On the equality of Hausdorff and box counting dimensions

By viewing the covers of a fractal as a statistical mechanical system, the exact capacity of a multifractal is computed. The procedure can be extended to any multifractal described by a scaling function to show why the capacity and Hausdorff dimension are expected to be equal.Comment: CYCLER Paper 93mar001 Latex file with 3 PostScript figures (needs psfig.sty

Palatini approach to Born-Infeld-Einstein theory and a geometric description of electrodynamics

The field equations associated with the Born-Infeld-Einstein action are derived using the Palatini variational technique. In this approach the metric and connection are varied independently and the Ricci tensor is generally not symmetric. For sufficiently small curvatures the resulting field equations can be divided into two sets. One set, involving the antisymmetric part of the Ricci tensor $R_{\stackrel{\mu\nu}{\vee}}$, consists of the field equation for a massive vector field. The other set consists of the Einstein field equations with an energy momentum tensor for the vector field plus additional corrections. In a vacuum with $R_{\stackrel{\mu\nu}{\vee}}=0$ the field equations are shown to be the usual Einstein vacuum equations. This extends the universality of the vacuum Einstein equations, discussed by Ferraris et al. \cite{Fe1,Fe2}, to the Born-Infeld-Einstein action. In the simplest version of the theory there is a single coupling constant and by requiring that the Einstein field equations hold to a good approximation in neutron stars it is shown that mass of the vector field exceeds the lower bound on the mass of the photon. Thus, in this case the vector field cannot represent the electromagnetic field and would describe a new geometrical field. In a more general version in which the symmetric and antisymmetric parts of the Ricci tensor have different coupling constants it is possible to satisfy all of the observational constraints if the antisymmetric coupling is much larger than the symmetric coupling. In this case the antisymmetric part of the Ricci tensor can describe the electromagnetic field, although gauge invariance will be broken.Comment: 12 page

A Time-Space Tradeoff for Triangulations of Points in the Plane

In this paper, we consider time-space trade-offs for reporting a triangulation of points in the plane. The goal is to minimize the amount of working space while keeping the total running time small. We present the first multi-pass algorithm on the problem that returns the edges of a triangulation with their adjacency information. This even improves the previously best known random-access algorithm

Efficient Coupling between Dielectric-Loaded Plasmonic and Silicon Photonic Waveguides

The realization of practical on-chip plasmonic devices will require efficient coupling of light into and out of surface plasmon waveguides over short length scales. In this letter, we report on low insertion loss for polymer-on-gold dielectric-loaded plasmonic waveguides end-coupled to silicon-on-insulator waveguides with a coupling efficiency of 79 ± 2% per transition at telecommunication wavelengths. Propagation loss is determined independently of insertion loss by measuring the transmission through plasmonic waveguides of varying length, and we find a characteristic surface-plasmon propagation length of 51 ± 4 μm at a free-space wavelength of λ = 1550 nm. We also demonstrate efficient coupling to whispering-gallery modes in plasmonic ring resonators with an average bending-loss-limited quality factor of 180 ± 8

Born-Regulated Gravity in Four Dimensions

Previous work involving Born-regulated gravity theories in two dimensions is extended to four dimensions. The action we consider has two dimensionful parameters. Black hole solutions are studied for typical values of these parameters. For masses above a critical value determined in terms of these parameters, the event horizon persists. For masses below this critical value, the event horizon disappears, leaving a ``bare mass'', though of course no singularity.Comment: LaTeX, 15 pages, 2 figure