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At least 73 records · Page 4

Statistics of Sxy estimates

The statistics of Sxy estimates derived from orthogonal-component measurements are examined. Based on results of Goodman (1957), the probability density function (pdf) for Sxy(f) estimates is derived, and a closed-form solution for arbitrary moments of the distribution is obtained. Characteristic functions are used to derive the exact pdf of Sxy(tot). In practice, a simple Gaussian approximation is found to be highly accurate even for relatively few degrees of freedom. Implications for experiment design are discussed, and a maximum-likelihood estimator for a posterior estimation is outlined.

Freilich, M. H.↗

Bootstrapping outperforms community‐weighted approaches for estimating the shapes of phenotypic distributions

Abstract Estimating phenotypic distributions of populations and communities is central to many questions in ecology and evolution. These distributions can be characterized by their moments (mean, variance, skewness and kurtosis) or diversity metrics (e.g. functional richness). Typically, such moments and metrics are calculated using community‐weighted approaches (e.g. abundance‐weighted mean). We propose an alternative bootstrapping approach that allows flexibility in trait sampling and explicit incorporation of intraspecific variation, and show that this approach significantly improves estimation while allowing us to quantify uncertainty. We assess the performance of different approaches for estimating the moments of trait distributions across various sampling scenarios, taxa and datasets by comparing estimates derived from simulated samples with the true values calculated from full datasets. Simulations differ in sampling intensity (individuals per species), sampling biases (abundance, size), trait data source (local vs. global) and estimation method (two types of community‐weighting, two types of bootstrapping). We introduce the traitstrap R package, which contains a modular and extensible set of bootstrapping and weighted‐averaging functions that use community composition and trait data to estimate the moments of community trait distributions with their uncertainty. Importantly, the first function in the workflow, trait_fill , allows the user to specify hierarchical structures (e.g. plot within site, experiment vs. control, species within genus) to assign trait values to each taxon in each community sample. Across all taxa, simulations and metrics, bootstrapping approaches were more accurate and less biased than community‐weighted approaches. With bootstrapping, a sample size of 9 or more measurements per species per trait generally included the true mean within the 95% CI. It reduced average percent errors by 26%–74% relative to community‐weighting. Random sampling across all species outperformed both size‐ and abundance‐biased sampling. Our results suggest randomly sampling ~9 individuals per sampling unit and species, covering all species in the community and analysing the data using nonparametric bootstrapping generally enable reliable inference on trait distributions, including the central moments, of communities. By providing better estimates of community trait distributions, bootstrapping approaches can improve our ability to link traits to both the processes that generate them and their effects on ecosystems.

Maitner, Brian S.↗

Comparison of generalized transport and Monte-Carlo models of the escape of a minor species

The steady-state diffusion of a minor species through a static background species is studied using a Monte Carlo model and a generalized 16-moment transport model. The two models are in excellent agreement in the collision-dominated region and in the 'transition region'. In the 'collisionless' region the 16-moment solution contains two singularities, and physical meaning cannot be assigned to the solution in their vicinity. In all regions, agreement between the models is best for the distribution function and for the lower-order moments and is less good for higher-order moments. Moments of order higher than the heat flow and hence beyond the level of description provided by the transport model have a noticeable effect on the shape of distribution functions in the collisionless region.

Demars, H. G.↗

Statistical properties of two sine waves in Gaussian noise.

A detailed study is presented of some statistical properties of a stochastic process that consists of the sum of two sine waves of unknown relative phase and a normal process. Since none of the statistics investigated seem to yield a closed-form expression, all the derivations are cast in a form that is particularly suitable for machine computation. Specifically, results are presented for the probability density function (pdf) of the envelope and the instantaneous value, the moments of these distributions, and the relative cumulative density function (cdf).

Esposito, R.↗

Probe and radar electron temperatures in an isotropic nonequilibrium plasma.

Electron temperatures measured by electrostatic probes and radar backscatter are distinct physical quantities, the temperature from each technique determined from a different moment of the electron-distribution function. Numerical inequality of temperatures results from a non-Maxwellian electron-distribution function or, equivalently, from a nonequilibrium electron plasma. Probe and backscatter electron temperatures are studied for low- and high-energy (isotropic) distortions of the distribution function. The nonequilibrium plasma generally produces higher probe than backscatter temperatures; however, the temperature difference is small for distortions due to realistic photoelectron populations. If the ionosphere is in a highly nonequilibrium state, probe and backscatter temperatures would differ from the temperature characterizing the average electron kinetic energy, and a single temperature applicable to a variety of physical processes would no longer exist.

Hoegy, W. R.↗

Energy partitioning of gaseous ions in an electric field.

The partitioning of ion energy among thermal energy, drift energy, and random-field energy is studied by solution of the Boltzmann equation. An expansion in powers of the square of the electric field strength is obtained by Kihara's method. Numerical calculations for several ion-neutral force laws show that Wannier's constant mean-free-time model gives a reasonable first approximation. The formal extension to multicomponent mixtures is also given. The matrix elements obtained are tabulated, and can be used to study the field dependence of other moments of the ion-distribution function.

Hahn, H.-S.↗

Far-infrared absorption in H2 and H2-He mixtures

Collision-induced absorption in the translation-rotation band of H2 and H2-He mixtures has been measured from 20 to 900 kaysers at 77.4, 195, and 292 K. To establish the accuracy of the results, various sources of error are investigated. The zeroth and first spectral moments are evaluated from experiment and theory for H2 at the various temperatures. To obtain theoretical moments consistent with the experimental values, the quantum pair-distribution function must be used. The major portion of the experimental moments can be accounted for by quadrupole-induced dipoles in H2 pairs. The remaining portion is attributable to an anisotropic overlap interaction, although its magnitude depends on the value of the molecular parameters required to calculate the quadrupole contribution.

Birnbaum, G.↗

The 1983 tail-era series. Volume 1: ISEE 3 plasma

Observations from the ISEE 3 electron analyzer are presented in plots. Electrons were measured in 15 continuous energy levels between 8.5 and 1140 eV during individual 3-sec spacecraft spins. Times associated with each data point are the beginning time of the 3 sec data collection interval. Moments calculated from the measured distribution function are shown as density, temperature, velocity, and velocity azimuthal angle. Spacecraft ephemeris is shown at the bottom in GSE and GSM coordinates in units of Earth radii, with vertical ticks on the time axis corresponding to the printed positions.

Fairfield, D. H.↗

P78-2 SCATHA environmental data atlas

The 100 eV to approximately 1 MeV plasma environment encountered by the P78-2 Spacecraft Charging at High Altitudes (SCATHA) satellite during its initial operation period was studied. Forty-four days of 10 minute averages of the four moments of the electron and ion distribution functions calculated from the SC5 and SC9 energetic particle measurements were analyzed to determine occurrence frequency, local time variation, geomagnetic activity variation, and L shell variation. The single and double Maxwellian parameters derived from the four moments were similarly analyzed. The interrelationships between the moments and derived parameters were computed and the results compared with the ATS-5 and ATS-6 atlas. Results of this analysis establish a baseline range for the SCATHA plasma environment.

Mulen, E. G.↗

Transverse-energy-energy correlations in deep inelastic scattering

Event shape observables have been widely used for precision QCD studies at various lepton and hadron colliders. We present the most accurate calculation of the transverse-energy-energy correlation event shape variable in deep-inelastic scattering. In the framework of soft-collinear effective theory the cross section is factorized as the convolution of the hard function, beam function, jet function and soft function in the back-to-back limit. A close connection to TMD factorization is established, as the beam function when combined with part of the soft function is identical to the conventional TMD parton distribution function, and the jet function is the second moment of the TMD fragmentation function matching coefficient. We validate our framework by comparing the obtained LO and NLO leading singular distributions to the full QCD calculations in the back-to-back limit. We report the resummed transverse-energy-energy correlation distributions up to N 3 LL accuracy matched with the NLO cross section for the production of a lepton and two jets. Our work provides a new way to precisely study TMD physics at the future Electron-Ion Collider.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Auroral ion velocity distributions using a relaxation model.

Calculation of ion velocity distributions for a weakly-ionized plasma subjected to crossed electric and magnetic fields for application to the auroral ionosphere. By replacing the Boltzmann collision integral with a simple relaxation model, an exact solution to Boltzmann's equation could be obtained. This solution has the advantage over a series expansion in that all the higher-order velocity moments are inherent in it. The exact solution is particularly advantageous when studying large departures of the distribution from its Maxwellian form, because these departures are caused by the higher velocity moments. In general, however, a simple relaxation model can only be used to obtain qualitative information on the distribution function. Consequently, it is possible to determine when the higher-order velocity moments affect the ion velocity distribution and the nature of their effect, but it is not possible to obtain accurate quantitative results.

St-Maurice, J.-P.↗

A novel conditional formulation of the Vlasov–Ampère equations: a conservative, positivity, asymptotic and Gauss law preserving scheme

We propose a novel reformulation of the Vlasov–Ampère equations for plasmas that reveals discrete symmetries that enables simultaneous conservation of mass, momentum and energy; preservation of Gauss’s law; positivity of the distribution function; and consistency with quasi-neutral asymptotics. The approach employs variable and coordinate transformations to yield a coupled system comprising a modified Vlasov equation and associated moment–field equations. The modified Vlasov equation advances a conditional distribution function that excludes mass, momentum and energy densities, which are instead evolved through moment equations enforcing the relevant symmetries, conservation laws and involution constraints. This reformulation aligns naturally with a recent slow-manifold reduction technique, which separates fast electron time scales and simplifies the treatment of the quasi-neutral limit within the reduced moment–field subsystem. Using this framework, we develop a numerical method for the reduced 1D1V subsystem that, for the first time in the literature, satisfies all key physical constraints while maintaining a quasi-neutral asymptotic behaviour. The advantages of the method are demonstrated on canonical electrostatic test problems, including the multiscale ion acoustic shock wave.

1D1V↗

Bayesian inference for the seismic moment tensor using regional waveforms and a data-derived distribution of velocity models

The largest source of uncertainty in any source inversion is the velocity model used to construct the transfer function employed in the forward model that relates observed ground motion to the seismic moment tensor. However, standard inverse procedures 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. We attempt to incorporate this uncertainty into an estimation of the seismic moment tensor using a distribution of velocity models calculated in a prior effort based on different and complementary data sets. The posterior distribution of velocity models is then used to construct Green’s functions for use in Bayesian inference of an unknown seismic moment tensor using regional waveform data. The combined likelihood is estimated using data-specific error models and the posterior of the seismic moment tensor is estimated and can be interpreted in terms of most-probable source-type.

58 GEOSCIENCES↗

Open-source library for performance-portable neutrino reaction rates: Application to neutron star mergers

A realistic and detailed description of neutrinos in binary neutron star (BNS) mergers is essential to build reliable models of such systems. To this end, we present bns_nurates, a novel open-source numerical library designed for the efficient on-the-fly computation of neutrino interactions, with particular focus on regimes relevant to BNS mergers. bns_nurates targets a higher level of accuracy and realism in the implementation of commonly employed reactions by accounting for relevant microphysics effects on the interactions, such as weak magnetism and mean field effects. It also includes the contributions of inelastic neutrino scattering off electrons and positrons and (inverse) nucleon decays. Finally, it offers a way to reconstruct the neutrino distribution function in the framework of moment-based transport schemes. As a first application, we compute both energy-dependent and energy-integrated neutrino emissivities and opacities for conditions extracted from a BNS merger simulation with m1 transport scheme. We find some qualitative differences in the results when considering the impact of the additional relevant reactions and of microphysics effects. For example, neutrino-electron/positron scattering reactions are important for the energy exchange of heavy-type neutrinos as they do not undergo semileptonic charged-current processes, when μ± are not accounted for. Moreover, weak magnetism and mean field effects can significantly modify the contribution of β processes for electron-type (anti)neutrinos, increasing at the same time the importance of (inverse) neutron decays. Here, the improved treatment for the reaction rates also modifies the conditions at which neutrinos decouple from matter in the system, potentially affecting their emission spectra.

79 ASTRONOMY AND ASTROPHYSICS↗

Statistical time-dependent model for the interstellar gas

We present models for temperature and ionization structure of low, uniform-density (approximately 0.3 per cu cm) interstellar gas in a galactic disk which is exposed to soft X rays from supernova outbursts occurring randomly in space and time. The structure was calculated by computing the time record of temperature and ionization at a given point by Monte Carlo simulation. The calculation yields probability distribution functions for ionized fraction, temperature, and their various observable moments. These time-dependent models predict a bimodal temperature distribution of the gas that agrees with various observations. Cold regions in the low-density gas may have the appearance of clouds in 21-cm absorption. The time-dependent model, in contrast to the steady-state model, predicts large fluctuations in ionization rate and the existence of cold (approximately 30 K), ionized (ionized fraction equal to about 0.1) regions.

Gerola, H.↗

Plasma electron analysis: Voyager plasma science experiment

The Plasma Science Experiment (PLS) on the Voyager spacecraft provide data on the plasma ions and electrons in the interplanetary medium and the magnetospheres of the giant planets Jupiter and Saturn. A description of the analysis used to obtain electron parameters (density, temperature, etc.) from the plasma science experiment PLS electron measurements which cover the energy range from 10 eV to 5950 eV is presented. The electron sensor (D cup) and its transmission characteristics are described. A derivation of the fundamental analytical expression of the reduced distribution function F(e) is given. The electron distribution function F(e), used in the moment integrations, can be derived from F(e). Positive ions produce a correction current (ion feedthrough) to the measured electron current, which can be important to the measurements of the suprathermal electron component. In the case of Saturn, this correction current, which can either add to or subtract from the measured electron current, is less than 20% of the measured signal at all times. Comments about the corrections introduced by spacecraft charging to the Saturn encounter data, which can be important in regions of high density and shadow when the spacecraft can become negatively charged are introduced.

Sittler, E. C., Jr.↗

Relationships among the harmonic coefficients of scan plane anisotropies

Frequently, a detector on a spinning spacecraft measures the flux of charged particles whose velocities lie in a plane containing the magnetic field. This flux may be Fourier analyzed as a function of the spacecraft roll angle. Relationships among the Fourier coefficients are derived using the adiabatic solution of the Vlasov equation. These relationships depend only on the fact that the lowest order (in gyroradius) of the distribution function is a function of the magnetic moment and that the first-order term is a function of the lowest order. These relationships may be used to separate the proton from the electron counts registered in Saturn's inner magnetosphere by the University of California's Cerenkov counter on Pioneer 11.

Northrop, T. G.↗