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The Flory–Stockmayer theory was the first theory investigating percolation processes. [2] The history of the percolation model as we know it has its root in the coal industry. Since the industrial revolution, the economical importance of this source of energy fostered many scientific studies to understand its composition and optimize its use.
During the last decades, percolation theory, the mathematical study of percolation, has brought new understanding and techniques to a broad range of topics in physics, materials science, complex networks, epidemiology, and other fields. For example, in geology, percolation
In percolation theory this cluster is named the percolating cluster. This phenomenon is quantified in percolation theory by a number of quantities, for example the average cluster size . This quantity represents the average size of all finite clusters and is given by the following equation.
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. Both problems are solved similarly and one can find distributions to use in auction theory.
Examples can be found not only in physical phenomena, but also in biology, neuroscience, ecology (e.g. evolution), and economics (e.g. diffusion of innovation). Percolation can be considered to be a branch of the study of dynamical systems or statistical mechanics. In particular, percolation networks exhibit a phase change around a critical ...
The percolation threshold is a mathematical concept in percolation theory that describes the formation of long-range connectivity in random systems. Below the threshold a giant connected component does not exist; while above it, there exists a giant component of the order of system size.
The clique percolation method [1] is a popular approach for analyzing the overlapping community structure of networks.The term network community (also called a module, cluster or cohesive group) has no widely accepted unique definition and it is usually defined as a group of nodes that are more densely connected to each other than to other nodes in the network.
Pages in category "Percolation theory" The following 13 pages are in this category, out of 13 total. This list may not reflect recent changes. ...