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DOE OSTI2023

Measurement of the branching fractions for Cabibbo-suppressed decays D + → K + K - π + π 0 and D ( s ) + → K + π - π + π 0 at Belle

We present measurements of the branching fractions for the singly Cabibbo-suppressed decays and , and the doubly Cabibbo-suppressed decay , based on of data recorded by the Belle experiment at the KEKB e + ⁢e - collider. We measure these modes relative to the Cabibbo-favored modes D + → K - ⁢π + ⁢π + ⁢π 0 and D$^{+}_{s}$ → K + ⁢K -⁢ π + ⁢π 0 . Our results for the ratios of branching fractions are $\mathscr{B}$⁡(D + →K + ⁢K -⁢ π + ⁢π 0 )/$\mathscr{B}$⁡(D + → K - ⁢π + ⁢π + ⁢π 0 ) =(11.32±0.13±0.26)%, $\mathscr{B}$⁡(D + →K + π - ⁢π + ⁢π 0 )/$\mathscr{B}$(D + →K -⁢ π + ⁢π + ⁢π 0 ) =(1.68±0.11±0.03)%, and $\mathscr{B}$⁡(D$^{+}_{s}$ → K + ⁢π - π + ⁢π 0 )/$\mathscr{B}$⁡(D$^{+}_{s}$ → K + ⁢K - π + π 0 ) =(17.13±0.62±0.51)%, where the uncertainties are statistical and systematic, respectively. The second value corresponds to (5.83 ±0.42) ×tan 4 ⁡θ C , where θ C is the Cabibbo angle; this value is larger than other measured ratios of branching fractions for a doubly Cabibbo-suppressed charm decay to a Cabibbo-favored decay. Multiplying these results by world average values for $\mathscr{B}$⁡(D + → K - ⁢π + ⁢π + ⁢π 0 ) and $\mathscr{B}$⁡(D$^{+}_{s}$ → K + ⁢K - π + π 0 ) yields $\mathscr{B}$( + →K + ⁢K -⁢ π + ⁢π 0 ) = (7.08±0.08±0.16±0.20)×10 -3 , $\mathscr{B}$⁡(D + → K +⁢ π - π + ⁢π 0 ) =(1.05±0.07±0.02±0.03)×10 -3 , and $\mathscr{B}$⁡(D$^{+}_{s}$ → K + ⁢π - π + ⁢π 0 ) =(9.44±0.34±0.28±0.32)×10 -3 , where the third uncertainty is due to the branching fraction of the normalization mode. The first two results are consistent with, but more precise than, the current world averages. The last result is the first measurement of this branching fraction.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

An Investigation of the Effects of Volume Fraction on Drag Coefficient of Non-Spherical Particles Using PR-DNS

Prediction of the drag coefficient is required in gas-particle multiphase flow modeling and simulation. Experimental data and correlations on the fixed-bed system of spherical particles with high volume fractions for various possible arrangements are available in the literature. However, the effect of volume fraction on the drag coefficient of non-spherical particles is not well studied. In solving the momentum equation, the volume fraction plays a vital role in determining the flow resistances. In this paper, we study the impact of volume fraction in the range of 0.069 to 0.65 on the drag coefficient using the computational fluid dynamics (CFD) simulation of air for Reynold number in the range of 10 to 10000 using particle resolved direct numerical solution (PR-DNS). Regular non-spherical particles such as a cube, tetrahedron, and spheroids are used in this study since their single particle’s drag coefficient data are available in the literature for comparison. For this work, the simulations are carried out in the Ansys Fluent using polyhedral mesh, which consumes significantly less computational time and power. The study showed the sphericity and volume fraction have significant impact on the bed pressure drop and average drag coefficient of the particles in the bed especially in high Reynolds number regime. The bed of the spheroid experiences the lowest drag being the most streamlined particle, and the particles with the edges result in a large drag coefficient due to flow separation at the discontinuity. The vector plots verify this behavior where large wake regions are observed behind the tetrahedron particle.

Mahyawansi, Pratik↗

DOE OSTI2024

Fractional Statistics

The quantum-mechanical description of assemblies of particles whose motion is confined to two (or one) spatial dimensions offers many possibilities that are distinct from bosons and fermions. We call such particles anyons. The simplest anyons are parameterized by an angular phase parameter θ. θ = 0, π correspond to bosons and fermions, respectively; at intermediate values, we say that we have fractional statistics. In two dimensions, θ describes the phase acquired by the wave function as two anyons wind around one another counterclockwise. It generates a shift in the allowed values for the relative angular momentum. Composites of localized electric charge and magnetic flux associated with an abelian U(1) gauge group realize this behavior. More complex charge-flux constructions can involve nonabelian and product groups acting on a spectrum of allowed charges and fluxes, giving rise to nonabelian and mutual statistics. Interchanges of nonabelian anyons implement unitary transformations of the wave function within an emergent space of internal states. Anyons of all kinds are described by quantum field theories that include Chern–Simons terms. The crossings of one-dimensional anyons on a ring are unidirectional, such that a fractional phase θ acquired upon interchange gives rise to fractional shifts in the relative momenta between the anyons. The quasiparticle excitations of fractional quantum Hall states have long been predicted to include anyons. Recently, the anyon behavior predicted for quasiparticles in the ν = 1/3 fractional quantum Hall state has been observed in both scattering and interferometric experiments. Excitations within designed systems, notably including superconducting circuits, can exhibit anyon behavior. Such systems are being developed for possible use in quantum information processing.

Physics↗

DOE OSTI2020

Analysis of Tempered Fractional Operators

Tempered fractional operators provide an improved predictive capability for modeling anomalous effects that cannot be captured by standard partial differential equations. These effects include subdiffusion and superdiffusion (i.e. the mean square displacement in a diffusion process is proportional to a fractional power of the time), that often occur in, e.g., geoscience and hydrology. We analyze tempered fractional operators within the nonlocal vector calculus framework in order to assimilate them to the rigorous mathematical structure developed for nonlocal models. First, we show they are special instances of generalized nonlocal operators by means of a proper choice of the nonlocal kernel. Then, we present a plan for showing tempered fractional operators are equivalent to truncated fractional operators. These truncated operators are useful because they are less computationally intensive than the tempered operators.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Conservative Release Fraction Correlation for Spray Releases

Washington River Protection Solutions, LLC (WRPS) is planning to conduct repairs in the Liquid Effluent Retention Facility (LERF), and prior to conducting this work they will re-evaluate the hazard category designation for LERF. As part of this evaluation, WRPS needs estimates of the release fraction of potential accidental sprays, because a spray release is a potential bounding accident. Pacific Northwest National Laboratory previously developed a conservative correlation for the cumulative generation rate (volume per time) of aerosol droplets less than or equal to specific sizes from spray releases as a function of the spray pressure, orifice area, and droplet diameter. To obtain release fraction estimates from the conservative generation rate correlation, the correlation needs to be recast by dividing the aerosol generation rate by the flow rate of a spray. In the current study, a conservative release fraction correlation was developed from the conservative aerosol generation rate correlation developed previously by dividing the generation rate correlation by the flow rate of a spray using an orifice flow rate equation and then this correlation was adjusted to be conservative. Test data were also extrapolated to a lower pressure than the lowest pressure tested (100 psig) for the spray data used for developing the previous conservative generation rate correlation. The new conservative release fraction correlation was then used to predict release fractions of respirable droplets (droplets = 10 µm) for four specific pipes that are part of LERF.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2020

Theoretical Analysis of Fractional Viscoelastic Flow in Circular Pipes: Parametric Study

Pipe flow is one of the most commonly used models to describe fluid dynamics. The concept of fractional derivative has been recently found very useful and much more accurate in predicting dynamics of viscoelastic fluids compared with classic models. In this paper, we capitalize on our previous study and consider space-time dynamics of flow velocity and stress for fractional Maxwell, Zener, and Burgers models. We demonstrate that the behavior of these quantities becomes much more complex (compared to integer-order classical models) when adjusting fractional order and elastic parameters. We investigate mutual influence of fractional orders and consider their limiting value combinations. Finally, we show that the models developed can be reduced to classical ones when appropriate fractional orders are set.

Gritsenko, Dmitry (ORCID:0000000248181512)↗

DOE OSTI2021

X-ray Imaging-Based Void Fraction Measurement in Saturated Flow Boiling Experiments with Seawater Coolant

Recent studies have shown that the presence of dissolved salts in water can exhibit peculiar flow boiling and two-phase flow regimes. Two-phase flow and convective flow boiling are typically characterized with the help of void fraction measurements. To quantitatively improve our understanding of two-phase flow and boiling phenomenon with seawater coolant, void fraction data are needed, which can not be obtained from optical imaging. In this paper, we present experimental void fraction measurements of saturated flow boiling of tap water and seawater using X-ray radiography. X-rays with a maximum energy level of 40 KeV were used for imaging the exit region of the heated test section. At lower heat flux levels, the two phase flow in seawater was bubbly and homogeneous in nature, resulting in higher void fractions as compared to tap water. With an increase in heat flux, the flow regime was similar to slug flow, and void fraction measurements approached similarity with tap water. The predicted pressure drop using the measured void faction shows good agreement with the measured total pressure drop across the test section, demonstrating the validity of the measurement process.

Eckels, Seth↗

DOE OSTI2026

The Binary Fraction of Stars in the Dwarf Galaxy Ursa Minor via Dark Energy Spectroscopic Instrument

We utilize multi-epoch line-of-sight velocity measurements from the Milky Way Survey of the Dark Energy Spectroscopic Instrument to estimate the binary fraction for member stars in the dwarf spheroidal galaxy Ursa Minor. Our dataset comprises 670 distinct member stars, with a total of more than 2,000 observations collected over approximately one year. We constrain the binary fraction for UMi to be $0.61^{+0.16}_{-0.20}$ and $0.69^{+0.19}_{-0.17}$, with the binary orbital parameter distributions based on solar neighborhood observation from Duquennoy & Mayor (1991) and Moe & Di Stefano (2017), respectively. Furthermore, by dividing our data into two subsamples at the median metallicity, we identify that the binary fraction for the metal-rich ([Fe/H]>-2.14) population is slightly higher than that of the metal-poor ([Fe/H]<-2.14) population. Based on the Moe & Di Stefano model, the best-constrained binary fractions for metal-rich and metal-poor populations in UMi are $0.86^{+0.14}_{-0.24}$ and $0.48^{+0.26}_{-0.19}$, respectively. After a thorough examination, we find that this offset cannot be attributed to sample selection effects. We also divide our data into two subsamples according to their projected radius to the center of UMi, and find that the more centrally concentrated population in a denser environment has a lower binary fraction of $0.33^{+0.30}_{-0.20}$, compared with $1.00^{+0.00}_{-0.32}$ for the subsample in more outskirts.

Qiu, Tian [Shanghai Jiao Tong Univ. (China); DESI ↗

DOE OSTI2025

Baryon fraction from the BAO amplitude: a consistent approach to parameterizing perturbation growth

Galaxy clustering constrains the baryon fraction Omega_b/Omega_m through the amplitude of baryon acoustic oscillations and the suppression of perturbations entering the horizon before recombination. This produces a different pre-recombination distribution of baryons and dark matter. After recombination, the gravitational potential responds to both components in proportion to their mass, allowing robust measurement of the baryon fraction. This is independent of new-physics scenarios altering the recombination background (e.g. Early Dark Energy). The accuracy of such measurements does, however, depend on how baryons and CDM are modeled in the power spectrum. Previous template-based splitting relied on approximate transfer functions that neglected part of information. We present a new method that embeds an extra parameter controlling the balance between baryons and dark matter in the growth terms of the perturbation equations in the CAMB Boltzmann solver. This approach captures the baryonic suppression of CDM prior to recombination, avoids inconsistencies, and yields a clean parametrization of the baryon fraction in the linear power spectrum, separating out the simple physics of growth due to the combined matter potential. We implement this framework in an analysis pipeline using Effective Field Theory of Large-Scale Structure with HOD-informed priors and validate it against noiseless LCDM and EDE cosmologies with DESI-like errors. The new scheme achieves comparable precision to previous splitting while reducing systematic biases, providing a more robust way to baryon-fraction measurements. In combination with BBN constraints on the baryon density and Alcock-Paczynski estimates of the matter density, these results strengthen the use of baryon fraction measurements to derive a Hubble constant from energy densities, with future DESI and Euclid data expected to deliver competitive constraints.

Crespi, Andrea [U. Waterloo (main); Waterloo U., I↗

DOE OSTI2020

Zeolitic catalytic conversion of alcohols to hydrocarbon fractions with reduced gaseous hydrocarbon content

A method for converting an alcohol to a hydrocarbon fraction reduced in gaseous hydrocarbon content, the method comprising: (i) contacting said alcohol with a metal-loaded zeolite catalyst under conditions suitable for converting said alcohol to a first hydrocarbon fraction containing liquid hydrocarbons having at least five carbon atoms along with gaseous hydrocarbons having less than five carbon atoms, wherein said metal-loaded zeolite catalyst is catalytically active for converting said alcohol to said first hydrocarbon fraction; and (ii) selectively removing said gaseous hydrocarbons from the first hydrocarbon fraction and contacting said gaseous hydrocarbons with a metal-loaded zeolite catalyst under conditions suitable for converting said gaseous hydrocarbons into liquid hydrocarbons having at least five carbon atoms to produce a second hydrocarbon fraction reduced in gaseous hydrocarbon content, wherein the metal-loaded zeolite catalyst in steps (i) and (ii) are the same or different.

09 BIOMASS FUELS↗

DOE OSTI2022

Fourier analysis of continuous fractional diffusion synthetic acceleration schemes in slab geometry

We propose two fractional extensions of continuous diffusion synthetic acceleration (DSA) with fractional derivative order α varying over the interval 2 ≥ α ≥ 1 . We investigate the spectral properties of the corresponding continuous families of fractional preconditioners by performing Fourier analysis for a model infinite homogeneous medium problem in slab geometry. The first family results in a fractional acceleration scheme, FrDSAo, that reduces to traditional DSA for .α = 2 and scattering ratio c limiting to a unit value (c → 1) but is otherwise optimized via the Fourier analysis, to obtain the smallest possible spectral radius, for c < 1 and 2 ≥ α ≥ 1. The second family corresponds to a fractional acceleration scheme, FrDSAs, that reduces to traditional DSA for α = 2 for all values of c. The latter scheme is not optimized but has the advantage of lending itself to a more straightforward implementation. For high values of c, the results of the Fourier analysis point to the existence of an interval 2 > α > ∼1.8 where both FrDSAo and FrDSAs can achieve a lower spectral radius than DSA. For example, DSA has a spectral radius of ∼0.2246 for c = 0.9999 while FrDSAo produces a value of ∼0.1616 at α = 1.92 and FrDSAs results in ∼0.2116 at α =1.93. (author)

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

A multiscale approach to analyze the effect of radial void fraction distributions on BWR neutronic lattice parameters

The goal of this study is to analyze the effect of radial void fraction distribution, considered at three degrees of fidelity, on lattice and 2-group homogenized cross sections. The novelty of this work lies in its use of experimentally-determined radial void fraction distributions which allows for fine-scale coolant density data with no predictive uncertainty and which could be prohibitively expensive to simulate over the range of operational parameters used in the experiments. The experimentally-determined radial void fraction distributions are also characterized using a statistical tool called a semi-variogram in order to determine the scale of continuity. Void fraction distributions are averaged at the lattice and subchannel level for comparison with the fine-scale model. Models averaged at the subchannel and lattice level show a difference in about 68% of the time. Also, by comparing 2-group homogenized cross-sections, the differences between the subchannel and homogeneous cases are measurable.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

Flow pattern and void fraction characterization in nitrogen/water flows through a diamond-type triply periodic minimal surface lattice

Here, this study presents, to the authors knowledge, the first experimental investigation on the void fraction and flow patterns in two-phase flows through a diamond-type Triply Periodic Minimal Surface (TPMS) lattice. An additively manufactured TPMS structure was tested under upward co-current flow of a water/nitrogen mixture. Superficial velocities varied for a total of 42 test conditions (gas: 0.01–2.4 m/s; liquid: 0.01–2.4 m/s; mass flux: 20–2370 kg/m 2 ·s). High-speed video and X-ray imaging enabled time-averaged void fraction measurements and identified six distinct flow regimes which were used to develop a flow pattern map. Comparison of the void fraction data with correlations from literature demonstrated the Rouhani and Axelsson (1970) [49] correlation modified by Steiner (1993) [52] provided the best agreement, which was improved with empirically fit coefficients. This approach predicted the void fraction with errors < ±20% for 64% of the data, with a mean absolute percent deviation (MAPD) of 23%. The measured frictional pressure drop was compared to correlations from literature which captured the observed trends but did not provide good accuracy. The best agreement was found after optimizing the empirical coefficients of the Muller-Steinhagen & Heck (1986) [56] correlation; this approach captured 33% of the data within ±20% with a MAPD of 46% over the full range and captured 71% of the data within ±20% a MAPD of 13.3% at mass fluxes >1100 kg/m 2 -s. These results provide foundational insight into TPMS two-phase flow behavior and inform modeling and design of advanced heat exchange components incorporating TPMS geometries.

42 - ENGINEERING↗

DOE OSTI2021

An optimization-based approach to parameter learning for fractional type nonlocal models

Nonlocal operators of fractional type are a popular modeling choice for applications that do not adhere to classical diffusive behavior; however, one major challenge in nonlocal simulations is the selection of model parameters. In this study we propose an optimization-based approach to parameter identification for fractional models with an optional truncation radius. We formulate the inference problem as an optimal control problem where the objective is to minimize the discrepancy between observed data and an approximate solution of the model, and the control variables are the fractional order and the truncation length. For the numerical solution of the minimization problem we propose a gradient-based approach, where we enhance the numerical performance by an approximation of the bilinear form of the state equation and its derivative with respect to the fractional order. Several numerical tests in one and two dimensions illustrate the theoretical results and show the robustness and applicability of our method.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Evaluation of several relevant fractionation processes as possible explanation for radioxenon isotopic activity ratios in samples taken near underground nuclear explosions in shafts and tunnels

Gas samples taken from two historic underground nuclear tests done in 1989 at the Nevada National Security Site (NNSS), formerly the Nevada Test Site (NTS), were examined to determine how xenon isotopes fractionate because of early-time cavity processes, transport through the rock, or dispersal through tunnels. Xenon isotopes are currently being used to distinguish civilian sources of xenon in the atmosphere from sources associated with underground nuclear explosions (UNEs). The two nuclear tests included (1) BARNWELL, a test conducted in a vertical shaft approximately 600 m below ground surface at Pahute Mesa, and (2) DISKO ELM, a horizontal line-of-sight test done in P-tunnel approximately 261 m below the surface of Aqueduct Mesa. Numerical flow and transport models developed for the two sites had mixed success when attempting to match the observed xenon isotope ratios. At the BARNWELL site, the simulated xenon isotope ratios were consistent with measurements from the chimney and ground surface and appeared to have been affected primarily by fractionation during subsurface transport. At the DISKO ELM site, samples taken from two elevations in the chimney failed to show the degree of fractionation predicted by the models during transport and did not show evidence for significant fractionation due to early-time condensation of refractory xenon-precursor radionuclides into the melt glass. Gas samples taken from the adjacent tunnels in the days following the test showed mixed evidence for early-time separation of xenon isotopes from their iodine precursors.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Elemental fractionation in aerosol laser-induced breakdown spectroscopy with nanosecond and femtosecond laser ablation

For the purpose of realizing atmospheric radiation plume tracking, laser-induced breakdown spectroscopy (LIBS) was performed to characterize Cs atomic emissions from airborne nanoparticles in a binary particle matrix using nanosecond and femtosecond laser ablation. As a surrogate to multi-element nuclear fallout particulates, both Cs and Na solutions were mixed with Cu at a 1:1.45 M concentration ratio and aerosolized to study elemental fractionation in atomic emissions, revealing Na I resonance emissions are enhanced whereas Cs I resonance emissions are reduced with Cu present despite sharing similar electronic and chemical properties. Femtosecond laser ablation reduced elemental fractionation effects by more than 50% while retaining the same temporal fractionation trends for Cs and Na. The origin of elemental fractionation in aerosol LIBS was further investigated using Al and Ti aerosols which revealed that the particle matrix induces changes to the local plasma temperature, population of atomic states, and subsequent molecular association and emission.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Distribution of Bound and Free Water in Anatomical Fractions of Pine Residues and Corn Stover as a Function of Biological Degradation

Biomass quality is influenced by water’s abundance, distribution, and status in relation to other chemical species within the polymer matrix. Water interacts with polymers that make up the cell walls, and these interactions govern the physical and chemical changes that occur during the storage and preprocessing of biomass feedstocks. Time-domain nuclear magnetic resonance (TD-NMR) was employed to explore variations in the physical constraints of water within the lignocellulosic microstructure in distinct anatomical fractions of biomass and as a function of biological degradation. The Carr–Purcell–Meiboom–Gill sequence, when combined with knowledge of the chemical composition and physical structure of pine residues and corn stover anatomical fractions, gives an accurate measurement of the bound and free water. In this work, the impacts of storage and biological degradation were investigated to elucidate changes in the status and distribution of water within distinct plant tissues. We also investigate how degradation during storage affects water interactions in different pine residues (e.g., bark, branch, and needle) and corn stover (e.g., cob, leaf, and stalk) anatomical fractions using transverse relaxation times (T2). As demonstrated herein, TD-NMR provides quantitative data on lignocellulosic biomass–water interactions within anatomical fractions, which can further aid in the investigation of preprocessing effects on feedstock quality. Our findings suggest that biological heating enhances biomass–water interactions at the cellular and macromolecular scale. In addition, analysis of three-dimensional scanning electron microscopy reconstructions indicates that surface roughness wavelengths align with microscale roughness, suggesting that pine forestry residue and corn stover particles have primarily hydrophobic exterior surfaces. Furthermore, this study offers multiscale insights into understanding the microstructure, wettability, and chemical environment that dictate diffusion, enzyme access, and recalcitrance of lignocellulosic biomass.

09 BIOMASS FUELS↗

DOE OSTI2025

Generalized fractional approach to solving partial differential equations with arbitrary dispersion relations

The dynamics of physical systems are typically modeled by partial differential equations (PDEs). Because of the complexity in physical systems, PDE models rely on approximations or limiting cases. To model the full complexity of physical systems, it is necessary to use multiscale approaches where appropriate models are used at each level. Alternatively, complexity can be directly tackled by fractional integrodifferential equations that must be derived for each system. Here, we argue that complexity can be restored in PDEs by describing them from a fractional calculus perspective. Rather than deriving a fractional integrodifferential equation, we reinterpret the dispersion relation of the system by use of the Riesz definition, which contains the required information relating the energy and momentum space of the system and thus fully describes their dynamics. The approach is demonstrated by two examples: the Landau–Lifshitz equation in a 1D ferromagnetic chain and a modified KdV equation supporting surface gravity waves or Euler dispersion. The presented approach is applicable to fluids, soft matter, and solid-state matter and can be readily generalized to higher dimensions and more complex systems. While numerical calculations are needed to determine the fractional operator, the approach is analytical and can be utilized to determine analytical solutions and investigate nonlinear problems.

97 MATHEMATICS AND COMPUTING↗