Brak, R and Essam, J W (1999) Directed compact percolation near a wall: III. Exact results for the mean length and number of contacts. Journal of Physics A: Mathematical and General, 32 (2).
Full text access: Open
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 and cluster size below p_c. The results for the cluster length satisfy previously conjectured differential equations. A closed expression is conjectured for the mean size above p_c in terms of a hypergeometric function.
This is a Published version This version's date is: 15/01/1999 This item is peer reviewed
https://repository.royalholloway.ac.uk/items/1e24d41b-f727-fc9f-cead-21702ee4aba5/1/
Deposited by () on 23-Dec-2009 in Royal Holloway Research Online.Last modified on 23-Dec-2009
Published as J. Phys. A: Math. Gen. 32 355-367. Journal of Physics A: Mathematical and General copyright 1999 IoP Publishing Ltd.
1. M.Abramowitz and I.A.Stegun, Handbook of Mathematical Functions, (Dover 1964) 2. R. Brak, J. W. Essam and A. L. Owczarek (submitted to J. Phys. A) 3. M-P. Delest and G. Viennot, Theor. Comput. Sci. 34 169-206 (1984) 4. E. Domany and W. Kinzel, Phys. Rev. Letters. 53, 311-4 (1984) 5. J.W.Essam and A. J. Guttmann, J. Phys. A:Math. Gen. 28 3591-3598 (1995) 6. J. W. Essam and D. Tanlakishani, J. Phys. A:Math. Gen. 27 3743-50 (1994) 7. J. C. Lin Phys. Rev. A 45 R3394-7 (1992) 8. P. Paule and M. Schorn, A Mathematica version of Zeilberger's algorithm for proving binomial coefficient identities, J. Symbolic Computation 20 (1995),673-698. 9. C. Snow Hypergeometric and Legendre Functions wit Applications, Natl. Bur. Stand. (U.S.) Circ. No. 19 (U.S. GPO, Washington, D.C.,1952). 10. D. J. Zeilberger, Computational and Applied Maths. 32,321-68 (1990)