Percolation with nearest neighbour interaction

Duckers, Les

doi:10.1016/0375-9601(78)90029-4

Cited by 20 publications

(10 citation statements)

References 4 publications

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“…In previous studies [2,3,6,7], the relation between the correlation strength and the percolation threshold was discussed. In our model, if we deem the polymer length as a measure of the correlation strength, we would conclude that the critical occupation probability decreases as the correlation strength goes up.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…This assumption simplifies the problem, but is not always satisfied in reality. The introduction of correlations into the percolation problem dates back to the 1970s, when Duckers [2,3] studied site percolation with correlations. These early simulation data seemed to suggest a non-monotonic behavior of the percolation threshold as a function of the correlation strength.…”

Section: Introductionmentioning

confidence: 99%

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Two-dimensional polymer networks near percolation

Schmittmann

Zia

2007

J. Phys. A: Math. Theor.

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We report an extensive finite-size study of polymer networks near the percolation threshold, using numerical techniques. The polymers are modeled by random walks occupying the bonds of a two-dimensional square lattice. We measure the percolation threshold and critical exponents of the networks for various polymer lengths. We find that the critical occupation probability is a decreasing function of the polymer length, and the percolation of polymers with a fixed polymer length belongs to the same universality class as ordinary bond percolation. By adding particles to the lattice cells we can study the diffusion process in polymer networks. Measuring the current near percolation, we observe that its critical exponent is also independent of polymer length.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Two-dimensional polymer networks near percolation

Schmittmann

Zia

2007

J. Phys. A: Math. Theor.

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“…To gain a deeper insight, it is fruitful to investigate how the percolation behavior depends on the intercomponent interaction, which affects the correlation of the domain patterns. It is known that the percolation threshold is sensitive to the correlation between elements, i.e., the number of vertices in bond percolation and the intersite interaction in annealed percolation [20,[35][36][37]. The most important report related to us is Ref.…”

Section: E Percolation Thresholdmentioning

confidence: 99%

Phase-ordering percolation and an infinite domain wall in segregating binary Bose-Einstein condensates

2015

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Percolation theory is applied to the phase-transition dynamics of domain pattern formation in segregating binary Bose-Einstein condensates in quasi-two-dimensional systems. Our finite-sizescaling analysis shows that the percolation threshold of the initial domain pattern emerging from the dynamic instability is close to 0.5 for strongly repulsive condensates. The percolation probability is universally described with a scaling function when the probability is rescaled by the characteristic domain size in the dynamic scaling regime of the phase-ordering kinetics, independent of the intercomponent interaction. It is revealed that an infinite domain wall sandwiched between percolating domains in the two condensates has an noninteger fractal dimension and keeps the scaling behavior during the dynamic scaling regime. This result seems to be in contrast to the argument that the dynamic scale invariance is violated in the presence of an infinite topological defect in numerical cosmology.PACS numbers: 67.85. Fg, 64.60.ah 47.37.+q, 98.80.Cq

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“…1(c) shows the same for the negative (repulsive) correlation ( k v = k h = 0.1). It is evident that strong attractive correlation promotes formation of dense clusters and that the percolation threshold in this case is achieved at a much larger concentration of damaged sites, excluding some low values of k , where p c may be even less than in the case of k v = k h = 1 (Duckers 1978).…”

Section: Percolation Structuresmentioning

confidence: 70%

Seismological criticality concept and percolation model of fracture

Chélidzé¹,

Kolesnikov²,

Matcharashvili³

2006

Geophysical Journal International

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S U M M A R YIn the present paper we consider an anisotropically correlated percolation model of fracture (PMF), namely, the geometry of fracture structures, the energy emission model and the evolution of scatter of emitted (effective) amplitudes at attaining the critical point (CP; percolation threshold). The sequences of effective amplitudes calculated from PMF are considered as proxies of seismic catalogues and are analysed by various linear and non-linear methods, developed in modern time-series analysis. It is shown that the drastic increase in the scatter of amplitudes is a good precursor of the impending CP even in the case of an individual percolation run. The Lempel-Ziv (LZ) complexity test reveals clear non-linear structure in the sequence of effective amplitudes; the value LZ = 0.750 is significantly less than LZ for random process (LZ = 1) and the Hurst exponent is in the range 0.8-0.85. Both these results point to the appearance of some order in the generation of effective emission events, due, probably, to the memory property of percolation processes. Various tests (curvature parameter, Shannon entropy) show that the acceleration of model seismicity close to the CP increases with the growth of anisotropic correlation (AC). The role of AC in the acceleration of energy emission, and Shannon entropy behaviour close to the CP, are analysed.

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Percolation with nearest neighbour interaction

Cited by 20 publications

References 4 publications

Two-dimensional polymer networks near percolation

Two-dimensional polymer networks near percolation

Phase-ordering percolation and an infinite domain wall in segregating binary Bose-Einstein condensates

Seismological criticality concept and percolation model of fracture

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