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Active Width at a Slanted Active Boundary in Directed Percolation

Chun-Chung Chen·Hyunggyu Park·Marcel den Nijs
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Abstract

The width W of the active region around an active moving wall in a directed percolation process diverges at the percolation threshold p_c as W \simeq A ε^{-ν_\parallel} \ln(ε_0/ε), with ε=p_c-p, ε_0 a constant, and ν_\parallel=1.734 the critical exponent of the characteristic time needed to reach the stationary state ξ_\parallel \sim ε^{-ν_\parallel}. The logarithmic factor arises from screening of statistically independent needle shaped sub clusters in the active region. Numerical data confirm this scaling behaviour.

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Chun-Chung Chen, Hyunggyu Park, Marcel den Nijs. 1999-04-28. Active Width at a Slanted Active Boundary in Directed Percolation. https://doi.org/10.1103/physreve.60.2496

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