Analysis 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 ca...
| Main Authors: | , , , |
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| Format: | Journal Article |
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IOP Publishing Ltd
2014
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| Online Access: | http://hdl.handle.net/20.500.11937/2895 |
| _version_ | 1848744078719582208 |
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| author | Lonsdale, Heather Jensen, I. Essam, J. Owczarek, A. |
| author_facet | Lonsdale, Heather Jensen, I. Essam, J. Owczarek, A. |
| author_sort | Lonsdale, Heather |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T05:55:45Z |
| format | Journal Article |
| id | curtin-20.500.11937-2895 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T05:55:45Z |
| publishDate | 2014 |
| publisher | IOP Publishing Ltd |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-28952018-03-29T09:05:21Z Analysis of mean cluster size in directed compact percolation near a damp wall Lonsdale, Heather Jensen, I. Essam, J. Owczarek, A. critical exponents and amplitudes (theory) percolation problems (theory) 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. 2014 Journal Article http://hdl.handle.net/20.500.11937/2895 10.1088/1742-5468/2014/03/P03004 IOP Publishing Ltd restricted |
| spellingShingle | critical exponents and amplitudes (theory) percolation problems (theory) Lonsdale, Heather Jensen, I. Essam, J. Owczarek, A. Analysis of mean cluster size in directed compact percolation near a damp wall |
| title | Analysis of mean cluster size in directed compact percolation near a damp wall |
| title_full | Analysis of mean cluster size in directed compact percolation near a damp wall |
| title_fullStr | Analysis of mean cluster size in directed compact percolation near a damp wall |
| title_full_unstemmed | Analysis of mean cluster size in directed compact percolation near a damp wall |
| title_short | Analysis of mean cluster size in directed compact percolation near a damp wall |
| title_sort | analysis of mean cluster size in directed compact percolation near a damp wall |
| topic | critical exponents and amplitudes (theory) percolation problems (theory) |
| url | http://hdl.handle.net/20.500.11937/2895 |