Related papers: Discontinuous transition in explosive percolation …
We consider the gelation of particles which are permanently connected by random crosslinks, drawn from an ensemble of finite-dimensional continuum percolation. To average over the randomness, we apply the replica trick, and interpret the…
Connectivity - or the lack thereof - is crucial for the function of many man-made systems, from financial and economic networks over epidemic spreading in social networks to technical infrastructure. Often, connections are deliberately…
In the presence of attraction, the jamming transition of packings of frictionless particles corresponds to the rigidity percolation. When the range of attraction is long, the distribution of the size of rigid clusters, $P(s)$, is continuous…
This Letter studies the critical point as well as the discontinuity of a class of explosive site percolation in Erd\"{o}s and R\'{e}nyi (ER) random network. The class of the percolation is implemented by introducing a best-of-m rule. Two…
We develop a percolation model motivated by recent experimental studies of gels with active network remodeling by molecular motors. This remodeling was found to lead to a critical state reminiscent of random percolation (RP), but with a…
The rigidity transition occurs when, as the density of microscopic components is increased, a disordered medium becomes able to transmit and ensure macroscopic mechanical stability, owing to the appearance of a space-spanning rigid…
Percolation plays an important role in fields and phenomena as diverse as the study of social networks, the dynamics of epidemics, the robustness of electricity grids, conduction in disordered media, and geometric properties in statistical…
When real networks are considered, coupled networks with connectivity and feedback-dependency links are not rare but more general. Here we develop a mathematical framework and study numerically and analytically percolation of interacting…
If we add links to a network at random, a critical threshold can be crossed where a giant connected component forms. Conversely, if links or nodes are removed at random, the giant component shrinks and eventually breaks. In this paper, we…
Many real-world multilayer systems such as critical infrastructure are interdependent and embedded in space with links of a characteristic length. They are also vulnerable to localized attacks or failures, such as terrorist attacks or…
We introduce a model for dynamic networks, where the links or the strengths of the links change over time. We solve the model by mapping dynamic networks to the problem of directed percolation, where the direction corresponds to the…
We introduce a growing network model---the copying model---in which a new node attaches to a randomly selected target node and, in addition, independently to each of the neighbors of the target with copying probability $p$. When…
Transient dynamics leading to the synchrony of pulse-coupled oscillators has previously been studied as an aggregation process of synchronous clusters, and a rate equation for the cluster size distribution has been proposed. However, the…
Critical phenomena of a second-order percolation transition are known to be independent of cluster merging or pruning process. However, those of a hybrid percolation transition (HPT), mixed properties of both first-order and second-order…
Hybrid percolation transitions (HPTs) induced by cascading processes have been observed in diverse complex systems such as $k$-core percolation, breakdown on interdependent networks and cooperative epidemic spreading models. Much effort has…
Spontaneous explosive is an abrupt transition to collective behavior taking place in heterogeneous networks when the frequencies of the nodes are positively correlated to the node degree. This explosive transition was conjectured to be…
Our current world is linked by a complex mesh of networks where information, people and goods flow. These networks are interdependent each other, and present structural and dynamical features different from those observed in isolated…
The evolution of the Erd\H{o}s-R\'enyi (ER) network by adding edges can be viewed as a cluster aggregation process. Such ER processes can be described by a rate equation for the evolution of the cluster-size distribution with the connection…
A fundamental problem in network science is to predict how certain individuals are able to initiate new networks to spring up "new ideas". Frequently, these changes in trends are triggered by a few innovators who rapidly impose their ideas…
We consider the correlations and the hydrodynamic description of random walkers with a general finite memory moving on a $d$ dimensional hypercubic lattice. We derive a drift-diffusion equation and identify a memory-dependent critical…