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Diffusion-Limited Aggregation

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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 - LimitedAggregationAbhranil DasSPRING 2012
  2. 2. Mineral DendritesDendron = plant.Naturally occurring fissures in limestone and other rock arepercolated by manganese and iron solutions. Often mistaken forfossils.
  3. 3. Branched ElectrodepositionDendritic structures also form when materials freeze or crystallize out ofequilibrium. e.g: high voltage metal electrodeposition.Picture: Copper aggregate in copper sulphate solution
  4. 4. SimulationThe first computer model was given by Tom Witten at the College dé France and LenSander at the University of Michigan (~2000 citations), to describe how dust particlesform clumps in the air.
  5. 5. Simulation: Point Seed Brownian Tree
  6. 6. Simulation: Point SeedSnapshot 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 SeedSnapshot at dynamic equilibrium with about 250 drifters and 1300 aggregates, eachof radius 0.005 units.
  10. 10. Formation of Mineral DendritesSolutions of metal and oxide ions diffuse through rockcracks.When they meet, they produce a soluble compound.Beyond a concentration, the compound forms a colouredprecipitate.On meeting a precipitate molecule, a dissolved compoundmolecule 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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