SEARCH · Search NASA

Results for “generalized spherical functions”

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 73 records · Page 4

All sources NASA NTRS DOE OSTI

NASA NTRS1993

Wigner functions for nonclassical states of a collection of two-level atoms

The general theory of atomic angular momentum states is used to derive the Wigner distribution function for atomic angular momentum number states, coherent states, and squeezed states. These Wigner functions W(theta,phi) are represented as a pseudo-probability distribution in spherical coordinates theta and phi on the surface of a sphere of radius the square root of j(j +1) where j is the total angular momentum.

Agarwal, G. S.↗

DOE OSTI2021

Nanoparticle cellular internalization is not required for RNA delivery to mature plant leaves

Rapidly growing interest in the nanoparticle-mediated delivery of DNA and RNA to plants requires a better understanding of how nanoparticles and their cargoes translocate in plant tissues and into plant cells. However, little is known about how the size and shape of nanoparticles influence transport in plants and the delivery efficiency of their cargoes, limiting the development of nanotechnology in plant systems. In this study we employed non-biolistically delivered DNA-modified gold nanoparticles (AuNPs) of various sizes (5-20 nm) and shapes (spheres and rods) to systematically investigate their transport following infiltration into Nicotiana benthamiana leaves. Generally, smaller AuNPs demonstrated more rapid, higher and longer-lasting levels of association with plant cell walls compared with larger AuNPs. We observed internalization of rod-shaped but not spherical AuNPs into plant cells, yet, surprisingly, 10 nm spherical AuNPs functionalized with small-interfering RNA (siRNA) were the most efficient at siRNA delivery and inducing gene silencing in mature plant leaves. These results indicate the importance of nanoparticle size in efficient biomolecule delivery and, counterintuitively, demonstrate that efficient cargo delivery is possible and potentially optimal in the absence of nanoparticle cellular internalization. Additionally, our results highlight nanoparticle features of importance for transport within plant tissues, providing a mechanistic overview of how nanoparticles can be designed to achieve efficacious biocargo delivery for future developments in plant nanobiotechnology.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS1975

Review of aircraft noise propagation

The current state of knowledge about the propagation of aircraft noise was reviewed. The literature on the subject is surveyed and methods for predicting the most important and best understood propagation effects are presented. Available empirical data are examined and the data's general validity is assessed. The methods used to determine the loss of acoustic energy due to uniform spherical spreading, absorption in a homogeneous atmosphere, and absorption due to ground cover are presented. A procedure for determining ground induced absorption as a function of elevation angle between source and receiver is recommended. Other factors that affect propagation, such as refraction and scattering due to turbulence, which were found to be less important for predicting the propagation of aircraft noise, are also evaluated.

Putnam, T. W.↗

NASA NTRS1989

Theory of local thermal instability in spherical systems

The gasdynamical properties of local thermal instability in optically thin astrophysical plasmas as it occurs in spherical accretion and winds is investigated. In a medium characterized by both thermal and hydrostatic equilibrium, if the cooling function is not an explicit function of position and does not display isentropic thermal instability, then isobaric thermal instability by the Field criterion is present if and only if convective instability is present by the Schwarzschild criterion. In this case, thermal overstability cannot occur. Convective instability by the Schwarzschild criterion will also occur in accretion flows locally dominated by external heating or in marginally unbound, radiatively cooling outflows. A very general Lagrangian equation for the development of nonradial thermal instability in flows with spherical symmetry is derived and is solved analytically in certain regimes. The results are applied to cluster X-ray cooling flows.

Balbus, Steven A.↗

NASA NTRS2023

Estimating the Subsolar Magnetopause Position from Soft X-Ray Images Using a Low-Pass Image Filter

The Lunar Environment heliospheric X-ray Imager (LEXI) and Solar wind Magnetosphere Ionosphere Link Explorer (SMILE) missions will image the Earth’s dayside magnetopause and cusps in soft X-rays after their respective launches in the near future, to specify global magnetic reconnection modes for varying solar wind conditions. To support the success of these scientific missions, it is critical to develop techniques that extract the magnetopause locations from the observed soft X-ray images. In this research, we introduce a new geometric equation that calculates the subsolar magnetopause position ( R s ) from a satellite position, the look direction of the instrument, and the angle at which the X-ray emission is maximized. Two assumptions are used in this method: (1) The look direction where soft X-ray emissions are maximized lies tangent to the magnetopause, and (2) the magnetopause surface near the subsolar point is almost spherical and thus R s is nearly equal to the radius of the magnetopause curvature. We create synthetic soft X-ray images by using the Open Geospace General Circulation Model (OpenGGCM) global magnetohydrodynamic model, the galactic background, the instrument point spread function, and Poisson noise. We then apply the fast Fourier transform and Gaussian low-pass filters to the synthetic images to remove noise and obtain accurate look angles for the soft X-ray peaks. From the filtered images, we calculate R 2 and its accuracy for different LEXI locations, look directions, and solar wind densities by using the OpenGGCM subsolar magnetopause location as ground truth. Our method estimates R s with an accuracy of <0.3 R E when the solar wind density exceeds >10 cm -3 . The accuracy improves for greater solar wind densities and during southward interplanetary magnetic fields. The method captures the magnetopause motion during southward interplanetary magnetic field turnings. Consequently, the technique will enable quantitative analysis of the magnetopause motion and help reveal the dayside reconnection modes for dynamic solar wind conditions. This technique will support the LEXI and SMILE missions in achieving their scientific objectives.

Hyangpyo Kim↗

DOE OSTI2026

The impact of optical measurement techniques on measured aerosol particle size distributions

Ambient aerosol particle size distributions measured by the Ultra-High Sensitivity Aerosol Spectrometer (UHSAS) at various sites around the world exhibit modes at optical diameters near 600 nm and 850 nm. These modes are not present in concurrent measurements with the Grimm 11-D Optical Particle Counter (OPC). Here, in this study, we argue that these modes result from the optical measurement technique itself, and we explain why they appear in measurements by the UHSAS but not in those by the Grimm OPC. We construct computer models of the UHSAS and Grimm (“digital UHSAS” and “digital Grimm”) and use these to investigate the size distribution that would result from measurements of artificial aerosol particle size distributions that do not contain modes. The appearance of modes for the structureless incoming size distributions sampled by the digital UHSAS is explained by the nonlinear behavior of partial scattering cross sections of uniform spherical particles as a function of their diameter. The absence of modes in the digital Grimm is explained by the coarser size resolution of that instrument. Detailed analysis of the relationship between optical and geometric diameters for uniform spherical particles reveals two important results. First, these diameters generally have different numerical values for the same particle, and second, the relationship is nonlinear; thus, widths of size bins in terms of optical diameter differ from those in geometric diameter. These results explain the modes observed in the ambient size distributions and highlight concerns with attempts to create a merged size distribution by combining measurements from different instruments.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Electron Dynamics Within a MITL Containing a Load

In this paper, we derive the vacuum electric fields within specific cylindrically symmetric magnetically insulated transmission lines (MITLs) in the limit of an infinite speed of light for an arbitrary time-dependent current. We focus our attention on two types of MITLs: the radial MITL and a spherically curved MITL. We then simulate the motion of charged particles, such as electrons, present in these MITLs due to the vacuum fields. In general, the motion of charged particles due to the vacuum fields is highly nonlinear since the fields are nonlinear functions of spatial coordinates and depend on an arbitrary time-dependent current drive. Using guiding center theory, however, one can describe the gross particle kinetics using a combination of $\textbf {E} \times \textbf {B}$ and $\nabla B$ drifts. In addition, we compare our approximate inner MITL field models and particle kinetics with those from a fully electromagnetic simulation code. We find that the agreement between the approximate model and the electromagnetic simulations is excellent.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1976

Design of efficient stiffened shells of revolution

A method to produce efficient piecewise uniform stiffened shells of revolution is presented. The approach uses a first order differential equation formulation for the shell prebuckling and buckling analyses and the necessary conditions for an optimum design are derived by a variational approach. A variety of local yielding and buckling constraints and the general buckling constraint are included in the design process. The local constraints are treated by means of an interior penalty function and the general buckling load is treated by means of an exterior penalty function. This allows the general buckling constraint to be included in the design process only when it is violated. The self-adjoint nature of the prebuckling and buckling formulations is used to reduce the computational effort. Results for four conical shells and one spherical shell are given.

Majumder, D. K.↗

NASA NTRS1993

Empirical wind model for the middle and lower atmosphere. Part 2: Local time variations

The HWM90 thermospheric wind model was revised in the lower thermosphere and extended into the mesosphere and lower atmosphere to provide a single analytic model for calculating zonal and meridional wind profiles representative of the climatological average for various geophysical conditions. Local time variations in the mesosphere are derived from rocket soundings, incoherent scatter radar, MF radar, and meteor radar. Low-order spherical harmonics and Fourier series are used to describe these variations as a function of latitude and day of year with cubic spline interpolation in altitude. The model represents a smoothed compromise between the original data sources. Although agreement between various data sources is generally good, some systematic differences are noted. Overall root mean square differences between measured and model tidal components are on the order of 5 to 10 m/s.

Hedin, A. E.↗

NASA NTRS1999

A Spherical Earth Solution for TOA Lightning Location Retrieval

With the advent of high-speed digital computers, the method of chi square minimization is a highly practical means for analyzing a wide variety of (otherwise intractable) nonlinear inversion problems in applied mathematical physics. Little thought or effort is required to apply the chi square method to obtain quick and reasonable estimates of a solution, and the method offers a means to assess retrieval errors. Because the method is simple and practical it is sometimes hastily applied to problems that can be solved by formal analytic or quasi-analytic means. Presently, Global Atmospherics Inc. (GAI) finds the minimum of a chi square function to analyze time-of-arrival (TOA) and magnetic bearing data derived from the National Lightning Detection Network (NLDN); ellipsoidal Earth geometry is assumed. An analytic solution to this problem has not yet been attained, but the consideration and solving of less general problem statements might eventually lead to a final solution. In the present study, the problem of retrieving lightning ground-strike location on a spherical Earth surface using a network of 4 or more time-of-arrival (TOA) sensors is considered. It is shown that this problem has an analytic solution and therefore does not require the use of nonlinear estimation theory (such as the chi square method mentioned above). The mathematical robustness of the analytic solution is tested using computer-generated lightning sources and simulated TOA measurement errors. A quasi-analytic extension of the spherical Earth solution for an oblate spheroidal Earth geometry is considered in a related study. The incorporation of magnetic bearing information into these analytic solutions would lead to a general and elegant analytic retrieval scheme that would most likely replace the chi square estimation theory currently employed by Global Atmospherics Inc. (GAI).

Koshak, William J,↗

DOE OSTI2020

Landau quantization of multilayer graphene on a Haldane sphere

Here, we consider the problem of multilayer graphene on a Haldane sphere and determine the Landau level spectrum for this family of systems. This serves as a generalization of the Landau quantization problem of ordinary nonrelativistic Haldane sphere and spherical graphene, or Dirac-like particles on a sphere. The Hamiltonian is diagonalized in a concise algebraic fashion exploiting two mutually commuting SU(2) algebras of the problem. Additionally, using exact wave functions we demonstrate computation of Haldane pseudopotentials in the second Landau level. These exact solutions add to the current toolkits of the numerical studies on fractional quantum Hall effects in systems of graphite multilayers.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1996

Distortion Representation of Forecast Errors for Model Skill Assessment and Objective Analysis

We study a novel characterization of errors for numerical weather predictions. In its simplest form we decompose the error into a part attributable to phase errors and a remainder. The phase error is represented in the same fashion as a velocity field and will be required to vary slowly and smoothly with position. A general distortion representation allows for the displacement and a bias correction of forecast anomalies. In brief, the distortion is determined by minimizing the objective function by varying the displacement and bias correction fields. In the present project we use a global or hemispheric domain, and spherical harmonics to represent these fields. In this project we are initially focusing on the assessment application, restricted to a realistic but univariate 2-dimensional situation. Specifically we study the forecast errors of the 500 hPa geopotential height field for forecasts of the short and medium range. The forecasts are those of the Goddard Earth Observing System data assimilation system. Results presented show that the methodology works, that a large part of the total error may be explained by a distortion limited to triangular truncation at wavenumber 10, and that the remaining residual error contains mostly small spatial scales.

Hoffman, Ross N.↗

NASA NTRS1977

General relativity and satellite orbits - The motion of a test particle in the Schwarzschild metric

The motion of a satellite of negligible mass about a massive spherically symmetric object in a space of Schwarzschild geometry is calculated by using ordinary Newtonian methods for an inverse-square gravitational field acted upon by an inverse-cube disturbing function. The disturbing function is expressed in terms of the Keplerian elements of the orbit and substituted in the Lagrange planetary equations. The equations can be integrated to calculate the displacement in position of the satellite due to the relativistic potential. For example, the Beacon Explorer C satellite is found to be displaced by about 17.4 cm after one revolution. For Mercury the advance of the perihelion is about 85 km after one orbit, and the maximum periodic displacement is about 13 km.

Rubincam, D. P.↗

DOE OSTI2020

Final Focus Solenoid Design Considerations

Radiography utilizing intense relativistic electron beams requires a final focus magnet to produce a small beam spot on the x-ray conversion target. A solenoid magnet is generally used for the final focus magnet. This note addresses design considerations of the final focus solenoid that impact the spot size. The spot size on target is a function of the beam size entering the final focus magnet, the beam emittance and energy spread and spherical aberration inherent in a solenoid magnet. The present final focus solenoid designs for both Axis 1 and Axis 2 of the DARHT facility are evaluated. A new design is proposed for both Axis 1 and Axis 2.

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

Lorentzian OPE inversion formula: A geometric perspective

We give a new perspective on the Lorentzian operator product expansion inversion formula [S. Caron-Huot, Analyticity in spin in conformal theories, .; D. Simmons-Duffin, D. Stanford, and E. Witten, A spacetime derivation of the Lorentzian OPE inversion formula, .], building on [P. Agarwal , companion paper, Embedding space approach to Lorentzian CFT amplitudes and causal spherical functions, .]. We introduce an “auxiliary” fourpoint function that can be related to the traditionally defined ones via a Radon transform. The Mellin amplitudes associated with this auxiliary function can be shown to be equivalent to the conventional partial wave amplitudes. This has the intuitive geometrical meaning of a generalization of the projection-slice theorem. Published by the American Physical Society 2025

Agarwal, Pulkit (ORCID:0000000346581691)↗

DOE OSTI2023

Quantifying molecular deformation in polymer melts by a generalized Zimm plot approach

The Zimm plot has been widely used to characterize the molecular dimensions of polymers from small-angle scattering experiments, where the reciprocal intensity is analyzed as a function of the square of the magnitude of the scattering wavevector Q. Here, this work explores the benefits of analyzing the reciprocal scattering intensity from deformed polymers, extending the original Zimm plot to anisotropic materials. In the small-angle limit, a tensorial extension of the Guinier law is found for the gyration tensor and the reciprocal single-chain structure factor. In the high-Q limit, application of the spherical harmonic expansion technique to the reciprocal structure factor permits direct model-independent analysis of spatially dependent molecular deformation of polymers. Additionally, the contributions from high-order spherical harmonics become insignificant in the reciprocal-intensity representation. The proposed generalized Zimm plot approach is demonstrated computationally with the affine deformation model and the Rouse model, and experimentally with small-angle neutron scattering measurements of deformed polystyrene melts.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Crystal mechanics-based thermo-elastic constitutive modeling of orthorhombic uranium using generalized spherical harmonics and first-order bounding theories

In earlier works, a mathematical procedure for invertible microstructure-property linkages was developed using computationally efficient spectral methods for polycrystalline cubic and hexagonal metals. This paper formulates such invertible microstructure–property linkages for orthorhombic polycrystalline metals relying on the generalized spherical harmonics (GSH) spectral basis. The procedure is used to compute property closures of orthorhombic polycrystals. The closures represent the complete set of theoretically possible combinations of effective properties for a selected material. The procedure relies on the first-order bounding theories and considers orientation distribution functions (ODFs) as the main microstructural descriptor influencing homogenized properties. Numerous examples of these closures involving second-rank thermal expansion and fourth-rank elastic stiffness tensorial properties over a broad range of temperatures are presented for α-uranium (α-U). In doing so, certain key properties of these closures are exploited to facilitate their computation with drastically reduced computational effort. Along with the recently developed GSH-based interpolation procedure for ODFs from coarsely spaced experimental measurement grids to finely spaced finite element mesh resolution grids presented in Barrett et al., the developed computationally efficient ODF-effective property linkages are used to establish a crystal mechanics-based simulation framework coupled with the finite element method (FEM). The ODF dependent thermal expansion and elastic stiffness tensors are efficiently calculated at every integration point and used by the FEM to predict the overall distortion of a hemispherical part made of α-U during heating. In conclusion, it is shown that the developed framework can be used to simulate microstructurally heterogeneous components under thermo-mechanical loadings in a computationally efficient manner.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Stability of hairy black holes in shift-symmetric scalar-tensor theories via the effective field theory approach

Shift-symmetric Horndeski theories admit an interesting class of Schwarzschild-de Sitter black hole solutions exhibiting time-dependent scalar hair. The properties of these solutions may be studied via a bottom-up effective field theory (EFT) based on the background symmetries. This is in part possible by making use of a convenient coordinate choice — Lemaître-type coordinates — in which the profile of the Horndeski scalar field is linear in the relevant time coordinate. We construct this EFT, and use it to understand the stability of hairy black holes in shift-symmetric Horndeski theories, providing a set of constraints that the otherwise-free functions appearing in the Horndeski Lagrangian must satisfy in order to admit stable black hole solutions. The EFT is analyzed in the decoupling limit to understand potential sources of instability. Further, we also perform a complete analysis of the EFT with odd-parity linear perturbations around general spherically symmetric space-time.

79 ASTRONOMY AND ASTROPHYSICS↗