Construct · 3 fields · 4 citations
One name. Different field. Different construct. One map.
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The mathematical study of the connected clusters that form when the sites or bonds of a random graph or lattice are independently occupied with probability p: as p rises past a critical value, the percolation threshold, a giant cluster that spans the whole system appears abruptly. Broadbent and Hammersley's 1957 Percolation processes introduced the model to capture how a fluid spreads through a random medium, and Stauffer and Aharony's textbook set out its scaling laws and critical exponents. The referent is a connectivity transition in an abstract random structure, quantified by a threshold probability, not water moving through real soil or a rumour moving through a crowd.[1][2]
The downward movement of water through unsaturated soil and porous rock under gravity, after it infiltrates at the surface and before it reaches the water table: the rate is governed by the pore structure and the current water content of the medium. Hillel's Environmental Soil Physics treats this deep percolation as a term in the soil water balance, distinct from infiltration at the surface and from saturated groundwater flow. The referent is real water draining through a physical medium, measured as a percolation rate in millimetres per hour, and it is the meaning probed in a septic-system perc test, not an abstract lattice or a social contagion.[3]
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Sociology and diffusion
the spread of information, products, or opinions through a population as each person passes it on past a personal threshold.The spread of information, a product, or an opinion through a population, modelled by treating each person as a site that passes the message to neighbours only when it clears their personal threshold: adoption becomes self-sustaining once a connected path of receptive individuals spans the network. Solomon, Weisbuch, de Arcangelis, Jan, and Stauffer's 2000 Social percolation models borrowed the percolation threshold to describe when a film or fashion turns into a market-wide hit rather than fading out. The referent is a social diffusion process across people, and although it reuses the mathematics of the lattice meaning, its object is influence moving between agents, not water in soil.[4]