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    Analysis of mean cluster size in directed compact percolation near a damp wall

    Access Status
    Fulltext not available
    Authors
    Lonsdale, Heather
    Jensen, I.
    Essam, J.
    Owczarek, A.
    Date
    2014
    Type
    Journal Article
    
    Metadata
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    Citation
    Lonsdale, 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.
    Source Title
    Journal of Statistical Mechanics: Theory and Experiment
    DOI
    10.1088/1742-5468/2014/03/P03004
    ISSN
    1742-5468
    URI
    http://hdl.handle.net/20.500.11937/2895
    Collection
    • Curtin Research Publications
    Abstract

    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.

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