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Continuum percolation thresholds for mixtures of spheres of different sizes. (English) Zbl 1008.60104
Summary: Using Monte-Carlo simulations, we find the continuum percolation threshold of a three-dimensional mixture of spheres of two different sizes. We fix the value of \(r\), the ratio of the volume of the smaller sphere to the volume of the larger sphere, and determine the percolation threshold for various values of \(x\), the ratio of the number of larger objects to the number of total objects. The critical volume fraction increases from \(\varphi_c=0.28955\pm 0.00007\) for equal-sized spheres to a maximum of \(\varphi_c^{\max}=0.29731\pm 0.00007\) for \(x\approx 0.11\), an increase of \(2.7 \%\).

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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