Related papers: Directed Percolation with a Wall or Edge
These notes fill in results about oriented percolation that are required for the paper [3] ("Forward clusters for degenerate random environments"). Since these are essentially modifications of results found in other sources (but adapted to…
We give the first properties of independent Bernoulli percolation, for oriented graphs on the set of vertices $\Z^d$ that are translation-invariant and may contain loops. We exhibit some examples showing that the critical probability for…
We extend a modal theory of diffraction by a set of parallel fibers to deal with the case of a hard boundary: that is a structure made for instance of air-holes inside a dielectric matrix. Numerical examples are given concerning some…
Edges are a basic and fundamental feature in image processing, that are used directly or indirectly in huge amount of applications. Inspired by the expansion of image resolution and processing power dilated convolution techniques appeared.…
An important class of real-world networks have directed edges, and in addition, some rank ordering on the nodes, for instance the "popularity" of users in online social networks. Yet, nearly all research related to explosive percolation has…
We study the two most common types of percolation process on a sparse random graph with a given degree sequence. Namely, we examine first a bond percolation process where the edges of the graph are retained with probability p and afterwards…
We present a review of the recent progress on percolation scaling limits in two dimensions. In particular, we will consider the convergence of critical crossing probabilities to Cardy's formula and of the critical exploration path to…
Percolation on two-dimensional small-world networks has been proposed as a model for the spread of plant diseases. In this paper we give an analytic solution of this model using a combination of generating function methods and high-order…
We show that Directed Percolation (DP) simulations in a pipe geometry in 3+1 dimensions fully capture the observed complex phenomenology of the transition to turbulence. At low Reynolds numbers (Re), turbulent puffs form and spontaneously…
Every realistic instance of a percolation problem is faced with some degree of polydispersity, e.g., the pore-size distribution of an inhomogeneous medium, the size distribution of filler particles in composite materials, or the vertex…
Percolation is a fundamental concept that brought new understanding on the robustness properties of complex systems. Here we consider percolation on weakly interacting networks, that is, network layers coupled together by much less…
In this work we consider five different lattice models which exhibit continuous phase transitions into absorbing states. By measuring certain universal functions, which characterize the steady state as well as the dynamical scaling…
The basic notion of percolation in physics assumes the emergence of a giant connected (percolation) cluster in a large disordered system when the density of connections exceeds some critical value. Until recently, the percolation phase…
In the last two decades there was a lot of progress in understanding the geometry of smooth Gaussian fields. This survey aims to cover one particular line of research: the large scale behaviour of level and excursion sets and their…
A theoretical and computational study analysing the initiation of yield-stress fluids percolation in porous media is presented. Yield-stress fluid flows through porous media are complicated due to the non-linear rheological behaviour of…
A well studied family of random fractals called fractal percolation is discussed. We focus on the projections of fractal percolation on the plane. Our goal is to present stronger versions of the classical Marstrand theorem, valid for almost…
The event graph representation of temporal networks suggests that the connectivity of temporal structures can be mapped to a directed percolation problem. However, similar to percolation theory on static networks, this mapping is valid…
In this paper, we consider the problem of assessing local clustering in complex networks. Various definitions for this measure have been proposed for the cases of networks having weighted edges, but less attention has been paid to both…
The study presented here addresses the challenging problem of laminar-turbulent flow transition in boundary layers. Directed percolation theory has emerged as a promising approach to understand and describe this transition in different…
We predict that self-bound clusters of particles exist in the supercritical phase of simple fluids. These clusters, whose internal temperature is lower than the global temperature of the system, define a percolation line that starts at the…