Related papers: Directed Percolation with a Wall or Edge
We study the influence of the boundary conditions at the solid liquid interface on diffusion in a confined fluid. Using an hydrodynamic approach, we compute numerical estimates for the diffusion of a particle confined between two planes.…
With the recent popularity of graphical clustering methods, there has been an increased focus on the information between samples. We show how learning cluster structure using edge features naturally and simultaneously determines the most…
We study the geometry of the critical clusters in fully coordinated percolation on the square lattice. By Monte Carlo simulations (static exponents) and normal mode analysis (dynamic exponents), we find that this problem is in the same…
Boundary layer flow over a realistic porous wall might contain both the effects of wall-permeability and wall-roughness. These two effects are typically examined in the context of a rough-wall flow, i.e., by defining a ``roughness'' length…
We present a scaling theory for the effect of thermal fluctuations on the characteristics of the depinning transition, and also in the closely related directed percolation model. Thermal effects act as a sort of external field that produces…
We study site and bond percolation on directed simple random graphs with a given degree distribution and derive the expressions for the critical value of the percolation probability above which the giant strongly connected component emerges…
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…
Spatial random graphs capture several important properties of real-world networks. We prove quenched results for the continuum space version of scale-free percolation introduced in [DW18]. This is an undirected inhomogeneous random graph…
Particle diffusion in a two dimensional curved surface embedded in $R_3$ is considered. In addition to the usual diffusion flow, we find a new flow with an explicit curvature dependence. New diffusion equation is obtained in $\epsilon$…
We consider here the percolation problem in thin films, both in the direction normal to the film and in the direction parallel to the film. We thereby describe here the cross-over between 2D and 3D percolation, which we do on cubic and…
In confined systems, such as the inside of a biological cell, the outer boundary or wall can affect the dynamics of internal particles. In many cases of interest both the internal particle and outer wall are approximately spherical.…
A new ``Percolation with Clustering'' (PWC) model is introduced, where (the probabilities of) site percolation configurations on the leaf set of a binary tree are rewarded exponentially according to a generic function, which measures the…
In order to clarify how the percolation theory governs the conductivities in real materials which consist of small conductive particles, e.g., nanoparticles, with random configurations in an insulator, we numerically investigate the…
In this article we discuss a set of geometric ideas which shed some light on the question of directed polymer pinning in the presence of bulk disorder. Differing from standard methods and techniques, we transform the problem to a particular…
In [Watanabe et al., Phys. Rev. Lett. 93 190601 (2004)], the authors show numerically that spanning and percolation probabilities in two-dimensional systems with different aspect ratios obey a form of "superscaling". In this comment, we…
Percolation is a cornerstone concept in physics, providing crucial insights into critical phenomena and phase transitions. In this study, we adopt a kinetic perspective to reveal the scaling behaviors of higher-order gaps in the largest…
Using a recently introduced algorithm for simulating percolation in microcanonical (fixed-occupancy) samples, we study the convergence with increasing system size of a number of estimates for the percolation threshold for an open system…
The two-dimensional site percolation problem is studied by transfer-matrix methods on finite-width strips with free boundary conditions. The relationship between correlation-length amplitudes and critical indices, predicted by conformal…
We study, on a square lattice, an extension to fully coordinated percolation which we call iterated fully coordinated percolation. In fully coordinated percolation, sites become occupied if all four of its nearest neighbors are also…
Analytical results are derived for the bond percolation threshold and the size of the giant connected component in a class of random networks with non-zero clustering. The network's degree distribution and clustering spectrum may be…