diffusion in disordered media
Download
Skip this Video
Download Presentation
Diffusion in Disordered Media

Loading in 2 Seconds...

play fullscreen
1 / 11

Diffusion in Disordered Media - PowerPoint PPT Presentation


  • 75 Views
  • Uploaded on

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.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Diffusion in Disordered Media' - keene


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
diffusion in disordered media

Diffusion in Disordered Media

Nicholas Senno

PHYS 527

12/12/2013

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.
slide10

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.
ad