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Results for “Multipole expansion”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Cumulative atomic multipole moments complement any atomic charge model to obtain more accurate electrostatic properties

The quality of several atomic charge models based on different definitions has been analyzed using cumulative atomic multipole moments (CAMM). This formalism can generate higher atomic moments starting from any atomic charges, while preserving the corresponding molecular moments. The atomic charge contribution to the higher molecular moments, as well as to the electrostatic potentials, has been examined for CO and HCN molecules at several different levels of theory. The results clearly show that the electrostatic potential obtained from CAMM expansion is convergent up to R-5 term for all atomic charge models used. This illustrates that higher atomic moments can be used to supplement any atomic charge model to obtain more accurate description of electrostatic properties.

NASA Discipline Number 52-20↗
NASA NTRS1999

Energy Levels of C IV: The Polarization Method

In a previous publication [Can. J. Phys. 75, 11 (1997)] we calculated the generalized polarizabilities up to multipole order 3 as well as certain higher-order hyperpolarizabilities for two-electron atoms and ions of Z=2-6 and 10. In this paper we apply some of these results to calculate excited-state energies in three times ionized (lithium-like) carbon. For states with angular momentum L greater than or equal to 3 accurate results are obtained using an asymptotic polarizability expansion that includes nonadiabatic effects. Comparison is made with recent optical measurements, and a critical discussion of the correct form of the expansion is given. In addition, the possibility of very accurate measurements of the fine-structure splitting encourages us to present a table of such splittings to very high accuracy. An appendix contains similar results for lithium-like oxygen and neon ions.

Bhatia, A. K.↗
NASA NTRS1978

A beaming model of the Io-independent Jovian decameter radiation based on multipole models of the Jovian magnetic field

A geometrical model is presented in which the apparent source locations of the Io-independent decameter radiation are computed. The calculations assume that the radiation is produced by stably trapped electrons radiating near the electron gyrofrequency and that the emission is then beamed onto a conical surface. The maximum occurrence probability of noise storms is associated with regions in the Jovian magnetosphere where the axis of the emission cone is most inclined toward the Jovian equatorial plane. The calculations utilize and compare two of the octupole spherical harmonic expansions of the Jovian magnetic field constructed from data accumulated by the fluxgate and vector helium magnetometers on board Pioneer 11.

Goldstein, M. L.↗
NASA NTRS1979

A beaming model of the Io-independent Jovian decameter radiation based on multipole models of the Jovian magnetic field

A geometrical model is presented in which the apparent source locations of the Io-independent decameter radiation are computed. The calculations assume that the radiation is produced by stably trapped electrons radiating near the local electron gyrofrequency and that the emission is then beamed onto a conical surface. The maximum occurrence probability of noise storms is associated with regions in the Jovian magnetosphere where the axis of the emission cone is most inclined toward the Jovian equatorial plane. The calculations utilize and compare two of the octopole spherical harmonic expansions of the Jovian magnetic field constructed from data accumulated by the fluxgate and vector helium magnetometers on board Pioneer 11.

Goldstein, M. L.↗
NASA NTRS1990

Multipole radiation in charged-particle scattering

This paper formulates the general problem of photon emission in particle scattering using a classical and quantum mechanical approach. The connection between the classical short collision time (SCT) and Born results is examined for various special classifications of problems. In the dipole case the two formulations yield results that can be expressed in the same form and for arbitrary scattering potential. For quadrupole emission the SCT and Born results are the same only for a short-range potential, however. The quadrupole problem is more sensitive to details in the process because the calculation requires an expansion of the total amplitude for the process to lowest order in the photon wave number or momentum. The special case of photon emission associated with spin-flip transitions during scattering is considered for spin-1/2 particles. Like classical magnetic dipole radiation, there is no infrared divergence feature for this type of emission.

Gould, Robert J.↗
NASA NTRS1975

High zonal harmonics of rapidly rotating planets

A new perturbation expansion is derived for the structure of rotating bodies in hydrostatic equilibrium. The method uses an expansion of the density on Legendre polynomial functions of angle, and can be developed analytically in a manner analogous to the standard level-surface perturbation theory. The new theory proceeds from a prescribed pressure-density relation rather than from a prescribed density distribution, and is both simpler and more physically transparent than the level-surface approach. High zonal harmonics are shown to arise via a transfer function involving derivatives of the interior sound velocity, and via mixing of multipole density components in the outer shell of the planet. Sample calculations for polytropic sequences are presented, as well as standard gravity models for Jupiter and Saturn. Mathematical subleties of the theory are discussed in an appendix.

Hubbard, W. B.↗
NASA NTRS1981

A 5 x 40 cm rectangular-beam multipole ion source

A rectangular ion source particularly suited for the continuous sputter processing of materials over a wide area is discussed. A multipole magnetic field configuration was used to design an ion source with a 5 x 40 cm beam area, while a three-grid ion optics system was used to maximize ion current density at the design ion energy of 500 eV. An average extracted current density of about 4 mA/sq cm could be obtained from 500 eV Ar ions. The difference between the experimental performance and the design value of 6 mA/sq cm is attributed to grid misalignment due to thermal expansion. The discharge losses at typical operating conditions ranged from about 600 to 1000 eV/ion, in reasonable agreement with the design value of 800 eV/ion. The use of multiple rectangular-beam ion sources to process wider areas than would be possible with a single source was also studied, and the most uniform coverage was found to be obtainable with a 0 to 2 cm overlap.

Robinson, R. S.↗
DOE OSTI2025

Quantifying bias due to non-Gaussian foregrounds in an optimal reconstruction of CMB lensing and temperature power spectra

We estimate the magnitude of the bias due to non-Gaussian extragalactic foregrounds on the optimal reconstruction of the cosmic microwave background (CMB) lensing potential and temperature power spectra. The reconstruction is performed using a Bayesian inference method known as the marginal unbiased score expansion (MUSE). We apply MUSE to a minimum variance combination of multifrequency maps drawn from the Agora publicly available simulations of the lensed CMB and correlated extragalactic foreground emission. Taking noise levels appropriate to the SPT-3G D1 release, we find non-Gaussian foregrounds may bias the MUSE reconstruction of the lensing potential amplitude at the level of (0.7 ± 0.3)σ when using modes up to ℓ max = 3500. We do not detect a statistically significant bias, finding a value of (-0.4 ± 0.3)σ, when restricted to lower angular multipoles, ℓ max = 3000. This work is a first step toward understanding the impact of extragalactic foregrounds on optimal reconstructions of CMB temperature and lensing potential power spectra.

Statistical sampling techniques↗
DOE OSTI2026

Alleviating prior dependencies for DESI DR1 clustering fits through reparameterization

Bayesian analyses of the full-shape clustering of Dark Energy Spectroscopic Instrument (DESI) Data Release 1 (DR1) exhibit prior-volume projection effects, whereby weakly constrained nuisance parameters of the Effective Field Theory of Large Scale Structure (EFTofLSS) shift marginalized cosmological posteriors away from the posterior maximum. We reanalyze DESI DR1 power spectrum multipoles using two complementary mitigation strategies: (i) nonlinear orthogonalization to decorrelate nuisance and cosmological parameter priors, and (ii) a fully reparameterization-invariant Jeffreys prior over all EFTofLSS coefficients, evaluated on-the-fly via closed-form Jacobians. Including data from DESI, Big-Bang Nuclesynthesis and a constraint on $n_{\mathrm{s}}$, baseline priors lead to multi-$σ$ projection in the Hubble parameter $H_{0}$ and dark energy equation of state parameters $w_{0}$ and $w_{a}$; the Jeffreys prior successfully recenters these posteriors to enclose the maximum a posteriori estimate within the 68% credible regions, demonstrating clear mitigation of projection effects for these late-time expansion parameters. A hybrid Jeffreys+baseline-Gaussian configuration controls residual over-broad tails in the physical cold dark matter density $ω_{\mathrm{c}}$ while preserving the volume correction, and is our favoured approach. We compare the credible intervals derived using our methodology to those obtained using Halo Occupation Distribution (HOD)-informed priors and to confidence intervals derived using frequentist profile likelihood analyses, finding agreement in both central values and degeneracy directions in the $w_{0}$--$w_{a}$ plane. This demonstrates that, once projection effects are properly controlled, we can make robust inferences about the late-time cosmological expansion independent of the statistical framework adopted.

Bonici, M. [Waterloo U.; Perimeter Inst. Theor. Ph↗
NASA NTRS1995

Fast Multipole Methods for Three-Dimensional N-body Problems

We are developing computational tools for the simulations of three-dimensional flows past bodies undergoing arbitrary motions. High resolution viscous vortex methods have been developed that allow for extended simulations of two-dimensional configurations such as vortex generators. Our objective is to extend this methodology to three dimensions and develop a robust computational scheme for the simulation of such flows. A fundamental issue in the use of vortex methods is the ability of employing efficiently large numbers of computational elements to resolve the large range of scales that exist in complex flows. The traditional cost of the method scales as Omicron (N(sup 2)) as the N computational elements/particles induce velocities at each other, making the method unacceptable for simulations involving more than a few tens of thousands of particles. In the last decade fast methods have been developed that have operation counts of Omicron (N log N) or Omicron (N) (referred to as BH and GR respectively) depending on the details of the algorithm. These methods are based on the observation that the effect of a cluster of particles at a certain distance may be approximated by a finite series expansion. In order to exploit this observation we need to decompose the element population spatially into clusters of particles and build a hierarchy of clusters (a tree data structure) - smaller neighboring clusters combine to form a cluster of the next size up in the hierarchy and so on. This hierarchy of clusters allows one to determine efficiently when the approximation is valid. This algorithm is an N-body solver that appears in many fields of engineering and science. Some examples of its diverse use are in astrophysics, molecular dynamics, micro-magnetics, boundary element simulations of electromagnetic problems, and computer animation. More recently these N-body solvers have been implemented and applied in simulations involving vortex methods. Koumoutsakos and Leonard (1995) implemented the GR scheme in two dimensions for vector computer architectures allowing for simulations of bluff body flows using millions of particles. Winckelmans presented three-dimensional, viscous simulations of interacting vortex rings, using vortons and an implementation of a BH scheme for parallel computer architectures. Bhatt presented a vortex filament method to perform inviscid vortex ring interactions, with an alternative implementation of a BH scheme for a Connection Machine parallel computer architecture.

Koumoutsakos, P.↗
DOE OSTI2025

Impact and mitigation of spectroscopic systematics on DESI DR1 clustering measurements

The large scale structure catalogs within DESI Data Release 1 (DR1) use nearly 6 million galaxies and quasars as tracers of the large-scale structure of the universe to measure the expansion history with baryon acoustic oscillations and the growth of structure with redshift-space distortions. In order to take advantage of DESI's unprecedented statistical power, we must ensure that the galaxy clustering measurements are unaffected by non-cosmological density fluctuations. One source of spurious fluctuations comes from variation in galaxy density with spectroscopic observing conditions, lowering the redshift efficiency (and thus galaxy density) in certain areas of the sky. We measure the uniformity of the redshift success rate for DESI luminous red galaxies (LRG), bright galaxies (BGS) and quasars (QSO), complementing the detailed discussion of emission line galaxy (ELG) systematics in a companion paper [1]. We find small but significant fluctuations of up to 3% in redshift success rate with the effective spectroscopic signal-to-noise, and create and describe weights that remove these fluctuations. We also describe the process to identify and remove data from certain poorly performing fibers from DESI DR1, and measure the stability of the redshift success rate with time. Finally, we find small but significant correlations of redshift success rate with position on the focal plane, survey speed, and number of exposures required, and show the impact of weights correcting these trends on the power spectrum multipoles and on cosmological parameters from BAO and RSD fits. These corrections change the best-fit parameters by <15% of their statistical errors, and thus contribute negligibly to the overall DESI error budget.

cosmological parameters from LSS↗