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dc.contributor.authorLonsdale, Heather
dc.contributor.authorJensen, I.
dc.contributor.authorEssam, J.
dc.contributor.authorOwczarek, A.
dc.identifier.citationLonsdale, H. and Jensen, I. and Essam, J. and Owczarek, A. 2014. Analysis of mean cluster size in directed compact percolation near a damp wall. Journal of Statistical Mechanics: Theory and Experiment. P03004.

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 a series expansion for the pw = 2p case to obtain a second-order inhomogeneous differential equation satisfied by the mean size, which exhibits a critical exponent gamma = 2, in common with the wet wall result. For the more general case of pw = rp, with r rational, we use a modular arithmetic method for finding ordinary differential equations (ODEs) and obtain a fourth-order homogeneous ODE satisfied by the series. The ODE is expressed exactly in terms of r. We find that in the damp region 0 < r < 2 the critical exponent gamma damp = 1, which is the same as the dry wall result.

dc.publisherIOP Publishing Ltd
dc.subjectcritical exponents and amplitudes (theory)
dc.subjectpercolation problems (theory)
dc.titleAnalysis of mean cluster size in directed compact percolation near a damp wall
dc.typeJournal Article
dcterms.source.titleJournal of Statistical Mechanics: Theory and Experiment
curtin.accessStatusFulltext not available

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