Occupancy-probability scaling in diffusion-limited aggregation
LA Turkevich, H Scher - Physical review letters, 1985 - APS
LA Turkevich, H Scher
Physical review letters, 1985•APSA continuous-time random-walk theory of diffusion-limited aggregation yields perimeter
occupancy probabilities. Scaling relates the fractal dimension D to the cluster-tip occupancy
probabilities. These agree with the analytic probabilities near cusps of a lattice-symmetric
array of traps. On a two-dimensional square lattice D= 5 3, whereas D= 2 for the Eden
model, and D= 4 3 for the η= 2 dielectric breakdown model. D is not universal: D= 7 4 for the
two-dimensional triangular lattice. The square and triangular lattices bracket (±2.5%) …
occupancy probabilities. Scaling relates the fractal dimension D to the cluster-tip occupancy
probabilities. These agree with the analytic probabilities near cusps of a lattice-symmetric
array of traps. On a two-dimensional square lattice D= 5 3, whereas D= 2 for the Eden
model, and D= 4 3 for the η= 2 dielectric breakdown model. D is not universal: D= 7 4 for the
two-dimensional triangular lattice. The square and triangular lattices bracket (±2.5%) …
Abstract
A continuous-time random-walk theory of diffusion-limited aggregation yields perimeter occupancy probabilities. Scaling relates the fractal dimension D to the cluster-tip occupancy probabilities. These agree with the analytic probabilities near cusps of a lattice-symmetric array of traps. On a two-dimensional square lattice D= 5 3, whereas D= 2 for the Eden model, and D= 4 3 for the η= 2 dielectric breakdown model. D is not universal: D= 7 4 for the two-dimensional triangular lattice. The square and triangular lattices bracket (±2.5%) Meakin's large off-lattice simulations (D= 1.71).
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