Growth by Random Walker Sampling, and Scaling of the Dielectric Breakdown Model

Abstract

Random walkers absorbing on a boundary sample the Harmonic Measure linearly and independently: we discuss how the recurrence times between impacts enable non-linear moments of the measure to be estimated. From this we derive a new technique to simulate Dielectric Breakdown Model growth which is governed nonlinearly by the Harmonic Measure. Recurrence times are shown to be accurate and effective in probing the multifractal growth measure of diffusion limited aggregation. For the Dielectric Breakdown Model our new technique grows large clusters efficiently and we are led to significantly revise earlier exponent estimates. Previous results by two conformal mapping techniques were less converged than expected, and in particular a recent theoretical suggestion of superuniversality is firmly refuted.

9 pages, 8 figures

References in corpus (11)

• Laplacian growth as one-dimensional turbulence
• Scaling and Crossovers in Diffusion Limited Aggregation
• Multifractal Structure of the Harmonic Measure of Diffusion Limited Aggregates
• Fractal to Nonfractal Phase Transition in the Dielectric Breakdown Model
• Growth Exponents with 3.99 Walkers
• Scaling exponent of the maximum growth probability in diffusion-limited aggregation
• Off-lattice noise reduction and the ultimate scaling of DLA in two dimensions
• Theory of Diffusion Controlled Growth
• Diffusion-limited aggregation in channel geometry
• Theory of Diffusion Controlled Growth
• Branched Growth with $\eta \approx 4$ Walkers

Cited by in corpus (3)

• Anisotropic diffusion limited aggregation in three dimensions - universality and non-universality
• Random walks, diffusion limited aggregation in a wedge, and average conformal maps
• The dynamics of the angular and radial density correlation scaling exponents in fractal to non-fractal morphodynamics