Research PapersNo Access

A THEORETICAL ANALYSIS OF A PERCOLATION MODEL

SENCER TANERI

Gazi Muhtar Paşa Cad. Kılıçarslan Çık, Manolya Apt. No. 1-A-7 Feneryolu Kadıköy 34724, Istanbul, Turkey

https://doi.org/10.1142/S0217984912501692Cited by:0 (Source: Crossref)

Abstract

This is an analytical analysis of a previously published research for a percolation simulation. In that research the effect of mutations on adaptability was investigated in a bit-string model of invading species in a random environment. However, analytical analysis was missing which will be the topic here. The Hausdorff dimensions are calculated for the fractals and the conditions on invasion are analyzed analytically by manipulation of partial differential equations. Thus, various conclusions may be reached without having to run long simulations.

Keywords:

PACS: 02.60.Lj, 05.10.Ln, 05.45.Df

References

G. Grimmett, Percolation, 2nd edn. (Springer, 1999) p. 8. Google Scholar
S. Taneri, Eur. Phys. J. B 47, 417 (2005). Web of Science, ADS, Google Scholar
J. M. Smith , Evolutionary Genetics ( Oxford University Press , Oxford , 1999 ) . Google Scholar
I. Jensen, H. C. Fogeby and R. Dickman, Phys. Rev. A R41, 3411 (1990). ADS, Google Scholar
C. F. Ferrara and J. F. Fontanari, Phys. Rev. E 65, 021902-1 (2002). Web of Science, Google Scholar
T. Vicsek , Fractal Growth Phenomena ( Utopia Press , Singapore , 1989 ) . Link, Google Scholar
R. N. Onody and R. A. Zara, Phys. Rev. E 56, 2548 (1997). Web of Science, ADS, Google Scholar
R. A. Zara and R. N. Onody, Int. J. Mod. Phys. C 10, 229 (1999). Google Scholar
K. J. Falconer, Fractal Geometry Mathematical Foundations and Applications (John Wiley, New York, 2003) p. 152. Google Scholar