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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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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Dynamic Multipoles in the RCS

The Rapid Cycling Synchrotron (RCS) of the Electron--Ion Collider (EIC) will accelerate polarized electrons up to 18 GeV at a repetition rate of 1 Hz. Dynamic multipoles driven by eddy currents in the vacuum chamber can affect beam dynamics and polarization preservation during the energy ramp. Building on the analytical treatment of S.Y. Lee for a ramped normal-conducting dipole magnet, we use conformal transformations to derive compact expressions for dynamic multipoles in higher-order ramped magnets with circular beam pipes. We further derive analytical frequency-domain transfer functions for both self-response and cross-response multipoles, providing compact dynamical models for their evolution during arbitrary ramp waveforms. The resulting analytical predictions are benchmarked against finite-element simulations, including the effects of practical pole geometry and beam-pipe misalignment. Finally, the expected dynamic multipoles in the RCS magnets are estimated and their implications for beam dynamics and polarization preservation are discussed.

43 PARTICLE ACCELERATORS↗
DOE OSTI2021

Natively Periodic Fast Multipole Method: Approximating the Optimal Green’s Function

The fast multipole method (FMM) obeys periodic boundary conditions "natively" if it uses a periodic Green's function for computing the multipole expansion in the interaction zone of each FMM oct-tree node. One can define the "optimal" Green's function for such a method that results in the numerical solution that converges to the equivalent particle-mesh (PM) solution in the limit of sufficiently high order of multipoles. A discrete functional equation for the optimal Green's function can be derived, but is not practically useful as methods for its solution are not known. Instead, this paper presents an approximation for the optimal Green's function that is accurate to better than 10 -3 in ${L}_{\mathrm{MAX}}$ norm and 10 -4 in L 2 norm for practically useful multipole counts. Such an approximately optimal Green's function offers a practical way for implementing the FMM with periodic boundary conditions natively, without the need to compute lattice sums or to rely on hybrid FMM-PM approaches.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
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↗
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 OSTI2017

Atom-partitioned multipole expansions for electrostatic potential boundary conditions

Applications such as grid-based real-space density functional theory (DFT) use the Poisson equation to compute electrostatics. However, the expected long tail of the electrostatic potential requires either the use of a large and costly outer domain or Dirichlet boundary conditions estimated via multipole expansion. We find that the oft-used single-center spherical multipole expansion is only appropriate for isotropic mesh domains such as spheres and cubes. In this work, we introduce a method suitable for high aspect ratio meshes whereby the charge density is partitioned into atomic domains and multipoles are computed for each domain. While this approach is moderately more expensive than a single-center expansion, it is numerically stable and still a small fraction of the overall cost of a DFT calculation. The net result is that when high aspect ratio systems are being studied, form-fitted meshes can now be used in lieu of cubic meshes to gain computational speedup.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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 OSTI2016

Tunable multipole resonances in plasmonic crystals made by four-beam holographic lithography

Plasmonic nanostructures confine light to sub-wavelength scales, resulting in drastically enhanced light-matter interactions. Recent interest has focused on controlled symmetry breaking to create higher-order multipole plasmonic modes that store electromagnetic energy more efficiently than dipole modes. Here we demonstrate that four-beam holographic lithography enables fabrication of large-area plasmonic crystals with near-field coupled plasmons as well as deliberately broken symmetry to sustain multipole modes and Fano-resonances. Compared with the spectrally broad dipole modes we demonstrate an order of magnitude improved Q-factors (Q = 21) when the quadrupole mode is activated. We further demonstrate continuous tuning of the Fano-resonances using the polarization state of the incident light beam. The demonstrated technique opens possibilities to extend the rich physics of multipole plasmonic modes to wafer-scale applications that demand low-cost and high-throughput.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

A single-site multipole model for liquid water

Accurate and efficient empirical potential energy models that describe the atomistic interactions between water molecules in the liquid phase are essential for computer simulations of many problems in physics, chemistry, and biology, especially when long length or time scales are important. However, while models with non-polarizable partial charges at four or five sites in a water molecule give remarkably good values for certain properties, deficiencies have been noted in other properties and increasing the number of sites decreases computational efficiency. An alternate approach is to utilize a multipole expansion of the electrostatic potential due to the molecular charge distribution, which is exact outside the charge distribution in the limits of infinite distances or infinite orders of multipoles while partial charges are a qualitative representation of electron density as point charges. Here, a single-site multipole model of water is presented, which is as fast computationally as three-site models but is also more accurate than four- and five-site models. The dipole, quadrupole, and octupole moments are from quantum mechanical–molecular mechanical calculations so that they account for the average polarization in the liquid phase, and represent both the in-plane and out-of-plane electrostatic potentials of a water molecule in the liquid phase. This model gives accurate thermodynamic, dynamic, and dielectric properties at 298 K and 1 atm, as well as good temperature and pressure dependence of these properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
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↗
DOE OSTI2017

Application of the inverse fast multipole method as a preconditioner in a 3D Helmholtz boundary element method

Here we investigate an efficient preconditioning of iterative methods (such as GMRES) for solving dense linear systems Ax = b that follow from a boundary element method (BEM) for the 3D Helmholtz equation, focusing on the low-frequency regime. While matrix–vector products in GMRES can be accelerated through the low-frequency fast multipole method (LFFMM), the BEM often remains computationally expensive due to the large number of GMRES iterations. We propose the application of the inverse fast multipole method (IFMM) as a preconditioner to accelerate the convergence of GMRES. The IFMM is in essence an approximate direct solver that uses a multilevel hierarchical decomposition and low-rank approximations. The proposed IFMM-based preconditioning has a tunable parameter ε that balances the cost to construct a preconditioner M, which is an approximation of A -1 , and the cost to perform the iterative process by means of M. Namely, using a small (respectively, large) value of ε takes a long (respectively, short) time to construct M, while the number of iterations can be small (respectively, large). A comprehensive set of numerical examples involving various boundary value problems with complicated geometries and mixed boundary conditions is presented to validate the efficiency of the proposed method. We show that the IFMM preconditioner (with a nearly optimal ε of 10 -2 ) clearly outperforms some common preconditioners for the BEM, achieving 1.2–10.8 times speed-up of the computations, in particular when the scale of the underlying scatterer is about five wavelengths or more. In addition, the IFMM preconditioner is capable of solving complicated problems (in a reasonable amount of time) that BD preconditioner can not.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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↗