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NASA NTRS1989

Semi-Lagrangian integration of a gridpoint shallow water model on the sphere

A stable, semi-Lagrangian, semi-implicit, two-time-level, gridpoint integration scheme for the shallow water equations on the sphere is presented. A rotated spherical coordinate system is used to integrate the equations of motion at each gridpoint poleward of a certain latitude, thus overcoming problems associated with the polar singularity. The results of medium term integrations of large scale test patterns using a long time step are presented.

Mcdonald, A.↗

NASA NTRS2000

Reduction of Sample Rotation in Electrostatic Levitation

In many containerless processing systems, control of sample rotation is an important issue. Sample rotation is even more important for microgravity containerless processing systems, where the centrifugal acceleration can approach 1 g for even a small rotation rate. Prior work on rotation control by Rhim focused on driving the sample rotation at a controlled rate for droplet dynamics experiments and measurement of electrical conductivity. His technique allows controlled, fast rotation, but for many microgravity experiments the goal is zero rotation. To minimize sample rotation, two approaches are apparent: first, to identify and balance or eliminate the driving forces for undesired sample rotation, or second, implement a feedback-based rotation control loop in parallel with the position control loop. In this work, we have taken the first approach. To minimize sample rotation, the simplest approach is to identify and balance or eliminate the driving forces for undesired sample rotation. Our experiments show that the dominant driving force for rotation of machined Zr spheres in the MSFC ESL is photon pressure from the heating laser. Experimental results showing the correlation between heating power and torque are compared to theoretical predictions, and a strategy for minimizing the torque due to photon pressure is presented.

Hyers, R. W↗

NASA NTRS2003

The Effect of Surface Topography on the Nonlinear Dynamics of Rossby Waves

Boussinesq convection in rotating systems attracts a sustained attention of the fluid dynamics community, because it has intricate non-linear dynamics (Cross & Hohenberg 1993) and plays an important role in geophysical and astrophysical applications, such as the motion of the liquid outer core of Earth, the Red Spot in Jupiter, the giant cells in the Sun etc. (Alridge et al. 1990). A fundamental distinction between the real geo- and astrophysical problems and the idealized laboratory studies is that natural systems are inhomogeneous (Alridge et al. 1990). Heterogeneities modulate the flow and influence significantly the dynamics of convective patterns (Alridge et al. 1990; Hide 1971). The effect of modulations on pattern formation and transition to turbulence in Boussinesq convection is far from being completely understood (Cross & Hohenberg 1993; Aranson & Kramer 2002). It is generally accepted that in the liquid outer core of the Earth the transport of the angular momentum and internal heat occurs via thermal Rossby waves (Zhang et al. 2001; Kuang & Bloxham 1999). These waves been visualized in laboratory experiments in rotating liquid-filled spheres and concentric spherical shells (Zhang et al. 2001; Kuang & Bloxham 1999). The basic dynamical features of Rossby waves have been reproduced in a cylindrical annulus, a system much simpler than the spherical ones (Busse & Or 1986; Or & Busse 1987). For convection in a cylindrical annulus, the fluid motion is two-dimensional, and gravity is replaced by a centrifugal force, (Busse & Or 1986; Or & Busse 1987). Hide (1971) has suggested that the momentum and heat transport in the core might be influenced significantly by so-called bumps, which are heterogeneities on the mantle-core boundary. To model the effect of surface topography on the transport of momentum and energy in the liquid outer core of the Earth, Bell & Soward (1996), Herrmann & Busse (1998) and Westerburg & Busse (2001) have studied the nonlinear dynamics of thermal Rossby waves in a cylindrical annulus with azimuthally modulated height.

Abarzhi, S. I.↗

NASA NTRS1986

Coating a Sphere With Evaporated Metal

In vacuum coating apparatus, metal evaporated onto sphere from small source located some distance away. Sphere held in path of metal vapor while rotated about axis that rocks back and forth. One tilting motion particularly easy to produce is sinusoidal rocking with frequency much lower than rotational frequency. Apparatus developed for coating single-crystal sapphire spheres with niobium.

Strayer, D. M.↗

DOE OSTI2022

Reducing Memory Consumption in Calico with Shared Memory

This document details the work to reduce memory consumption in Calico. Calico is SimTools’ Constructive Solid Geometry (CSG) and geometry painting library. It is primarily used to paint material volume fractions in the Eulerian meshes of the physics codes. Calico provides point-in-body checks for the geometry supplied by an Oso model, which are then aggregated by the host codes. In addition, Calico can be used to build Oso models and is used by Ingen for that purpose. Oso models, and thus Calico, provide support for various CSG primitives such as spheres, cylinders, surfaces generated by rotating tabular curve data, and STL files as well as binary combinations of those primitives. Prior to refactoring Calico will run out of memory on CTS-1 machines when 36 MPI ranks are used per node when reading STL models on the order of 1.5 GB. This limitation is a bottleneck in designer workflow. This problem has been alleviated through the use of data structures to both reduce memory consumption and to leverage MPI-3 shared memory. This report details the data structures targeted for refactoring in Calico, the methods and implementation details for reducing memory consumption and leveraging shared memory, and results for one test problem. Results show a memory reduction when loading a 1 GB STL file by a factor of 27.5, from 93.4 to 3.4 GB.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1980

Nonlinear axially symmetric circulations in a nearly inviscid atmosphere

The structure of certain axially symmetric circulations in a stably stratified, differentially heated, rotating Boussinesq fluid on a sphere is analyzed. A simple approximate theory (similar to that introduced by Schneider (1977)) is developed for the case in which the fluid is sufficiently inviscid that the poleward flow in the Hadley cell is nearly angular momentum conserving. The theory predicts the width of the Hadley cell, the total poleward heat flux, the latitude of the upper level jet in the zonal wind, and the distribution of surface easterlies and westerlies. Fundamental differences between such nearly inviscid circulations and the more commonly studied viscous axisymmetric flows are emphasized. The theory is checked against numerical solutions to the model equations.

Held, I. M.↗

NASA NTRS1942

The stability of laminar flow past a sphere

As a contribution to the problem of turbulence on a surface of rotation, the method of small oscillation is applied to the flow past a sphere. It was found that the method developed for two-dimensional flow is applicable without modifications. The frictional layer in the vicinity of the stagnation point of a surface of rotation is less stable against small two-dimensional disturbances than in the stagnation point itself, as proved from an analysis of the velocity distribution made by Homann.

Pretsch, J↗

DOE OSTI2022

Bridging the Bondi and Event Horizon Scales: 3D GRMHD Simulations Reveal X-shaped Radio Galaxy Morphology

X-shaped radio galaxies (XRGs) produce misaligned X-shaped jet pairs and make up ≲10% of radio galaxies. XRGs are thought to emerge in galaxies featuring a binary supermassive black hole (SMBH), SMBH merger, or large-scale ambient medium asymmetry. We demonstrate that XRG morphology can naturally form without such special, preexisting conditions. Our 3D general-relativistic magnetohydrodynamic (GRMHD) simulation for the first time follows magnetized rotating gas from outside the SMBH sphere of influence of radius RB to the SMBH of gravitational radius Rg at the largest scale separation, RB/Rg = 103, to date. Initially, our axisymmetric system of constant-density hot gas contains a weak vertical magnetic field and rotates in the equatorial plane of a rapidly spinning SMBH. We seed the gas with small-scale 2% level pressure perturbations. Infalling gas forms an accretion disk, and the SMBH launches relativistically magnetized collimated jets reaching well outside RB. Under the pressure of the infalling gas, the jets intermittently turn on and off, erratically wobble, and inflate pairs of cavities in different directions, resembling an X-shaped jet morphology. Synthetic X-ray images reveal multiple pairs of jet-powered shocks and cavities. Large-scale magnetic flux accumulates on the SMBH, becomes dynamically important, and leads to a magnetically arrested disk state. The SMBH accretes at 2% of the Bondi rate ($\dot{M}\simeq 2.4\times {10}^{-3}{M}_{\odot }\,{\mathrm{yr}}^{-1}$ for M87*) and launches twin jets at η = 150% efficiency. These jets are powerful enough (P jets ≃ 2 × 10 44 erg s -1 ) to escape along the SMBH spin axis and end the short-lived intermittent jet state, whose transient nature can account for the rarity of XRGs.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

One-dimensional neutron diffraction from layered graphite: Reciprocal space structure and grating behavior

In this work we report observations of one-dimensional neutron diffraction from highly oriented pyrolytic graphite (HOPG), where the scattering angle varies continuously with incident angle following classical grating-like behavior. The 2D polycrystalline structure of HOPG—with highly aligned layers along the 𝑐 axis but random in-plane rotations—creates planes of scattering intensity in reciprocal space at 𝑄 𝑐 =𝑛⁢(2⁢𝜋/𝑑) where 𝑑=3.35Å is the interlayer spacing. As the Ewald sphere sweeps through reciprocal space during sample rotation, it continuously intersects these planes, producing the observed angular dispersion. We observe both first-order (𝑛=1) and second-order (𝑛=2) diffraction at conventional scattering angles (25°–70°), with peak positions that remain temperature-independent between 10 K and 294 K and follow quantitative agreement with momentum conservation 𝑄 𝑐 =𝑘⁢[sin⁡𝜓−sin⁡𝜓 𝑓 ]=𝑛⁢(2⁢𝜋/𝑑). X-ray diffraction under similar conditions shows no comparable behavior, confirming that sharp nuclear-vacuum contrast is essential. While diffraction intensities are weak (∼10 −6 of Bragg peaks), the observations demonstrate how the interplay of atomic-scale periodicity, nuclear contrast, and structural disorder enables observation of continuous diffraction curves at thermal neutron wavelengths, illustrating how HOPG's unique microstructure determines its scattering properties beyond conventional Bragg diffraction.

2-dimensional systems↗

NASA NTRS1993

Near-Threshold Rovibrational Excitation of HF by Electron Impact

The pronounced threshold peaks found in cross sections for electron-impact excitation of the vibrational levels of HF have been studied using an R-matrix method, in which electron exchange, correlation effects and polarization are included. Vibration is modelled inside the R-matrix sphere using the energy-modified adiabatic phase matrix method (EMAP). Rotation of the target molecule is treated outside the R-matrix sphere, using the frame transformation method. The external rovibronic close-coupling equations are solved by analytic methods. Analysis of the multichannel threshold structures indicates that the peaks found for rovibrational excitation of nu = 1 can be interpreted as virtual states while those for nu = 2 correspond to nuclear-excited Feshbach resonances. These two different results correspond simply to a change of sign of a small parameter that is determined by the threshold analysis. Whereas the overall shapes of the excitation peaks agree with earlier theoretical results, we have found detailed rotational fine structures for scattering energies on the order of the rotational constant above and below the opening of the vibrational channels. The partial and total cross sections for rovibrational state-to-state transitions in the energy region of the peaks are analysed. Characteristic cusp structures and excitation peaks are found at the rovibrational thresholds for transitions with small angular momentum transfer (Delta)j =0, 1 and 2. Differential cross sections are similar to recent measurements. These experimental data do not show the relatively sharp rise at the vibrational thresholds indicated by theory. Theory and experiment are in good agreement for the shape and magnitude of the angular dependence of cross sections for rovibrational state-to-state transitions, especially at larger energies.

Thummel, Helmar T.↗

NASA NTRS2010

Evaluating Descent and Ascent Trajectories Near Non-Spherical Bodies

Spacecraft landing on small bodies pass through regions where conventional gravitation formulations using exterior spherical harmonics are inaccurate. An investigation shows that a formulation using interior solid spherical harmonics might be satisfactory. Interior spherical harmonic expansions are usable inside an imaginary, empty sphere. For this application, such a sphere could be positioned in empty space above the intended landing site and rotating with the body. When the spacecraft is inside this sphere, the interior harmonic expansion would be used instead of the conventional, exterior harmonic expansion. Coefficients can be determined by a least-squares fit to gravitation measurements synthesized from conventional formulations. Due to their unfamiliarity, recurrences for interior, as well as exterior, expansions are derived. Hotine's technique for partial derivatives of exterior spherical harmonics is extended to interior harmonics.

Werner, Robert A.↗

NASA NTRS1973

Spacecraft attitude sensor

A system for sensing the attitude of a spacecraft includes a pair of optical scanners having a relatively narrow field of view rotating about the spacecraft x-y plane. The spacecraft rotates about its z axis at a relatively high angular velocity while one scanner rotates at low velocity, whereby a panoramic sweep of the entire celestial sphere is derived from the scanner. In the alternative, the scanner rotates at a relatively high angular velocity about the x-y plane while the spacecraft rotates at an extremely low rate or at zero angular velocity relative to its z axis to provide a rotating horizon scan. The positions of the scanners about the x-y plane are read out to assist in a determination of attitude. While the satellite is spinning at a relatively high angular velocity, the angular positions of the bodies detected by the scanners are determined relative to the sun by providing a sun detector having a field of view different from the scanners.

Davidson, A. C.↗

DOE OSTI2021

Geodesic motion around hairy black holes

In a recent paper Ovalle et al. (2021) it has been obtained new static black hole solutions with primary hairs by the Gravitational Decoupling. In this work we either study the geodesic motion of massive and massless particles around those solutions and restrict the values of the primary hairs by observational data. In particular, we obtain the effective potential, the innermost stable circular orbits, the marginally bounded orbit, and the periastron advance for time-like geodesics. In order to restrict the values taken by the primary hairs we explore their relationship with the rotation parameter of the Kerr black hole giving the same innermost stable circular orbit radius and give the numerical values for the supermassive black holes at Ark 564 and NGC 1365. The photon sphere and the impact parameter associated to null geodesics are also discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

A conservative discontinuous Galerkin algorithm for particle kinetics on smooth manifolds

A novel, conservative discontinuous Galerkin algorithm is presented for particle kinetics on manifolds. The motion of particles on the manifold is represented using both canonical and non-canonical Hamiltonian formulations. Our schemes apply to both formulations, but the canonical formulation results in a particularly efficient scheme that also conserves particle density and energy exactly. The collisionless update is coupled to a Bhatnagar-Gross-Krook (BGK) collision operator that provides a simplified model for relaxation to local thermodynamic equilibrium. An iterative scheme is constructed to ensure collisional invariants (density, momentum and energy) are preserved numerically. Rotation of the manifold is incorporated by modifying the Hamiltonian while ensuring a canonical formulation. Several test problems, including a kinetic version of the classical Sod shock problem, Kelvin-Helmholtz instability on the surfaces of a sphere and a hyperboloid, with and without rotations, are presented. A prospectus for further development of this approach to simulation of kinetic theory in general relativity is presented.

Discontinuous Galerkin↗

NASA NTRS1965

Unconventional inertial sensors.

Inertial sensors reviewing ring laser, electrostatic fluid sphere, magnetic resonance, superconductivity gyroscope, relativistic rotating tensor, vortex rate and quantum mechanical effect sensing

INERTIAL ACCELEROMETER↗

NASA NTRS1984

The Solid Model Geometry Generator (SMGG)

The Solid Model Geometry Generator (SMGG) system provides the capacity to model complex solid objects through the composition of primitive parts. The parts are specified through input of dimension and orientation parameters. The parts may later be edited, the model may be displayed (through a variety of display options), and the resulting geometry formatted for subsequent analysis. The SMGG system was originally constructed for use in the preliminary stages of space station and other spacecraft design. Because the system models a design through the use of basic shapes common to many solid objects and provides limited capabilities for producing irregularly shaped parts, it can be used for a variety of applications. Currently, seven primitive parts may be specified and produced through SMGG. These include boxes, spheres, cones, paraboloids, tori, and translationally or rotationally swept parts. Each part may be specified by the user through input of basic part dimensions and a local orientation. For example, a box is specified by its length, width, height and orientation in space (rotation, translation, and scaling).

Jones, K. H.↗

NASA NTRS1984

The collapse of the cores of slowly rotating isothermal clouds

A generalized model which accounts for the effects of initially uniform and slow rotation is defined for the spherical collapse of a singular isothermal sphere such as protosolar and binary nebulae. An initial unstable equilibrium state is described for a sound speed of 0.35 km/sec and a rotation rate of 10 to the -14th/sec for the molecular cloud surrounding the accreting core. The total angular momentum and mass of the inner cloud is set equal to solar system values. The evolution of the collapse is traced by applying a perturbation analysis to the similarity solution for a nonrotating condition, and matched asymptotic expansions solve the hydrodynamic equations. The model is concluded a valid tool for studying star and nebular disk formation.

Terebey, S.↗

NASA NTRS1999

Laser Induced Rotation of a Levitated Sample in Vacuum

A method of systematically controlling the rotational state of a sample levitated in a high vacuum using the photon pressure is described. A zirconium sphere was levitated in the high-temperature electrostatic levitator and it was rotated by irradiating it with a narrow beam of a high power laser on a spot off the center of mass.

laser induced rotation electrostatic levitator↗