Backbends in directed percolation
نویسندگان
چکیده
When directed percolation in a bond percolation process does not occur, any path to innnity on the open bonds will zigzag back and forth through the lattice. Backbends are the portions of the zigzags that go against the percolation direction. They are important in the physical problem of particle transport in random media in the presence of a eld, as they act to limit particle ow through the medium. The critical probability for percolation along directed paths with backbends no longer than a given length n is deened as p n. We prove that (p n) is strictly decreasing and converges to the critical probability for undi-rected percolation p c. We also investigate some variants of the basic model, such as by replacing the standard d-dimensional cubic lattice with a (d ? 1)-dimensional slab or with a Bethe lattice; and we discuss the mathematical consequences of alternative ways to formalise the physical concepts of`percolation' and`backbend'. Acknowledgments We thank Ronald Meester and Ramakrishna Ramaswamy for many helpful discussions. Sarkar and White thank everyone at the Indian Statistical Institute in New Delhi for their kind hospitality.
منابع مشابه
Model for Anisotropic Directed Percolation
We propose a simulation model to study the properties of directed percolation in two-dimensional (2D) anisotropic random media. The degree of anisotropy in the model is given by the ratio μ between the axes of a semiellipse enclosing the bonds that promote percolation in one direction. At percolation, this simple model shows that the average number of bonds per site in 2D is an invariant equal ...
متن کاملThe Directed Polymer — Directed Percolation Transition
We study the relation between the directed polymer and the directed percolation models, for the case of a disordered energy landscape where the energies are taken from bimodal distribution. We find that at the critical concentration of the directed percolation, the directed polymer undergoes a transition from the directed polymer universality class to the directed percolation universality class...
متن کاملIntermittency studies in directed bond percolation
The self-similar cluster fluctuations of directed bond percolation at the percolation threshold are studied using techniques borrowed from intermittency-related analysis in multi-particle production. Numerical simulations based on the factorial moments for large 1 + 1-dimensional lattices allow to handle statistical and boundary effects and show the existence of weak but definite intermittency ...
متن کاملFirst-Passage Percolation, Semi-Directed Bernoulli Percolation, and Failure in Brittle Materials
0022-4715/98/0500-0603$15.00/0 © 1998 Plenum Publishing Corporation We present a two-dimensional, quasistatic model of fracture in disordered brittle materials that contains elements of first-passage percolation, i.e., we use a minimum-energy-consumption criterion for the fracture path. The first-passage model is employed in conjunction with a "semi-directed" Bernoulli percolation model, for wh...
متن کامل