Related papers: Sharpness versus robustness of the percolation tra…
In this work we consider the two-dimensional percolation model arising from the majority dynamics process at a given time $t\in\mathbb{R}_+$. We show the emergence of a sharp threshold phenomenon for the box crossing event at the critical…
During the past two decades, percolation has long served as a basic paradigm for network resilience, community formation and so on in complex systems. While the percolation transition is known as one of the most robust continuous…
Percolation in systems made up of randomly placed impermeable grains is often examined in the context of system spanning clusters of connected solids forming above a relatively low critical grain density $\rho_{c1}$ or networks of…
We consider the directed percolation process as a prototype of systems displaying a nonequilibrium phase transition into an absorbing state. The model is in a critical state when the activation probability is adjusted at some precise value…
Spreading from a seed is studied by Monte Carlo simulation on a square lattice with two types of sites affecting the rates of birth and death. These systems exhibit a critical transition between survival and extinction. For time- dependent…
Quenched disorder - in the sense of the Harris criterion - is generally a relevant perturbation at an absorbing state phase transition point. Here using a strong disorder renormalization group framework and effective numerical methods we…
Many non-equilibrium systems display dynamic phase transitions from active to absorbing states, where fluctuations cease entirely. Based on a field theory representation of the master equation, the critical behavior can be analyzed by means…
Consider growing a network, in which every new connection is made between two disconnected nodes. At least one node is chosen randomly from a subset consisting of $g$ fraction of the entire population in the smallest clusters. Here we show…
We present a study of connectivity percolation in suspensions of hard spherocylinders by means of Monte Carlo simulation and connectedness percolation theory. We focus attention on polydispersity in the length, the diameter and the…
We consider self-avoiding walk and percolation in $\Zd$, oriented percolation in $\Zd\times\Zp$, and the contact process in $\Zd$, with $p D(\cdot)$ being the coupling function whose range is denoted by $L<\infty$. For percolation, for…
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.…
Using three-dimensional representation of confluent cell layers, we map the amorphous solid to fluid phase transition in active cell layers onto the two-dimensional (2D) site percolation universality class. Importantly, we unify two…
We present a new type of phase-change behavior relevant for information storage applications, that can be observed in 2D systems with cluster-forming ability. The temperature-based control of the ordering in 2D particle systems depends on…
Given a weighted graph, we introduce a partition of its vertex set such that the distance between any two clusters is bounded from below by a power of the minimum weight of both clusters. This partition is obtained by recursively merging…
Percolation on complex networks is used both as a model for dynamics on networks, such as network robustness or epidemic spreading, and as a benchmark for our models of networks, where our ability to predict percolation measures our ability…
In this paper we introduce a novel description of the equilibrium state of a bond percolation process on random graphs using the exact method of generating functions. This allows us to find the expected size of the giant connected component…
We study intersection properties of two or more independent tree-like random graphs. Our setting encompasses critical, possibly long range, Bernoulli percolation clusters, incipient infinite clusters, as well as critical branching random…
In many real, directed networks, the strongly connected component of nodes which are mutually reachable is very small. This does not fit with current theory, based on random graphs, according to which strong connectivity depends on mean…
We perform a novel analysis of the granular texture of a granular bed close to stability limit. Our analysis is based on a unique criterion of friction mobilisation in a simulated two-dimensional packing. In this way, we recover the bimodal…
Cell deformability is an essential determinant for tissue-scale mechanical nature, such as fluidity and rigidity, and is thus crucial for understanding tissue homeostasis and stable developmental processes. However, numerical simulations…