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Finite-size effects and percolation properties of Poisson geometries

Abstract : Random tessellations of the space represent a class of prototype models of heterogeneous media, which are central in several applications in physics, engineering and life sciences. In this work, we investigate the statistical properties of d-dimensional isotropic Poisson geometries by resorting to Monte Carlo simulation, with special emphasis on the case d = 3. We first analyse the behaviour of the key features of these stochastic geometries as a function of the dimension d and the linear size L of the domain. Then, we consider the case of Poisson binary mixtures, where the polyhedra are assigned two 'labels' with complementary probabilities. For this latter class of random geometries, we numerically characterize the percolation threshold, the strength of the percolating cluster and the average cluster size.
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C. Larmier, E. Dumonteil, F. Malvagi, A. Mazzolo, Andrea Zoia. Finite-size effects and percolation properties of Poisson geometries. Physical Review E , American Physical Society (APS), 2016, 94 (1), pp.012130. ⟨10.1103/PhysRevE.94.012130⟩. ⟨cea-02388628⟩

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