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At least 379 records · Page 21

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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.↗

NASA NTRS1998

The Dynamical Evolution of the Earth-Moon Progenitors: Results and Interpretation - 2

Substantial evidence indicates that the Earth-Moon system formed about 100 m.y. after the oldest meteorites and that the inner solar system had five terrestrial planets for several tens of millions of years before the hypothesized Moon-forming impact. We present and discuss some results from a series of N-body integrations in which the mass ratio of the Earth-Moon progenitors is 8:1 or 1:1. We want to know if it is plausible to have the Earth-Moon progenitors collide between 8 m.y. and 200 m.y. after the other planets had formed and to have the resulting system look "similar" to the solar system. If a collision occurs, the integrations tell us which two bodies collide and the time of the collision. We also determine the angular momentum deficit (AMD) of the resulting terrestrial planets. Additionally, we calculate several parameters of the collision. We use the AMD of the terrestrial planets to compare the resulting system to our own. The AMD or a planet is the difference between its orbital angular momentum and its orbital angular momentum if it were in a circular orbit with zero inclination.

Rivera, E.↗

DOE OSTI2022

Efficient computation of N -point correlation functions in D dimensions

We present efficient algorithms for computing the N-point correlation functions (NPCFs) of random fields in arbitrary D-dimensional homogeneous and isotropic spaces. Such statistics appear throughout the physical sciences and provide a natural tool to describe stochastic processes. Typically, algorithms for computing the NPCF components have $\mathscr O$(n N ) complexity (for a dataset containing n particles); their application is thus computationally infeasible unless N is small. By projecting the statistic onto a suitably defined angular basis, we show that the estimators can be written in a separable form, with complexity $\mathscr O$(n 2 ) or $\mathscr O$(n g log n g ) if evaluated using a Fast Fourier Transform on a grid of size n g . Our decomposition is built upon the D-dimensional hyperspherical harmonics; these form a complete basis on the (D – 1) sphere and are intrinsically related to angular momentum operators. Concatenation of (N – 1) such harmonics gives states of definite combined angular momentum, forming a natural separable basis for the NPCF. As N and D grow, the number of basis components quickly becomes large, providing a practical limitation to this (and all other) approaches: However, the dimensionality is greatly reduced in the presence of symmetries; for example, isotropic correlation functions require only states of zero combined angular momentum. We provide a Julia package implementing our estimators and show how they can be applied to a variety of scenarios within cosmology and fluid dynamics. The efficiency of such estimators will allow higher-order correlators to become a standard tool in the analysis of random fields.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1991

Numerical models of giant planet formation with rotation

A 1D quasi-spherical approximation is presently used under the assumption of hydrostatic equilibrium to model giant-planet formation processes that encompass the accretion and transport of angular momentum for both radiative and convective zones. These calculations have been conducted up to masses comparable to those of Saturn. Angular momentum transport is strong, leading to strong concentration of angular momentum in the outer convective zones which develop envelope masses greater than 30 earth masses. When the models are allowed to contract near the calculation's end, the ratio of centrifugal force to gravity at the outer radius rises sufficiently to validate the quasi-spherical approximation.

Korycansky, D. G.↗

NASA NTRS1984

Ballistic transport in Saturn's rings - An analytic theory

Ejecta from impacts of micrometeoroids on Saturn's ring particles will, in most cases, remain in orbit about Saturn and eventually be reaccreted by the rings, possibly at a different radial location. The resulting mass transport has been suggested as the cause of some of the features observed in Saturn's rings. Previous attempts to model this transport have used numerical simulations which have not included the effects of the angular momentum transport coincident with mass transport. An analytical model for ballistic mass transport in Saturn's rings is developed. The model includes the effects of angular momentum advection and shows that the net material movement due to angular momentum advection is comparable to that caused by direct ballistic mass transport.

Lissauer, J. J.↗

NASA NTRS1993

Algorithm for IAU north poles and rotation parameters

In 1970 the International Astronomical Union (IAU) defined any object's north pole to be that axis of rotation which lies north of the solar system's invariable plane. A competing definition in widespread use at some institutions followed the 'right hand rule' whereby the 'north' axis of rotation was generally said to be that of the rotational angular momentum. In the case of the latter definition, the planet Neptune and its satellite Triton would have their 'north' poles in opposite hemispheres because Triton's angular momentum vector is in the hemisphere opposite from that of Neptune's rotation angular momentum. The IAU resolutions have been somewhat controversial in some quarters ever since their adoption. A Working Group has periodically updated the recommended values of planet and satellite poles and rotation rates in accordance with the IAU definition of north and the IAU definition of prime meridian. Neither system is completely satisfactory in the perception of all scientists, and some confusion has been generated by publishing data in the two different systems. In this paper we review the IAU definitions of north and of the location of prime meridian and we present the algorithm which has been employed in determining the rotational parameters of the natural satellites. The IAU definition of the prime meridian contains some ambiguities which in practice have been 'specified' by the numerical values published by the IAU working group but which have not yet been explicitly documented. The purpose of this paper is to explicitly document the algorithm employed by the IAU working group in specifying satellite poles and rotation rates.

Lieske, J. H.↗

DOE OSTI2023

Exact quantization and analytic continuation

In this paper we give a streamlined derivation of the exact quantization condition (EQC) on the quantum periods of the Schrödinger problem in one dimension with a general polynomial potential, based on Wronskian relations. We further generalize the EQC to potentials with a regular singularity, describing spherical symmetric quantum mechanical systems in a given angular momentum sector. We show that the thermodynamic Bethe ansatz (TBA) equations that govern the quantum periods undergo nontrivial monodromies as the angular momentum is analytically continued between integer values in the complex plane. The TBA equations together with the EQC are checked numerically against Hamiltonian truncation at real angular momenta and couplings, and are used to explore the analytic continuation of the spectrum on the complex angular momentum plane in examples.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Phonon Helicity Induced by Electronic Berry Curvature in Dirac Materials

In two-dimensional insulators with time-reversal (TR) symmetry, a nonzero local Berry curvature of low-energy massive Dirac fermions can give rise to nontrivial spin and charge responses, even though the integral of the Berry curvature over all occupied states is zero. In this Letter, we present a new effect induced by the electronic Berry curvature. By studying electron-phonon interactions in BaMnSb2, a prototype two-dimensional Dirac material possessing two TR-related massive Dirac cones, we find that the nonzero local Berry curvature of electrons can induce a phonon angular momentum. The direction of this phonon angular momentum is locked to the phonon propagation direction, and thus we refer to it as “phonon helicity” in a way that is reminiscent of electron helicity in spin-orbit-coupled electronic systems. We discuss possible experimental probes of such phonon helicity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1993

Molecular processes in comets

Classical trajectory calculations of the cross sections for vibrational and rotational energy exchange in direct and reactive collisions of hydrogen atoms and hydrogen molecules have been carried out. To test the sensitivity, three potential energy surfaces have been used. For the exchange transitions which occur at small internuclear distances, the rate coefficients for the three surfaces agree quite well. For the direct transitions, there are significant differences for the pure rotational transitions from j=0 to 2 and from j=1 to j=3 in which there is no change in vibration. For higher j the differences tend to disappear, suggesting that the rotational angular momentum can couple to the orbital angular momentum to overcome the centrifugal barrier. Complete numerically exact quantum mechanical calculations for the process in which vJ changes have been performed. Dr. M. A'Hearn has provided data on the fluorescent population of the NH rotational and fine-structure levels from which we should be able to predict accurate photodissociation lifetimes. The distribution rate of C2 is being investigated. A review of H3(+) in terrestrial and extraterrestrial environments was prepared for a volume of Advances in Atomic, Molecular and Optical Physics.

Dalgarno, A.↗

NASA NTRS1994

Yet another model of soft gamma repeaters

We develop a model of soft gamma repeaters (SGRs) in which a supernova leaves planets orbiting a neutron star in intersecting orbits. These planets will collide in approximately 10(exp 4) yr if their orbits are coplanar. Some fragments of debris lose their angular momentum in the collision and fall onto the neutron star, producing a SGR. The initial accretion of matter left by the collision with essntially no angular momentum may produce a superburst like that of 1979 March 5, while debris fragments which later lose their angular momentum produce an irregular but non-Poissonian pattern of smaller bursts resembling those observed in spectrum and duration.

Katz, J. I.↗

NASA NTRS1991

Three-dimensional simulations of black hole tori

The global hydrodynamic nonaxisymmetric instabilities in thick constant angular momentum (l) accretion gas tori in orbit around a Schwarzschild black hole are investigated via 2D and 3D numerical simulations. A radially-wide torus is found to develop and m = 1 nonaxisymmetric density perturbation near the pressure maximum and a trailing spiral wave that extends through the outer part of the torus. This global wave transports angular momentum through the torus, causing the average angular momentum distribution to evolve slowly away from l = constant. The unstable mode drives an accretion flow from the torus into the black hole. The role of accretion is investigated by modeling a wide torus with an inner boundary at the cusp of the Schwarzschild effective potential. In such a torus, accretion is present throughout the evolution; only modest unstable mode growth is observed, and saturation occurs at low amplitude. Comparison simulations performed in the torus equatorial plane show qualitative similarities between the 2D and 3D system, although the 3D modes have a function dependence on height.

Hawley, John F.↗

NASA NTRS1982

Sharp edges of planetary rings

The ring systems of Saturn and Uranus exhibit several sharp edges, across which the optical depth drops from order unity to essentially zero. At least two and perhaps all of these features are associated with the location of orbital resonances between a satellite and the ring particles. It is remarkable that the optical depth varies on a distance scale which is much finer than that over which angular momentum can be transferred between a satellite and the ring material. The important features of this phenomenon are: (1) a perturbed band of width Delta a/a of about (satellite mass/planetary mass) to the 1/2 power adjacent to the edge within which the angular momentum transfer occurs, (2) streamlines perturbed such that the angular momentum luminosity decreases smoothly across the band to zero at the edge even though the optical depth remains constant, and (3) dynamical equilibrium requires a relation between the random velocity, the rate of deformation and the optical depth.

Borderies, N.↗

NASA NTRS1989

The ages of globular cluster stars - Effects of rotation on pre-main-sequence, main-sequence, and turnoff evolution

Evolutionary sequences for low-metallicity stars (Z ranging from 0.001 to 0.0001) to study the effects of internal stellar rotation on the evolutionary time scales in the pre-main sequence, the main sequence (MS), and around the MS turnoff. Although a substantial amount of angular momentum remains in the interior, rotation is only a minor perturbation on the structure and ages of globular cluster stars. Even models with large initial angular momenta have MS lifetimes that are within 1 percent of those of standard models of the same mass and composition. Therefore, rotation does not affect age estimates of globular clusters from isochrone fitting. Furthermore, the models suggest that because rotation is not likely to affect horizontal-branch (HB) morphology, it does not affect significantly age estimates from the Delta-V method. Nevertheless, the internal angular momentum in the models is consistent with observations of surface rotational velocities on the HB, which require the preservation of a large reservoir of internal angular momentum.

Deliyannis, Constantine P.↗

NASA NTRS1988

Attitude motion of a non-attitude-controlled cylindrical satellite

In 1985, two non-attitude-controlled satellites were each placed in a low earth orbit by the Scout Launch Vehicle. The satellites were cylindrical in shape and contained reservoirs of hydrazine fuel. Three-axis magnetometer measurements, telemetered in real time, were used to derive the attitude motion of each satellite. Algorithms are generated to deduce possible orientations (and magnitudes) of each vehicle's angular momentum for each telemetry contact. To resolve ambiguities at each contact, a force model was derived to simulate the significant long-term effects of magnetic, gravity gradient, and aerodynamic torques on the angular momentum of the vehicles. The histories of the orientation and magnitude of the angular momentum are illustrated.

Wilkinson, C. K.↗

NASA NTRS1980

Disk-satellite interactions

The rate at which angular momentum and energy are transferred between a disk and a satellite which orbit a central mass is calculated. It is shown that the angular momentum and energy transfer at Lindblad resonances tends to increase the satellite's orbit to lowest order in eccentricity, whereas the transfer at corotation resonances tends to decrease it. The results are applied to the interaction between Jupiter and the protoplanetary disk. The angular momentum transfer is shown to be so rapid that substantial changes in both the structure of the disk and the orbit of Jupiter must have taken place on a time scale of a few thousand years.

Goldreich, P.↗

NASA NTRS1989

Accretion discs around young stellar objects and the proto-sun

Observed IR and UV excesses have widely been interpreted as signatures for accretion disks around young stellar objects. Analyses of the observed properties of these disks are important for the investigation of star formation as well as the dynamics of the protoplanetary disk out of which the solar system was formed. Accretion-disk theories suggest that evolution of protoplanetary disks is determined by the efficiency of angular momentum transport. During the formation stages, the disk dynamics are regulated by mixing of infalling material and disk gas. In the outermost regions of the disk, self-gravity may promote the growth of nonaxisymmetric perturbations which can transfer angular momentum outwards. After infall has ceased, convectively driven turbulence can redistribute angular momentum with an evolutionary timescale of 0.1 - 1 Myr. Convection in protoplanetary disks may eventually be stabilized by surface heating as the disk material is depleted.

Lin, D. N. C.↗

DOE OSTI2020

Effect of the orientation of Rydberg atoms on their collisional ionization cross section

Collisional ionization between two Rydberg atoms in relative motion is examined. A classical trajectory Monte Carlo method is used to determine the cross sections associated with Penning ionization. The dependence of the ionization cross section on the magnitude and the direction of orbital angular momentum of the electrons and the direction of the Laplace-Runge-Lenz vector of the electrons is studied. For a given magnitude of angular momentum, there can exist a difference of a factor of up to ~2.5 in the ionization cross section between the orientations with the highest and the lowest ionization cross section. As a result, the case of exchange ionization is examined and its dependence on the magnitude of angular momentum is studied.

74 ATOMIC AND MOLECULAR PHYSICS↗

NASA NTRS2008

Compact Dielectric-Rod White-Light Delay Lines

Optical delay lines of a proposed type would be made from rods of such dielectric materials as calcium fluoride, fused silica, or sapphire. These would offer advantages over prior optical delay lines, as summarized below. Optical delay lines are key components of opto-electronic microwave oscillators, narrow-band opto-electronic microwave filters, evanescent-field optical biochemical detectors, and some Fourier-Transform spectrum analyzers. Heretofore, optical delay lines used in such applications have been of two types: resonators and coiled long optical fibers, both of which have disadvantages: Resonators are compact, but excitation must be provided by narrow-band lasers. Wide-band (including noisy) laser light cannot be coupled efficiently to narrow-band resonators. When light is coupled into a narrowband resonator from a source of reasonably high power, a significant amount of optical energy circulates within the resonator, causing nonlinear loss and significant noise. Typically, a coil-type optical delay line is made of fused-silica fiber, which exhibits fundamental loss. To overcome the limit imposed by the optical loss in fused silica, it would be necessary to use fibers having crystalline cores. Although space is saved by winding fibers into coils, fiber-coil delay lines are still inconveniently bulky. The proposed compact dielectric-rod delay lines would exploit the special class of non-diffracting light beams that are denoted Bessel beams because their amplitudes are proportional to Bessel functions of the radii from their central axes. High-order Bessel beams can have large values of angular momentum. They can be generated with the help of whispering-gallery-mode optical resonators, as described, for example, in "Simplified Generation of High-Angular-Momentum Light Beams" (NPO-42965) NASA Tech Briefs, Vol. 31, No. 3 (March 2007), page 8a. In a delay line according to the proposal, the dielectric rod would be dimensioned to function as a multimode waveguide. Suitably chosen high-angular-momentum modes in such a waveguide exhibit low group velocity (hence, long delay) and no resonance. Such a delay line could perform well at any wavelength or range of wavelengths within the transparency wavelength band of the dielectric material, and the maximum possible group delay achievable through suitable design would be limited only by the optical loss in the rod material.

Maleki, Lute↗