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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Carbon content of soil fractions varies with season, rainfall, and soil fertility across a lowland tropical moist forest gradient

Tropical forests contain some of the largest soil carbon (C) stocks on Earth, making them broadly relevant to terrestrial-climate feedbacks, yet our understanding of how their soil organic C (SOC) fractions vary over space and time is limited. We studied effects of season, fertility, and mean annual precipitation (MAP) on the C contents of soil fractions across 14 lowland forests in Panama. We measured free-debris, occluded-debris, and mineral-associated SOC fractions, as well as soluble C associated with each fraction. We hypothesized that mineral-associated SOC would be greatest in infertile, strongly weathered soils with large reactive mineral contents. We also hypothesized that the debris SOC fractions would accumulate during the dry season, reflecting seasonal increases in litterfall. To address this, we compared soil fractions in wet and dry seasons from fertile and infertile soils across a range of 1809 – 2864 mm MAP. The C content (mg C / g soil) of all soil fractions varied with fertility and MAP: specifically, free-debris SOC was greatest in wet, high-fertility soils, and occluded-debris SOC was greater in high-fertility than low-fertility soils. The mineral-associated SOC fraction, which contained the majority of bulk soil C, showed increasing C content with greater MAP in infertile sites, presumably driving similar spatial patterns in the bulk soil. Only the free-debris SOC fraction showed strong seasonal variation, increasing in mass during the dry season. Nitrogen behaved similarly to C. In summary, soil C contents increased with MAP in infertile sites but not fertile sites, driven by the mineral-associated SOC fraction. The dry season had greater free-debris SOC, but this seasonal trend was not apparent in bulk soil C, likely because of the small size of the free-debris SOC fraction. Furthermore, changes in the quantity and seasonality of precipitation, which are projected for tropical forests, might shift spatial and temporal patterns of soil C storage, which would in turn influence forest-climate feedbacks for this C-rich biome.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2012

Microbial Enhanced Oil Recovery in Fractional-Wet Systems: A Pore-Scale Investigation

Microbial enhanced oil recovery (MEOR) is a technology that could potentially increase the tertiary recovery of oil from mature oil formations. However, the efficacy of this technology in fractional-wet systems is unknown, and the mechanisms involved in oil mobilization therefore need further investigation. Our MEOR strategy consists of the injection of ex situ produced metabolic byproducts produced by Bacillus mojavensis JF-2 (which lower interfacial tension (IFT) via biosurfactant production) into fractional-wet cores containing residual oil. Two different MEOR flooding solutions were tested; one solution contained both microbes and metabolic byproducts while the other contained only the metabolic byproducts. The columns were imaged with X-ray computed microtomography (CMT) after water flooding, and after MEOR, which allowed for the evaluation of the pore-scale processes taking place during MEOR. Results indicate that the larger residual oil blobs and residual oil held under relatively low capillary pressures were the main fractions recovered during MEOR. Residual oil saturation, interfacial curvatures, and oil blob sizes were measured from the CMT images and used to develop a conceptual model for MEOR in fractional-wet systems. Overall, results indicate that MEOR was effective at recovering oil from fractional-wet systems with reported additional oil recovered (AOR) values between 44 and 80%; the highest AOR values were observed in the most oil-wet system.

02 PETROLEUM↗
DOE OSTI2018

Linear fractional differential equations and eigenfunctions of fractional differential operators

Eigenfunctions associated with Riemann–Liouville and Caputo fractional differential operators are obtained by imposing a restriction on the fractional derivative parameter. Those eigenfunctions can be used to express the analytical solution of some linear sequential fractional differential equations. As a first application, we discuss analytical solutions for the so-called fractional Helmholtz equation with one variable, obtained from the standard equation in one dimension by replacing the integer order derivative by the Riemann–Liouville fractional derivative. A second application consists of an initial value problem for a fractional wave equation in two dimensions in which the integer order partial derivative with respect to the time variable is replaced by the Caputo fractional derivative. The classical Mittag-Leffler functions are important in the theory of fractional calculus because they emerge as solutions of fractional differential equations. Starting with the solution of a specific fractional differential equation in terms of these functions, we find a way to express the exponential function in terms of classical Mittag-Leffler functions. A remarkable characteristic of this relation is that it is true for any value of the parameter n appearing in the definition of the functions, i.e., we have an infinite family of different expressions for e{sup x} in terms of classical Mittag-Leffler functions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Numerical approach based on fractional-order Lagrange polynomials for solving a class of fractional differential equations

In this study, we propose a new set of fractional functions based on the Lagrange polynomials to solve a class of fractional differential equations. Fractional differential equations are the best tools for modelling natural phenomenon that are elaborated by fractional calculus. Therefore, we need an accurate and efficient technique for solving them. The main purpose of this article is to generalize new functions based on Lagrange polynomials to the fractional calculus. At first, we present a new representation of Lagrange polynomials and in continue, we propose a new set of fractional-order functions which are called fractional-order Lagrange polynomials (FLPs). Besides, a general formulation for operational matrices of fractional integration and derivative of FLPs on arbitrary nodal points are extracted. These matrices are obtained using Laplace transform. The initial value problems is reduced to the system of algebraic equations using the operational matrix of fractional integration and collocation method. Also, we find the upper bound of error vector for the fractional integration operational matrix and we indicate convergence of approximations of FLPs. Illustrative examples are included to demonstrate the validity and applicability of the proposed technique.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Tackling the curse of dimensionality in fractional and tempered fractional PDEs with physics-informed neural networks

Fractional and tempered fractional partial differential equations (PDEs) are effective models of long-range interactions, anomalous diffusion, and non-local effects. Traditional numerical methods for these problems are mesh-based, thus struggling with the curse of dimensionality (CoD). Physics-informed neural networks (PINNs) offer a promising solution due to their universal approximation, generalization ability, and mesh-free training. In principle, Monte Carlo fractional PINN (MC-fPINN) estimates fractional derivatives using Monte Carlo methods and thus could lift CoD. However, this may cause significant variance and errors, hence affecting convergence; in addition, MC-fPINN is sensitive to hyperparameters. In general, numerical methods and specifically PINNs for tempered fractional PDEs are under-developed. Herein, we extend MC-fPINN to tempered fractional PDEs to address these issues, resulting in the Monte Carlo tempered fractional PINN (MC-tfPINN). To reduce possible high variance and errors from Monte Carlo sampling, we replace the one-dimensional (1D) Monte Carlo with 1D Gaussian quadrature, applicable to both MC-fPINN and MC-tfPINN. We validate our methods on various forward and inverse problems of fractional and tempered fractional PDEs, scaling up to 100,000 dimensions. Our improved MC-fPINN/MC-tfPINN using quadrature consistently outperforms the original versions in accuracy and convergence speed in very high dimensions.

42 ENGINEERING↗
DOE OSTI2017

Molybdenum isotope fractionation and speciation in a euxinic lake—Testing ways to discern isotope fractionation processes in a sulfidic setting

The molybdenum (Mo) isotope composition in euxinic shales has been used as a proxy for the global distribution of anoxic conditions in ancient oceans, and since more recently also as a proxy for sulfide concentrations in depositional environments. However, there is currently no way to distinguish isotope fractionation at low bottom water sulfide concentrations in ‘local’ basins from ‘global’ secular isotope variations associated with changing seawater composition. This uncertainty is challenging the use of Mo isotopes for paleoceanographic reconstructions. To explore this further, we present new data from sediments deposited over the past ~ 9800 years in one of the best studied euxinic localities in the world: Lake Cadagno in Switzerland. The sample set allows us to test ways to discern isotope fractionation processes at play in a highly restricted euxinic basin. Most of our drill core samples (n = 18) show high δ98Mo values similar to previously studied shallow sediments, indicative of quantitative Mo removal from the water column (Dahl et al. 2010a). However, a few samples (n = 3) deposited between about 1200 and 3400 years ago carry low δ98Mo values and have been isotopically fractionated in the lake. Sedimentological and geochemical characterizations show that these δ98Mo-fractionated sediments formed during times of frequent injection of O2- and sediment-rich river water into the deep sulfidic water column. A positive correlation between δ98Mo and sedimentary Mo contents suggests that isotope fractionation occurred during times of non-quantitative Mo removal, although Mn-oxide cycling at the chemocline might also contribute a subordinate proportion of (98Mo-depleted) molybdenum into the sulfidic zone. Sedimentary Mo/U enrichments relative to oxic lake water further supports the hypothesis that a particulate Mo shuttle was most efficient during times of quantitative Mo removal. Therefore, periods with inefficient Mo capture are ascribed to incomplete conversion of molybdate to particle reactive Mo species when bottom water H2S levels were low or less stable than today. Using XAFS spectroscopy, we found that the two distinct Mo compounds predominating in the sediments (MoIV-S and MoVI-OS) are not diagnostic for isotope fractionation that has occurred in Lake Cadagno. Instead, we infer that δ98Mo-fractionated products (forming via a low-sulfide Mo pathway) can be subsequently altered with little or no isotopic imprint during remobilization and re-precipitation (e.g., at higher sulfide levels in the sediments) as well as during post-depositional oxidation. Future work could investigate local δ98Mo-fractionation processes expressed in other euxinic settings and explore other sedimentary metrics to constrain the steps involved in the euxinic burial pathway(s). One tantalizing prospect of this is to distinguish between local bottomwater sulfide levels and variations in the fraction of global seafloor anoxia from the Mo isotope composition in ancient euxinic mudrocks.

58 GEOSCIENCES↗
DOE OSTI2013

THE CLUSTER AND FIELD GALAXY ACTIVE GALACTIC NUCLEUS FRACTION AT z = 1-1.5: EVIDENCE FOR A REVERSAL OF THE LOCAL ANTICORRELATION BETWEEN ENVIRONMENT AND AGN FRACTION

The fraction of cluster galaxies that host luminous active galactic nuclei (AGNs) is an important probe of AGN fueling processes, the cold interstellar medium at the centers of galaxies, and how tightly black holes and galaxies co-evolve. We present a new measurement of the AGN fraction in a sample of 13 clusters of galaxies (M {>=} 10{sup 14} M{sub Sun }) at 1 < z < 1.5 selected from the Spitzer/IRAC Shallow Cluster Survey, as well as the field fraction in the immediate vicinity of these clusters, and combine these data with measurements from the literature to quantify the relative evolution of cluster and field AGN from the present to z {approx} 3. We estimate that the cluster AGN fraction at 1 < z < 1.5 is f{sub A} = 3.0{sup +2.4}{sub -1.4}% for AGNs with a rest-frame, hard X-ray luminosity greater than L{sub X,{sub H}} {>=} 10{sup 44} erg s{sup -1}. This fraction is measured relative to all cluster galaxies more luminous than M{sup *}{sub 3.6}(z) + 1, where M{sup *}{sub 3.6}(z) is the absolute magnitude of the break in the galaxy luminosity function at the cluster redshift in the IRAC 3.6 {mu}m bandpass. The cluster AGN fraction is 30 times greater than the 3{sigma} upper limit on the value for AGNs of similar luminosity at z {approx} 0.25, as well as more than an order of magnitude greater than the AGN fraction at z {approx} 0.75. AGNs with L{sub X,{sub H}} {>=} 10{sup 43} erg s{sup -1} exhibit similarly pronounced evolution with redshift. In contrast to the local universe, where the luminous AGN fraction is higher in the field than in clusters, the X-ray and MIR-selected AGN fractions in the field and clusters are consistent at 1 < z < 1.5. This is evidence that the cluster AGN population has evolved more rapidly than the field population from z {approx} 1.5 to the present. This environment-dependent AGN evolution mimics the more rapid evolution of star-forming galaxies in clusters relative to the field.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

SU-E-T-480: Radiobiological Dose Comparison of Single Fraction SRS, Multi-Fraction SRT and Multi-Stage SRS of Large Target Volumes Using the Linear-Quadratic Formula

Purpose: To compare the radiobiological effect on large tumors and surrounding normal tissues from single fraction SRS, multi-fractionated SRT, and multi-staged SRS treatment. Methods: An anthropomorphic head phantom with a centrally located large volume target (18.2 cm{sup 3}) was scanned using a 16 slice large bore CT simulator. Scans were imported to the Multiplan treatment planning system where a total prescription dose of 20Gy was used for a single, three staged and three fractionated treatment. Cyber Knife treatment plans were inversely optimized for the target volume to achieve at least 95% coverage of the prescription dose. For the multistage plan, the target was segmented into three subtargets having similar volume and shape. Staged plans for individual subtargets were generated based on a planning technique where the beam MUs of the original plan on the total target volume are changed by weighting the MUs based on projected beam lengths within each subtarget. Dose matrices for each plan were export in DICOM format and used to calculate equivalent dose distributions in 2Gy fractions using an alpha beta ratio of 10 for the target and 3 for normal tissue. Results: Singe fraction SRS, multi-stage plan and multi-fractionated SRT plans had an average 2Gy dose equivalent to the target of 62.89Gy, 37.91Gy and 33.68Gy, respectively. The normal tissue within 12Gy physical dose region had an average 2Gy dose equivalent of 29.55Gy, 16.08Gy and 13.93Gy, respectively. Conclusion: The single fraction SRS plan had the largest predicted biological effect for the target and the surrounding normal tissue. The multi-stage treatment provided for a more potent biologically effect on target compared to the multi-fraction SRT treatments with less biological normal tissue than single-fraction SRS treatment.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

Fractionation of Organosolv Lignin Using Acetone:Water and Properties of the Obtained Fractions

In this study, lignin fractions with different molecular weight were prepared using a simple and almost green method from switchgrass and pine organosolv lignin. Different proportions of acetone in water, ranging from 30 to 60%, were used for lignin fractionation. A higher concentration of acetone dissolved higher molecular weight fractions of the lignin. Fractionated organosolv lignin showed different molecular weight and functional groups. Higher molecular weight fractions exhibited more aliphatic and less phenolic OH than lower molecular weight fractions. Lower molecular weight fractions lead to more homogeneous structure compared to samples with a higher molecular weight. In conclusion, all fractions showed strong antioxidant activity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2012

Thomson scattering diagnostic for the measurement of ion species fraction

Simultaneous Thomson scattering measurements of collective electron-plasma and ion-acoustic fluctuations have been utilized to determine ion species fraction from laser produced CH plasmas. The CH{sub 2} foil is heated with 10 laser beams, 500 J per beam, at the Omega Laser facility. Thomson scattering measurements are made 4 mm from the foil surface using a 30 J 2{omega} probe laser with a 1 ns pulse length. Using a series of target shots the plasma evolution is measured from 2.5 ns to 9 ns after the rise of the heater beams. Measuring the electron density and temperature from the electron-plasma fluctuations constrains the fit of the two-ion species theoretical form factor for the ion feature such that the ion temperature, plasma flow velocity and ion species fraction are determined. The ion species fraction is determined to an accuracy of {+-}0.06 in species fraction.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2013

Repopulation of interacting tumor cells during fractionated radiotherapy: Stochastic modeling of the tumor control probability

Purpose: Optimal treatment planning for fractionated external beam radiation therapy requires inputs from radiobiology based on recent thinking about the “five Rs” (repopulation, radiosensitivity, reoxygenation, redistribution, and repair). The need is especially acute for the newer, often individualized, protocols made feasible by progress in image guided radiation therapy and dose conformity. Current stochastic tumor control probability (TCP) models incorporating tumor repopulation effects consider “stem-like cancer cells” (SLCC) to be independent, but the authors here propose that SLCC-SLCC interactions may be significant. The authors present a new stochastic TCP model for repopulating SLCC interacting within microenvironmental niches. Our approach is meant mainly for comparing similar protocols. It aims at practical generalizations of previous mathematical models. Methods: The authors consider protocols with complete sublethal damage repair between fractions. The authors use customized open-source software and recent mathematical approaches from stochastic process theory for calculating the time-dependent SLCC number and thereby estimating SLCC eradication probabilities. As specific numerical examples, the authors consider predicted TCP results for a 2 Gy per fraction, 60 Gy protocol compared to 64 Gy protocols involving early or late boosts in a limited volume to some fractions. Results: In sample calculations with linear quadratic parameters α = 0.3 per Gy, α/β = 10 Gy, boosting is predicted to raise TCP from a dismal 14.5% observed in some older protocols for advanced NSCLC to above 70%. This prediction is robust as regards: (a) the assumed values of parameters other than α and (b) the choice of models for intraniche SLCC-SLCC interactions. However, α = 0.03 per Gy leads to a prediction of almost no improvement when boosting. Conclusions: The predicted efficacy of moderate boosts depends sensitively on α. Presumably, the larger values of α are the ones appropriate for individualized treatment protocols, with the smaller values relevant only to protocols for a heterogeneous patient population. On that assumption, boosting is predicted to be highly effective. Front boosting, apart from practical advantages and a possible advantage as regards iatrogenic second cancers, also probably gives a slightly higher TCP than back boosting. If the total number of SLCC at the start of treatment can be measured even roughly, it will provide a highly sensitive way of discriminating between various models and parameter choices. Updated mathematical methods for calculating repopulation allow credible generalizations of earlier results.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2013

A NOVEL APPROACH TO CONSTRAIN THE ESCAPE FRACTION AND DUST CONTENT AT HIGH REDSHIFT USING THE COSMIC INFRARED BACKGROUND FRACTIONAL ANISOTROPY

The Cosmic Infrared Background (CIB) provides an opportunity to constrain many properties of the high-redshift (z > 6) stellar population as a whole. This background, specifically from 1 to 200 {mu}m, should contain information about the era of reionization and the stars that are responsible for these ionizing photons. In this paper, we look at the fractional anisotropy ({delta}I/I) of this high-redshift population, where {delta}I is the ratio of the magnitude of the fluctuations and I is the mean intensity. We show that this can be used to constrain the escape fraction of the population as a whole, because the magnitude of the fluctuations of the CIB depends on the escape fraction, while the mean intensity does not. This results in lower values of the escape fraction producing higher values of the fractional anisotropy. This difference is predicted to be larger at longer wavelength bands (above 10 {mu}m), albeit it is also much harder to observe in that range. We show that the fractional anisotropy can also be used to separate a dusty from a dust-free population. Finally, we discuss the constraints provided by current observations on the CIB fractional anisotropy.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

Fractionated Wide-Field Radiation Therapy Followed by Fractionated Local-Field Irradiation for Treating Widespread Painful Bone Metastasis

Purpose: Wide-field radiation therapy (WFRT) is an effective treatment for widespread bone metastasis. We evaluated local-field irradiation (LFI) after fractionated WFRT (f-WFRT) for treating the patients with multiple painful bone lesions. Methods and Materials: From 1998 to 2007, 32 patients with multiple bone metastases were treated with fractionated LFI (f-LFI) after f-WFRT. All patients initially received 15 Gy in 5 fractions to a wide field, followed by LFI (9-15 Gy in 3 Gy fractions). Response was assessed by evaluating the degree of pain relief using a visual analog scale before radiotherapy, after f-WFRT, and after f-LFI. Results: Fractionated LFI following f-WFRT yielded an overall relief rate of 93.8% and a complete relief rate of 43.8%. The rate of the appearance of new disease was 6.3% for the patients with complete relief, 20.5% for the patients with a partial relief, and 50% for the patients with no relief. Conclusion: Fractionated LFI after f-WFRT is a well-tolerated and effective treatment for multiple metastatic bone disease.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2012

Cu isotope fractionation during bornite dissolution: An in situ X-ray diffraction analysis

Low-temperature ore deposits exhibit a large variation in {delta}{sup 65}Cu ({approx}12{per_thousand}), and this range has been attributed, in part, to isotope fractionation during weathering reactions of primary minerals such as chalcocite and chalcopyrite. Here, we examine the fractionation of Cu isotopes during dissolution of another important Cu ore mineral, bornite, using a novel approach that combines time-resolved X-ray diffraction (XRD) and isotope analysis of reaction products. During the initial stages of bornite oxidative dissolution by ferric sulfate (< 5 mol% of total Cu leached), dissolved Cu was enriched in isotopically heavy Cu ({sup 65}Cu) relative to the solid, with an average apparent isotope fractionation ({Delta}{sub aq - min} = {delta}{sup 65}Cu{sub aq} - {delta}{sup 65}Cu{sub min}{sup 0}) of 2.20 {+-} 0.25{per_thousand}. When > 20 mol% Cu was leached from the solid, the difference between the Cu isotope composition of the aqueous and mineral phases approached zero, with {Delta}{sub aq - min}{sup 0} values ranging from - 0.21 {+-} 0.61{per_thousand} to 0.92 {+-} 0.25{per_thousand}. XRD analysis allowed us to correlate changes in the atomic structure of bornite with the apparent isotope fractionation as the dissolution reaction progressed. These data revealed that the greatest degree of apparent fractionation is accompanied by a steep contraction in the unit-cell volume, which we identified as a transition from stoichiometric to non-stoichiometric bornite. We propose that the initially high {Delta}{sub aq - min} values result from isotopically heavy Cu ({sup 65}Cu) concentrating within Cu{sup 2+} during dissolution. The decrease in the apparent isotope fractionation as the reaction progresses occurs from the distillation of isotopically heavy Cu ({sup 65}Cu) during dissolution or kinetic isotope effects associated with the depletion of Cu from the surfaces of bornite particles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Quality carbon fibers from fractionated lignin

The application of lignin carbon fibers was hindered by their low quality and mechanical performance. We addressed this challenge by developing a new approach to fractionate and modify lignin to produce quality carbon fibers using an enzyme-mediator system, which derives lignin fractions with different molecular weights, functional groups, and interunitary linkages. The fractionated lignin in general improves the miscibility and spinnability of lignin. In particular, the insoluble lignin fraction renders carbon fibers with a significantly improved turbostratic carbon structure as revealed by XRD and Raman spectroscopy. The improvement in the carbon structure leads to the significantly improved elastic modulus. The results suggest that higher molecular weights, less –OH groups, and more linear structures may contribute to the improved crystallization and mechanical performance of lignin carbon fibers. Finally, the technical breakthrough produces lignin-based carbon fibers with a similar elastic modulus to commercial carbon fibers for the first time, and paves the path for replacing PAN with lignin for producing quality carbon fibers.

Enzymatic fractionation↗
DOE OSTI2016

Measurements of the S-wave fraction in $B^0$ → $K^+π^-μ^+μ^-$ decays and the $B^0 → K^*(892)^0μ^+μ^-$ differential branching fraction

A measurement of the differential branching fraction of the decay $B^0 → K^*(892)^0$ $μ^+μ^-$ is presented together with a determination of the S-wave fraction of the $K^+π^-$ system in the decay $B^0 → K^+π^-μ^+μ^-$. The analysis is based on pp-collision data corresponding to an integrated luminosity of 3 fb -1 collected with the LHCb experiment. The measurements are made in bins of the invariant mass squared of the dimuon system, q 2 . Precise theoretical predictions for the differential branching fraction of $B^0 → K^*(892)^0 μ^+μ^-$ decays are available for the q 2 region 1.1 < q 2 < 6.0 GeV 2 / c 4 . In this q 2 region, for the $K^+π^-$ invariant mass range 796 < $m_{K_π}$ < 996 MeV/c 2 , the S-wave fraction of the $K^+π^-$ system in $B^0 → K^+π^-μ^+μ^-$ decays is found to be F S = 0.101 &#x00B1;<!-- ± --> 0.017 ( s t a t ) &#x00B1;<!-- ± --> 0.009 ( s y s t ) , and the differential branching fraction of $B^0 → K^*(892)^0 μ^+μ^-$ decays is determined to be d B / d q 2 = ( 0. 392 &#x2212;<!-- - --> 0.019 + 0.020 ( s t a t ) &#x00B1;<!-- ± --> 0.010 ( s y s t ) &#x00B1;<!-- ± --> 0.027 ( n o r m ) ) &#x00D7;<!-- × --> 1 0 &#x2212;<!-- - --> 7 c 4 / G e V 2 . The differential branching fraction measurements presented are the most precise to date and are found to be in agreement with Standard Model predictions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗