Michael J Kearney 2003 J. Phys. A: Math. Gen. 36 2663 doi:10.1088/0305-4470/36/11/302
Michael J Kearney
Show affiliationsA two-parameter model on a directed lattice is introduced to represent the growth and spread of clusters on the half-plane. The model exhibits a phase transition in the compact directed percolation universality class between a state where clusters are finite with probability one and a state where clusters are infinite with non-zero probability. In the finite regime, exact expressions are given for the mean perimeter length and area of the generated clusters for a variety of different boundary conditions. An illustrative example is considered, namely a forest fire spreading before a prevailing wind along the floor and sides of an idealized valley.
60Axx Foundations of probability theory
Issue 11 (21 March 2003)
Received 24 January 2003
Published 6 March 2003
Michael J Kearney 2003 J. Phys. A: Math. Gen. 36 2663
S Okamura et al 2004 Plasma Phys. Control. Fusion 46 A113
Fèlix Casanova et al 2008 Nanotechnology 19 315709
R. C. Duncan and Hui Li 1997 ApJ 484 720
V A De Lorenci et al 1999 Class. Quantum Grav. 16 3047
Hidetomo Sawai et al. 2008 ApJ 672 465
Vladimir Al Osipov and Eugene Kanzieper 2009 J. Phys. A: Math. Theor. 42 475101
César Briceño et al. 2002 ApJ 580 317
W Prellier et al 2005 J. Phys.: Condens. Matter 17 R803
Thomas E. Harrison et al. 2007 ApJ 656 444