Related papers: Percolation transition in correlated static model
We use molecular dynamics simulations to study a model of the gelation transition with a dynamic bond forming procedure. After establishing evidence for 3D percolation as the static universality class, we turn our attention to the dynamics…
K-core percolation is a fundamental dynamical process in complex networks with applications that span numerous real-world systems. Earlier studies focus primarily on random networks without spatial constraints and reveal intriguing…
We study a coupled dynamics of a network and a particle system. Particles of density $\rho$ diffuse freely along edges, each of which is rewired at a rate given by a decreasing function of particle flux. We find that the coupled dynamics…
The urban networks of London and New York City are investigated as directed graphs within the paradigm of graph percolation. It has been recently observed that urban networks show a critical percolation transition when a fraction of edges…
Existing studies on the degree correlation of evolving networks typically rely on differential equations and statistical analysis, resulting in only approximate solutions due to inherent randomness. To address this limitation, we propose an…
The study of the Ising model from a percolation perspective has played a significant role in the modern theory of critical phenomena. We consider the celebrated square-lattice Ising model and construct percolation clusters by placing bonds,…
Recently, the percolation transition has been characterized on interacting networks both in presence of interdependent and antagonistic interactions. Here we characterize the phase diagram of the percolation transition in two Poisson…
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…
We compare phase transition and critical phenomena of bond percolation on Euclidean lattices, nonamenable graphs, and complex networks. On a Euclidean lattice, percolation shows a phase transition between the nonpercolating phase and…
We investigate the onset of the discontinuous percolation transition in small-world hyperbolic networks by studying the systems-size scaling of the typical largest cluster approaching the transition, $p\nearrow p_{c}$. To this end, we…
The structure of interconnected systems and its impact on the system dynamics is a much-studied cross-disciplinary topic. Although various critical phenomena have been found in different models, the study on the connections between…
Many biological tissues feature a heterogeneous network of fibers whose tensile and bending rigidity contribute substantially to these tissues' elastic properties. Rigidity percolation has emerged as a important paradigm for relating these…
Percolation is an emblematic model to assess the robustness of interconnected systems when some of their components are corrupted. It is usually investigated in simple scenarios, such as the removal of the system's units in random order, or…
We observed a phase transition-like behavior that is marked by the onset of the realization of the connectivity between two sites on a two-dimensional cross-section of a three-dimensional percolation cluster. This was found using…
Rigidity percolation (RP) occurs when mechanical stability emerges in disordered networks as constraints or components are added. Here we discuss RP with structural correlations, an effect ignored in classical theories albeit relevant to…
In this paper we examine the percolation properties of higher-order networks that have non-trivial clustering and subgraph-based assortative mixing (the tendency of vertices to connect to other vertices based on subgraph joint degree). Our…
In this work we explore degree assortativity in complex networks, and extend its usual definition beyond that of nearest neighbours. We apply this definition to model networks, and describe a rewiring algorithm that induces assortativity.…
The percolation threshold of the network model by Barabasi and Albert (BA-model) [Science 286, 509 (1999)] has thus far only been 'guessed' based on simulations and comparison with other models. Due to the still uncertain influence of…
We introduce a simple model of active transport for an ensemble of particles driven by an external shear flow. Active refers to the fact that the flow of the particles is modified by the distribution of particles itself. The model consists…
The dynamics of a 2D site percolation model on a square lattice is studied using the hierarchical approach introduced by Gabrielov et al., Phys. Rev. E, 60, 5293-5300, 1999. The key elements of the approach are the tree representation of…