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Percolation in Evolving Media
In the previous chapters, we described the applications of percolation theory to flow and transport in porous media. The phenomena that we described...
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Primitive Loops, Loop Clusters, and Loop Percolation
Sets of discrete loops can be decomposed into connected clusters. This chapter focuses on loop clusters distribution and related Markovian...
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Directed Percolation and Its Applications
As described briefly in Chap. 3, a variant of the classical percolation called directed percolation (DP), has been shown to have fascinating...
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Applications of Percolation Theory
The first edition of this book was published in 1994. Since then considerable progress has been made in both theoretical developments of percolation...
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Inhomogeneous long-range percolation in the weak decay regime
We study a general class of percolation models in Euclidean space including long-range percolation, scale-free percolation, the weight-dependent...
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Extensions of the Classical Percolation Model
The classical percolation model described in Chap. 2 is appropriate when there are no correlations between...
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Percolation in Large-Scale Systems
Many of the applications of percolation theory that were described in the previous chapters are now well established in the sense that percolation is...
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Vector Percolation and Rigidity of Materials
In this chapter, elastic percolation models of disordered materials, which represent a significant extension of the resistor and pore-network models...
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Explosive Percolation and Its Applications
In Chap. 3 , we described many variants of the classical random bond or site percolation. Such variants...
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Percolation of three fluids on a honeycomb lattice
In this paper, we consider a generalization of percolation: percolation of three related fluids on a honeycomb lattice. Izyurov and Magazinov proved...
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Triangle Percolation on the Grid
We consider a geometric percolation process partially motivated by recent work of Hejda and Kala. Specifically, we start with an initial set
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Percolation of Repulsive Particles on Graphs
What are the percolation properties of a repulsive point process on an infinite connected graph? To treat this question, one starts by clearly state...
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More on Bond Percolation
In this chapter, we gather a few more results and open problems concerning percolations on random maps.
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Applications of Invasion Percolation
A highly important problem in engineering, physics, and chemistry is develo** efficient computational algorithms for studying complex phenomena....
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Site-bond percolation model of epidemic spreading with vaccination in complex networks
To study disease transmission with vaccination based on the network, we map an SIR model to a site-bond percolation model. In the case where the...
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Isoperimetric Inequalities and Supercritical Percolation on High-Dimensional Graphs
It is known that many different types of finite random subgraph models undergo quantitatively similar phase transitions around their percolation...
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Percolation in Biological Systems
Most biological systems are so complex that they preclude any reasonable description in terms of the exact interactions among their fundamental...