30,330 research outputs found
The d=6, (2,0)-tensor multiplet coupled to self-dual strings
We show that the central charges that group theory allows in the (2,0)
supersymmetry translations algebra arise from a string and a 3-brane by
commuting two supercharges. We show that the net force between two such
parallel strings vanishes. We show that all the coupling constants are fixed
numbers, due to supersymmetry, and self-duality of the three-form field
strength. We obtain a charge quantization for the self-dual field strength, and
show that when compactifying on a two-torus, it reduces to the usual
quantization condition of N=4 SYM with gauge group SU(2), and with coupling
constant and theta angle given by the tau-parameter of the two-torus, provided
that we pick that chiral theory which corresponds to a theta function with zero
characteristics, as expected on manifolds of this form.Comment: 18 pages, reference adde
Jacobi Elliptic Functions and the Complete Solution to the Bead on the Hoop Problem
Jacobi elliptic functions are flexible functions that appear in a variety of
problems in physics and engineering. We introduce and describe important
features of these functions and present a physical example from classical
mechanics where they appear: a bead on a spinning hoop. We determine the
complete analytical solution for the motion of a bead on the driven hoop for
arbitrary initial conditions and parameter values.Comment: Accepted for publication in American Journal of Physics. 9 pages, 6
figure
R-process and alpha-elements in the Galactic disk: Kinematic correlations
Recent studies of elemental abundances in the Galactic halo and in the
Galactic disk have underscored the possibility to kinematically separate
different Galactic subcomponents. Correlations between the galactocentric
rotation velocity and various element ratios were found, providing an important
means to link different tracers of star formation and metal enrichment to the
Galactic components of different origin (collapse vs. accretion). In the
present work we determine stellar kinematics for a sample of 124 disk stars,
which we derive from their orbits based on radial velocities and proper motions
from the the literature. Our stars form a subsample of the Edvardsson et al.
(1993) sample and we concentrate on three main tracers: (i) Europium as an
r-process element is predominantly produced in Supernovae of type II. (ii)
Likewise, alpha-elements, such as Ca, Si, Mg, are synthesised in SNe II,
contrary to iron, which is being produced preferentially in SNe Ia. (iii) The
s-process element Barium is a measure of the relative contribution of AGB stars
to the Galaxy's enrichment history and has been shown to be an indicator for
distinguishing between thin and thick disk stars. All such studies reveal,
basically, that stars with low galactocentric rotational velocity tend to have
high abundances of alpha-elements and Eu, but lower abundances of, e.g., Ba.Comment: 5 pages, 2 figures, Poster contribution to appear in "Planets To
Cosmology: Essential Science In Hubble's Final Years", proceedings of the May
2004 STScI Symposium, M. Livio (ed.), (Cambridge University Press
Characteristic and Ehrhart polynomials
Let A be a subspace arrangement and let chi(A,t) be the characteristic
polynomial of its intersection lattice L(A). We show that if the subspaces in A
are taken from L(B_n), where B_n is the type B Weyl arrangement, then chi(A,t)
counts a certain set of lattice points. One can use this result to study the
partial factorization of chi(A,t) over the integers and the coefficients of its
expansion in various bases for the polynomial ring R[t]. Next we prove that the
characteristic polynomial of any Weyl hyperplane arrangement can be expressed
in terms of an Ehrhart quasi-polynomial for its affine Weyl chamber. Note that
our first result deals with all subspace arrangements embedded in B_n while the
second deals with all finite Weyl groups but only their hyperplane
arrangements.Comment: 16 pages, 1 figure, Latex, to be published in J. Alg. Combin. see
related papers at http://www.math.msu.edu/~saga
The total mass of super-Brownian motion upon exiting balls and Sheu's compact support condition
We study the total mass of a d-dimensional super-Brownian motion as it first
exits an increasing sequence of balls. The process of the total mass is a
time-inhomogeneous continuous-state branching process, where the increasing
radii of the balls are taken as the time parameter. We are able to characterise
its time-dependent branching mechanism and show that it converges, as time goes
to infinity, towards the branching mechanism of the total mass of a
one-dimensional super-Brownian motion as it first crosses above an increasing
sequence of levels. Our results allow us to identify the compact support
criterion given in Sheu (1994) as a classical Grey condition (1974) for the
aforementioned limiting branching mechanism.Comment: 28 pages, 2 figure
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