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DOE OSTI2025

Bayesian Inference for the Seismic Moment Tensor Using Regional Waveforms and Teleseismic- P Polarities with a Data-Derived Distribution of Velocity Models and Source Locations

The largest source of uncertainty in any source inversion is the velocity model used in the transfer function that relates observed ground motion to the seismic moment tensor. However, standard inverse procedure often does not quantify uncertainty in the seismic moment tensor due to error in the Green’s functions from uncertain event location and Earth structure. Here, we incorporate this uncertainty into an estimation of the seismic moment tensor using a data-derived distribution of velocity models based on complementary geophysical data sets, including thickness constraints, velocity profiles, gravity data, surface-wave group velocities, and regional body-wave travel times. The data-derived distribution of velocity models is then used as a prior distribution of Green’s functions for use in Bayesian inference of an unknown seismic moment tensor using regional and teleseismic-P waveforms. The use of multiple data sets is important for gaining resolution to different components of the moment tensor. The combined likelihood is estimated using data-specific error models and the posterior of the seismic moment tensor is estimated and interpreted in terms of the most probable source type.

58 GEOSCIENCES↗

DOE OSTI2020

Calculation of the First Moment of Energy Using D-T Reactivity Formalisms Under the Maxwell-Boltzmann Distribution (Pt. 1)

Nuclear fusion science is an example of a scientific field with a rich history of expert involvement and scientific publications, which together, form an expert-knowledge base. One example of this history is the utilization of published reaction rates from a variety of authors. Investigators for Deuterium-Tritium (D-T) ion fusion can choose from using frequently cited methods: the Bosch and Hale reactivity, thermonuclear reaction rates from Caughlan and Fowler, and the reactivity evaluation from Miley, Towner & Ivich which forms the basis of the Naval Research Lab (NRL) formulary. There are other choices available. Each of the reactivity formulations considered here, are based upon the Maxwell- Boltzmann velocity distribution for D-T fusion ion reactants. Numerical methods for computer codes simulating hot, energetic plasmas, include tabulations of the reactivity, and the first moment of energy. The purpose of this study is to answer the question: what is the first moment of energy, and how has it been formulated? This report is part of a series of reports by the authors on D-T fusion-reaction formalism. The present focus is on defining the mathematical relationship of the first moment of D-T fusion ion kinetic energy, $\langle$E$\rangle$, with the fusion crosssection, fusion reactivity and its derivative with respect to ion-temperature. Three variants of the first moment $\langle$E$\rangle$ are analytically developed and explored: 1) constant cross-section, 2) a normalized first moment, and 3) a particular function of the first moment. Much of the mathematical development is relegated to the Appendices, for a concise presentation of topics and results. A research component of this discussion is our comparison of some of the reactivity and its derivative results between evaluations (1) versus (2) and (3), which the authors have not found in any other publication to date. This investigation is useful for validation, verification (V&V) and uncertainty quantification (UQ) as it compares the work of several authors.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1976

Magnetic moments of charmed baryons. I, II

The magnetic moments of all charmed baryons belonging to the totally symmetric 20 (underlined) representation, the mixed symmetry 20 prime (underlined) and the totally antisymmetric 4 (underlined) representation have been compared under U(4) symmetry, assuming that the magnetic-moment operator is proportional to the charge operator. The magnetic moments of all charmed particles have been expressed in terms of the moments of proton, neutron and delta particles in the case of U(4) symmetry. Then assuming that the magnetic moment operator is a tensor transforming as the (15,3) members of a 63 (underlined) representation of U(8) or SU(8), the magnetic moments of all the baryons belonging to the 120 (underlined) representation are compared.

Choudhury, A. L.↗

NASA NTRS1986

Third-moment closure of turbulence for predictions of separating and reattaching shear flows: A study of Reynolds-stress closure model

A numerical study of computations in backward-facing steps with flow separation and reattachment, using the Reynolds stress closure is presented. The highlight of this study is the improvement of the Reynold-stress model (RSM) by modifying the diffusive transport of the Reynolds stresses through the formulation, solution and subsequent incorporation of the transport equations of the third moments, bar-u(i)u(j)u(k), into the turbulence model. The diffusive transport of the Reynolds stresses, represented by the gradients of the third moments, attains greater significance in recirculating flows. The third moments evaluated by the development and solution of the complete transport equations are superior to those obtained by existing algebraic correlations. A low-Reynolds number model for the transport equations of the third moments is developed and considerable improvement in the near-wall profiles of the third moments is observed. The values of the empirical constants utilized in the development of the model are recommended. The Reynolds-stress closure is consolidated by incorporating the equations of k and e, containing the modified diffusion coefficients, and the transport equations of the third moments into the Reynolds stress equations. Computational results obtained by the original k-e model, the original RSM and the consolidated and modified RSM are compared with experimental data. Overall improvement in the predictions is seen by consolidation of the RMS and a marked improvement in the profiles of bar-u(i)u(j)u(k) is obtained around the reattachment region.

Amano, R. S.↗

NASA NTRS1959

A Dynamic Model Investigation of the Effect of a Sharp-Edge Vertical Gust on Blade Periodic Flapping Angles and Bending Moments of a Two-Blade Rotor

A two-blade rotor having a diameter of 4 feet and a solidity of 0.037 was subjected to sharp-edge vertical gusts while being operated at various forward speeds to study the effect of the gusts on the blade periodic bending moments and flapping angles. Variables studied included gust velocity, collective pitch angle, flapping hinge offset, and tip-speed ratio. Dimensionless coefficients are derived for the periodic components of the incremental changes in blade flapping angles and bending moments which arise when a rotor blade penetrates a sharp-edge gust. Mental changes in both the flapping angles and bending moments are essentially proportional to gust velocity, and the coefficients express the ratio of these increments to gust velccity. The results show that the flapping coefficient usually increases with an increase in collective pitch angle, is generally dependent on tip-speed ratio, and is essentially independent of the amount of flapping hinge offset. The bending-moment coefficient is also dependent on collective pitch angle and tip-speed ratio. Expected reductions in bending moments are realized by the use of flapping hinges, and further reductions in bending moments are achieved as the amount of flapping hinge offset is increased. Comparison of the experimental results of this investigation with limited available theoretical results shows substantial agreement but indicates that the assumption that the response of the rotor to a sharp-edge gust is independent of the collective pitch angle prior to gust entry is probably inadequate.

McCarty, John Locke↗

NASA NTRS1937

Theoretical span loading and moments of tapered wings produced by aileron deflection

The effect of tapered ailerons on linearly tapered wings is theoretically determined. Four different aileron spans are considered for each of three wing aspect ratios and each of four wing taper ratios. The change in lift on one half of the wing, the rolling moment, the additional induced drag, and the yawing moment, due to aileron deflection, are represented by non dimensional coefficients. Similar coefficients are given for the damping and yawing moments, the additional drag, and the change in lift, due to rolling. It was found possible to effect a fairly close agreement between the theoretical and experimental rolling moments by introducing into the theoretical expression for the rolling moment an effective change in angle of attack obtained from an analysis of flap data. The theoretical curves show that the highly tapered wing with long ailerons has a lower ratio of yawing to rolling moment and a lower additional induced drag than wings with less taper.

Pearson, H A↗

NASA NTRS1954

Experimental investigation of the forces and moments due to sideslip of a series of triangular vertical and horizontal tail combinations at Mach numbers

An experimental investigation was made at Mach numbers of 1.62, 1.93, and 2.41 of a series of tail combinations consisting of triangular vertical tail attached symmetrically to a triangular horizontal tail to determine the lateral force, yawing moment, and rolling moment due to sideslip. The apex angles of both the vertical- and horizontal-tail surfaces were varied systematically in order to obtain results for an appreciable range of operating conditions. The results of the investigation indicated that, for tails having subsonic leading edges and supersonic trailing edges, the lateral-force derivative and the yawing-moment derivative were predicted satisfactorily by the method presented in NACA TN 3071 except when the leading edges approach a sonic condition. The theoretical rolling-moment derivative was in fair agreement with the experimental derivative. For the limited tests in which both the leading and trailing edges were supersonic, the prediction of the lateral-force derivative and the yawing-moment derivative obtained from NACA TN 2412 was in good agreement with the experimental derivatives, whereas the prediction of the rolling-moment derivative was fair.

Coletti, Donald E↗

NASA NTRS2010

Low-Friction, Low-Profile, High-Moment Two-Axis Joint

The two-axis joint is a mechanical device that provides two-degrees-of-freedom motion between connected components. A compact, moment-resistant, two-axis joint is used to connect an electromechanical actuator to its driven structural members. Due to the requirements of the overall mechanism, the joint has a low profile to fit within the allowable space, low friction, and high moment-reacting capability. The mechanical arrangement of this joint can withstand high moments when loads are applied. These features allow the joint to be used in tight spaces where a high load capability is required, as well as in applications where penetrating the mounting surface is not an option or where surface mounting is required. The joint consists of one base, one clevis, one cap, two needle bearings, and a circular shim. The base of the joint is the housing (the base and the cap together), and is connected to the grounding structure via fasteners and a bolt pattern. Captive within the housing, between the base and the cap, are the rotating clevis and the needle bearings. The clevis is attached to the mechanical system (linear actuator) via a pin. This pin, and the rotational movement of the clevis with respect to the housing, provides two rotational degrees of freedom. The larger diameter flange of the clevis is sandwiched between a pair of needle bearings, one on each side of the flange. During the assembly of the two-axis joint, the circular shims are used to adjust the amount of preload that is applied to the needle bearings. The above arrangement enables the joint to handle high moments with minimal friction. To achieve the high-moment capability within a low-profile joint, the use of depth of engagement (like that of a conventional rotating shaft) to react moment is replaced with planar engagement parallel to the mounting surface. The needle bearings with the clevis flange provide the surface area to react the clevis loads/moments into the joint housing while providing minimal friction during rotation. The diameter of the flange and the bearings can be increased to react higher loads and still maintain a compact surface mounting capability. This type of joint can be used in a wide variety of mechanisms and mechanical systems. It is especially effective where precise, smooth, continuous motion is required. For example, the joint can be used at the end of a linear actuator that is required to extend and rotate simultaneously. The current design application is for use in a spacecraft docking-system capture mechanism. Other applications might include industrial robotic or assembly line apparatuses, positioning systems, or in the motion-based simulator industry that employs complex, multi-axis manipulators for various types of motions.

Lewis, James L.↗

NASA NTRS2011

A Procedure for Accurately Measuring the Shaker Overturning Moment During Random Vibration Tests

Motivation: For large system level random vibration tests, there may be some concerns about the shaker's capability for the overturning moment. It is the test conductor's responsibility to predict and monitor the overturning moment during random vibration tests. If the predicted moment is close to the shaker's capability, test conductor must measure the instantaneous moment at low levels and extrapolate to higher levels. That data will be used to decide whether it is safe to proceed to the next test level. Challenge: Kistler analog formulation for computing the real-time moment is only applicable to very limited cases in which we have 3 or 4 load cells installed at shaker interface with hardware. Approach: To overcome that limitation, a simple procedure was developed for computing the overturning moment time histories using the measured time histories of the individual load cells.

predict overturning↗

NASA NTRS2013

Measurements of DSD Second Moment Based on Laser Extinction

Using a technique recently developed for estimating the density of surface dust dispersed during a rocket landing, measuring the extinction of a laser passing through rain (or dust in the rocket case) yields an estimate of the 2nd moment of the particle cloud, and rainfall drop size distribution (DSD) in the terrestrial meteorological case. With the exception of disdrometers, instruments that measure rainfall make in direct measurements of the DSD. Most common of these instruments are the rainfall rate gauge measuring the 1 1/3 th moment, (when using a D(exp 2/3) dependency on terminal velocity). Instruments that scatter microwaves off of hydrometeors, such as the WSR-880, vertical wind profilers, and microwave disdrometers, measure the 6th moment of the DSD. By projecting a laser onto a target, changes in brightness of the laser spot against the target background during rain, yield a measurement of the DSD 2nd moment, using the Beer-Lambert law. In order to detect the laser attenuation within the 8-bit resolution of most camera image arrays, a minimum path length is required, depending on the intensity of the rainfall rate. For moderate to heavy rainfall, a laser path length of 100 m is sufficient to measure variations in optical extinction using a digital camera. A photo-detector could replace the camera, for automated installations. In order to spatially correlate the 2nd moment measurements to a collocated disdrometer or tipping bucket, the laser's beam path can be reflected multiple times using mirrors to restrict the spatial extent of the measurement. In cases where a disdrometer is not available, complete DSD estimates can be produced by parametric fitting of DSD model to the 2nd moment data in conjunction with tipping bucket data. In cases where a disdrometer is collocated, the laser extinction technique may yield a significant improvement to insitu disdrometer validation and calibration strategies

Lane, John E.↗

DOE OSTI2022

Majorana versus Dirac Constraints on the Neutrino Dipole Moments

Massive neutrinos are guaranteed to have nonzero electromagnetic moments and, since there are at least three neutrino species, these dipole moments define a matrix. Here, we estimate the current upper bounds on all independent neutrino electromagnetic moments, concentrating on Earth-bound experiments and measurements with solar neutrinos, including the very recent results reported by XENONnT. We make no simplifying assumptions and compare the hypotheses that neutrinos are Majorana fermions or Dirac fermions. In particular, we fully explore constraints in the Dirac-neutrino parameter space. Majorana and Dirac neutrinos are different; for example, the upper bounds on the magnitudes of the elements of the dipole moment matrix are weaker for Dirac neutrinos, relative to Majorana neutrinos. The potential physics reach of next-generation experiments also depends on the nature of the neutrino. We find that a next-generation experiment two orders of magnitude more sensitive to the neutrino electromagnetic moments via $\nu_{\mu}$ elastic scattering may discover that the neutrino electromagnetic moments are nonzero if the neutrinos are Dirac fermions. Instead, if the neutrinos are Majorana fermions, such a discovery is ruled out by existing solar neutrino data, unless there are more than three light neutrinos.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

Moment-Fourier approach to ion parallel fluid closures and transport for a toroidally confined plasma

A general method of solving the drift kinetic equation is developed for an axisymmetric magnetic field. Expanding a distribution function in general moments, a set of ordinary differential equations is obtained. Successively expanding the moments and magnetic-field involved quantities in Fourier series, a set of linear algebraic equations is obtained. The set of full (Maxwellian and non-Maxwellian) moment equations is solved to express the first-order density, temperature, and flow velocity in terms of radial gradients of the zeroth-order pressure and temperature. Closure relations that connect parallel heat flux density and viscosity to the radial gradients and parallel gradients of temperature and flow velocity are also obtained by solving the non-Maxwellian moment equations. The closure relations combined with the linearized fluid equations reproduce the same solution obtained directly from the full moment equations. Furthermore, the method can be generalized to derive closures and transport for an electron-ion plasma and a multi-ion plasma in a general magnetic field.

neoclassical transport↗

DOE OSTI2025

Dilute magnetic impurity-induced effective phonon magnetic moment in Fe-doped monolayer MoS 2

Realization of large effective phonon magnetic moment in monolayer MoS 2 has established an important route for exploring intriguing magnetic phenomena in a nonmagnetic material. The sizable coupling between the orbital transition and the circularly polarized phonon results in the large effective phonon magnetic moment. In this work, using magneto-Raman spectroscopy, we investigate substitutional doping of magnetic atoms as a tuning knob of the electronic and phononic properties of MoS 2 . We show that Fe-doping polarizes the spin of the conduction bands and introduces a localized Fe band underneath the conduction band. As a result, an additional orbital transition between the Mo 4d and Fe 3d states emerges, producing an orbital-phonon hybridized mode at 283 cm −1 . Our magnetic field dependent measurements demonstrate that this new mode carries 2.8 $\mu_{\mathrm{B}}$ effective phonon magnetic moment, which is comparable to that of the undoped MoS 2 . Moreover, even though a long-range magnetic order is absent in Fe-doped MoS 2 , the local magnetic moment of Fe modifies the nature of the spin fluctuation, producing monotonically increasing quasielastic scattering spectral weight as temperature decreases. Our results highlight two-dimensional dilute magnetic semiconductors synthesized by substitutional doping as a promising material platform to manipulate the phonon magnetic moment through orbital-phonon coupling.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Tuning the melting point of selected ionic liquids through adjustment of the cation’s dipole moment.

In prior research with thermally robust salts [Cassity et al., PCCP, 2017, 19, 31560] it was noted that an increase in the dipole moment of the cation generally led to a decrease in the melting point. Molecular dynamics simulations of the liquid state revealed that an increased dipole moment reduces cation-cation repulsions through dipole-dipole alignment. This was believed to reduce the liquid phase enthalpy, which would tend to lower the melting point of the IL. Here, we also test this principle by replacing hydrogen atoms with fluorine atoms at selected positions within the cation. This allows us to alter the electrostatics of the cation without substantially affecting the sterics. Furthermore, the strength of the dipole moment can be controlled by choosing different positions within the cation for replacement. We studied variants of four different parent cations paired with bistriflimide and determined their melting points, and enthalpies and entropies of fusion through DSC experiments. The decreases in the melting point were determined to be enthalpically driven. We found that the dipole moment of the cation, as determined by quantum chemical calculations, is inversely correlated with the melting point of the given compound. Molecular dynamics simulations of the crystalline and solid states of two isomers showed differences in their enthalpies of fusion that closely matched those seen experimentally. Moreover, this reduction in the enthalpy of fusion was determined to be caused by an increase in the enthalpy of the crystalline state. We provide evidence that dipole-dipole interactions between cations leads to the formation of cationic domains in the crystalline state. These cationic associations partially block favourable cation–anion interactions, which are recovered upon melting. If, however, the dipole- dipole interactions between cations is too strong they have a tendency to form glasses. This study provides a design rule for lowering the melting point of structurally similar ILs by altering their dipole moment.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2022

Electron cyclotron drift instability and anomalous transport: two-fluid moment theory and modeling

In the presence of a strong electric field perpendicular to the magnetic field, the electron cross-field (E × B) flow relative to the unmagnetized ions can cause the so-called electron cyclotron drift instability (ECDI) due to resonances of the ion acoustic mode and the electron cyclotron harmonics. This occurs in, for example, collisionless shock ramps in space, and in E × B discharge devices such as Hall thrusters. A prominent feature of ECDI is its capability to induce an electron flow parallel to the background >E field at a speed greatly exceeding predictions by classical collision theory. Such anomalous transport is important due to its role in particle thermalization at space shocks, and in causing plasma flows towards the walls of E × B devices, leading to unfavorable erosion and performance degradation, etc. The development of ECDI and anomalous transport is often considered requiring a fully kinetic treatment. In this work, however, we demonstrate that a reduced variant of this instability, and more importantly, the associated anomalous transport, can be treated self-consistently in a collisionless two-fluid framework without any adjustable collision parameter. By treating both electron and ion species on an equal footing, the free energy due to the inter-species velocity shear allows the growth of an anomalous electron flow parallel to the background E field. We will first present linear analyses of the instability in the two-fluid five- and ten-moment models, and compare them against the fully-kinetic theory. At low temperatures, the two-fluid models predict the fastest-growing mode in good agreement with the kinetic result. Also, by including more (> = 10) moments, secondary (and possibly higher) unstable branches can be recovered. The dependence of the instability on ion-to-electron mass ratio, plasma temperature, and background B field strength is also thoroughly explored. We then carry out direct numerical simulations of the cross-field setup using the five-moment model. The development of the instability, as well as the anomalous transport, is confirmed and in excellent agreement with theoretical predictions. The force balance properties are also studied using the five-moment simulation data. Here this work casts new insights into the nature of ECDI and the associated anomalous transport and demonstrates the potential of the two-fluid moment model in efficient modeling of E × B plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Optimization of foreground moment deprojection for semi-blind CMB polarization reconstruction

Abstract Upcoming Cosmic Microwave Background (CMB) experiments, aimed at measuring primordial CMB polarization B-modes, require exquisite control of instrumental systematics and Galactic foreground contamination. Blind minimum-variance techniques, like the Needlet Internal Linear Combination (NILC), have proven effective in reconstructing the CMB polarization signal and mitigating foregrounds and systematics across diverse sky models without suffering from foreground mismodelling errors. Still, residual foreground contamination from NILC may bias the recovered CMB polarization at large angular scales when confronted with the most complex foreground scenarios.By adding constraints to NILC to deproject statistical moments of the Galactic emission, the Constrained Moment ILC (cMILC) method has been demonstrated to further enhance foreground subtraction, albeit with an associated increase in overall noise variance. Faced with this trade-off between foreground bias reduction and overall variance minimization, there is still no recipe on which moments to deproject and which are better suited for blind variance minimization. To address this, we introduce the optimized cMILC (ocMILC) pipeline, which performs full automated optimization of the required number and set of foreground moments to deproject, pivot parameter values, and deprojection coefficients across the sky and angular scales, depending on the actual sky complexity, available frequency coverage, and experiment sensitivity. The optimal number of moments for deprojection, before paying significant noise penalty, is determined through a data diagnosis inspired by the Generalized NILC (GNILC) method.Validated on B-mode simulations of thePICOspace mission concept with four challenging foreground models, ocMILC exhibits lower Galactic foreground contamination compared to NILC and cMILC at all angular scales, with limited noise penalty. This multi-layer optimization enables the ocMILC pipeline to achieve unbiased posteriors of the tensor-to-scalar ratio, regardless of foreground complexity.

Astronomy & Astrophysics↗

DOE OSTI2020

Dark Energy Survey Year 3 results: cosmology with moments of weak lensing mass maps – validation on simulations

ABSTRACT We present a simulated cosmology analysis using the second and third moments of the weak lensing mass (convergence) maps. The second moment, or variances, of the convergence as a function of smoothing scale contains information similar to standard shear two-point statistics. The third moment, or the skewness, contains additional non-Gaussian information. The analysis is geared towards the third year (Y3) data from the Dark Energy Survey (DES), but the methodology can be applied to other weak lensing data sets. We present the formalism for obtaining the convergence maps from the measured shear and for obtaining the second and third moments of these maps given partial sky coverage. We estimate the covariance matrix from a large suite of numerical simulations. We test our pipeline through a simulated likelihood analyses varying 5 cosmological parameters and 10 nuisance parameters and identify the scales where systematic or modelling uncertainties are not expected to affect the cosmological analysis. Our simulated likelihood analysis shows that the combination of second and third moments provides a 1.5 per cent constraint on S8 ≡ σ8(Ωm/0.3)0.5 for DES Year 3 data. This is 20 per cent better than an analysis using a simulated DES Y3 shear two-point statistics, owing to the non-Gaussian information captured by the inclusion of higher order statistics. This paper validates our methodology for constraining cosmology with DES Year 3 data, which will be presented in a subsequent paper.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Impact of point spread function higher moments error on weak gravitational lensing

ABSTRACT Weak gravitational lensing is one of the most powerful tools for cosmology, while subject to challenges in quantifying subtle systematic biases. The point spread function (PSF) can cause biases in weak lensing shear inference when the PSF model does not match the true PSF that is convolved with the galaxy light profile. Although the effect of PSF size and shape errors – i.e. errors in second moments – is well studied, weak lensing systematics associated with errors in higher moments of the PSF model require further investigation. The goal of our study is to estimate their potential impact for LSST weak lensing analysis. We go beyond second moments of the PSF by using image simulations to relate multiplicative bias in shear to errors in the higher moments of the PSF model. We find that the current level of errors in higher moments of the PSF model in data from the Hyper Suprime-Cam survey can induce a ∼0.05 per cent shear bias, making this effect unimportant for ongoing surveys but relevant at the precision of upcoming surveys such as LSST.

79 ASTRONOMY AND ASTROPHYSICS↗