Monte Carlo experiments on cluster size distribution in percolation

Hoshen, Joseph; Stauffer, Dietrich; Bishop, George H.; Harrison, R. J.; Quinn, George D.

doi:10.1088/0305-4470/12/8/022

Cited by 84 publications

(19 citation statements)

References 51 publications

(50 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For q = 3, deviations from linearity are already perceptible and, moreover, the hull-enclosed and domain area distributions can be resolved. For sufficiently low p (but probably valid for all p < p c ) the distribution tail is exponential [36,37,38,39,40,41] and the simulation data is compatible with [42,43] n rp (A, p) ∼ A −θ exp[−f (p)A], where the exponent θ depends on the dimension only (θ = 1 for d = 2). Since all q states are equally present, the domains are typically smaller the larger the value of q and the occupation dependent coefficient f (p) thus increases for increasing q or decreasing p. The data for the different distributions shown in Fig.…”

Section: T0 → ∞supporting

confidence: 52%

Curvature-driven coarsening in the two-dimensional Potts model

et al. 2010

View full text Add to dashboard Cite

We study the geometric properties of polymixtures after a sudden quench in temperature. We mimic these systems with the q-states Potts model on a square lattice with and without weak quenched disorder, and their evolution with Monte Carlo simulations with nonconserved order parameter. We analyze the distribution of hull-enclosed areas for different initial conditions and compare our results with recent exact and numerical findings for q =2 ͑Ising͒ case. Our results demonstrate the memory of the presence or absence of long-range correlations in the initial state during the coarsening regime and exhibit superuniversality properties.

show abstract

Section: T0 → ∞supporting

confidence: 52%

Curvature-driven coarsening in the two-dimensional Potts model

et al. 2010

View full text Add to dashboard Cite

show abstract

“…So, at p 0 = p 0c (N 0 ,α,µ), there is a serious jump in the number of bankruptcies necessary to destabilize the system from N 0 to N f ∼ 4N 0 (since γ ∼ 2, cf Hoschen et al 1979, Margolina et al 1984. However, if p 0 remains just below p 0c (N 0 ,α,µ), the initial N 0 bankruptcies of phase I are enough to trigger a macroscopic crisis.…”

Section: Analytical Predictionsmentioning

confidence: 99%

When the collective acts on its components: economic crisis autocatalytic percolation

Cantono

Solomon

2010

New J. Phys.

View full text Add to dashboard Cite

Agent-based models have improved the standards for empirical support and validation criteria in social, biological, cognitive and human sciences. Yet, the inclusion, in these models, of vertical interactions between various aggregation levels remains a challenge. We study analytically, numerically and by simulation the generic consequences of interactions between the collective and its individual components: the appearance of an autocatalytic loop between the dynamics of the collective and its components; the system, which is dominated by a limited number of factors amplified by this collective↔individuals autocatalytic loop; the microscopic features, which are not involved in the autocatalytic loop and are irrelevant at the systemic level; and how the above clarify the interplay between macroscopic predictable features and the ones dependent on random unpredictable individual events. Using the social and market percolation framework, we study the dramatic effects of the collective↔individuals autocatalytic loop on economic crisis propagation: the percolation transition becomes discontinuous; there are a few relevant regions and regimes corresponding to a quite diverse range of response policy options; there are stability ranges where appropriate policies can help to avoid macroscopic crisis percolation; and beyond those regions the systemic crisis might become unstoppable.

show abstract

“…Equation (6) suggests the slope τ − 1 ≈ 1.05, while the observed slope 0.96 is somewhat less than that. This is due to the impact of two concurrent phenomena: so-called "deviation from scaling" at small m [14] and finite-size effects at large m [17,14]; they are discussed below in Sect. 4.4.…”

Section: Distribution At Percolationmentioning

confidence: 99%

“…This phenomenon is especially important when the system is close to percolation and clusters of arbitrary large sizes have already been formed. The appropriate scale corrections for the mass distribution were studied by Hoshen et al [14] and Margolina et al [17].…”

Section: Corrected Scaling At Percolationmentioning

confidence: 99%

See 1 more Smart Citation

Inverse cascade in a percolation model: Hierarchical description of time-dependent scaling

2005

View full text Add to dashboard Cite

The dynamics of a 2D site percolation model on a square lattice is studied using the hierarchical approach introduced by Gabrielov et al., Phys. Rev. E, 60, 5293-5300, 1999. The key elements of the approach are the tree representation of clusters and their coalescence, and the Horton-Strahler scheme for cluster ranking. Accordingly, the evolution of percolation model is considered as a hierarchical inverse cascade of cluster aggregation. A three-exponent time-dependent scaling for the cluster rank distribution is derived using the Tokunaga branching constraint and classical results on percolation in terms of cluster masses. Deviations from the pure scaling are described. An empirical constraint on the dynamics of a rank population is reported based on numerical simulations.

show abstract

Monte Carlo experiments on cluster size distribution in percolation

Abstract: Abstract. Cluster statistics in two-and three-dimensional site percolation problems are derived here by Monte Carlo methods. The average number n, of percolation clusters with s occupied sites each is calculated by up to 19 runs on a 4000 X 4000 triangular lattice near p c .

Cited by 84 publications

References 51 publications

Curvature-driven coarsening in the two-dimensional Potts model

Curvature-driven coarsening in the two-dimensional Potts model

When the collective acts on its components: economic crisis autocatalytic percolation

Inverse cascade in a percolation model: Hierarchical description of time-dependent scaling

Contact Info

Product

Resources

About