Mid-IR period-magnitude relations for AGB stars

Asymptotic Giant Branch variables are found to obey period-luminosity relations in the mid-IR similar to those seen at K_S (2.14 microns), even at 24 microns where emission from circumstellar dust is expected to be dominant. Their loci in the M, logP diagrams are essentially the same for the LMC and for NGC6522 in spite of different ages and metallicities. There is no systematic trend of slope with wavelength. The offsets of the apparent magnitude vs. logP relations imply a difference between the two fields of 3.8 in distance modulus. The colours of the variables confirm that a principal period with log P > 1.75 is a necessary condition for detectable mass-loss. At the longest observed wavelength, 24 microns, many semi-regular variables have dust shells comparable in luminosity to those around Miras. There is a clear bifurcation in LMC colour-magnitude diagrams involving 24 micron magnitudes.Comment: 5 pages, 4 figure

Energy Transport in the Vaidya System

Energy transport mechanisms can be generated by imposing relations between null tetrad Ricci components. Several kinds of mass and density transport generated by these relations are studied for the generalized Vaidya system.Comment: J.Math. Phys. (to appear

A Spacetime in Toroidal Coordinates

We present an exact solution of Einstein's field equations in toroidal coordinates. The solution has three regions: an interior with a string equation of state; an Israel boundary layer; an exterior with constant isotropic pressure and constant density, locally isometric to anti-de Sitter spacetime. The exterior can be a cosmological vacuum with negative cosmological constant. The size and mass of the toroidal loop depend on the size of the cosmological constant.Comment: to appear in J. Math. Phy

Quasigeometric Distributions and Extra Inning Baseball Games

Each July, the eyes of baseball fans across the country turn to Major League Baseball’s All-Star Game, gathering the best and most popular players from baseball’s two leagues to play against each other in a single game. In most sports, the All-Star Game is an exhibition played purely for entertainment. Since 2003, the baseball All-Star Game has actually ‘counted’, because the winning league gets home field advantage in the World Series. Just one year before this rule went into effect, there was no winner in the All-Star Game, as both teams ran out of pitchers in the 11th inning and the game had to be stopped at that point. Under the new rules, the All-Star Game must be played until there is a winner, no matter how long it takes, so the managers need to consider the possibility of a long extra inning game. This should lead the managers to ask themselves what the probability is that the game will last 12 innings. What about 20 innings? Longer? In this paper, we address these questions and several other questions related to the game of baseball. Our methods use a variation on the well-studied geometric distribution called the quasigeometric distribution. We begin by reviewing some of the literature on applications of mathematics to baseball. In the second section we will define the quasigeometric distribution and examine several of its properties. The final two sections examine the applications of this distribution to models of scoring patterns in baseball games and, more specifically, the length of extra inning games

Scale Symmetries of Spherical String Fluids

We consider homothetic maps in a family of spherical relativistic star models. A generalization of Vaidya's radiating metric provides a fluid atmosphere of radiation and strings. The similarity structure of the string fluid is investigated.Comment: to appear in J. Math. Physic

Adding Twist to Anisotropic Fluids

We present a solution generating technique for anisotropic fluids which preserves specific Killing symmetries. Anisotropic matter distributions that can be used with the one parameter Ehlers-Geroch transform are discussed. Example spacetimes that support the appropriate anisotropic stress-energy are found and the transformation applied. The 3+1 black string solution is one of the spacetimes with the appropriate matter distribution. Use of the transform with a black string seed is discussed.Comment: to appear in J. Math. Phy

Two-Fluid Atmosphere for Relativistic Stars

We have extended the Vaidya radiating metric to include both a radiation fluid and a string fluid. This paper expands our brief introduction to extensions of the Schwarzschild vacuum which appeared in 1998 Phys. Rev. D Vol 57, R5945. Assuming diffusive transport for the string fluid, we find new analytic solutions of Einstein's field equations.Comment: to appear in Classical and Quantum Gravit