SEARCH · Search NASA

Results for “MULTIPOLES”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2

All sources NASA NTRS DOE OSTI

DOE OSTI2019

Hierarchical Particle Mesh: An FFT-accelerated Fast Multipole Method

I observe a modification to the original Fast Multipole Method (FMM) of Greengard & Rokhlin that approximates the gravitation field of an FMM cell as a small uniform grid (a “gridlet”) of effective masses. The effective masses on a gridlet are set from the requirement that the multipole moments of the FMM cells are reproduced exactly, thus preserving the accuracy of the gravitational field representation. The measurement of the gravitational field from a multipole expansion can then be computed for all multipole orders simultaneously, with a single Fast Fourier Transform, significantly reducing the computational cost at a given value of the required accuracy. The described approach belongs to the class of “kernel independent” variants of the FMM method and works with any Green function.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1987

Complex space multipole theory for scattering and diffraction problems

Classical multipole theory can be extended to multipoles located in complex space and applied in scattering and diffraction problems with the advantage that, if the point of the multipole is correctly chosen, the first term may give an order of magnitude better approximation to the source than when the multipole is in real space. The basic theory, given elsewhere, is presented here in a more straightforward manner and the improvement in radiation pattern is demonstrated for sources of constant polarization. Applications on scattering by spheroidal dielectric bodies and diffraction by a dielectric half-space are discussed.

Lindell, Ismo V.↗

DOE OSTI2019

An adaptive fast multipole method in Cartesian basis, enabled by algorithmic differentiation

A novel form of the fast multipole method is realized by the combination of adaptive data structures with implementation of the multipole expansions and their translations in Cartesian basis, and enabled by algorithmic differentiation. It may be possible to generalize it to any kernel that allows its formulation as a function of small quantities with respect to which they can be expanded. There is no hard and fast rule recipe that works for all cases. However, it is shown how to do it for the softened Coulomb kernel, which is different from the Coulomb kernel. The characteristics and performance of the method are mapped and shown to provide an attractive option for a generic fast multipole algorithm in a wide region of the parameter space. The algorithm is illustrated with a beam dynamics application.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Multipole Expansion of Atomic Electron Density Fluctuation Interactions in the Density-Functional Tight-Binding Method

The accuracy of the density-functional tight-binding (DFTB) method in describing noncovalent interactions is limited due to its reliance on monopole-based spherical charge densities. In this study, we present a multipole-extended second-order DFTB (mDFTB2) method that takes into account atomic dipole and quadrupole interactions. Furthermore, we combine the multipole expansion with the monopole-based third-order contribution, resulting in the mDFTB3 method. To assess the accuracy of mDFTB2 and mDFTB3, we evaluate their performance in describing noncovalent interactions, proton transfer barriers, and dipole moments. Here, our benchmark results show promising improvements even when using the existing electronic parameters optimized for the original DFTB3 model. Both mDFTB2 and mDFTB3 outperform their monopole-based counterparts, DFTB2 and DFTB3, in terms of accuracy. While mDFTB2 and mDFTB3 perform comparably for neutral and positively charged systems, mDFTB3 exhibits superior performance over mDFTB2 when dealing with negatively charged systems and proton transfers. Overall, the incorporation of the multipole expansion significantly enhances the accuracy of the DFTB method in describing noncovalent interactions and proton transfers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Resonance Scattering Treatment with the Windowed Multipole Formalism

A new method for directly sampling the resonance upscattering effect is presented. Alternatives have relied on inefficient rejection sampling techniques or large tabular storage of relative velocities. None of these approaches, which require pointwise energy data, are particularly well suited to the windowed multipole cross-section representation. The new method, called multipole analytic resonance scattering, overcomes these limitations by inverse transform sampling from the target relative velocity distribution where the cross section is expressed in the multipole formalism. The closed-form relative speed distribution contains a novel special function we deem the incomplete Faddeeva function, and we present the first results on its efficient numerical evaluation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Mixing bispectrum multipoles under geometric distortions

We derive general expressions for how the Alcock–Paczynski distortions affect the power spectrum and the bispectrum of cosmological fields. We compute explicit formulas for the mixing coefficients of bispectrum multipoles in the linear approximation. The leading-order effect for the bispectrum is the uniform dilation of all three wavevectors. The mixing coefficients depend on the shape of the bispectrum triplet. Our results for the bispectrum multipoles are framed in terms of the ‘natural’ basis of the lengths of three wavevectors but can be easily generalized for other bases and reduction schemes. Our validation tests confirm that the linear approximation is extremely accurate for all power spectrum multipoles. The linear approximation is accurate for the bispectrum monopole but results in sub-per cent level inaccuracies for the bispectrum quadrupole and fails for the bispectrum hexadecapole. Our results can be used to simplify the analysis of the bispectrum from galaxy surveys, especially the measurement of the baryon acoustic oscillation peak position. They can be used to replace numeric schemes with exact analytical formulae.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

CMB low multipole alignments across WMAP and Planck data releases

ABSTRACT The first observations of the cosmic microwave background (CMB) from NASA's Wilkinson Microwave Anisotropy Probe (WMAP) led to finding ‘alignment’ anomalies not expected from fluctuations in the isotropic cosmological model. We study the data of all 8 full-sky public releases since then to test for anomalous alignments and shapes of the first 60 multipoles, i.e. over the range $2\le l \le 61$. We use rotationally invariant and covariant statistics to test isotropy of all subsequent WMAP data releases, along with those from the ESA’s Planck mission. Anomalous alignments among the multipoles $l=1, 2, 3$ are very consistent and robust. More alignments are detected, some of them new, while significance is diluted by the large range of the search. Power entropy, a measure of the randomness of the multipoles, is consistently anomalous at about $2\sigma$ level or better across all data releases. It appears that the CMB is not as random as the cosmological principle predicts on large angular scales.

Patel, Sanjeet Kumar↗

DOE OSTI2020

Nuclear multipole responses from chiral effective field theory interactions

We probe nuclear multipole resonances in the framework of the random-phase approximation by using the interaction obtained from the chiral effective field theory. The three-nucleon force is included in a form of the in-medium two-nucleon interaction, which was derived from the chiral three-nucleon force. The isoscalar monopole, isoscalar dipole, isovector dipole, and isoscalar quadrupole resonances of the closed-shell 56,68,78 Ni have been investigated. The calculations reasonably reproduce the experimental multipole resonances of 56,68 Ni, and well describe the pygmy dipole resonance and dipole polarizability measured in 68 Ni. The multipole resonances of 78 Ni, including pygmy dipole resonance and dipole polarizability, are predicted. The detailed effects of the tensor force and three-body force are analyzed by dissecting the chiral interaction. In this work, we find that in general the tensor force effect on electric giant resonances is not as significant as the effect from the three-body force, although the tensor force provides more than half of the binding energy. The effect from three-body force is strong in light nuclei. Particularly, three-body force is crucial for the formation of the pygmy resonance in calculations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

BICEP/Keck XXI: Constraints on early-Universe parity violation from multipole-dependent birefringence

We present the first constraints on multipole-dependent cosmic birefringence using CMB polarization data from the BK18 dataset, which combines observations from BICEP2, Array, and BICEP3 at frequencies of 95, 150, and 220 GHz. Photon coupling to an axionlike field leads to the rotation of CMB polarization, inducing nonzero cross-correlations. We show that a multipole-dependent rotation imprints a distinct signature in the polarization spectra that can be constrained. Specifically, we consider an early dark energy (EDE) scenario in which a pseudoscalar field couples to photons through a Chern-Simons interaction, generating a polarization rotation with multipole dependence. We introduce a phenomenological as a step function, obtaining constraints on the step function size consistent with zero, with uncertainties less than (68% CL). In addition, using multi-frequency , , and cross spectra, along with robust BICEP/ foreground treatment and likelihood framework, we derive constraints on the axion-photon coupling amplitude for several choices of EDE parameters. For the baseline best-fit value from the 2018 analysis, we obtain (68% CL), consistent with previous limits.

Ade, P A R↗

DOE OSTI2020

Multipole-based cable braid electromagnetic penetration model: magnetic penetration case

The goal of this paper is to present, for the first time, calculations of the magnetic penetration case of a first principles multipole-based cable braid electromagnetic penetration model. As a first test case, a one-dimensional array of perfect electrically conducting wires, for which an analytical solution is known, is investigated: we compare both the self-inductance and the transfer inductance results from our first principles cable braid electromagnetic penetration model to those obtained using the analytical solution. These results are found in good agreement up to a radius to half spacing ratio of about 0.78, demonstrating a robustness needed for many commercial and non-commercial cables. We then analyze a second set of test cases of a square array of wires whose solution is the same as the one-dimensional array result and of a rhomboidal array whose solution can be estimated from Kley's model. As a final test case, we consider two layers of one-dimensional arrays of wires to investigate porpoising effects analytically. We find good agreement with analytical and Kley's results for these geometries, verifying our proposed multipole model. Note that only our multipole model accounts for the full dependence on the actual cable geometry which enables us to model more complicated cable geometries.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1977

Multipole gas thruster design

The development of a low field strength multipole thruster operating on both argon and xenon is described. Experimental results were obtained with a 15-cm diameter multipole thruster and are presented for a wide range of discharge-chamber configurations. Minimum discharge losses were 300-350 eV/ion for argon and 200-250 eV/ion for xenon. Ion beam flatness parameters in the plane of the accelerator grid ranged from 0.85 to 0.93 for both propellants. Thruster performance is correlated for a range of ion chamber sizes and operating conditions as well as propellant type and accelerator system open area. A 30-cm diameter ion source designed and built using the procedure and theory presented here-in is shown capable of low discharge losses and flat ion-beam profiles without optimization. This indicates that by using the low field strength multipole design, as well as general performance correlation information provided herein, it should be possible to rapidly translate initial performance specifications into easily fabricated, high performance prototypes.

Isaacson, G. C.↗

NASA NTRS1978

15 cm mercury multipole thruster

A 15 cm multipole ion thruster was adapted for use with mercury propellant. During the optimization process three separable functions of magnetic fields within the discharge chamber were identified: (1) they define the region where the bulk of ionization takes place, (2) they influence the magnitudes and gradients in plasma properties in this region, and (3) they control impedance between the cathode and main discharge plasmas in hollow cathode thrusters. The mechanisms for these functions are discussed. Data from SERT II and cusped magnetic field thrusters are compared with those measured in the multipole thruster. The performance of this thruster is shown to be similar to that of the other two thrusters. Means of achieving further improvement in the performance of the multipole thruster are suggested.

Longhurst, G. R.↗

NASA NTRS1993

Multipole correction of atomic monopole models of molecular charge distribution. I. Peptides

The defects in atomic monopole models of molecular charge distribution have been analyzed for several model-blocked peptides and compared with accurate quantum chemical values. The results indicate that the angular characteristics of the molecular electrostatic potential around functional groups capable of forming hydrogen bonds can be considerably distorted within various models relying upon isotropic atomic charges only. It is shown that these defects can be corrected by augmenting the atomic point charge models by cumulative atomic multipole moments (CAMMs). Alternatively, sets of off-center atomic point charges could be automatically derived from respective multipoles, providing approximately equivalent corrections. For the first time, correlated atomic multipoles have been calculated for N-acetyl, N'-methylamide-blocked derivatives of glycine, alanine, cysteine, threonine, leucine, lysine, and serine using the MP2 method. The role of the correlation effects in the peptide molecular charge distribution are discussed.

NASA Discipline Exobiology↗

NASA NTRS1991

Ab initio study of the electrostatic multipole nature of torsional potentials in CH3SSCH3, CH3SSH, and HOOH

The origin of torsional potentials in H3CSSCH3, H3CSSH, and HOOH and the anisotropy of the local charge distribution has been analyzed in terms of atomic multipoles calculated from the ab initio LCAO-MO-SCF wave function in the 6-31G* basis set. The results indicate that for longer -S-S-bonds the major contribution to these torsional barriers are electrostatic interactions of the atomic multipoles located on two atoms forming the rotated bond. This finding demonstrates the important role of electrostatic 1-2 interatomic interactions, usually neglected in conformational studies. It also opens the possibility to derive directly from accurate ab initio wave functions a simple nonempirical torsional potential involving atomic multipoles of two bonded atoms defining the torsional angle. For shorter -O-O- bonds, use of more precise models and inclusion of 1-3 interactions seems to be necessary.

NASA Program Exobiology↗

NASA NTRS2003

Global Aspects of Charged Particle Motion in Axially Symmetric Multipole Magnetic Fields

The motion of a single charged particle in the space outside of a compact region of steady currents is investigated. The charged particle is assumed to produce negligible electromagnetic radiation, so that its energy is conserved. The source of the magnetic field is represented as a point multipole. After a general description, attention is focused on magnetic fields with axial symmetry. Lagrangian dynamical theory is utilized to identify constants of the motion as well as the equations of motion themselves. The qualitative method of Stonner is used to examine charged particle motion in axisymmetric multipole fields of all orders. Although the equations of motion generally have no analytical solutions and must be integrated numerically to produce a specific orbit, a topological examination of dynamics is possible, and can be used, d la Stonner, to completely describe the global aspects of the motion of a single charged particle in a space with an axisymmetric multipole magnetic field.

Shebalin, John V.↗

DOE OSTI2025

A Green’s function fast multipole method for computation of micromechanical fields in heterogeneous materials

Computation of micromechanical fields in heterogeneous materials is usually performed using either the finite element method or the Green’s function method based on FFTs. The finite element method allows for accurate discretization and for non-periodic boundary conditions but is computationally expensive. On the other hand, the FFT-based method is computationally efficient but requires discretization on a regular grid of hexahedral voxels. In this paper, a Green’s function method allowing for accurate discretization using tetrahedral elements and for non-periodic boundary conditions is proposed. The convolution is computed using the fast multipole method, which provides good accuracy even for low-order expansion due to the fast decay of interactions between elements. The proposed Green’s function fast multipole method is verified by comparison with analytical and FFT-based solutions. Furthermore, the computational time is analyzed and compared to the FFT-based method for non-periodic convolution. Finally, effective properties of an elastic polycrystalline microstructure containing thin intergranular cracks are computed and analyzed.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Multipole interaction in spectral line broadening by plasmas

A long-standing ambiguity in spectral line broadening theory related to the electric field divergence in the quadrupole term of the screened Coulomb radiator-plasma interaction is examined. This is accomplished with multipole expansions from a Taylor series as well as a partial wave analysis of the screened Coulomb interaction. Here, it is explicitly shown that the two approaches agree up to the octupole term for an effective radiator size small compared to the plasma screening length. Furthermore, the ambigous corrections are confirmed appearing naturally in both methods. For higher multipoles the agreement is demonstrated numerically with a computer program using exact arithmetic.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Shadow molecular dynamics for flexible multipole models

Shadow molecular dynamics provide an efficient and stable atomistic simulation framework for flexible charge models with long-range electrostatic interactions. Shadow molecular dynamics simulations are driven by approximate “shadow” Born–Oppenheimer potentials for which the exact charges and forces are directly accessible without relying on costly (and approximate) iterative solvers. While previous implementations have been limited to atomic monopole charge distributions, we extend this approach to flexible multipole models. We derive detailed expressions for the shadow energy functions, potentials, and force terms, explicitly incorporating monopole–monopole, dipole–monopole, and dipole–dipole interactions. In our formulation, both atomic monopoles and atomic dipoles are treated as extended dynamical variables alongside the propagation of the nuclear degrees of freedom. We demonstrate that introducing the additional dipole degrees of freedom preserves the stability and accuracy previously seen in monopole-only shadow molecular dynamics simulations. In addition, we present a shadow molecular dynamics scheme where the monopole charges are held fixed while the dipoles remain flexible. Our extended shadow dynamics provide a framework for stable, computationally efficient, and versatile molecular dynamics simulations involving long-range interactions between flexible multipoles. This is of particular current interest in combination with machine-learned interatomic potentials, including long-range electrostatic interactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗