Fractal Dimensions of Confined Clusters in Two-Dimensional Directed   Percolation
  The fractal structure of directed percolation clusters, grown at the percolation threshold inside parabolic-like systems, is studied in two dimensions via Monte Carlo simulations. With a free surface at y=\pm Cx^k and a dynamical exponent z, the surface shape is a relevant perturbation when k<1/z and the fractal dimensions of the anisotropic clusters vary continuously with k. Analytic expressions for these variations are obtained using a blob picture approach. 
C. Kaiser (1 and 2), L. Turban (2) ((1) F. U. Berlin, (2) Henri   Poincare University, Nancy)