On directed compact percolation near a damp wall
نویسندگان
چکیده
منابع مشابه
On directed compact percolation near a damp wall
The percolation probability for directed, compact percolation near a damp wall, which interpolates between the previously examined cases, is derived exactly. We find that the critical exponent β = 2 in common with the dry wall, rather than the value previously found in the wet wall and bulk cases. The solution is found via a mapping to a particular model of directed walks. We evaluate the exact...
متن کاملDirected compact percolation near a damp wall: mean length and mean number of wall contacts
Key aspects of the cluster distribution in the case of directed, compact percolation near a damp wall are derived as functions of the bulk occupation probability p and the wall occupation probability pw. The mean length of finite clusters and mean number of contacts with the wall are derived exactly, and we find that both results involve elliptic integrals and further multiple sum functions of ...
متن کاملAnalysis of mean cluster size in directed compact percolation near a damp wall
We investigate the behaviour of the mean size of directed compact percolation clusters near a damp wall in the low-density region, where sites in the bulk are wet (occupied) with probability p while sites on the wall are wet with probability pw. Methods used to find the exact solution for the dry case (pw = 0) and the wet case (pw = 1) turn out to be inadequate for the damp case. Instead we use...
متن کاملMean length of finite clusters in directed compact percolation near a damp wall
The mean length of finite clusters is derived exactly for the case of directed compact percolation near a damp wall. We find that the result involves elliptic integrals and exhibits similar critical behaviour to the dry wall case.
متن کاملDirected Compact Percolation near a wall: III. Exact results for the mean length and number of contacts
Existing exact results for the percolation probability and mean cluster size for compact percolation near a dry wall are extended to the mean cluster length and the mean number of contacts with the wall. The results are derived from our previous work on vesicles near an attractive wall and involve elliptic integrals as opposed to the simple rational forms found for the percolation probability a...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2009
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/42/12/125001