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what


lattice grid


connections


balls in place when p=0.63

     

PERCOLATION MODEL

  • Physicists make models.
    1. Put the balls on a lattice grid
    2. Put either a metal or a glass ball in each square of a grid
    3. Balls are ``connected'' to a ball above, below, right and left
    4. We want the sample to have top to bottom and right to left connections to conduct electricity - diagonal does not work in the standard model
    5. A ball would be metal with probability p between 0 and 1.0 and p_c is the critical value above which the sample is conducting
    6. We find this on a computer by calculating a random number between 0 and 1.0 for each square.
      We test if some p is the right one by checking which sites have metal balls by
      observing if p is greater than our number - if it is
      we put a metal ball there. If not a glass ball would go there.
  • Lets try p=1.0 - is there percolation?
  • Lets try p=0 - is there percolation?
  • What is the smallest p that works for our square grid???