What is Percolation: Definition and 14 Discussions

In physics, chemistry and materials science, percolation (from Latin percolare, "to filter" or "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.

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  1. Mikkel

    I How Does Finite Size Scaling Reveal Cluster Behavior in 1D Percolation?

    Hello I am struggeling with a problem, or perhaps more with understanding the problem. I have to simulate a one dimensional percolation in Python and that part I can do. The issue is understanding the next line of the problem, which I will post here: "For the largest cluster size S, use finite...
  2. A

    A Could the 3D percolation model explain Regge-Trajectories?

    Regge-theory succesfully explains the latest LHC ##pp## elastic scattering experimental results and total cross-sections: https://arxiv.org/pdf/1711.03288 https://arxiv.org/abs/1808.08580 Three different Regge-trajectories are needed: one Reggeon, one (soft) Pomeron and one Odderon. The...
  3. M

    I Bootstrap percolation and percolation

    I read about bootstrap percolation and I would like to find links and similarities between bootstrap percolation and percolation (the initial model). I wonder if there is any result in percolation that is still valid in the bootstrap model.
  4. bananabandana

    Percolation Problem Homework: Probability of Cluster Size s

    Homework Statement We have a 1-D lattice [a line] of ##L## sites. Sites are occupied with probability ##p##. Find the probability that a given site is a member of a cluster of size ##s##. (A cluster is a set of adjacent occupied sites. The cluster size is the number of occupied sites in the...
  5. J

    Metal insulator transition and percolation

    Hello, For the past 2 days I've been looking for a resource discussing the metal insulator transition using percolation theory. (The next part treats the Anderson and Mott models) I'm studying for a course of solid state physics where this is mentioned/summarized. The problem is that the...
  6. D

    Systems simulated by a simple percolation model using python

    I'm a first year physics student, and one of my assignment for my programming class is about percolation. I need to create some disks randomly distributed in an area (this is a 2-D), and then by varying the density of the disk, I need to figure out the percolation threshold such that the two...
  7. S

    Visualization package for percolation paths

    Hello! Could you give me an example of visualization package or smth like that where i can get this kind of figure percolation paths ? Thanks!
  8. F

    MHB Percolation - Measure - Probability

    In $\Omega = \{0,1\}^{\mathbb{Z}^{2}}$, consider the class $C$ of cylinders. Show that $C$ is algebra. At $w\in \Omega$, we call cluster point $x$ all points $z\in \mathbb{Z}^{2}$ that can be attained from $x$ by a path that only passes by open dots. In the $\sigma$-algebra generated by $C...
  9. D

    What is Menshikov's Theorem and How Does it Relate to Percolation?

    Hi, I am trying to learn some stuff about percolation, specifically what Menshikov's theorem is about. On wiki http://en.wikipedia.org/wiki/Percolation_theory it says: "when p<pc, the probability that a specific point (for example, the origin) is contained in an open cluster of size r...
  10. H

    Percolation Theory: Any one know more?

    I am currently working in using the Ising model to study magnetization, and almost wrapping it up. The professor I am working with said I should get into percolation theory, so, my questions are: Has anyone worked with this, in what perspective? Currently i am an undergrad,I am planning to...
  11. B

    Understanding Percolation Threshold p_c on Triangular Lattices

    i am having some trouble understanding the meaning of what a percolation threshold is p_{c}. apparently on triangular lattices a threshold of 0.5 is the result on any sized lattice. however i can definitely think of a way to fill in half the points on a triangle lattice and not have it span...
  12. U

    Understanding Percolation Threshold and Periodic Boundary in Particle Systems

    I have two questions related to statistical physics or particle physics, could somebody help ?If this is not the right place for these questions, please advise. 1 What does 'percolation threshold' means for a system of particles? 2 What is "periodic boundary" in a particulate system? Is it...
  13. R

    Information on the percolation threshold

    Can anyone help me find information on the percolation threshold, i.e for when particle concentration is increased to a point when electrical pathways are created and resistance decreases by many orders, for metals loaded polymers. Cheers :smile: :-p :approve: :zzz: :blushing...
  14. C

    Tutorials for percolation simulations?

    Do you know any tutorials for percolation simulations? Thanks a ton! Carter Note: sorry, just don't know the correct place to post in.