Abstract

CAVALCANTE DA SILVA, P; CORSO, G  and  DA SILVA, L.R. Lattices with variable and constant occupation density and q-exponential distribution. Rev. mex. fis. [online]. 2008, vol.54, n.6, pp.459-463. ISSN 0035-001X.

In this paper we test the hypothesis that q-exponential distribution fits better on distributions arising from lattices with a heterogeneous topology than a homogeneous topology. We compare two lattices: the first is the typical square lattice with a constant occupation density p (the lattice used in standard percolation theory), and the second is a lattice constructed with a gradient of p. In the homogeneous lattice the occupied number of neighbors of each cell is the same (on average) for the full lattice, otherwise in the p-gradient lattice this number changes along the lattice. In this sense the p-gradient lattice shows a more complex topology than the homogeneous lattice. We fit the q-exponential and the stretched exponential distribution on the cluster size distribution that arises in the lattices. We observe that the q-exponential fits better on the p-gradient lattice than on a constant p lattice. On the other hand, the stretched exponential distribution fits equally well on both lattices.

Keywords : q-exponential distribution; gradient lattices; stretched exponential; topology.

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