Search results for "Continuum percolation theory"
showing 4 items of 4 documents
Percolation on correlated random networks
2011
We consider a class of random, weighted networks, obtained through a redefinition of patterns in an Hopfield-like model and, by performing percolation processes, we get information about topology and resilience properties of the networks themselves. Given the weighted nature of the graphs, different kinds of bond percolation can be studied: stochastic (deleting links randomly) and deterministic (deleting links based on rank weights), each mimicking a different physical process. The evolution of the network is accordingly different, as evidenced by the behavior of the largest component size and of the distribution of cluster sizes. In particular, we can derive that weak ties are crucial in o…
Percolation and Schramm–Loewner evolution in the 2D random-field Ising model
2011
Abstract The presence of random fields is well known to destroy ferromagnetic order in Ising systems in two dimensions. When the system is placed in a sufficiently strong external field, however, the size of clusters of like spins diverges. There is evidence that this percolation transition is in the universality class of standard site percolation. It has been claimed that, for small disorder, a similar percolation phenomenon also occurs in zero external field. Using exact algorithms, we study ground states of large samples and find little evidence for a transition at zero external field. Nevertheless, for sufficiently small random-field strengths, there is an extended region of the phase d…
Dynamic percolation transition induced by phase separation: A Monte Carlo analysis
1987
The percolation transition of geometric clusters in the three-dimensional, simple cubic, nearest neighbor Ising lattice gas model is investigated in the temperature and concentration region inside the coexistence curve. We consider “quenching experiments,” where the system starts from an initially completely random configuration (corresponding to equilibrium at infinite temperature), letting the system evolve at the considered temperature according to the Kawasaki “spinexchange” dynamics. Analyzing the distributionnl(t) of clusters of sizel at timet, we find that after a time of the order of about 100 Monte Carlo steps per site a percolation transition occurs at a concentration distinctly l…
On multi-scale percolation behaviour of the effective conductivity for the lattice model
2015
Macroscopic properties of heterogeneous media are frequently modelled by regular lattice models, which are based on a relatively small basic cluster of lattice sites. Here, we extend one of such models to any cluster's size kxk. We also explore its modified form. The focus is on the percolation behaviour of the effective conductivity of random two- and three-phase systems. We consider only the influence of geometrical features of local configurations at different length scales k. At scales accessible numerically, we find that an increase in the size of the basic cluster leads to characteristic displacements of the percolation threshold. We argue that the behaviour is typical of materials, w…