Analysis of mean cluster size in directed compact percolation near a damp wall
dc.contributor.author | Lonsdale, Heather | |
dc.contributor.author | Jensen, I. | |
dc.contributor.author | Essam, J. | |
dc.contributor.author | Owczarek, A. | |
dc.date.accessioned | 2017-01-30T10:26:58Z | |
dc.date.available | 2017-01-30T10:26:58Z | |
dc.date.created | 2015-09-01T20:00:45Z | |
dc.date.issued | 2014 | |
dc.identifier.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. | |
dc.identifier.uri | http://hdl.handle.net/20.500.11937/2895 | |
dc.identifier.doi | 10.1088/1742-5468/2014/03/P03004 | |
dc.description.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. | |
dc.publisher | IOP Publishing Ltd | |
dc.subject | critical exponents and amplitudes (theory) | |
dc.subject | percolation problems (theory) | |
dc.title | Analysis of mean cluster size in directed compact percolation near a damp wall | |
dc.type | Journal Article | |
dcterms.source.volume | 2014 | |
dcterms.source.number | 3 | |
dcterms.source.issn | 1742-5468 | |
dcterms.source.title | Journal of Statistical Mechanics: Theory and Experiment | |
curtin.accessStatus | Fulltext not available |