Related papers: Multiple and Asymmetric Scalings in Explosive Perc…

We study the percolation transition in growing networks under an Achlioptas process (AP). At each time step, a node is added in the network and, with the probability $\delta$, a link is formed between two nodes chosen by an AP. We find that…

We consider cumulative merging percolation (CMP), a long-range percolation process describing the iterative merging of clusters in networks, depending on their mass and mutual distance. For a specific class of CMP processes, which…

Percolation processes on random networks have been the subject of intense research activity over the last decades: the overall phenomenology of standard percolation on uncorrelated and unclustered topologies is well known. Still some…

The presence of scaling variables in experimental observables provide very valuable indications of the dynamics underlying a given physical process. In the last years, the search for geometric scaling, that is the presence of a scaling…

We extend the Achlioptas model for the delay of criticality in the percolation problem. Instead of having a completely random connectivity pattern, we generalize the idea of the two-site probe in the Achlioptas model for connecting smaller…

Clusters generated by the product-rule growth model of Achlioptas, D'Souza, and Spencer on a two-dimensional square lattice are shown to obey qualitatively different scaling behavior than standard (random growth) percolation. The threshold…

Data series generated by complex systems exhibit fluctuations on many time scales and/or broad distributions of the values. In both equilibrium and non-equilibrium situations, the natural fluctuations are often found to follow a scaling…

We apply a variant of the explosive percolation procedure to large real-world networks, and show with finite-size scaling that the university class, ordinary or explosive, of the resulting percolation transition depends on the structural…

By introducing a simple competition mechanism for bond insertion in random graphs, explosive percolation exhibits a sharp phase transition with rich critical phenomena. We investigate high-order connectivity in explosive percolation using…

Percolation has long served as a model for diverse phenomena and systems. The percolation transition, that is, the formation of a giant cluster on a macroscopic scale, is known as one of the most robust continuous transitions. Recently,…

Percolation and synchronization are two phase transitions that have been extensively studied since already long ago. A classic result is that, in the vast majority of cases, these transitions are of the second-order type, i.e. continuous…

Multiparticle production processes provide valuable information about the mechanism of the conversion of the initial energy of projectiles into a number of secondaries by measuring their multiplicity distributions and their distributions in…

Multifractal systems usually have singularity spectra defined on bounded sets of H\"older exponents. As a consequence, their associated multifractal scaling exponents are expected to depend linearly upon statistical moment orders at high…

The percolation phase transitions of two-dimensional lattice networks under a generalized Achlioptas process (GAP) are investigated. During the GAP, two edges are chosen randomly from the lattice and the edge with minimum product of the two…

When strained beyond the linear regime, soft colloidal glasses yield to steady-state plastic flow in a way that is similar to the deformation of conventional amorphous solids. Due to the much larger size of the colloidal particles with…

Explosive percolation in a network is a phase transition where a large portion of nodes becomes connected with an addition of a small number of edges. Although extensively studied in random network models and reconstructed real networks,…

We approximate a 2D Ising spin glass by tiling an infinite square lattice with large identical unit cells. The interactions within the unit cell are random. Each such sample shows one or more critical points. We examine the scaling of the…

We propose a novel finite size scaling analysis for percolation transition observed in complex networks. While it is known that cooperative systems in growing networks often undergo an infinite order transition with inverted…

Fractal structures appear in a vast range of physical systems. A literature survey including all experimental papers on fractals which appeared in the six Physical Review journals (A-E and Letters) during the 1990's shows that experimental…

Motivated by the importance of geometric information in real systems, a new model for long-range correlated percolation in link-adding networks is proposed with the connecting probability decaying with a power-law of the distance on the…