Continuum percolation with holes

Finite-Size Scaling in Two-dimensional Continuum Percolation Models

We test the universal finite-size scaling of the cluster mass order parameter in two-dimensional (2D) isotropic and directed continuum percolation models below the percolation threshold by computer simulations. We found that the simulation data in the 2D continuum models obey the same scaling expression of massM to sample size L as generally accepted for isotropic lattice problems, but with a p...

No-Enclave Percolation Corresponds to Holes in the Cluster Backbone.

The no-enclave percolation (NEP) model introduced recently by Sheinman et al. can be mapped to a problem of holes within a standard percolation backbone, and numerical measurements of such holes give the same size-distribution exponent τ=1.82(1) as found for the NEP model. An argument is given that τ=1+d_{B}/2≈1.822 for backbone holes, where d_{B} is the backbone dimension. On the other hand, a...

Existence of phase transition for heavy-tailed continuum percolation

Let (Xn, rn)n≥1 be a marked Poisson process with intensity λ in Rd, d ≥ 2. The marks (rn) are radii of closed Euclidean balls centered at the points (Xn). Two points Xi and Xj of the Poisson process X are adjacent, Xi ∼ Xj , if D(Xi, ri) ∩ D(Xj , rj) 6= ∅, where D(x,R) = {y ∈ Rd : ||x− y||2 ≤ R}. We say that x, y ∈ Rd are connected, x↔ y, if there are Xi1 , . . . , Xil ∈ X such that x ∈ D(Xi1 ,...

Studies in statistical physics: Stochastic strategies in a minority game and continuum percolation of overlapping discs

Basic transport properties in natural porous media: Continuum percolation theory and fractal model