We define a percolation problem on the basis of spin configurations of the two-dimensional XY model. Neighboring spins belong to the same percolation cluster if their orientations differ less than a certain threshold called the conducting angle. The percolation properties of this model are studied by means of Monte Carlo simulations and a finite-size scaling analysis. Our simulations show the e...

Abstract Nowadays, as accepted as the era of information or digital, time has changed and has invited all people to a new world in which everybody must define himself. Avoiding from getting benefit from this human progress is useless; Rather, we must know this great technology best and adapt ourselves with its consequences. In fact, in many countries and among many nations there had been peopl...

A water-table dependent reservoir model to investigate the effect of drought and vascular plant invasion on peatland hydrology. Author manuscript, published in "Journal of Hydrology (2013) 32 p." 2 ABSTRACT: This paper investigates the water table dynamics in a peatland showing a wide range of water table fluctuations. A reservoir model of water table fluctuations in a double-porosity peat is p...

Electrical conductivity and permittivity of carbon black-polyvinyl chloride composites were studied over a wide frequency spectrum (dc, 1.3 GHz). Conductivity of the bulk composites increases with higher volume fraction of carbon black as expected. However, the functional dependence of the increasing conductivity with carbon black loading is different below and above the percolation threshold b...

We study percolation in the hierarchical lattice of order N where the probability of connection between two points separated by distance k is of the form ck/N , δ > −1. Since the distance is an ultrametric, there are significant differences with percolation in the Euclidean lattice. We consider three regimes: δ < 1, where percolation occurs, δ > 1, where it does not occur, and δ = 1 which is th...

The location and nature of the percolation transition in random networks is a subject of intense interest. Recently, a series of graph evolution processes have been introduced that lead to discontinuous percolation transitions where the addition of a single edge causes the size of the largest component to exhibit a significant macroscopic jump in the thermodynamic limit. These processes can hav...

We describe in detail an efficient algorithm for studying site or bond percolation on any lattice. The algorithm can measure an observable quantity in a percolation system for all values of the site or bond occupation probability from zero to one in an amount of time that scales linearly with the size of the system. We demonstrate our algorithm by using it to investigate a number of issues in p...

There has been a great deal of interest and activity in percolation theory since the two Saint-Flour courses, [76, 111], of 1984 and 1996 reprinted in this new edition. We present here a summary of progress since the first publications of our lecture notes. The second edition of Percolation, [77], was published in 1999 as a fairly complete, contemporary account of ‘classical’ percolation (but w...