Search results
Results From The WOW.Com Content Network
In statistical physics and mathematics, percolation theory describes the behavior of a network when nodes or links are added. This is a geometric type of phase transition , since at a critical fraction of addition the network of small, disconnected clusters merge into significantly larger connected , so-called spanning clusters.
The percolation threshold is a mathematical concept in percolation theory that describes the formation of long-range connectivity in ... In discrete mathematics, this ...
Outside mathematics, the Eden growth model is used to model bacteria growth and deposition of material. Another example is comparing a minimized cost from the Vickrey–Clarke–Groves auction (VCG-auction) to a minimized path from first passage percolation to gauge how pessimistic the VCG-auction is at its lower limit.
Typically, a family of universality classes will have a lower and upper critical dimension: below the lower critical dimension, the universality class becomes degenerate (this dimension is 2d for the Ising model, or for directed percolation, but 1d for undirected percolation), and above the upper critical dimension the critical exponents ...
In two dimensional square lattice percolation is defined as follows. A site is "occupied" with probability p or "empty" (in which case its edges are removed) with probability 1 – p; the corresponding problem is called site percolation, see Fig. 2. Percolation typically exhibits universality.
Percolation clusters become self-similar precisely at the threshold density for sufficiently large length scales, entailing the following asymptotic power laws: . The fractal dimension relates how the mass of the incipient infinite cluster depends on the radius or another length measure, () at = and for large probe sizes, .
Thus the Erdős–Rényi process is the mean-field case of percolation. Some significant work was also done on percolation on random graphs. From a physicist's point of view this would still be a mean-field model, so the justification of the research is often formulated in terms of the robustness of the graph, viewed as a communication network.
Percolation centrality is a version of weighted betweenness centrality, but it considers the 'state' of the source and target nodes of each shortest path in calculating this weight. Percolation of a ‘contagion’ occurs in complex networks in a number of scenarios.