Boundary effects for invasion percolation are introduced and discussed here. The presence of boundaries determines a set of critical exponents characteristic of the boundary. In this paper we present numerical simulations showing a remarkably different fractal dimension for the region of the percolating cluster near the boundary. In fact, near the surface we find a value of D-sar= 1.67 +/- 0.03, with respect to the bulk value of D-bul = 1.87 +/- 0.01. Furthermore, we are able to present a theoretical computation of the fractal dimension near the boundary in fairly good agreement with numerical data.
Cafiero, R., Caldarelli, G., Gabrielli, A. (1997). Surface effects in invasion percolation. PHYSICAL REVIEW E, 56(2), R1291-R1294 [10.1103/PhysRevE.56.R1291].
Surface effects in invasion percolation
Gabrielli A.
1997-01-01
Abstract
Boundary effects for invasion percolation are introduced and discussed here. The presence of boundaries determines a set of critical exponents characteristic of the boundary. In this paper we present numerical simulations showing a remarkably different fractal dimension for the region of the percolating cluster near the boundary. In fact, near the surface we find a value of D-sar= 1.67 +/- 0.03, with respect to the bulk value of D-bul = 1.87 +/- 0.01. Furthermore, we are able to present a theoretical computation of the fractal dimension near the boundary in fairly good agreement with numerical data.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
