Related papers: Explosive Percolation Obeys Standard Finite-Size S…
Finite size fluctuations are a crucial ingredient in kinetic theory of long-range interacting collisionless systems. In this Letter, we introduce a phenomenological theory which predicts an anomalous scaling close to marginal stability for…
We study the percolation properties of the growing clusters model. In this model, a number of seeds placed on random locations on a lattice are allowed to grow with a constant velocity to form clusters. When two or more clusters eventually…
We study the explosive character of the percolation transition in a real-world network. We show that the emergence of a spanning cluster in the Human Protein Homology Network (H-PHN) exhibits similar features to an Achlioptas-type process…
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…
A approach of finite size scaling theory for discontinous percolation with multiple giant clusters is developed in this paper. The percolation in generalized Bohman-Frieze-Wormald (BFW) model has already been proved to be discontinuous…
In a recent Letter, Friedman and Landsberg discussed the underlying mechanism of explosive phase transitions on complex networks [Phys. Rev. Lett. 103, 255701 (2009)]. This Brief Report presents a modest, though more insightful extension of…
Percolation is the simplest fundamental model in statistical mechanics that exhibits phase transitions signaled by the emergence of a giant connected component. Despite its very simple rules, percolation theory has successfully been applied…
A set of discrete individual points located in an embedding continuum space can be seen as percolating or non-percolating, depending on the radius of the discs/spheres associated with each of them. This problem is relevant in theoretical…
As the variety of systems displaying scale invariant characteristics are matched only by their number, it is becoming increasingly important to understand their fundamental and universal elements. Much work has attempted to apply 2nd order…
An explosive percolation transition is the abrupt emergence of a giant cluster at a threshold caused by a suppression of the growth of large clusters. In this paper, we consider the information entropy of the cluster size distribution,…
We define a continuum percolation model that provides a collection of random ellipses on the plane and study the behavior of the covered set and the vacant set, the one obtained by removing all ellipses. Our model generalizes a construction…
The recent proliferation of correlated percolation models---models where the addition of edges/vertices is no longer independent of other edges/vertices---has been motivated by the quest to find discontinuous percolation transitions. The…
Emergent behaviors occur in a vast array of systems across many scales, and are of fundamental physical importance because of the intrinsic difficulty in linking microscopic system properties to macroscopic behaviors. Here we study the…
Consider the indicator function $f$ of a two-dimensional percolation crossing event. In this paper, the Fourier transform of $f$ is studied and sharp bounds are obtained for its lower tail in several situations. Various applications of…
Event-by-event fluctuations of hadronic patterns in heavy-ion collisions are studied in search for signatures of quark-hadron phase transition. Attention is focused on a narrow strip in the azimuthal angle with small $\Delta y$. The…
Traditional percolation theory assumes static microscopic rules, limiting its ability to describe real-world complex systems where macroscopic order actively regulates local interactions. Here, we introduce feedback percolation, an unified…
The universal theory of order parameter fluctuations (delta scaling laws) is applied to a wide range of intermediate energy heavy-ion collision data obtained with INDRA. This systematic study confirms that the observed fragment production…
In this work, we study explosive percolation (EP) in Barab\'{a}si-Albert (BA) network, in which nodes are born with degree $k=m$, for both product rule (PR) and sum rule (SR) of the Achlioptas process. For $m=1$ we find that the critical…
We investigate sample-to-sample fluctuations of the shear modulus in ensembles of particle packings near the jamming transition. Unlike the average modulus, which exhibits distinct scaling behaviours depending on the interparticle…
The intermittent burst dynamics during the slow drainage of a porous medium is studied experimentally. We have shown that this system satisfies a set of conditions known to be true for critical systems, such as intermittent activity with…