Percolation

Percolation is a mathematical model and theory used in statistical physics and material science. It is used to describe the behavior of connected clusters in a random graph. The theory of percolation is directly related to the study of phase transition, random graph, and critical phenomena.

Definition

Percolation, in the broadest sense, refers to the movement and filtering of fluids through porous materials. In the context of statistical physics, it is a mathematical model that describes the formation of long-range connectivity in random systems.

Percolation Theory

Percolation theory is a mathematical field that studies the behavior of connected clusters in a random graph. The theory was first introduced by Broadbent and Hammersley in 1957. It has since been applied to a wide range of physical and biological systems, including the spread of diseases, the movement of fluids in porous materials, and the behavior of neural networks.

Percolation Threshold

The percolation threshold is a mathematical constant that describes the point at which a system transitions from a disconnected state to a connected one. It is a critical parameter in percolation theory and has been studied extensively in both two and three dimensions.

Applications

Percolation theory has a wide range of applications in both physics and beyond. It is used to model the behavior of disordered materials, the spread of diseases, the flow of fluids in porous materials, and the behavior of neural networks, among other things.

See Also

• Phase transition
• Random graph
• Critical phenomena
• Percolation threshold
• Neural networks

References

Percolation Resources
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