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– Percolation theory has applications in physics, materials science, complex networks, and epidemiology.
– In geology, percolation involves water filtration through soil and rocks to recharge groundwater.
– Two-dimensional square lattice percolation involves site occupation probabilities.
– Universality is a common feature of percolation phenomena.
– Computer simulations are often used due to the complexity of obtaining exact analytical results.

Coffee percolation involves water passing through coffee grounds.
– Weathered material movement on slopes.
– Cracking of trees under sunlight and pressure.
– Robustness of biological virus shells to subunit removal.
– Percolation in porous media and disease spread.

**Efficient Algorithms:**
– The fastest percolation algorithm was developed by Mark Newman and Robert Ziff in 2000.
– Statistical physics concepts like scaling theory and critical phenomena are used.
– Combinatorics is employed to study percolation thresholds.
– Computer simulations are commonly used due to analytical model complexity.
– Percolation properties are characterized using renormalization and fractals.

**Applications and Studies:**
– Dental percolation increases decay rate under crowns.
– Percolation tests are essential for planning septic systems.
– Studies reveal biophysical properties of virus-like particles.
– Critical behavior of epidemic processes is studied.
– Spread of epidemic diseases on networks is analyzed.

**Further Reading:**
– “What is percolation?” by Harry Kesten.
– “Applications of Percolation Theory” by Muhammad Sahimi.
– “Percolation” (2nd ed.) by Geoffrey Grimmett.
– “Introduction to Percolation Theory” by Dietrich Stauffer and Ammon Aharony.
– “Percolation and Conduction” by Scott Kirkpatrick.

Percolation (Wikipedia)

In physics, chemistry, and materials science, percolation (from Latin percolare 'to filter, trickle through') refers to the movement and filtering of fluids through porous materials. It is described by Darcy's law. Broader applications have since been developed that cover connectivity of many systems modeled as lattices or graphs, analogous to connectivity of lattice components in the filtration problem that modulates capacity for percolation.

In coffee percolation, soluble compounds leave the coffee grounds and join the water to form coffee. Insoluble compounds (and granulates) remain within the coffee filter.
Percolation in a square lattice.
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