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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

How Bayesian methods can improve R -matrix analyses of data: The example of the d t reaction

The 3 H(d, n) 4 He reaction is of significant interest in nuclear astrophysics and nuclear applications. It is an important, early step in big-bang nucleosynthesis and a key process in nuclear fusion reactors. We use one- and two-level R-matrix approximations to analyze data on the cross section for this reaction at center-of-mass energies below 215 keV. We critically examine the data sets using a Bayesian statistical model that allows for both common-mode and additional point-to-point un- certainties. We use Markov Chain Monte Carlo sampling to evaluate this R-matrix-plus-statistical model and find two-level R-matrix results that are stable with respect to variations in the channel radii. The S factor at 40 keV evaluates to 25.36(19) MeV b (68% credibility interval). We discuss our Bayesian analysis in detail and provide guidance for future applications of Bayesian methods to R-matrix analyses. We also discuss possible paths to further reduction of the S-factor uncertainty.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Transfer learning for metamaterial design and simulation

Abstract We demonstrate transfer learning as a tool to improve the efficacy of training deep learning models based on residual neural networks (ResNets). Specifically, we examine its use for study of multi-scale electrically large metasurface arrays under open boundary conditions in electromagnetic metamaterials. Our aim is to assess the efficiency of transfer learning across a range of problem domains that vary in their resemblance to the original base problem for which the ResNet model was initially trained. We use a quasi-analytical discrete dipole approximation (DDA) method to simulate electrically large metasurface arrays to obtain ground truth data for training and testing of our deep neural network. Our approach can save significant time for examining novel metasurface designs by harnessing the power of transfer learning, as it effectively mitigates the pervasive data bottleneck issue commonly encountered in deep learning. We demonstrate that for the best case when the transfer task is sufficiently similar to the target task, a new task can be effectively trained using only a few data points yet still achieve a test mean absolute relative error of 3 % with a pre-trained neural network, realizing data reduction by a factor of 1000.

Peng, Rixi↗
NASA NTRS1989

Trends in ozone profile measurements

From an examination of the agreements and differences between different satellite instruments, it is difficult to believe that existing satellite instruments determine upper stratospheric ozone much better than 4 pct.; by extension, it probably would require at least a 4 pct. change to be reliably detected as a change. The best estimates of the vertical profiles of ozone change in the upper stratosphere between 1979 and 1986 are judged to be those given by the two SAGE satellite instruments. SAGE-2 minus SAGE-1 gives a much lower ozone reduction than that given by the archived Solar Backscatter UV data. The average SAGE profiles of ozone changes between 20 and 50 degs north and between 20 and 50 degs south are given. The SAGE-1 and SAGE-2 comparison gives an ozone reduction of about 4 pct. at 25 km over temperate latitudes. Five ground based Umkehr stations between 36 and 52 degs north, corrected for the effects of volcanic aerosols, report an ozone reduction between 1979 and 1987 at Umkehr layer 8 of 9 + or - 5 pct. The central estimate of upper stratospheric ozone reduction given by SAGE at 40 km is less than the central value estimated by the Umkehr method at layer 8.

Johnston, H.↗
NASA NTRS1995

The sensitivity of various mode sets for probing differential rotation shear zones

The potential of future data sets from global oscillations network group (GONG) and solar oscillations investigation (SOI) for resolving long-lived azimuthal jets and shearing flows, is investigated. Various artificial data sets are constructed, containing noise resembling that of a one-year observation run. These are inverted using a two dimensional regularized least squares inversion. The ability of this method to form well localized averages of the rotation rate, as measured by the averaging kernels, is investigated using an extensive mode set and subsets. It is shown that it is possible to keep the noise in the solution down to a few nHz in much of the solar interior, while obtaining a reasonable resolution for a GONG-like data set. At low latitudes in the middle of the convection zone, an angular resolution of less than 10 deg and a radial resolution of about 0.04 solar radii, are obtained. The averaging kernels depend on the mode set, and a reduction in the number of modes tends to introduce small-scale near surface structures into the averaging kernels which would adversely affect the inferred rotation rate.

Christensen-Dalsgaard, Joergen↗
NASA NTRS1994

Acquisition and processing of data for isotope-ratio-monitoring mass spectrometry

Methods are described for continuous monitoring of signals required for precise analyses of 13C, 18O, and 15N in gas streams containing varying quantities of CO2 and N2. The quantitative resolution (i.e. maximum performance in the absence of random errors) of these methods is adequate for determination of isotope ratios with an uncertainty of one part in 10(5); the precision actually obtained is often better than one part in 10(4). This report describes data-processing operations including definition of beginning and ending points of chromatographic peaks and quantitation of background levels, allowance for effects of chromatographic separation of isotopically substituted species, integration of signals related to specific masses, correction for effects of mass discrimination, recognition of drifts in mass spectrometer performance, and calculation of isotopic delta values. Characteristics of a system allowing off-line revision of parameters used in data reduction are described and an algorithm for identification of background levels in complex chromatograms is outlined. Effects of imperfect chromatographic resolution are demonstrated and discussed and an approach to deconvolution of signals from coeluting substances described.

NASA Discipline Exobiology↗
NASA NTRSDate not supplied

Jig Twist Optimization of Mach 0.8 Transonic Truss-Braced Wing Aircraft

This paper presents a jig twist optimization study of Mach 0.8 Transonic Truss-Braced Wing (TTBW) aircraft using FUN3D. The solver has been validated against wind tunnel test data. An aeroelastic model deformation correction method is developed for the wind tunnel model to improve the validation. The flight condition corresponding to Mach 0.8 and design lift coefficient 0.695 is selected for the TTBW aircraft jig twist optimization to reduce the drag coefficient. The static aeroelastic simulation module in FUN3D is used for the aeroelastic simulation. Three different orders of the Chebyshev polynomials are used as shape function to represent the variations of the jig twist distribution along the wing span. The preliminary optimization results show that the Mach 0.8 TTBW aircraft with the optimized jig twist achieves a drag reduction of about 5.7 counts at the design condition when 5 𝑡ℎ order Chebyshev polynomials are used as shape function.

TTBW↗
NASA NTRS2022

Evaluating Mineral Lattices as Evolutionary Proxies for Metalloprotein Evolution

Protein coordinated iron-sulfur clusters drive electron flow within metabolic pathways for organisms throughout the tree of life. It is not known how iron-sulfur clusters were first incorporated into proteins. Structural analogies to iron-sulfde minerals present on early Earth, suggest a connection in the evolution of both proteins and minerals. The availability of large protein and mineral crystallographic structure data sets, provides an opportunity to explore co-evolution of proteins and minerals on a large-scale using informatics approaches. However, quantitative comparisons are confounded by the infnite, repeating nature of the mineral lattice, in contrast to metal clusters in proteins, which are fnite in size. We address this problem using the Niggli reduction to transform a mineral lattice to a fnite, unique structure that when translated reproduces the crystal lattice. Protein and reduced mineral structures were represented as quotient graphs with the edges and nodes corresponding to bonds and atoms, respectively. We developed a graph theory-based method to calculate the maximum common connected edge subgraph (MCCES) between mineral and protein quotient graphs. MCCES can accommodate differences in structural volumes and easily allows additional chemical criteria to be considered when calculating similarity. To account for graph size differences, we use the Tversky similarity index. Using consistent criteria, we found little similarity between putative ancient iron-sulfur protein clusters and iron-sulfur mineral lattices, suggesting these metal sites are not as evolutionarily connected as once thought. We discuss possible evolutionary implications of these findings in addition to suggesting an alternative proxy, mineral surfaces, for better understanding the coevolution of the geosphere and biosphere

Kenneth N. McGuinness↗
NASA NTRS2006

Small Hot Jet Acoustic Rig Validation

The Small Hot Jet Acoustic Rig (SHJAR), located in the Aeroacoustic Propulsion Laboratory (AAPL) at the NASA Glenn Research Center in Cleveland, Ohio, was commissioned in 2001 to test jet noise reduction concepts at low technology readiness levels (TRL 1-3) and develop advanced measurement techniques. The first series of tests on the SHJAR were designed to prove its capabilities and establish the quality of the jet noise data produced. Towards this goal, a methodology was employed dividing all noise sources into three categories: background noise, jet noise, and rig noise. Background noise was directly measured. Jet noise and rig noise were separated by using the distance and velocity scaling properties of jet noise. Effectively, any noise source that did not follow these rules of jet noise was labeled as rig noise. This method led to the identification of a high frequency noise source related to the Reynolds number. Experiments using boundary layer treatment and hot wire probes documented this noise source and its removal, allowing clean testing of low Reynolds number jets. Other tests performed characterized the amplitude and frequency of the valve noise, confirmed the location of the acoustic far field, and documented the background noise levels under several conditions. Finally, a full set of baseline data was acquired. This paper contains the methodology and test results used to verify the quality of the SHJAR rig.

Brown, Cliff↗
NASA NTRSDate not supplied

Applicability of Loads Estimation Techniques Using Sparse Acceleration Sensor Data to Spacecraft Structural Health Monitoring

The use of structural health monitoring systems on spacecraft structures can play a crucial role in ensuring the safety, reliability, and longevity of the structure by gathering and analyzing onboard sensor data. Of specific importance is monitoring for excessive loading at critical interfaces as any off-nominal structural excitations experienced by spacecraft structures can cause early unpredicted high structural life consumption or damage. The availability and cost of flight-certified sensors along with the size of spacecraft structures and allowable payload mass drives the need for a method to estimate loads using sparsely-located sensors. Numerous approaches such as physics-based, statistical learning, and physics-enhanced statistical learning algorithms have gained popularity among structural prognostics applications. However, developing noise-robust prediction models to assess loads and structural life predictions from a sparse multi-sensor data acquisition system can be a challenging task. This paper discusses the evaluation of physics-based versus machine-learning algorithms for predicting loads and structural life at mission critical locations on the spacecraft structure using a finite element loads analysis with the application of simulated noise and noise reduction techniques. To estimate the loads from accelerations, the physics-based algorithm leverages a loads transformation matrix from a Craig-Bampton reduced finite element model. A System Equivalent Reduction Expansion Process (SEREP) and a pseudo-inverse approach are considered to expand from the onboard sensor degrees of freedom to the Craig-Bampton model degrees of freedom. The machine learning algorithm provides a data driven solution/mapping of the sensor accelerations to the loads at the mission critical locations using a high dimensionality analysis. Although these strategies produce comparable loads prediction without noise, the limitations of these strategies with incorporating simulated noise and noise reduction techniques with low signal to noise ratio signals are evaluated. The study demonstrates the immense potential of statistical learning algorithms for sparse structural prognostic models and enhancing signal denoising techniques. These findings also highlight the need for noise-resilient prognostic models and low-noise data acquisition systems onboard spacecraft structures.

Spacecraft Structural Health Monitoring↗
DOE OSTI2022

A 1D–0D–3D coupled model for simulating blood flow and transport processes in breast tissue

In this work, we present mixed dimensional models for simulating blood flow and transport processes in breast tissue and the vascular tree supplying it. These processes are considered, to start from the aortic inlet to the capillaries and tissue of the breast. Large variations in biophysical properties and flow conditions exist in this system necessitating the use of different flow models for different geometries and flow regimes. In total, we consider four different model types. First, a system of 1D nonlinear hyperbolic partial differential equations (PDEs) is considered to simulate blood flow in larger arteries with highly elastic vessel walls. Second, we assign 1D linearized hyperbolic PDEs to model the smaller arteries with stiffer vessel walls. The third model type consists of ODE systems (0D models). It is used to model the arterioles and peripheral circulation. Finally, homogenized 3D porous media models are considered to simulate flow and transport in capillaries and tissue within the breast volume. Sink terms are used to account for the influence of the venous and lymphatic systems. Combining the four model types, we obtain two different 1D–0D–3D coupled models for simulating blood flow and transport processes: The first model results in a fully coupled 1D–0D–3D model covering the complete path from the aorta to the breast combining a generic arterial network with a patient specific breast network and geometry. The second model is a reduced one based on the separation of the generic and patient specific parts. The information from a calibrated fully coupled model is used as inflow condition for the patient specific sub-model allowing a significant computational cost reduction. Several numerical experiments are conducted to calibrate the generic model parameters and to demonstrate realistic flow simulations compared to existing data on blood flow in the human breast and vascular system. Moreover, we use two different breast vasculature and tissue data sets to illustrate the robustness of our reduced sub-model approach.

multiscale blood flow models↗
DOE OSTI2022

Data for Solvent-Free Enzymatic Esterification of Free Fatty Acids with Glycerol for Biodiesel Application: Optimized Using the Taguchi Experimental Method

Presence of free fatty acids along with glycerides poses a technical difficulty for biodiesel production. This work used a Taguchi L9 design to optimize the solvent-free enzymatic process to result in the esterification of oleic acid with glycerol. Under optimal conditions the esterification reaction temperature of 60°C, enzyme dose of 5 wt%, glycerol: oleic acid molar ratio of 5:1, and reaction time of 3 h, a 75.235 ± 2.19% conversion of oleic acid to esters was achieved. With the addition of molecular sieves, the conversion increased to 86.73% ± 1.09%. However, using the parameters predicted by Taguchi design (60°C, 5 wt%, 5:1, and 4.5 h), 88.5% ± 1.11% of oleic acid could be converted to esters derivative. Diglycerides were the major product, and the reaction equilibrium was attained after 4 h. The immobilized enzyme could be used up to seven times with only a 10% reduction in the conversion. Thus, the process can efficiently reduce the free fatty acid content of oil to make it suitable for biodiesel production.

Conversion↗
DOE OSTI2020

Explainable and trustworthy artificial intelligence for correctable modeling in chemical sciences

Data science has primarily focused on big data, but for many physics, chemistry, and engineering applications, data are often small, correlated and, thus, low dimensional, and sourced from both computations and experiments with various levels of noise. Typical statistics and machine learning methods do not work for these cases. Expert knowledge is essential, but a systematic framework for incorporating it into physics-based models under uncertainty is lacking. Here, we develop a mathematical and computational framework for probabilistic artificial intelligence (AI)–based predictive modeling combining data, expert knowledge, multiscale models, and information theory through uncertainty quantification and probabilistic graphical models (PGMs). We apply PGMs to chemistry specifically and develop predictive guarantees for PGMs generally. Our proposed framework, combining AI and uncertainty quantification, provides explainable results leading to correctable and, eventually, trustworthy models. The proposed framework is demonstrated on a microkinetic model of the oxygen reduction reaction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2009

Smart and Intelligent Sensors

John C. Stennis Space Center (SSC) provides rocket engine propulsion testing for NASA's space programs. Since the development of the Space Shuttle, every Space Shuttle Main Engine (SSME) has undergone acceptance testing at SSC before going to Kennedy Space Center (KSC) for integration into the Space Shuttle. The SSME is a large cryogenic rocket engine that uses Liquid Hydrogen (LH2) as the fuel. As NASA moves to the new ARES V launch system, the main engines on the new vehicle, as well as the upper stage engine, are currently base lined to be cryogenic rocket engines that will also use LH2. The main rocket engines for the ARES V will be larger than the SSME, while the upper stage engine will be approximately half that size. As a result, significant quantities of hydrogen will be required during the development, testing, and operation of these rocket engines.Better approaches are needed to simplify sensor integration and help reduce life-cycle costs. 1.Smarter sensors. Sensor integration should be a matter of "plug-and-play" making sensors easier to add to a system. Sensors that implement new standards can help address this problem; for example, IEEE STD 1451.4 defines transducer electronic data sheet (TEDS) templates for commonly used sensors such as bridge elements and thermocouples. When a 1451.4 compliant smart sensor is connected to a system that can read the TEDS memory, all information needed to configure the data acquisition system can be uploaded. This reduces the amount of labor required and helps minimize configuration errors. 2.Intelligent sensors. Data received from a sensor be scaled, linearized; and converted to engineering units. Methods to reduce sensor processing overhead at the application node are needed. Smart sensors using low-cost microprocessors with integral data acquisition and communication support offer the means to add these capabilities. Once a processor is embedded, other features can be added; for example, intelligent sensors can make a health assessment to inform the data acquisition client when sensor performance is suspect. 3.Distributed sample synchronization. Networks of sensors require new ways for synchronizing samples. Standards that address the distributed timing problem (for example, IEEE STD 1588) provide the means to aggregate samples from many distributed smart sensors with sub-microsecond accuracy. 4. Reduction in interconnect. Alternative means are needed to reduce the frequent problems associated with cabling and connectors. Wireless technologies offer the promise of reducing interconnects and simultaneously making it easy to quickly add a sensor to a system.

Lansaw, John↗
NASA NTRS2011

Validation of On-Orbit Methodology for the Assessment of Cardiac Function and Changes in the Circulating Volume Using "Braslet-M" Occlusion Cuffs

BACKGROUND: The transition to microgravity eliminates the hydrostatic gradients in the vascular system. The resulting fluid redistribution commonly manifests as facial edema, engorgement of the external neck veins, nasal congestion, and headache. This experiment examined the responses to modified Valsalva and Mueller maneuvers as measured by cardiac and vascular ultrasound in a baseline microgravity steady state, and under the influence of thigh occlusion cuffs (Braslet cuffs). METHODS: Nine International Space Station crewmember subjects (Expeditions 16 - 20) were examined in 15 experiment sessions 101 46 days after launch (mean SD; 33 - 185). 27 cardiac and vascular parameters were obtained under three respiratory conditions (baseline, Valsalva, and Mueller) before and after tightening of the Braslet cuffs for a total of 162 data points per session. The quality of cardiac and vascular ultrasound examinations was assured through remote monitoring and guidance by Investigators from the NASA Telescience Center in Houston, TX, USA. RESULTS: Fourteen of the 81 measured conditions were significantly different with Braslet application and were apparently related to cardiac preload reduction or increase in the venous volume sequestered in the lower extremity. These changes represented 10 of the 27 parameters measured. In secondary analysis, 7 of the 27 parameters were found to respond differently to respiratory maneuvers depending on the presence or absence of thigh compression, with a total of 11 differences. CONCLUSIONS: Acute application of Braslet occlusion cuffs causes lower extremity fluid sequestration and exerts proportionate measurable effects on cardiac performance in microgravity. Ultrasound techniques measuring the hemodynamic effects of thigh cuffs in combination with respiratory maneuvers may serve as an effective tool in determining the volume status of a cardiac or hemodynamically compromised patient in microgravity.

Hamilton, D. R.↗
DOE OSTI2021

Learning an Algebriac Multrigrid Interpolation Operator Using a Modified GraphNet Architecture

This work, building on previous efforts, develops a suite of new graph neural network machine learning architectures that generate data-driven prolongators for use in Algebraic Multigrid (AMG). Algebraic Multigrid is a powerful and common technique for solving large, sparse linear systems. Its effectiveness is problem dependent and heavily depends on the choice of the prolongation operator, which interpolates the coarse mesh results onto a finer mesh. Previous work has used recent developments in graph neural networks to learn a prolongation operator from a given coefficient matrix. In this paper, we expand on previous work by exploring architectural enhancements of graph neural networks. A new method for generating a training set is developed which more closely aligns to the test set. Asymptotic error reduction factors are compared on a test suite of 3-dimensional Poisson problems with varying degrees of element stretching. Results show modest improvements in asymptotic error factor over both commonly chosen baselines and learning methods from previous work.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1983

Analysis of Nonplanar Wing-tip-mounted Lifting Surfaces on Low-speed Airplanes

Nonplanar wing tip mounted lifting surfaces reduce lift induced drag substantially. Winglets, which are small, nearly vertical, winglike surfaces, are an example of these devices. To achieve reduction in lift induced drag, winglets produce significant side forces. Consequently, these surfaces can seriously affect airplane lateral directional aerodynamic characteristics. Therefore, the effects of nonplanar wing tip mounted surfaces on the lateral directional stability and control of low speed general aviation airplanes were studied. The study consists of a theoretical and an experimental, in flight investigation. The experimental investigation involves flight tests of winglets on an agricultural airplane. Results of these tests demonstrate the significant influence of winglets on airplane lateral directional aerodynamic characteristics. It is shown that good correlations exist between experimental data and theoretically predicted results. In addition, a lifting surface method was used to perform a parametric study of the effects of various winglet parameters on lateral directional stability derivatives of general aviation type wings.

Vandam, C. P.↗
NASA NTRS1987

Geometric description and grid generation for space vehicles

The understanding and analysis of three dimensional fluid behavior around reentry vehicles, like the Space Shuttle Orbiter, is of considerable importance for flight applications. Vehicle designers need pressure, heat transfer, and shear distributions to support design activities. Traditionally these have been obtained by experimental data. Significant reduction in design costs can be obtained if the calculated results based on finite difference procedures are used to verify and supplement experimental results. Computing the flow field over Space Shuttle Orbiter, which has complex cross sectional geometries is a major problem. A first step in this direction is development of body definition and grid generation procedure. In this project a digitized body definition and grid generation procedure, developed earlier at JSC, is modified and applied to the Shuttle Orbiter X24C-10D. Two dimensional grid and body definition for various sections of the space vehicle is obtained using the differential equation method. This study demonstrates that this geometry and grid generation procedure can be applied to other aerospace vehicles such as aerospaceplanes.

Krishna, Madakasira G.↗
DOE OSTI2020

Hadronic contributions to (g - 2) µ

The Muon g-2 Experiment at Fermilab, which recently started running, plans to reduce the uncertain- ties on the already very precisely measured anomalous magnetic moment of the muon by a factor of four. The goal of this effort is to probe the observed difference of more than three standard deviations between Standard-Model theory and experiment, one of the few persistent hints for physics beyond the Standard Model. The Fermilab experiment collected data from their first run last year with statistics comparable to BNL E821. They expect to release the measurement result in 2019. On the theoretical side, because the muon g - 2 arises from quantum- mechanical loop contributions in the Standard Model, it is sensitive to virtual effects of new particles, and places important constraints on Standard-Model extensions. To leverage the anticipated reduction in experimental errors, and determine unambiguously whether or not new-physics effects contribute to this quantity, the theoretical errors must be made more reliable and reduced to a commensurate precision. The Muon g-2 Theory Initiative was created to facilitate this development. The dominant sources of uncertainty in the Standard-Model prediction of the muon g -2 are from the hadronic contributions. The hadronic vacuum polarization (HVP) provides the leading correction followed by hadronic light-by-light (HLbL) scattering. There are a number of complementary theoretical efforts underway to better understand and quantify these contributions, including dispersive and data driven methods, lattice QCD, and effective field theories. Given the precision goals and the phenomenological importance, it is important to have more than one independent method for each of the two hadronic corrections, each with fully quantified uncertainties. Fostering the development of such methods is a prime goal of the initiative, as this will enable critical cross checks, and, upon combination, may yield gains in precision, to maximize the impact of E989. An important aspect of the Muon g-2 Theory Initiative’s activities are providing platforms that facilitate interactions between the different groups, as well as between the theoretical and experimental g - 2 communities. To this end, several workshops were organized in 2017 and 2018. The first meeting, held at Fermilab (June 3–6, 2017, St. Charles, IL, USA), served to kick-off the Initiative’s activities. Two meetings in early 2018 were focused respectively on the HVP and HLbL corrections. The HVP meeting was held at KEK (February 12–14, 2018, Tsukuba, Japan) and the HLbL meeting at the University of Connecticut (March 12–14, 2018, Storrs, CT, USA). The most recent workshop, which served as the second plenary meeting of the Initiative, was held at the University of Mainz (June 18–22, 2018, Mainz, Germany). An important outcome of these meetings are concrete plans for a first white paper, which is currently being written. We aim to post the white paper just prior to the release of the first E989 measurement, to present a clean theoretical prediction. The first white paper is focused on assessing and improving the reliability of the SM prediction. The purpose of the INT workshop in September 2019 is to start the next stage of the Initiative, focusing on the development of strategies to improve the theory uncertainties beyond the current level towards the E989 precision goal. We aim to accelerate theoretical developments on the hadronic contributions to the muon g - 2 so that the Standard-Model theory error can be brought to the needed precision, again in advance of the next release from E989. Hence the workshop will provide crucial theory support for a US experiment with broad impact. The Muon g-2 Theory Initiative relies on input from representatives of all the different communities that are engaged in this effort. It is therefore important that all these areas are properly represented. The funds from this grant will be used to enable more people, especially early-career scientists, to participate and make essential contributions to the workshop discussions. Since the workshop’s main goal is to kick-off the next stage of the theory initiative’s activities, support for this workshop from the DOE will help the theory community provide crucial theoretical support to the Fermilab Muon g-2 Experiment.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗