Some Applications of the Percolation Theory. Brief Review of the Century Beginning

Abstract

The review is a brief description of the state of problems in percolation theory and their numerous applications, which are analyzed on base of interesting papers published in the last 15-20 years. At the submitted papers are studied both the cluster system of the physical body and its impact on the object in general, and adequate mathematical tools for description of critical phenomena too. Of special interest are the data, first, the point of phase transition of certain of percolation system is not really a point, but it is a critical interval, and second, in vicinity of percolation threshold observed many different infinite clusters instead of one infinite cluster that appears in traditional consideration.

arXiv admin note: text overlap with arXiv:1104.5376, arXiv:1205.0691 by other authors

References in corpus (4)

• "Explosive Percolation" Transition is Actually Continuous
• Gaussian model of explosive percolation in three and higher dimensions
• New universality class in percolation on multifractal scale-free planar stochastic lattice
• On multi-scale percolation behaviour of the effective conductivity for the lattice model

Cited by in corpus (2)

• Percolative scale-free behavior in the boiling crisis
• Hydrogen bonding and percolation in propan-2-ol -- water liquid mixtures: X-ray diffraction experiments and computer simulations