Algorithm 1018: FaVeST—Fast Vector Spherical Harmonic Transforms

Vector spherical harmonics on the unit sphere of ℝ 3 have broad applications in geophysics, quantum mechanics, and astrophysics. In the representation of a tangent vector field, one needs to evaluate the expansion and the Fourier coefficients of vector spherical harmonics. In this article, we develop fast algorithms (FaVeST) for vector spherical harmonic transforms on these evaluations. The forward FaVeST evaluates the Fourier coefficients and has a computational cost proportional to N log √ N for N number of evaluation points. The adjoint FaVeST, which evaluates a linear combination of vector spherical harmonics with a degree up to ⊡ M for M evaluation points, has cost proportional to M log √ M . Numerical examples of simulated tangent fields illustrate the accuracy, efficiency, and stability of FaVeST.

Inertial Waves in a Rotating Spherical Shell with Homogeneous Boundary Conditions

We find the analytical form of inertial waves in an incompressible, rotating fluid constrained by concentric inner and outer spherical surfaces with homogeneous boundary conditions on the normal components of velocity and vorticity. These fields are represented by Galerkin expansions whose basis consists of toroidal and poloidal vector functions, i.e., products and curls of products of spherical Bessel functions and vector spherical harmonics. These vector basis functions also satisfy the Helmholtz equation and this has the benefit of providing each basis function with a well-defined wavenumber. Eigenmodes and associated eigenfrequencies are determined for both the ideal and dissipative cases. These eigenmodes are formed from linear combinations of the Galerkin expansion basis functions. The system is truncated to numerically study inertial wave structure, varying the number of eigenmodes. The largest system considered in detail is a 25 eigenmode system and a graphical depiction is presented of the five lowest dissipation eigenmodes, all of which are non-oscillatory. These results may be useful in understanding data produced by numerical simulations of fluid and magnetofluid turbulence in a spherical shell that use a Galerkin, toroidal–poloidal basis as well as qualitative features of liquids confined by a spherical shell.

Spherical harmonic based noise rejection and neuronal sampling with multi-axis OPMs

In this study we explore the interference rejection and spatial sampling properties of multi-axis Optically Pumped Magnetometer (OPM) data. We use both vector spherical harmonics and eigenspectra to quantify how well an array can separate neuronal signal from environmental interference while adequately sampling the entire cortex. We found that triaxial OPMs have superb noise rejection properties allowing for very high orders of interference (L=6) to be accounted for while minimally affecting the neural space (2dB attenuation for a 60-sensor triaxial system). To adequately model the signals arising from the cortex, we show that at least 11th order (143 spatial degrees of freedom) irregular solid harmonics or 95 eigenvectors of the lead field are needed to model the neural space for OPM data (regardless of number of axes measured). This can be adequately sampled with 75-100 equidistant triaxial sensors (225-300 channels) or 200 equidistant radial channels. In other words, ordering the same number of channels in triaxial (rather than purely radial) configuration gives significant advantages not only in terms of external noise rejection but also minimizes cost, weight and cross-talk.

Negative optical force field on supercavitating titanium nitride nanoparticles by a single plane wave

A pulling motion of supercavitating plasmonic nanoparticle (NP) by a single plane wave has received attention for the fundamental physics and potential applications in various fields (e.g., bio-applications, nanofabrication, and nanorobotics). Here, the supercavitating NP depicts a state where a nanobubble encapsulates the NP, which can be formed via the photo-thermal heating process in a liquid. In this letter, we theoretically study the optical force on a supercavitating titanium nitride (TiN) NP by a single plane wave at near-infrared wavelengths to explore optical conditions that can potentially initiate the backward motion of the NP against the wave-propagating direction. An analysis with vector spherical harmonics is used to quantify the optical force on the NP efficiently. Next, the vector field line of the optical force is introduced to visualize the light-driven motion of the NP in a nanobubble. Finally, we characterize the vector field lines at various optical conditions (e.g., various sizes of NP and nanobubble, and wavelength), and we find a suitable window of the optical state which can potentially activate the backward motion of the supercavitating TiN NP.

Total angular momenta quantization of dielectric sphere modes

Spherical particles both dielectric and metallic are essential building blocks in nanophotonics. During the recent rapid development of Mie-tronic — nanophotonics devices heavily using various features of the Mie-resonances — the deep fundamental investigation of the eigenmodes of such particles by using the novel tools is still relevant and currently important. Moreover, eigenmodes of a sphere are closely related to the Vector Spherical Harmonics (VSH) which are widely used in the multipolar decomposition to analyze less symmetric structures. In this work, we study in detail the canonical spin and angular momenta (AM), helicity, and other properties of the eigenmodes of dielectric (nondispersive) and metallic (dispersive) spheres. We show that the canonical momentum density of the AM is quantized and has a close relation to the quantum picture of a single photon. Our work provides a solid platform for future studies and applications of the AM transfer from near fields of spherical particles to the matter in its vicinity.

Three-dimensional DKP oscillator in a curved Snyder space

The Snyder–de Sitter model is an extension of the Snyder model to a de Sitter background. It is called triply special relativity (TSR) because it is based on three fundamental parameters: speed of light, Planck mass and cosmological constant. In this paper, we study the three-dimensional DKP oscillator for spin-0 and spin-1 in the framework of Snyder–de Sitter algebra in momentum space. By using the technique of vector spherical harmonics the energy spectrum and the corresponding eigenfunctions are obtained for the both cases.

Global estimation of ionospheric drivers during extreme storms

<p>During geomagnetic storms, the space environment can be drastically altered as the plasma in the upper atmosphere, or ionosphere, moves globally. This plasma redistribution is mainly caused by storm-time electric fields, but another important driver of the velocity of the ions in the plasma is the neutral winds. These winds refer to the movement of the neutral particles that are part of the thermospheric layer of the atmosphere, that can drag the plasma. Geomagnetic storms increase the neutral winds, due to the heating of the thermosphere that comes from the storm. In this study we want to understand how these ionospheric drivers affect the ionosphere behavior because, among other reasons, during geomagnetic storms the plasma can refract and diffract trans-ionospheric signals and, consequently, can cause problems in the navigation systems such as GNSS (Global Navigation Satellite System)/GPS (Global Positioning System) that use the information from the signals.</p><p>In this work, our objective is to estimate the electric fields and neutral winds globally during a geomagnetic storm. Global GNSS TEC (total electron content) measurements are ingested by the Ionospheric Data Assimilation 4-Dimensional (IDA4D) algorithm [1], whose output is the electron density rate over a grid at different time steps during a geomagnetic storm. The density rates are treated as “observations” in EMPIRE (Estimating Model Parameters from Ionospheric Reverse Engineering), which is a data assimilation algorithm based on the plasma continuity equation [2,3,4]. Then, the EMPIRE “observations” are used to estimate corrections to the electric field and neutral winds by solving a Kalman filter. To study these drivers with EMPIRE, basis functions are used to describe them. For the global potential field, spherical harmonics are used.</p><p>To have a global estimation of the neutral winds, we introduce vector spherical harmonics as the basis function for the first time in EMPIRE. The vector spherical harmonics are used to model orthogonal components of neutral wind in the zonal (east-west) and meridional (north-south) directions. EMPIRE’s Kalman filter needs the error covariance of the vector spherical harmonics decomposition. To calculate it, the basis function is fitted to the model HWM14 (Horizonal Wind Model) values of the neutral winds and the error between the fitting and the model is studied. Later, we study the global potential field and global neutral winds over time to understand how much each driver contributes to the plasma redistribution during the geomagnetic storm on October 25<sup>th</sup> 2011. We compare the results to FPI (Fabry-Perot Interferometer) neutral winds measurements to validate the results.   </p><p>[1] G.S.Bust, G.Crowley, T.W.Garner, T.L.G.II, R.W.Meggs, C.N.Mitchell, P.S.J.Spencer, P.Yin, and B.Zapfe, Four-dimensional gps imaging of space weather storms, Space Weather, 5 (2007),  doi:10.1029/2006SW000237.</p><p>[2] D.S.Miladinovich, S.Datta-Barua, G.S.Bust, and J.J.Makela, Assimilation of thermospheric measurements for ionosphere-thermosphere state estimation, Radio Science, 51 (2016).</p><p>[3] D.S.Miladinovich, S.Datta-Barua, A.Lopez, S. Zhang, and G.S.Bust, Assimilation of gnss measurements for estimation of high-latitude convection processes, Space Weather, 18 (2020).</p><p>[4] G.S.Bust and S.Datta-Barua, Scientific investigations using ida4d and empire, in Modeling the Ionosphere-Thermosphere System, J. Huba, R. Schunk, and G. Khazanov, eds., John Wiley & Sons, Ltd, 1 ed., 2014.</p>