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We perform Monte-Carlo simulations to study the Bernoulli ($p$) bond percolation on the enhanced binary tree which belongs to the class of nonamenable graphs with one end. Our numerical results show that the system has two different…
The enhanced binary tree (EBT) is a nontransitive graph which has two percolation thresholds $p_{c1}$ and $p_{c2}$ with $p_{c1}<p_{c2}$. Our Monte Carlo study implies that the second threshold $p_{c2}$ is significantly lower than a recent…
Percolation for a planar lattice has a single percolation threshold, whereas percolation for a negatively curved lattice displays two separate thresholds. The enhanced binary tree (EBT) can be viewed as a prototype model displaying two…
We propose a novel finite size scaling analysis for percolation transition observed in complex networks. While it is known that cooperative systems in growing networks often undergo an infinite order transition with inverted…
The main purpose of percolation theory is to model phase transitions in a variety of random systems, which is highly valuable in fields related to materials physics, biology, or otherwise unrelated areas like oil extraction or even quantum…
We study the percolative properties of bi-dimensional systems generated by a random sequential adsorption of line-segments on a square lattice. As the segment length grows, the percolation threshold decreases, goes through a minimum and…
A two parameter percolation model with nucleation and growth of finite clusters is developed taking the initial seed concentration \rho and a growth parameter g as two tunable parameters. Percolation transition is determined by the final…
By studying its subgraphs, it is argued that the lower critical percolation threshold of the enhanced binary tree (EBT) is bounded as $p_{c1} < 0.355059$, while the upper threshold is bounded both from above and below by 1/2 according to…
In [Watanabe et al., Phys. Rev. Lett. 93 190601 (2004)], the authors show numerically that spanning and percolation probabilities in two-dimensional systems with different aspect ratios obey a form of "superscaling". In this comment, we…
The finite-size scaling theory for continuous phase transition plays an important role in determining critical point and critical exponents from the size-dependent behaviors of quantities in the thermodynamic limit. For percolation phase…
Monte Carlo simulations alone could not clarify the corrections to scaling for the size-dependent p_c(L) above the upper critical dimension. Including the previous series estimate for the bulk threshold $p_c(\infty)$ gives preference for…
We study the percolation properties of the growing clusters model. In this model, a number of seeds placed on random locations on a lattice are allowed to grow with a constant velocity to form clusters. When two or more clusters eventually…
Scale transformations have played an extremely successful role in studies of cosmological large-scale structure by relating the non-linear spectrum of cosmological density fluctuations to the linear primordial power at longer wavelengths.…
We have studied the phase transition of the contact process near a multiple junction of $M$ semi-infinite chains by Monte Carlo simulations. As opposed to the continuous transitions of the translationally invariant ($M=2$) and semi-infinite…
Binary mixtures prepared in an homogeneous phase and quenched into a two-phase region phase-separate via a coarsening process whereby domains of the two phases grow in time. With a numerical study of a spin-exchange model we show that this…
We present a review of the recent progress on percolation scaling limits in two dimensions. In particular, we will consider the convergence of critical crossing probabilities to Cardy's formula and of the critical exploration path to…
Recently, a simple non-interacting-electron model, combining local quantum tunneling via quantum point contacts and global classical percolation, has been introduced in order to describe the observed ``metal-insulator transition'' in two…
Using a recently developed method to simulate percolation on large clusters of distributed machines [N. R. Moloney and G. Pruessner, Phys. Rev. E 67, 037701 (2003)], we have numerically calculated crossing, spanning and wrapping…
Cascading failures in complex systems have been studied extensively using two different models: $k$-core percolation and interdependent networks. We combine the two models into a general model, solve it analytically and validate our…
We have developed a 3-D Monte Carlo radiative transfer model which computes line and continuum polarization variability for a binary system with an optically thick non-axisymmetric envelope. This allows us to investigate the complex…