Discrete Newtonian Cosmology

In this paper we lay down the foundations for a purely Newtonian theory of cosmology, valid at scales small compared with the Hubble radius, using only Newtonian point particles acted on by gravity and a possible cosmological term. We describe the cosmological background which is given by an exact solution of the equations of motion in which the particles expand homothetically with their comoving positions constituting a central configuration. We point out, using previous work, that an important class of central configurations are homogeneous and isotropic, thus justifying the usual assumptions of elementary treatments. The scale factor is shown to satisfy the standard Raychaudhuri and Friedmann equations without making any fluid dynamic or continuum approximations. Since we make no commitment as to the identity of the point particles, our results are valid for cold dark matter, galaxies, or clusters of galaxies. In future publications we plan to discuss perturbations of our cosmological background from the point particle viewpoint laid down in this paper and show consistency with much standard theory usually obtained by more complicated and conceptually less clear continuum methods. Apart from its potential use in large scale structure studies, we believe that out approach has great pedagogic advantages over existing elementary treatments of the expanding universe, since it requires no use of general relativity or continuum mechanics but concentrates on the basic physics: Newton's laws for gravitationally interacting particles.Comment: 33 pages; typos fixed, references added, some clarification

Dyadic Green's Functions and Guided Surface Waves for a Surface Conductivity Model of Graphene

An exact solution is obtained for the electromagnetic field due to an electric current in the presence of a surface conductivity model of graphene. The graphene is represented by an infinitesimally-thin, local and isotropic two-sided conductivity surface. The field is obtained in terms of dyadic Green's functions represented as Sommerfeld integrals. The solution of plane-wave reflection and transmission is presented, and surface wave propagation along graphene is studied via the poles of the Sommerfeld integrals. For isolated graphene characterized by complex surface conductivity, a proper transverse-electric (TE) surface wave exists if and only if the imaginary part of conductivity is positive (associated with interband conductivity), and a proper transverse-magnetic (TM) surface wave exists when the imaginary part of conductivity is negative (associated with intraband conductivity). By tuning the chemical potential at infrared frequencies, the sign of the imaginary part of conductivity can be varied, allowing for some control over surface wave properties.Comment: 9 figure

The Cooperative VAS Program with the Marshall Space Flight Center

Work was divided between the analysis/forecast model development and evaluation of the impact of satellite data in mesoscale numerical weather prediction (NWP), development of the Multispectral Atmospheric Mapping Sensor (MAMS), and other related research. The Cooperative Institute for Meteorological Satellite Studies (CIMSS) Synoptic Scale Model (SSM) has progressed from a relatively basic analysis/forecast system to a package which includes such features as nonlinear vertical mode initialization, comprehensive Planetary Boundary Layer (PBL) physics, and the core of a fully four-dimensional data assimilation package. The MAMS effort has produced a calibrated visible and infrared sensor that produces imager at high spatial resolution. The MAMS was developed in order to study small scale atmospheric moisture variability, to monitor and classify clouds, and to investigate the role of surface characteristics in the production of clouds, precipitation, and severe storms

Evolution of planetesimal velocities

A self-consistent set of equations for the velocity evolution of a general planetesimal population is presented. The equations are given in a form convenient for calculations of the early stages of planetary accumulation when it is necessary to model the planetesimal swarm by methods of gas dynamics, rather than follow the orbital evolution of individual bodies. Steady state velocities of a simple planetesimal population consisting of two different sizes of bodies are calculated. Dynamical friction is found to be an important mechanism for transferring kinetic energy from the larger planetesimals to the smaller ones. When the small planetesimals are relatively abundant, gas drag and inelastic collisions among the smaller bodies are of comparable importance for dissipating energy from the population

Investigation of the large scale coherent structure in a jet and its relevance to jet noise

A study was conducted to determine the causes of aircraft noise in large jet aircraft. It was determined that jet noise varies strongly with velocity and that significant pure tones are generated by rotor-stator interaction in the jet engines. An objective method for deducing the large eddy structure in a large jet is described. The provisions of lighthill's theory are analyzed and applied to investigating the nature of jet noise. There is considerable evidence that a large scale coherent structure exists in a jet and that this structure can play a major role in sound radiation. Mathematical models are developed to define the parameters of orthogonal decomposition, finite extent velocity field, homogeneous fields, and periodic velocity fields

The Structure and C=C Vibrational Frequencies of the all- trans Polyenes C2nH2n+2(n=2-15), C2nH2n(Me)2(n=2-13), and C2nH2n(tert-Butyl)2(n=2-5): Computational Results

Carbon-carbon bond lengths and C=C vibrational frequencies are reported for the linear, all-trans unsubstituted C2nH2n+2 (n=2-15), methyl capped C2nH2nMe2 (n=2-13), and tert-butyl capped C2nH2n(tert-butyl)2 (n=2-5) polyenes (C2h) calculated at the B3LYP/6-311++G(d,p) level. The C=C/C-C bond length alternation remains evident at this level for the unsubstituted and methyl capped polyenes as the chain length increases; the center-most difference in the length of the C-C/C=C bonds is ~0.06 Å for C30H32 and C26H26Me2. The Ag, in-phase, harmonic C=C Raman frequency for the unsubstituted polyenes decreases from 1699.2 cm-1 (n = 2) to 1528.9 cm-1 (n=15); the anharmonic frequency decreases from 1651.5 cm-1 (n = 2) to 1547.7 cm-1 (n = 8). The harmonic C=C frequency for the methyl capped polyenes decreases from 1717.9 cm-1 (n = 2) to 1539.6 cm- 1 (n= 13), and the anharmonic C=C frequency decreases from 1675.0 cm-1 (n = 2) to 1562.8 cm-1 (n = 7)