Towards a theory of automated elliptic mesh generation

The theory of elliptic mesh generation is reviewed and the fundamental problem of constructing computational space is discussed. It is argued that the construction of computational space is an NP-Complete problem and therefore requires a nonstandard approach for its solution. This leads to the development of graph-theoretic, combinatorial optimization and integer programming algorithms. Methods for the construction of two dimensional computational space are presented

Schur Indices, BPS Particles, and Argyres-Douglas Theories

We conjecture a precise relationship between the Schur limit of the superconformal index of four-dimensional $\mathcal{N}=2$ field theories, which counts local operators, and the spectrum of BPS particles on the Coulomb branch. We verify this conjecture for the special case of free field theories, $\mathcal{N}=2$ QED, and $SU(2)$ gauge theory coupled to fundamental matter. Assuming the validity of our proposal, we compute the Schur index of all Argyres-Douglas theories. Our answers match expectations from the connection of Schur operators with two-dimensional chiral algebras. Based on our results we propose that the chiral algebra of the generalized Argyres-Douglas theory $(A_{k-1},A_{N-1})$ with $k$ and $N$ coprime, is the vacuum sector of the $(k,k+N)$ $W_{k}$ minimal model, and that the Schur index is the associated vacuum character.Comment: 46 pages, 12 figures. v2: revisions to section 1, references adde

X-ray Variability and Period Determinations in the Eclipsing Polar DP Leo

An analysis of ROSAT observations for the eclipsing magnetic cataclysmic binary DP Leo provides constraints on the origin, size, temperature, variability and structure of the soft X-ray emission region on the surface of the white dwarf. These data, when combined with prior observations, show a progression of approximately 2 degrees per year in the impact position of the accretion stream onto the white dwarf. One explanation for the observed drift in stream position is that a magnetic activity cycle on the secondary produces orbital period oscillations. These oscillations result in an orbital period which cycles above and below the rotational period of the nearly synchronous white dwarf. The accretion stream and X-ray emission regions are modeled to fit the observational data. A distance to the system is also calculated. [An erroneous value for the cyclotron luminosity, included in an earlier paper version of the preprint, is corrected here.]Comment: uuencoded PostScript file (25 pages) + 8 figures available by anonymous ftp to ftp.astro.psu.edu (in the directory /pub/robinson), to appear in ApJ, PSU preprint 1994-1