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 [Formula Presented] with respect to the bulk value of [Formula Presented] Furthermore, we are able to present a theoretical computation of the fractal dimension near the boundary in fairly good agreement with numerical data. © 1997 The American Physical Society.
Surface effects in invasion percolation
Caldarelli G.;
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 [Formula Presented] with respect to the bulk value of [Formula Presented] Furthermore, we are able to present a theoretical computation of the fractal dimension near the boundary in fairly good agreement with numerical data. © 1997 The American Physical Society.
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