Topic
Percolation
About: Percolation is a research topic. Over the lifetime, 11031 publications have been published within this topic receiving 283312 citations.
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TL;DR: In this article, the electrical conductivity of polyamide-6 and carbon nanotubes (NT) composites was analyzed and compared to carbon black filled polyamide 6 composites.
695 citations
TL;DR: It is shown both analytically and numerically that reducing the coupling between the networks leads to a change from a first order percolation phase transition to a second orderpercolation transition at a critical point.
Abstract: We study a system composed from two interdependent networks A and B, where a fraction of the nodes in network A depends on nodes of network B and a fraction of the nodes in network B depends on nodes of network A. Because of the coupling between the networks, when nodes in one network fail they cause dependent nodes in the other network to also fail. This invokes an iterative cascade of failures in both networks. When a critical fraction of nodes fail, the iterative process results in a percolation phase transition that completely fragments both networks. We show both analytically and numerically that reducing the coupling between the networks leads to a change from a first order percolation phase transition to a second order percolation transition at a critical point. The scaling of the percolation order parameter near the critical point is characterized by the critical exponent � ¼ 1.
669 citations
TL;DR: In this article, the authors prove the statement in the title of the paper and prove it in the paper's Appendix A, Section 2, Section 3, Section 4, Section 5.
Abstract: We prove the statement in the title of the paper.
666 citations
TL;DR: In this article, the electrical conductivity of mixtures of conductive and insulating materials is reviewed and different models have been proposed aimed at the prediction of the conductivity or the percolation concentration.
Abstract: The electrical conductivity of mixtures of conductive and insulating materials is reviewed In general, the conductivity of such mixtures increases drastically at a certain concentration of the conductive component, the so-called percolation concentration Among the parameters influencing the percolation concentration, the filler distribution, filler shape, filler/matrix interactions and the processing technique are the most important ones On the basis of these parameters, different models have been proposed aimed at the prediction of the conductivity or the percolation concentration It will be shown here that statistical, geometric or thermodynamic models explain the conductivity behaviour of specific mixtures on the basis of insufficient assumptions However, the conductivity seems to be predictable with the help of structure-oriented models
651 citations
TL;DR: In this article, the particle density has long-range correlations of the same form in iron, zinc or silicon dioxide aggregates, and the correlation data suggest a power-law spatial dependence giving a Hausdorff dimension between 1.7 and 1.9.
Abstract: Ultrafine smoke particles stick together to form chain-like aggregates. We find that the particle density has long-range correlations of the same form in iron, zinc or silicon dioxide aggregates. The correlation data suggest a power-law spatial dependence giving a Hausdorff dimension between 1.7 and 1.9. We discuss the consistency of these results with a model based on percolation. We also compare our results with a random-walk model, which has a nominal Hausdorff dimension of 2.
637 citations