No-enclave percolation corresponds to holes in the cluster backbone

Abstract

The no-enclave percolation (NEP) model introduced recently by Sheinman et al. can be mapped to a problem of holes within a standard percolation backbone, and numerical measurements of these holes gives the size-distribution exponent $\tau =1.82(1)$ of the NEP model. An argument is given that $\tau =1+d_B/2\approx 1.822$ where $d_B$ is the backbone dimension. On the other hand, a model of simple holes within a percolation cluster implies $\tau =1+d_f/2=187/96\approx 1.948$, where $d_f$ is the fractal dimension of the cluster, and this value is consistent with Sheinman et al.'s experimental results of gel collapse which gives $\tau =1.91(6)$. Both models yield a discontinuous maximum hole size at $p_c$, signifying explosive percolation behavior. At $p_c$, the largest hole fills exactly half the system, due to symmetry. Extensive numerical simulations confirm our results.

5 pages, 6 figures

References in corpus (12)

• Explosive percolation via control of the largest cluster
• Tricritical point in explosive percolation
• Modeling the dynamics of a tracer particle in an elastic active gel
• Connectivity disruption sparks explosive epidemic spreading
• Exact extreme value statistics at mixed order transitions
• Long-range random transverse-field Ising model in three dimensions
• Oscillating hysteresis in the q-neighbor Ising model
• Comment on "Anomalous Discontinuity at the Percolation Critical Point of Active Gels"
• A Minimal description of morphological hierarchy in two-dimensional aggregates
• Percolation with trapping mechanism drives active gels to the critically connected state
• Jamming vs. Caging in Three Dimensional Jamming Percolation
• Reply to Comment on "Anomalous Discontinuity at the Percolation Critical Point of Active Gels"

Cited by in corpus (11)

• Novel physics arising from phase transitions in biology
• Critical percolation clusters in seven dimensions and on a complete graph
• Finite-size scaling of critical avalanches
• Emergence of biconnected clusters in explosive percolation
• Barrier-Controlled Non-Equilibrium Criticality in Reactive Particle Systems
• Deterministic scale-invariant dynamics in a logistic Game-of-Life model
• A branching random-walk model of disease outbreaks and the percolation backbone
• Characterizing spatial point processes by percolation transitions
• Morphological transitions in supercritical generalized percolation and moving interfaces in media with frozen randomness
• No-exclaves percolation on random networks
• Iterative Site Percolation on Triangular Lattice