Related papers: Directed Spiral Percolation Hull on the Square and…
In the first paper of this series [S. Torquato, J. Chem. Phys. {\bf 136}, 054106 (2012)], analytical results concerning the continuum percolation of overlapping hyperparticles in $d$-dimensional Euclidean space $\mathbb{R}^d$ were obtained,…
We study site percolation on lattices confined to a semi-infinite strip. For triangular and square lattices we find that the probability that a cluster touches the three sides of such a system at the percolation threshold has the continuous…
Kinematic surveys of the dwarf spheroidal (dSph) satellites of the Milky Way are revealing tantalising hints about the structure of dark matter (DM) haloes at the low-mass end of the galaxy luminosity function. At the bright end, modelling…
We introduce a simple lattice model in which percolation is constructed on top of critical percolation clusters, and show that it can be repeated recursively any number $n$ of generations. In two dimensions, we determine the percolation…
Transient dynamics leading to the synchrony of pulse-coupled oscillators has previously been studied as an aggregation process of synchronous clusters, and a rate equation for the cluster size distribution has been proposed. However, the…
We analyse the critical region of finite-($d$)-dimensional Ising spin glass, in particular the limit of $d$ closely above the lower critical dimension $d_\ell$. At criticality the thermally active degrees of freedom are surfaces (of width…
We study a percolation problem based on critical loop configurations of the O($n$) loop model on the honeycomb lattice. We define dual clusters as groups of sites on the dual triangular lattice that are not separated by a loop, and…
We numerically investigate the electric potential distribution over a two-dimensional continuum percolation model between the electrodes. The model consists of overlapped conductive particles on the background with an infinitesimal…
A simple finite-size scaling theory is proposed here for anisotropic percolation models considering the cluster size distribution function as generalized homogeneous function of the system size and two connectivity lengths. The proposed…
2D Percolation path exponents $x^{\cal P}_{\ell}$ describe probabilities for traversals of annuli by $\ell$ non-overlapping paths, each on either occupied or vacant clusters, with at least one of each type. We relate the probabilities…
Recent theoretical and computational progress has led to unprecedented understanding of symmetry-breaking instabilities in 2D dynamic fracture. At the heart of this progress resides the identification of two intrinsic, near crack tip length…
We introduce the notion of topological electronic states on random lattices in non-integer dimensions. By considering a class $D$ model on critical percolation clusters embedded in two dimensions, we demonstrate that these topological…
The concept of splitting tessellations and splitting tessellation processes in spherical spaces of dimension $d\geq 2$ is introduced. Expectations, variances and covariances of spherical curvature measures induced by a splitting…
We introduce a technique that uses projection properties of fractal percolation to establish dimension conservation results for sections of deterministic self-similar sets. For example, let $K$ be a self-similar subset of $\mathbb{R}^2$…
We performed extensive numerical simulation of diffusion-limited aggregation in two dimensional channel geometry. Contrary to earlier claims, the measured fractal dimension D = 1.712 +- 0.002 and its leading correction to scaling are the…
We argue the exact universal result for the three-point connectivity of critical percolation in two dimensions. Predictions for Potts clusters and for the scaling limit below p_c are also given.
We investigate the in-spiraling timescales of globular clusters in dwarf spheroidal (dSph) and dwarf elliptical (dE) galaxies, due to dynamical friction. We address the problem of these timescales having been variously estimated in the…
Motivated by recent experiments, we investigate the scattering properties of percolation clusters generated by numerical simulations on a three dimensional cubic lattice. Individual clusters of given size are shown to present a fractal…
We show that only considering the largest cluster suffices to obtain a first-order percolation transition. As opposed to previous realizations of explosive percolation our models obtain Gaussian cluster distributions and compact clusters as…
The distribution of masses of clusters smaller than the infinite cluster is evaluated at the percolation threshold. The clusters are ranked according to their masses and the distribution $P(M/L^D,r)$ of the scaled masses M for any rank r…