Perkolationspfaden

Perkolationspfaden, often translated as percolation paths, are a fundamental concept in percolation theory. They refer to a connected cluster of occupied sites or bonds in a random lattice. In simpler terms, imagine a grid where some squares are filled (occupied) and others are empty. A percolation path is a sequence of adjacent filled squares that connect one side of the grid to another, or a central point to the edge. The existence and properties of these paths are crucial for understanding how a fluid can flow through a porous medium, how electrical current can pass through a disordered material, or how diseases can spread through a population.

The formation of percolation paths is governed by a critical probability, often denoted as pc. Below this probability, the occupied sites are too sparse to form a spanning cluster. Above pc, a connected cluster of infinite size, or a spanning cluster, emerges and percolates across the entire system. The study of percolation paths involves analyzing their length, tortuosity, and connectivity properties. These characteristics change dramatically near the percolation threshold. Researchers use simulations and analytical methods to determine pc and to characterize the behavior of these paths in various dimensions and lattice structures. Understanding percolation paths has applications in diverse fields, including material science, hydrology, and epidemiology.