Related papers: Distribution functions in percolation problems
These lectures give an introduction to the methods of conformal field theory as applied to deriving certain results in two-dimensional critical percolation: namely the probability that there exists at least one cluster connecting two…
We study the effects of nonreciprocity and network structure on percolation. To this end, we investigate nonreciprocal random networks - directed networks for which the probability of a link occurring from node i to node j differs from the…
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…
The average number $S_N(t)$ of distinct sites visited up to time t by N noninteracting random walkers all starting from the same origin in a disordered fractal is considered. This quantity $S_N(t)$ is the result of a double average: an…
We develop a theoretical approach to percolation in random clustered networks. We find that, although clustering in scale-free networks can strongly affect some percolation properties, such as the size and the resilience of the giant…
We study the distributions of traveling length l and minimal traveling time t through two-dimensional percolation porous media characterized by long-range spatial correlations. We model the dynamics of fluid displacement by the convective…
We study random networks of nonlinear resistors, which obey a generalized Ohm's law, $V\sim I^r$. Our renormalized field theory, which thrives on an interpretation of the involved Feynman Diagrams as being resistor networks themselves, is…
The functionality of nodes in a network is often described by the structural feature of belonging to the giant component. However, when dealing with problems like transport, a more appropriate functionality criterion is for a node to belong…
Focusing on multifractal properties we investigate electric transport on random resistor diode networks at the phase transition between the non-percolating and the directed percolating phase. Building on first principles such as symmetries…
Real networks are vulnerable to random failures and malicious attacks. However, when a node is harmed or damaged, it may remain partially functional, which helps to maintain the overall network structure and functionality. In this paper, we…
Crackling noise is a common feature in many systems that are pushed slowly, the most familiar instance of which is the sound made by a sheet of paper when crumpled. In percolation and regular aggregation clusters of any size merge until a…
Survival and percolation probabilities are most important quantities in the theory and in the application of growth models with spreading. We construct field theoretical expressions for these probabilities which are feasible for…
We consider the simple random walk on the (unique) infinite cluster of super-critical bond percolation in $\Z^d$ with $d\ge2$. We prove that, for almost every percolation configuration, the path distribution of the walk converges weakly to…
We consider propagation models that describe the spreading of an attribute, called "damage", through the nodes of a random network. In some systems, the average fraction of nodes that remain undamaged vanishes in the large system limit, a…
Analytical results are derived for the bond percolation threshold and the size of the giant connected component in a class of random networks with non-zero clustering. The network's degree distribution and clustering spectrum may be…
We construct a theory of distributions in the setting of analysis on post-critically finite self-similar fractals, and on fractafolds and products based on such fractals. The results include basic properties of test functions and…
While classical percolation is well understood, percolation effects in randomly packed or jammed structures are much less explored. Here we investigate both experimentally and theoretically the electrical percolation in a binary composite…
We consider the percolation problem of sites on an $L\times L$ square lattice with periodic boundary conditions which were unvisited by a random walk of $N=uL^2$ steps, i.e. are vacant. Most of the results are obtained from numerical…
Movements of molecular motors on cytoskeletal filaments are described by directed walks on a line. Detachment from this line is allowed to occur with a small probability. Motion in the surrounding fluid is described by symmetric random…
Statistical properties of the critical current distribution in superconductor with fractal clusters of a normal phase are considered. It is found that there is the range of fractal dimensions in which the variance and expectation for this…