Capabilities and applications of the Program to Optimize Simulated Trajectories (POST). Program summary document

The capabilities and applications of the three-degree-of-freedom (3DOF) version and the six-degree-of-freedom (6DOF) version of the Program to Optimize Simulated Trajectories (POST) are summarized. The document supplements the detailed program manuals by providing additional information that motivates and clarifies basic capabilities, input procedures, applications and computer requirements of these programs. The information will enable prospective users to evaluate the programs, and to determine if they are applicable to their problems. Enough information is given to enable managerial personnel to evaluate the capabilities of the programs and describes the POST structure, formulation, input and output procedures, sample cases, and computer requirements. The report also provides answers to basic questions concerning planet and vehicle modeling, simulation accuracy, optimization capabilities, and general input rules. Several sample cases are presented

Twisted K-theory and K-theory of bundle gerbes

In this note we introduce the notion of bundle gerbe K-theory and investigate the relation to twisted K-theory. We provide some examples. Possible applications of bundle gerbe K-theory to the classification of D-brane charges in non-trivial backgrounds are discussed.Comment: 29 pages, corrected typos, added references, included new section on twisted Chern character in non-torsion cas

On the Existence of the Quantum Action

We have previously proposed a conjecture stating that quantum mechanical transition amplitudes can be parametrized in terms of a quantum action. Here we give a proof of the conjecture and establish the existance of a local quantum action in the case of imaginary time in the Feynman-Kac limit (when temperature goes to zero). Moreover we discuss some symmetry properties of the quantum action.Comment: revised version, Text (LaTeX

Contribution of brown dwarfs and white dwarfs to recent microlensing observations and to the halo mass budget

We examine the recent results of the MACHO collaboration towards the Large Magellanic Cloud (Alcock et al. 1996) in terms of a halo brown dwarf or white dwarf population. The possibility for most of the microlensing events to be due to brown dwarfs is totally excluded by large-scale kinematic properties. The white dwarf scenario is examined in details in the context of the most recent white dwarf cooling theory (Segretain et al. 1994) which includes explicitely the extra source of energy due to carbon-oxygen differentiation at crystallization, and the subsequent Debye cooling. We show that the observational constraints arising from the luminosity function of high-velocity white dwarfs in the solar neighborhood and from the recent HST deep field counts are consistent with a white dwarf contribution to the halo missing mass as large as 50 %, provided i) an IMF strongly peaked around 1.7 Msol and ii) a halo age older than 18 Gyr.Comment: 14 pages, 2 Postscript figures, to be published in Astrophysical Journal Letters, minor revision in tex

Hydromagnetic constraints on deep zonal flow in the giant planets

The observed zonal flows of the giant planets will, if they penetrate below the visible atmosphere, interact significantly with the planetary magnetic field outside the metallized core. The appropriate measure of this interaction is the Chandrasekhar number Q = H^2 /4πρνα^2 λ (H = radial component of the magnetic field, ν = eddy viscosity, λ = magnetic diffusivity, α^-1 = length scale on which λ varies); at depths where Q ≳ 1, the velocity will be forced to oscillate on a small length scale or decay to zero. We estimate the conductivity due to semiconduction in H_2 (Jupiter, Saturn) and ionization in H_(2)0 (Uranus, Neptune) as a function of depth; the value λ ≈ 10^10 cm^2 s^-1 needed for Q = 1 is readily obtained well outside the metallic core (where A ≈ 10^2 cm^2 s^-1). These assertions are quantified by a simple model of the equatorial zonal jet in which the flow is assumed uniform on cylinders concentric with the spin axis, and viscous and magnetic torques on each cylinder are balanced. We solve this "Taylor constraint" simultaneously with the dynamo equation to obtain the velocity and magnetic field in the equatorial plane. With this model we reproduce the widely differing jet widths of Jupiter and Saturn (though not the flow at very high or low latitudes) using v = 2500 cm^2 s^-1, consistent with the requirement that viscous dissipation not exceed the specific luminosity. A model Uranian jet consistent with the limited Voyager data can also be constructed, with appropriately smaller v, but only if one assumes a two-layer interior. We tentatively predict a wide Neptunian jet. For Saturn (but not Jupiter or Uranus) the model has a large magnetic Reynolds number where Q = 1 and hence exhibits substantial axisymmetrization of the field in the equatorial plane. This effect may or may not persist at higher latitudes. The one-dimensional model presented is only a first step. Variation of the velocity and magnetic field parallel to the spin axis must be modeled in order to answer several important questions, including: (1) What is the behavior of flows at high latitudes, whose Taylor cylinders are interrupted by the region with Q > 1? (2) To what extent is differential rotation in the envelope responsible for the spinaxisymmetry of Saturn's magnetic field

A time-dependent Hartree-Fock study of triple-alpha dynamics

Time-dependent Hartree-Fock calculations have been performed for fusion reactions of He-4 + He-4 -> Be*-8, followed by He-4 + Be*-8 . Depending on the orientation of the initial state, a linear chain vibrational state or a triangular vibration is found in 12C, with transitions between these states observed. The vibrations of the linear chain state and the triangular state occur at ~9 and 4 MeV respectively.Comment: Re-submission to SciPost Proceedings following referee comment

Evolutionary calculations of phase separation in crystallizing white dwarf stars

We present an exploration of the significance of Carbon/Oxygen phase separation in white dwarf stars in the context of self-consistent evolutionary calculations. Because phase separation can potentially increase the calculated ages of the oldest white dwarfs, it can affect the age of the Galactic disk as derived from the downturn in the white dwarf luminosity function. We find that the largest possible increase in ages due to phase separation is 1.5 Gyr, with a most likely value of approximately 0.6 Gyr, depending on the parameters of our white dwarf models. The most important factors influencing the size of this delay are the total stellar mass, the initial composition profile, and the phase diagram assumed for crystallization. We find a maximum age delay in models with masses of 0.6 solar masses, which is near the peak in the observed white dwarf mass distribution. We find that varying the opacities (via the metallicity) has little effect on the calculated age delays. In the context of Galactic evolution, age estimates for the oldest Galactic globular clusters range from 11.5 to 16 Gyr, and depend on a variety of parameters. In addition, a 4 to 6 Gyr delay is expected between the formation of the globular clusters and that of the Galactic thin disk, while the observed white dwarf luminosity function gives an age estimate for the thin disk of 9.5 +/-1.0 Gyr, without including the effect of phase separation. Using the above numbers, we see that phase separation could add between 0 to 3 Gyr to the white dwarf ages and still be consistent with the overall picture of Galaxy formation. Our calculated maximum value of 1.5 Gyr fits within these bounds, as does our best guess value of 0.6 Gyr.Comment: 13 total pages, 8 figures, 3 tables, accepted for publication in the Astrophysical Journal on May 25, 199

Infusing literacy and math into a socioculturally responsive summer science camp

Presentation given by Georgia Southern faculty members Alma Stevenson and Shelli Casler-Failing at National Youth At-Risk Conference, Savannah, GA

Program to Optimize Simulated Trajectories (POST). Volume 1: Formulation manual

A general purpose FORTRAN program for simulating and optimizing point mass trajectories (POST) of aerospace vehicles is described. The equations and the numerical techniques used in the program are documented. Topics discussed include: coordinate systems, planet model, trajectory simulation, auxiliary calculations, and targeting and optimization