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# Diffusion in Disordered Media - PowerPoint PPT Presentation

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

Nicholas Senno

PHYS 527

12/12/2013

• 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

• 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

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• When p = pc the asymptotic behavior changes to <R2> ∝ t0.79

• 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.

• 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 ant if enough clusters are averaged over.

• 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.