of turns a particle takes to get extracted once it is in the unstable region in the phase space, i.e., outside the triangular separatrix in case of third-integer resonance. The study of transit time is important because transit time directly contributes to the beam response time during resonant extraction and thus knowing it apriori would be practically useful in designing of the extraction system. In this work, we shall investigate the analytical derivation of the transit time of particles (to the first order Kobayashi Hamiltonian) in different parts of the phase space distribution and compare against the analytical results. We also compare the simulation result of the transit time of particles (with higher statistics) for the static as well as dynamic extraction conditions cases, particularly in the context of resonant extraction parameters for Mu2e experiment at Fermilab.

Narayanan, Aakaash [Fermilab] (ORCID:0000000157944↗
DOE OSTI2022

Mass Transport Limitations and Kinetic Consequences of Corn Stover Deacetylation

Alkaline pretreatment of herbaceous feedstocks such as corn stover prior to mechanical refining and enzymatic saccharification improves downstream sugar yields by removing acetyl moieties from hemicellulose. However, the relationship between transport phenomena and deacetylation kinetics is virtually unknown for such feedstocks and this pretreatment process. Here, we report the development of an experimentally validated reaction–diffusion model for the deacetylation of corn stover. A tissue-specific transport model is used to estimate transport-independent kinetic rate constants for the reactive extraction of acetate, hemicellulose and lignin from corn stover under representative alkaline conditions (5–7 g L -1 NaOH, 10 wt% solids loadings) and at low to mild temperatures (4–70°C) selected to attenuate individual component extraction rates under differential kinetic regimes. The underlying transport model is based on microstructural characteristics of corn stover derived from statistically meaningful geometric particle and pore measurements. These physical descriptors are incorporated into distinct particle models of the three major anatomical fractions (cobs, husks and stalks) alongside an unsorted, aggregate corn stover particle, capturing average Feret lengths of 917–1239 μm and length-to-width aspect ratios of 1.8–2.9 for this highly heterogeneous feedstock. Individual reaction–diffusion models and their resulting particle model ensembles are used to validate and predict anatomically-specific and bulk feedstock performance under kinetic-controlled vs. diffusion-controlled regimes. In general, deacetylation kinetics and mass transfer processes are predicted to compete on similar time and length scales, emphasizing the significance of intraparticle transport phenomena. Critically, we predict that typical corn stover particles as small as ~2.3 mm in length are entirely diffusion-limited for acetate extraction, with experimental effectiveness factors calculated to be 0.50 for such processes. Debilitatingly low effectiveness factors of 0.021–0.054 are uncovered for cobs—implying that intraparticle mass transfer resistances may impair observable kinetic measurements of this anatomical fraction by up to 98%. These first-reported quantitative maps of reaction vs. diffusion control link fundamental insights into corn stover anatomy, biopolymer composition, practical size reduction thresholds and their kinetic consequences. These results offer a guidepost for industrial deacetylation reactor design, scale-up and feedstock selection, further establishing deacetylation as a viable biorefinery pretreatment for the conversion of lignocellulosics into value-added fuels and chemicals.

09 BIOMASS FUELS↗
DOE OSTI2021

The Effect of Warm Dark Matter on Early Star Formation Histories of Massive Galaxies: Predictions from the CROC Simulations

Several massive (M * > 108 M ⊙ ), high-redshift (z = 8–10) galaxies have recently been discovered to contain stars with ages of several hundred million years, pushing the onset of star formation in these galaxies back to z ~ 15. The very existence of stars formed so early may serve as a test for cosmological models with suppressed small-scale power (and, hence, late formation of cosmic structure). We explore the ages of the oldest stars in numerical simulations from the Cosmic Reionization On Computers project with cold dark matter (CDM) and two warm dark matter (WDM) cosmologies with 3 and 6 keV particles. There are statistically significant differences of ~5 Myr between average stellar ages of massive galaxies in CDM and 3 keV WDM, while CDM and 6 keV WDM are statistically indistinguishable. Even this 5 Myr difference, however, is much less than current observational uncertainties on the stellar population properties of high-redshift galaxies. The age distributions of all galaxies in all cosmologies fail to produce a substantial Balmer break, although uncertainties in dust attenuation are a potentially significant factor. Finally, we assess the convergence of our simulation predictions and find that the systematic uncertainties on individual galaxy properties are comparable to the differences between cosmologies, suggesting these differences may not be numerically robust.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Variance reduction techniques for Monte Carlo neutron noise simulations

The small fluctuations of the neutron flux caused by small perturbations of the macroscopic cross-sections take the name of neutron noise. Advanced Monte Carlo methods have been recently proposed in order to solve the neutron noise equations in the frequency domain, which allows establishing reference solutions to validate faster but approximate deterministic solvers. Due to the presence of particles carrying two statistical weights (for the real and imaginary components of the noise field), both of which may be positive or negative, Monte-Carlo simulations of neutron noise pose distinct challenges in terms of variance reduction. In this work we investigate two variance-reduction techniques, namely branchless collisions and weight cancellation, and probe their effectiveness for a benchmark con- figuration concerning the noise field induced by a pin with oscillating cross sections in a fuel assembly.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Proof that Combining the Forced-collision and DXTRAN Monte Carlo Variance-reduction Techniques is Fair

This report provides mathematical proof that the MCNP DXTRAN (also known in other codes as forced-flight) and forced-collision variance-reduction techniques do not bias the expected value of Monte Carlo simulation estimates when combined. Proof is also provided that the techniques are unbiased when used independently. To prove that the techniques are unbiased, this report derives the first History Score Moment Equation (HSME) for non-multiplying media employing only forced collisions, only DXTRAN, and then both the variance-reduction techniques combined, as defined next. The HSMEs are found by forming the History Score Probability Density Functions (HSPDFs) and then taking the first score moment. Following its derivation, each HSME with a variance-reduction technique employed is reduced to the HSME for an analog simulation. Because the HSME represents the expected contribution to estimators in the simulation, reducing the HSME with variance reduction to the analog HSME shows that the simulation is unbiased despite the variance-reduction technique considered in the HSME. Analysis regarding higher-score moments of each technique is the subject of prior work and is not addressed herein. Throughout this work, the phase space p is defined to be the particle position x, direction-of-flight unit vector $\hat{Ω}$, energy E, and statistical weight w, $$p ≡ (x; \hat{Ω}; E; w).$$ A reduced phase-space excluding the statistical weight of the particle, $$r ≡ (x; \hat{Ω}; E),$$ is also used.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Integrated photonic Galton board and its application for photon counting

The Galton board is a desktop probability machine traditionally used to visualize the principles of statistical physics from classical particles. Here, we demonstrate a photonic Galton board that enables on-chip observation of statistics from single-photon interference. The photonic Galton board consists of a directional coupler matrix terminated by an array of superconducting nanowire detectors to provide spatiotemporal resolution. This design also allows for photon-number-resolving capability, making it suitable for high-speed photon counting. Our results demonstrate the compatibility between single-photon detector array and photonic integrated circuits, paving the way for implementing on-chip large-scale quantum optics experiments and photonic quantum computing.

Qin, Hezheng (ORCID:0009000139348800)↗