4,256 research outputs found
A Probablistic Origin for a New Class of Bivariate Polynomials
We present here a probabilistic approach to the generation of new polynomials
in two discrete variables. This extends our earlier work on the 'classical'
orthogonal polynomials in a previously unexplored direction, resulting in the
discovery of an exactly soluble eigenvalue problem corresponding to a bivariate
Markov chain with a transition kernel formed by a convolution of simple
binomial and trinomial distributions. The solution of the relevant
eigenfunction problem, giving the spectral resolution of the kernel, leads to
what we believe to be a new class of orthogonal polynomials in two discrete
variables. Possibilities for the extension of this approach are discussed.Comment: This is a contribution to the Special Issue on Dunkl Operators and
Related Topics, published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA
VLTI/MIDI 10 micron interferometry of the forming massive star W33A
We report on resolved interferometric observations with VLTI/MIDI of the
massive young stellar object (MYSO) W33A. The MIDI observations deliver
spectrally dispersed visibilities with values between 0.03 and 0.06, for a
baseline of 45m over the wavelength range 8-13 micron. The visibilities
indicate that W33A has a FWHM size of approximately 120AU (0.030'') at 8 micron
which increases to 240AU at 13 micron, scales previously unexplored among
MYSOs. This observed trend is consistent with the temperature falling off with
distance. 1D dust radiative transfer models are simultaneously fit to the
visibility spectrum, the strong silicate feature and the shape of the mid
infrared spectral energy distribution (SED). For any powerlaw density
distribution, we find that the sizes (as implied by the visibilities) and the
stellar luminosity are incompatible. A reduction to a third of W33A's
previously adopted luminosity is required to match the visibilities; such a
reduction is consistent with new high resolution 70 micron data from Spitzer's
MIPSGAL survey. We obtain best fits for models with shallow dust density
distributions of r^(-0.5) and r^(-1.0) and for increased optical depth in the
silicate feature produced by decreasing the ISM ratio of graphite to silicates
and using optical grain properties by Ossenkopf et al. (1992).Comment: 4 pages, 4 figures. Accepted for ApJ letter
IR Dust Bubbles: Probing the Detailed Structure and Young Massive Stellar Populations of Galactic HII Regions
We present an analysis of wind-blown, parsec-sized, mid-infrared bubbles and
associated star-formation using GLIMPSE/IRAC, MIPSGAL/MIPS and MAGPIS/VLA
surveys. Three bubbles from the Churchwell et al. (2006) catalog were selected.
The relative distribution of the ionized gas (based on 20 cm emission), PAH
emission (based on 8 um, 5.8 um and lack of 4.5 um emission) and hot dust (24
um emission) are compared. At the center of each bubble there is a region
containing ionized gas and hot dust, surrounded by PAHs. We identify the likely
source(s) of the stellar wind and ionizing flux producing each bubble based
upon SED fitting to numerical hot stellar photosphere models. Candidate YSOs
are also identified using SED fitting, including several sites of possible
triggered star formation.Comment: 37 pages, 17 figure
Some Further Results for the Stationary Points and Dynamics of Supercooled Liquids
We present some new theoretical and computational results for the stationary
points of bulk systems. First we demonstrate how the potential energy surface
can be partitioned into catchment basins associated with every stationary point
using a combination of Newton-Raphson and eigenvector-following techniques.
Numerical results are presented for a 256-atom supercell representation of a
binary Lennard-Jones system. We then derive analytical formulae for the number
of stationary points as a function of both system size and the Hessian index,
using a framework based upon weakly interacting subsystems. This analysis
reveals a simple relation between the total number of stationary points, the
number of local minima, and the number of transition states connected on
average to each minimum. Finally we calculate two measures of localisation for
the displacements corresponding to Hessian eigenvectors in samples of
stationary points obtained from the Newton-Raphson-based geometry optimisation
scheme. Systematic differences are found between the properties of eigenvectors
corresponding to positive and negative Hessian eigenvalues, and localised
character is most pronounced for stationary points with low values of the
Hessian index.Comment: 16 pages, 2 figure
A Branching Time Model of CSP
I present a branching time model of CSP that is finer than all other models
of CSP proposed thus far. It is obtained by taking a semantic equivalence from
the linear time - branching time spectrum, namely divergence-preserving coupled
similarity, and showing that it is a congruence for the operators of CSP. This
equivalence belongs to the bisimulation family of semantic equivalences, in the
sense that on transition systems without internal actions it coincides with
strong bisimilarity. Nevertheless, enough of the equational laws of CSP remain
to obtain a complete axiomatisation for closed, recursion-free terms.Comment: Dedicated to Bill Roscoe, on the occasion of his 60th birthda
Velocity dependence of friction and Kramers relaxation rates
We study the influence of the velocity dependence of friction on the escape
of a Brownian particle from the deep potential well (,
is the barrier height, is the Boltzmann constant, is the
bath temperature). The bath-induced relaxation is treated within the Rayleigh
model (a heavy particle of mass in the bath of light particles of mass
) up to the terms of the order of ,
. The term is equivalent to the Fokker-Planck
dissipative operator, and the term is responsible for the
velocity dependence of friction. As expected, the correction to the Kramers
escape rate in the overdamped limit is proportional to and is
small. The corresponding correction in the underdamped limit is proportional to
and is not necessarily small. We thus suggest that
the effects due to the velocity-dependent friction may be of considerable
importance in determining the rate of escape of an under- and moderately damped
Brownian particle from a deep potential well, while they are of minor
importance for an overdamped particle
Vermiforichnus (Polychaeta) Borings in Paraspirifer Bownockeri (Brachiopoda: Devonian)
Author Institution: Department of Geology, Bowling Green UniversityShells of Paraspirifer bownockeri (Stewart) from the Silica Formation, Middle Devonian of northwestern Ohio, commonly contain numerous borings of a polychaete worm forming the endolithic trace fossil Vermiforichnus clarki Cameron (1969a) which can be exposed by acidizing the specimens. The borings are most abundant on the brachial valve, and their surface openings tend to be concentrated along major growth lines thence extending dominantly in the general direction of the beaks of the valves. Infestations of the polychaete occurred at 2 different time intervals as indicated by the spacing of the borings on 2 major growth lines with renewed shell growth between them. Growth of the host was severely reduced immediately following the infestation and in some areas damage to the mantle caused deformation in the shell of the host
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