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