Directed percolation in the two-dimensional continuum

We report the first study of directed percolation in the continuum. The percolation threshold is found to be at Bc=5.00.1, where Bc is the average number of intersections per diode at the threshold. This is to be compared with Bc=3.20.1 in the corresponding nondirected problem. It is found that the critical exponents of this system are para=0.740.05, =0.460.08, =0.330.07, and =(2.00 0.05). The good agreement with values found for directed lattices appears to be a confirmation of universality for these systems as well as a demonstration that geometrical and physical properties of directed systems in the continuum can be computed.