Invasion percolation on a tree and queueing models
نویسندگان
چکیده
منابع مشابه
Invasion Percolation in Presence of Gravity
Simultaneous capillary dominated displacement of the wetting and non-wetting phases are processes of interest in many disciplines including modeling of the penetration of polluting liquids in hydrology or the secondary migration in petroleum reservoir engineering. Percolation models and in particular invasion percolation is well suited to characterize the slow immiscible displaceme...
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This thesis concerns itself with three different stochastic models: the selfdestructive percoaltion model, the invasion percolation model and a stochastic dynamic for the incipient infinite cluster model. These models are all defined on a graph in the plane denoted by Z, which is obtained by taking the points of R with integer coordinates as vertices and two vertices are connected with an edge ...
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We consider invasion percolation on a rooted regular tree. For the infinite cluster invaded from the root, we identify the scaling behaviour of its r-point function for any r ≥ 2 and of its volume both at a given height and below a given height. In addition, we derive scaling estimates for simple random walk on the cluster starting from the root. We find that while the power laws of the scaling...
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simultaneous capillary dominated displacement of the wetting and non-wetting phases are processes of interest in many disciplines including modeling of the penetration of polluting liquids in hydrology or the secondary migration in petroleum reservoir engineering. percolation models and in particular invasion percolation is well suited to characterize the slow immiscible displacement of two flu...
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Starting from the root, extend k branches and append k children with probability p, or terminate with probability q = 1− p. Then, we have a finite k-ary tree with probability one if 0 ≤ p ≤ 1/k. Moreover, we give the expectation and variance of the length of ideal codewords for representing the finite trees. Furthermore, we establish the probability of obtaining infinite tree, that is, of penet...
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ژورنال
عنوان ژورنال: Physical Review E
سال: 2009
ISSN: 1539-3755,1550-2376
DOI: 10.1103/physreve.79.041133