percolerend

Percolerend is a term used in discussions of percolation theory and related network dynamics to designate a state or process in which percolation-like connectivity governs system behavior. It is a neologism formed from percolation with the suffix -erend to indicate a property or tendency, and its exact usage can vary across disciplines.

Definition and scope: A percolerend regime refers to a situation where macroscopic transport, diffusion, or activation spreads through a medium primarily via connected clusters formed by random occupation or interaction. This regime sits between subcritical conditions, where clusters remain small, and supercritical conditions, where a single spanning cluster dominates. The percolerend perspective emphasizes the influence of network geometry and cluster structure on observed phenomena.

Applications: In porous media, percolerend dynamics describe transport near the percolation threshold, where conductivity and flow are controlled by the emergent spanning cluster. In neural and social networks, the term can describe cascades or spreading processes that depend on the formation of a connected pathway across the system. In materials science, percolerend conduction highlights the role of conductive pathways in determining overall conductivity.

Key properties: Percolerend systems often exhibit critical-like scaling, fractal features of clusters, and sensitivity to system size. Analyses typically employ finite-size scaling, cluster size distributions, and measurements of transport coefficients to characterize the regime.

Limitations and usage: The term is not uniformly standardized and may be used differently by researchers. It can overlap with phrases such as “percolation-dominated” or “percolating regime,” depending on the context and disciplinary conventions.

See also: Percolation theory, percolation threshold, cluster, diffusion in porous media, network contagion.