Topological types of real regular jacobian elliptic surfaces

We present the topological classification of real parts of real regular elliptic surfaces with a real section.Comment: 17 pages, 7 figures, to appear in Geometriae Dedicat

Exact Results for Average Cluster Numbers in Bond Percolation on Lattice Strips

We present exact calculations of the average number of connected clusters per site, , as a function of bond occupation probability $p$, for the bond percolation problem on infinite-length strips of finite width $L_y$, of the square, triangular, honeycomb, and kagom\'e lattices $\Lambda$ with various boundary conditions. These are used to study the approach of , for a given $p$ and $\Lambda$, to its value on the two-dimensional lattice as the strip width increases. We investigate the singularities of in the complex $p$ plane and their influence on the radii of convergence of the Taylor series expansions of about $p=0$ and $p=1$.Comment: 16 pages, revtex, 7 eps figure

Strong Interactions and Stability in the DGP Model

The model of Dvali, Gabadadze, and Porrati (DGP) gives a simple geometrical setup in which gravity becomes 5-dimensional at distances larger than a length scale \lambda_{DGP}. We show that this theory has strong interactions at a length scale \lambda_3 ~ (\lambda_{DGP}^2 / M_P)^{1/3}. If \lambda_{DGP} is of order the Hubble length, then the theory loses predictivity at distances shorter than \lambda_3 ~ 1000 km. The strong interaction can be viewed as arising from a longitudinal `eaten Goldstone' mode that gets a small kinetic term only from mixing with transverse graviton polarizations, analogous to the case of massive gravity. We also present a negative-energy classical solution, which can be avoided by cutting off the theory at the same scale scale \lambda_3. Finally, we examine the dynamics of the longitudinal Goldstone mode when the background geometry is curved.Comment: 24 pages, LaTeX2e, no figure