Related papers: Critical phenomena in heterogeneous k-core percola…
Light is shown to exhibit critical and tricritical behavior in passive mode-locked lasers with externally injected pulses. It is a first and unique example of critical phenomena in a one-dimensional many body light-mode system. The phase…
Many man-made networks support each other to provide efficient services and resources to the customers, despite that this support produces a strong interdependency between the individual networks. Thus an initial failure of a fraction $1-p$…
Networks in the real world do not exist as isolated entities, but they are often part of more complicated structures composed of many interconnected network layers. Recent studies have shown that such mutual dependence makes real networked…
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…
Metal wire networks rely on percolation paths for electrical conduction, and by suitably introducing break-make junctions on a flexible platform, a network can be made to serve as a resistive strain sensor. Several experimental designs have…
We investigate percolation on growing networks where the evolution of connected components resembles a non-equilibrium version of the multiplicative coalescent. The supercritical $\pi> \pi_c$ regime for a host of such models was conjectured…
Bootstrap percolation is a well-known model to study the spreading of rumors, new products or innovations on social networks. The empirical studies show that community structure is ubiquitous among various social networks. Thus, studying…
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…
Descriptors that characterize the geometry and topology of the pore space of porous media are intimately linked to their transport properties. We quantify such descriptors, including pore-size functions and the critical pore radius…
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…
We study phase transition and percolation at criticality for three random graph models on the plane, viz., the homogeneous and inhomogeneous enhanced random connection models (RCM) and the Poisson stick model. These models are built on a…
Percolation in a scale-free hierarchical network is solved exactly by renormalization-group theory, in terms of the different probabilities of short-range and long-range bonds. A phase of critical percolation, with algebraic…
To enable the study of criticality in multicomponent fluids, the standard spherical model is generalized to describe an $\ns$-species hard core lattice gas. On introducing $\ns$ spherical constraints, the free energy may be expressed…
Signatures of critical behaviour in nuclear fragmentation are often based on arguments from percolation theory. We demonstrate with general thermodynamic considerations and studies of the Ising model that the reliance on percolation as a…
We numerically study bootstrap percolation on Kleinberg's spatial networks, in which the probability density function of a node to have a long-range link at distance $r$ scales as $P(r)\sim r^{\alpha}$. Setting the ratio of the size of the…
We consider bond percolation on the square lattice with perfectly correlated random probabilities. According to scaling considerations, mapping to a random walk problem and the results of Monte Carlo simulations the critical behavior of the…
One of the most remarkable social phenomena is the formation of communities in social networks corresponding to families, friendship circles, work teams, etc. Since people usually belong to several different communities at the same time,…
Using perturbative renormalization group we study the influence of random velocity field on the critical behaviour of directed bond percolation process near its second-order phase transition between absorbing and active phase. We consider…
In complex systems, external parameters often determine the phase in which the system operates, i.e., its macroscopic behavior. For nearly a century, statistical physics has extensively studied systems' transitions across phases,…
We analytically explore the scaling properties of a general class of nested subgraphs in complex networks, which includes the $K$-core and the $K$-scaffold, among others. We name such class of subgraphs $K$-nested subgraphs due to the fact…