Related papers: "Explosive Percolation" Transition is Actually Con…
We give an account of matter and (basically) a solution of a new class of problems synthesizing percolation theory and branching diffusion processes. They led us to realizing a novel type of stochastic processes, namely branching processes…
While classical percolation is well understood, percolation effects in randomly packed or jammed structures are much less explored. Here we investigate both experimentally and theoretically the electrical percolation in a binary composite…
The motility-induced phase separation exhibited by active particles with repulsive interactions is well known. We show that the interaction softness of active particles destabilizes the highly ordered dense phase, leading to the formation…
Percolation problems appear in a large variety of different contexts ranging from the design of composite materials to vaccination strategies on community networks. The key observable for many applications is the percolation threshold.…
We describe the critical window for percolation in the universality class of sparse growing random graphs. In our models, vertices arrive sequentially and connect independently to each earlier vertex $v$ with probability proportional to a…
Recently it has been shown that the transition of the 1+1-dimensional annihilation-fission process 2X->3X, 2X->0 exhibits an unusual type of nonequilibrium critical behavior. The phenomenological properties of critical clusters are…
An essential prerequisite for quark-gluon plasma production in nuclear collisions is cross-talk between the partons from different nucleons in the colliding nuclei. The initial density of partons is determined by the parton distribution…
The state space of our model is the Euclidean space in dimension d = 2. Simultaneously, from all points of a homogeneous Poisson point process, we let grow independent and identically distributed random continuum paths. Each path stops…
Multiplex networks describe a large variety of complex systems including infrastructures, transportation networks and biological systems. Most of these networks feature a significant link overlap. It is therefore of particular importance to…
A hybrid percolation transition (HPT) exhibits both discontinuity of the order parameter and critical behavior at the transition point. Such dynamic transitions can occur in two ways: by cluster pruning with suppression of loop formation of…
We consider a sequence of Poisson cluster point processes on $\mathbb{R}^d$: at step $n\in\mathbb{N}_0$ of the construction, the cluster centers have intensity $c/(n+1)$ for some $c>0$, and each cluster consists of the particles of a…
Abrupt transitions are ubiquitous in the dynamics of complex systems. Finding precursors, i.e. early indicators of their arrival, is fundamental in many areas of science ranging from electrical engineering to climate. However, obtaining…
The occurrence of system-scale coherent structures, so-called condensates, is a well-known phenomenon in two-dimensional turbulence. Here, the transition to condensate formation is investigated as a function of the magnitude of the force…
I report on the experimental confirmation that critical percolation statistics underlie the ordering kinetics of twisted nematic phases in the Allen-Cahn universality class. Soon after the ordering starts from a homogeneous disordered phase…
As a generation of the classical percolation, clique percolation focuses on the connection of cliques in a graph, where the connection of two $k$-cliques means that they share at least $l<k$ vertices. In this paper, we develop a theoretical…
We study the percolation of strongly connected clusters (SCCs), in which sites are mutually reachable through directed paths, in systems with randomly oriented bonds by extensive simulations on hypercubic lattices from dimension $d=2$ to…
It is widely believed that certain simple modifications of the random graph process lead to discontinuous phase transitions. In particular, starting with the empty graph on $n$ vertices, suppose that at each step two pairs of vertices are…
Depending on the type of flow, the transition to turbulence can take one of two forms: either turbulence arises from a sequence of instabilities or from the spatial proliferation of transiently chaotic domains, a process analogous to…
Collapse and reverse to collapse explosion transition in self-gravitating systems are studied by molecular dynamics simulations. A microcanonical ensemble of point particles confined to a spherical box is considered; the particles interact…
It has been shown that a hot and dense deconfined nuclear matter state produced in ultra-relativistic heavy-ion collisions, can be quantitatively described by the String Percolation phenomenological model. The model address the phase…