Surface effects for percolation

Surface effects for percolation

2014 If a (d 2014 1)-dimensional surface of a d-dimensional semi-infinite medium has a concentration pS different from the bulk concentration pB one may imagine that percolation is possible even if both pB and pS are below the dand (d 2014 1)-dimensional threshold, respectively. We give simple arguments, partly confirmed by Monte Carlo experiment, why this effect occurs for d = 3 but not for d ...

Surface effects and percolation : the repulsive case

Surface critical phenomena in three-dimensional percolation.

Using Monte Carlo methods and finite-size scaling, we investigate surface critical phenomena in the bond-percolation model on the simple-cubic lattice with two open surfaces in one direction. We decompose the whole lattice into percolation clusters and sample the surface and bulk dimensionless ratios Q1 and Qb, defined on the basis of the moments of the cluster-size distribution. These ratios a...

Surface and bulk criticality in midpoint percolation.

The concept of midpoint percolation has recently been applied to characterize the double percolation transitions in negatively curved structures. Regular d-dimensional hypercubic lattices are investigated in the present work using the same concept. Specifically, the site-percolation transitions at the critical thresholds are investigated for dimensions up to d=10 by means of the Leath algorithm...

THE SCALING LAW FOR THE DISCRETE KINETIC GROWTH PERCOLATION MODEL

The Scaling Law for the Discrete Kinetic Growth Percolation Model The critical exponent of the total number of finite clusters α is calculated directly without using scaling hypothesis both below and above the percolation threshold pc based on a kinetic growth percolation model in two and three dimensions. Simultaneously, we can calculate other critical exponents β and γ, and show that the scal...