Related papers: Inhomogeneous long-range percolation in the weak d…
Biased (degree-dependent) percolation was recently shown to provide new strategies for turning robust networks fragile and vice versa. Here we present more detailed results for biased edge percolation on scale-free networks. We assume a…
We investigate the effective properties (conductivity, diffusivity and elastic moduli) of model random composite media derived from Gaussian random fields and overlapping hollow spheres. The morphologies generated in the models exhibit low…
Using molecular dynamics computer simulations we investigate the structural and dynamical properties of a simple model for a colloidal gel at low volume fraction. We find that at low T the system is forming an open percolating cluster,…
Global physical properties of random media change qualitatively at a percolation threshold, where isolated clusters merge to form one infinite connected component. The precise knowledge of percolation thresholds is thus of paramount…
Dependency links in single-layer networks offer a convenient way of modeling nonlocal percolation effects in networked systems where certain pairs of nodes are only able to function together. We study the percolation properties of the weak…
Percolation is the paradigm for random connectivity and has been one of the most applied statistical models. With simple geometrical rules a transition is obtained which is related to magnetic models. This transition is, in all dimensions,…
Classical blockmodel is known as the simplest among models of networks with community structure. The model can be also seen as an extremely simply example of interconnected networks. For this reason, it is surprising that the percolation…
Recently increasing attention has been addressed to the fluctuations observed in percolation defined in single and multiplex networks. These fluctuations are extremely important to characterize the robustness of real finite networks but…
We study the charge-density dynamics within the two-dimensional extended Hubbard model in the presence of long-range Coulomb interaction across the metal-insulator transition point. To take into account strong correlations we start from…
We study the behavior of the random walk on the infinite cluster of independent long range percolation in dimensions $d=1,2$, where $x$ and $y$ a re connected with probability $\sim\beta/\|x-y\|^{-s}$. We show that when $d<s<2d$ the walk is…
The competition of depletion attractions and longer-ranged repulsions between colloidal particles in colloid-polymer mixtures leads to the formation of heterogeneous gel-like structures. For instance, gel networks, i.e., states where the…
The presence of long-ranged correlations in a fluid undergoing uniform shear flow is investigated. An exact relation between the density autocorrelation function and the density-mometum correlation function implies that the former must…
We investigate continuum percolation for Cox point processes, that is, Poisson point processes driven by random intensity measures. First, we derive sufficient conditions for the existence of non-trivial sub- and super-critical percolation…
The global energy fluctuations of a low density gas granular gas in the homogeneous cooling state near its clustering instability are studied by means of molecular dynamics simulations. The relative dispersion of the fluctuations is shown…
Systems of particles in a confining potential exhibit a spatially dependent density which fundamentally alters the nature of phase transitions that occur. A specific instance of this situation, which is being extensively explored currently,…
Disagreement percolation connects a Gibbs lattice gas and i.i.d. site percolation on the same lattice such that non-percolation implies uniqueness of the Gibbs measure. This work generalises disagreement percolation to the hard-sphere model…
We introduce a novel percolation model that generalizes the classical Random Connection Model (RCM) to a random simplicial complex, allowing for a more refined understanding of connectivity and emergence of large-scale structures in random…
We investigate properties of the correlation function of clusters of galaxies using geometrical models. On small scales the correlation function depends on the shape and the size of superclusters. On large scales it describes the geometry…
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…
We study the percolation phase transition in hierarchical scale-free nets. Depending on the method of construction, the nets can be fractal or small-world (the diameter grows either algebraically or logarithmically with the net size),…