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Diffusion-Limited Aggregation

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Lecture 09
Lecture 09
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Diffusion-Limited Aggregation

A simulation of diffusion-limited aggregation (DLA) processes that give fractal shapes to mineral dendrites, electrodeposition etc.

A simulation of diffusion-limited aggregation (DLA) processes that give fractal shapes to mineral dendrites, electrodeposition etc.

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Diffusion-Limited Aggregation

  1. 1. Diffusion - Limited Aggregation Abhranil Das SPRING 2012
  2. 2. Mineral Dendrites Dendron = plant. Naturally occurring fissures in limestone and other rock are percolated by manganese and iron solutions. Often mistaken for fossils.
  3. 3. Branched Electrodeposition Dendritic structures also form when materials freeze or crystallize out of equilibrium. e.g: high voltage metal electrodeposition. Picture: Copper aggregate in copper sulphate solution
  4. 4. Simulation The first computer model was given by Tom Witten at the College dé France and Len Sander at the University of Michigan (~2000 citations), to describe how dust particles form clumps in the air.
  5. 5. Simulation: Point Seed Brownian Tree
  6. 6. Simulation: Point Seed Snapshot with 944 drifters and 1131 aggregates, each of radius 0.005 units.
  7. 7. Why this shape? • Why do the branches form? • Why are they retained? Why doesn’t the shape get filled in?
  8. 8. Diffusion to Capture
  9. 9. Simulation: Line Seed Snapshot at dynamic equilibrium with about 250 drifters and 1300 aggregates, each of radius 0.005 units.
  10. 10. Formation of Mineral Dendrites Solutions of metal and oxide ions diffuse through rock cracks. When they meet, they produce a soluble compound. Beyond a concentration, the compound forms a coloured precipitate. On meeting a precipitate molecule, a dissolved compound molecule sticks to it and adds to the precipitate. Therefore, the mechanism is the same as electrodeposition.
  11. 11. Fractal Dimension
  12. 12. Sources • Branches, Philip Ball, Oxford University Press 2009 • Diffusion-limited aggregation, T.A. Witten, L.M. Sander, Physical Review B 1983 • classes.yale.edu/fractals

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