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Diffusion in Disordered Media. Nicholas Senno PHYS 527 12/12/2013. Random Walk. Need to consider relationship between average displacement and time: <R 2 >  4Dt Can define diffusion constant from properties of classical random walk.

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diffusion in disordered media

Diffusion in Disordered Media

Nicholas Senno

PHYS 527


random walk
Random Walk
  • Need to consider relationship between average displacement and time:

<R2>  4Dt

  • Can define diffusion constant from properties of classical random walk.
  • However, because each cluster has different structure we need to average over many random walkers per cluster and then again over many clusters
blind ant
Blind Ant
  • Consider a random walker that can choose to move to any neighboring site with equal probability
  • If the move is possible it makes the move
  • If not the ant remains at the current location for the time step





myopic ant
Myopic Ant
  • What if the ant can see which neighboring sites are available?
  • Then we can save some computational steps by allowing the ant to move every time.
exact enumeration
Exact Enumeration
  • So far we have considered averages over many walkers but what if consider the probability distribution of every random walk?
  • The probability of being at a cluster site i at a time t+1 (call this number Wt+1(i)) only depends on the probability of the neighboring sites at time t.
  • This makes exact enumeration a recursive algorithm not a Monte Carlo Simulation.

Exact enumeration produces the same results as the myopic ant if enough clusters are averaged over.

diffusion in random media
Diffusion In Random Media
  • It is possible to define a diffusion constant in analogy to the classical random walk
  • The blind ant, myopic ant, and exact enumeration methods all give similar results but the implantation of each increases in complexity
  • The Monte Carlo simulations are good for large systems that scale well while the Recursive approach is better for smaller work stations.