We test the universal finite-size scaling of the cluster mass order parameter in two-dimensional (2D) isotropic and directed continuum percolation models below the percolation threshold by computer simulations. We found that the simulation data in the 2D continuum models obey the same scaling expression of massM to sample size L as generally accepted for isotropic lattice problems, but with a p...

In this paper, we outline the theory of epidemic percolation networks and their use in the analysis of stochastic susceptible-infectious-removed (SIR) epidemic models on undirected contact networks. We then show how the same theory can be used to analyze stochastic SIR models with random and proportionate mixing. The epidemic percolation networks for these models are purely directed because und...

Percolation has recently been proposed as a key component of an advanced program execution model for future generation high-end machines featuring adaptive data/code transformation and movement for effective latency tolerance. Percolation is related to conventional prefetch technique, but is more aggressive and smarter. A program unit (e.g. a procedure instance) is not ready to be scheduled for...

Numerical and analytical studies of the onset of percolation in high-aspect-ratio fiber fiber systems such as nanotube reinforced polymers available in the literature have consistently modeled fibers as penetrable, straight, capped cylinders, also referred to as spherocylinders. In reality, however, fibers of very high-aspect ratio embedded in a polymer do not come into direct physical contact ...

For biased random walk on the infinite cluster in supercritical i.i.d. percolation on Z, where the bias of the walk is quantified by a parameter β > 1, it has been conjectured (and partly proved) that there exists a critical value βc > 1 such that the walk has positive speed when β < βc and speed zero when β > βc. In this paper, biased random walk on the infinite cluster of a certain translatio...

We explicitly construct an uncountable class of infinite aperiodic plane graphs which have equal, and explicitly computable, bond percolation thresholds. Furthermore for both bond percolation and the random-cluster model all large scale properties, such as the values of the percolation threshold and the critical exponents, of the graphs are equal. This equivalence holds for all values of p and ...

The void percolation and conduction problems for equisized overlapping ellipsoids of revolution are investigated using the discretization method. The method is validated by comparing the estimated percolation threshold of spheres with the precise result found in literature. The technique is then extended to determine the threshold of void percolation as a function of the geometric aspect ratio ...

Percolation has recently been proposed as a key component of an advanced program execution model for future generation high-end machines featuring adaptive data/code transformation and movement for effective latency tolerance. An early evaluation of the performance effect of percolation is very important in the design space exploration of future generations of supercomputers. In this paper, we ...

We study the percolation properties of embedded topological defects, Z–vortices, and the occurrence of the corresponding Nambu monopoles in the electroweak theory for a Higgs mass MH ≈ 100 GeV, near to the crossover temperature. Although there is no phase transition anymore at such strong selfcoupling, we observe that the Z–vortices still exhibit a percolation transition that has been found rec...