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 Dsur=1.67±0.03, with respect to the bulk value of Dbul=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.
Surface effects in Invasion Percolation
Guido Caldarelli;Andrea Gabrielli
1997
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 Dsur=1.67±0.03, with respect to the bulk value of Dbul=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.File in questo prodotto:
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