Related papers: The elastic and directed percolation backbone
The elastic backbone is the set of all shortest paths. We found a new phase transition at $p_{eb}$ above the classical percolation threshold at which the elastic backbone becomes dense. At this transition in $2d$ its fractal dimension is…
We present high statistics simulations for 2-d percolation clusters in the "bus bar" geometry at the critical point, for site and for bond percolation. We measured their backbone sizes and electrical conductivities. For all sets of…
We study the statistics of the backbone cluster between two sites separated by distance $r$ in two-dimensional percolation networks subjected to spatial long-range correlations. We find that the distribution of backbone mass follows the…
Directed spiral percolation (DSP), percolation under both directional and rotational constraints, is studied on the triangular lattice in two dimensions (2D). The results are compared with that of the 2D square lattice. Clusters generated…
We study the recently-introduced directed percolation depinning (DPD) model for interface roughening with quenched disorder for which the interface becomes pinned by a directed percolation (DP) cluster for $d = 1$, or a directed surface…
We present a new view of Feynman diagrams for the field theory of transport on percolation clusters. The diagrams for random resistor networks are interpreted as being resistor networks themselves. This simplifies the field theory…
A new site percolation model, directed spiral percolation (DSP), under both directional and rotational (spiral) constraints is studied numerically on the square lattice. The critical percolation threshold $p_c\approx 0.655$ is found between…
Rephrasing the backbone of two-dimensional percolation as a monochromatic path crossing problem, we investigate the latter by a transfer matrix approach. Conformal invariance links the backbone dimension D_b to the highest eigenvalue of the…
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…
We consider directed percolation with an absorbing boundary in 1+1 and 2+1 dimensions. The distribution of cluster lifetimes and sizes depend on the boundary. The new scaling exponents can be related to the exponents characterizing standard…
The incipient infinite cluster appearing at the bond percolation threshold can be decomposed into singly-connected ``links'' and multiply-connected ``blobs.'' Here we decompose blobs into objects known in graph theory as 3-blocks. A 3-block…
Directed spiral percolation (DSP) is a new percolation model with crossed external bias fields. Since percolation is a model of disorder, the effect of external bias fields on the properties of disordered systems can be studied numerically…
While for standard percolation directionality is known to increase the combinatorial complexity of percolation, here we show that when connectivity is ensured by paths of length $R\geq 2$, network directionality, impeding backtracking, can…
Explosive percolation (EP) has received significant research attention due to its rich and anomalous phenomena near criticality. In our recent study [Phys. Rev. Lett. 130, 147101 (2023)], we demonstrated that the correct critical behaviors…
We investigate percolation on a randomly directed lattice, an intermediate between standard percolation and directed percolation, focusing on the isotropic case in which bonds on opposite directions occur with the same probability. We…
Directed Percolation (DP) is a classic model for nonequilibrium phase transitions into a single absorbing state (fixation). It has been extensively studied by analytical and numerical techniques in diverse contexts. Recently, DP has…
We carry out a high-precision Monte Carlo study of the shortest-path fractal dimension $\dm$ for percolation in two and three dimensions, using the Leath-Alexandrowicz method which grows a cluster from an active seed site. A variety of…
We investigate the role of disorder on the fracturing process of heterogeneous materials by means of a two-dimensional fuse network model. Our results in the extreme disorder limit reveal that the backbone of the fracture at collapse,…
We investigate a recent suggestion that the spatial distribution of earthquake hypocenters makes a fractal set with a structure and fractal dimensionality close to those of the backbone of critical percolation clusters, by analyzing four…
The fractal structure of directed percolation clusters, grown at the percolation threshold inside parabolic-like systems, is studied in two dimensions via Monte Carlo simulations. With a free surface at y=\pm Cx^k and a dynamical exponent…