"Generalized des Cloizeaux" exponent for self-avoiding walks on the incipient percolation cluster.

We study the asymptotic shape of self-avoiding random walks (SAW) on the backbone of the incipient percolation cluster in d-dimensional lattices analytically. It is generally accepted that the configurational averaged probability distribution function for the end-to-end distance r of an N step SAW behaves as a power law for r-->0. In this work, we determine the corresponding exponent using scaling arguments, and show that our suggested "generalized des Cloizeaux" expression for the exponent is in excellent agreement with exact enumeration results in two and three dimensions.

Critical packing fraction of rectangular particles on the square lattice

The random packing of identical and nonoverlapping rectangular particles of size nxm (10 for L-->infinity, while when p(f)>p(c)(f),P(infinity)-->1 when L-->infinity and an infinite cluster exists. The value for p(c)(f) is found to be consistent with the continuum percolation threshold p(c) congruent with0.67 for overlapping particles in two dimensions.