Finite size effect of harmonic measure estimation in a DLA model: Variable size of probe particles

TL;DR

This paper investigates how the size of probe particles affects the estimation of harmonic measure in DLA models, introducing a variable probe size method that improves accuracy in fractal dimension estimation.

Contribution

It introduces a variable probe particle size approach to accurately estimate the harmonic measure and fractal dimension in DLA simulations, considering two limiting cases.

Findings

Enhanced accuracy in fractal dimension estimation.

Variation in probability distribution with probe particle size.

Successful simulation of large DLA clusters with improved measurement.

Abstract

A finite size effect in the probing of the harmonic measure in simulation of diffusion-limited aggregation (DLA) growth is investigated. We introduce a variable size of probe particles, to estimate harmonic measure and extract the fractal dimension of DLA clusters taking two limits, of vanishingly small probe particle size and of infinitely large size of a DLA cluster. We generate 1000 DLA clusters consisting of 50 million particles each, using an off-lattice killing-free algorithm developed in the early work. The introduced method leads to unprecedented accuracy in the estimation of the fractal dimension. We discuss the variation of the probability distribution function with the size of probing particles.