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The existence or not of a percolation threshold on power law correlated graphs is a fundamental question for which a general criterion is lacking. In this work we investigate the problems of site and bond percolation on graphs with degree…
We investigated numerically the distribution of participation numbers in the 3d Anderson tight-binding model at the localization-delocalization threshold. These numbers in {\em one} disordered system experience strong level-to-level…
Complex networks display various types of percolation transitions. We show that the degree distribution and the degree-degree correlation alone are not sufficient to describe diverse percolation critical phenomena. This suggests that a…
For random percolation at p_c, the probability distribution P(n) of the number of spanning clusters (n) has been studied in large scale simulations. The results are compatible with $P(n) \sim \exp(-an^2)$ for all dimensions. We also study…
We study gradient percolation for site percolation on the triangular lattice. This is a percolation model where the percolation probability depends linearly on the location of the site. We prove the results predicted by physicists for this…
In composite materials composed of soft polymer matrix and stiff, high-aspect-ratio particles, the composite undergoes a transition in mechanical strength when the inclusion phase surpasses a critical density. This phenomenon (rheological…
In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially…
We study the percolation of FINITE-SIZED objects on two- and three-dimensional lattices. Our motivation stems, on one hand from some recent interesting experimental results on transport properties of impurity-doped oxide perovskites and on…
We study the effect of a transport current on the vortex-line lattice in isotropic type-II superconductors in the presence of strong thermal fluctuations by means of 'driven-diffusion' Monte Carlo simulations of a discretized London theory…
In this work we derive and study the analytical solution of the voltage and current diffusion equation for the case of a finite-length resistor-constant phase element (CPE) transmission line (TL) network that can represent a model for…
The problem of continuum percolation in dispersions of rods is reformulated in terms of weighted random geometric graphs. Nodes (or sites or vertices) in the graph represent spatial locations occupied by the centers of the rods. The…
We determine thresholds $p_c$ for random site percolation on a triangular lattice for neighbourhoods containing nearest (NN), next-nearest (2NN), next-next-nearest (3NN), next-next-next-nearest (4NN) and next-next-next-next-nearest (5NN)…
The earlier work of the author on Frequency estimation in three-phase power systems ( that is included as the reference number 1) is expanded to the distributed setting in order present a framework for the implementation of such a frequency…
The correct definition of the conductance of finite systems implies a connection to the system of the massive ideal leads. Influence of the latter on the properties of the system appears to be rather essential and is studied below on the…
We use very efficient algorithms to calculate low-density series for bond and site percolation on the directed triangular, honeycomb, kagom\'e, and $(4.8^2)$ lattices. Analysis of the series yields accurate estimates of the critical point…
Two distinct distribution functions $P_{sp}(m)$ and $P_{ns}(m)$ of the scaled largest cluster sizes $m$ are obtained at the percolation threshold by numerical simulations, depending on the condition whether the lattice is actually spanned…
Diffusion of electrons in three dimensional disordered systems is investigated numerically for all the three universality classes, namely, orthogonal, unitary and symplectic ensembles. The second moment of the wave packet $<\vv{r}^2(t)>$ at…
The dynamics of magnetic flux distributions across a YBaCuO strip carrying transport current is measured using magneto-optical imaging at 20 K. The current is applied in pulses of 40-5000 ms duration and magnitude close to the critical one,…
The distribution of return intervals of extreme events is studied in time series characterized by finite-term correlations with non-exponential decay. Precisely, it has been analyzed the statistics of the return intervals of extreme values…
We consider diffusive lattice gases on a ring and analyze the stability of their density profiles conditionally to a current deviation. Depending on the current, one observes a phase transition between a regime where the density remains…