Stationary growth and unique invariant harmonic measure of cylindrical DLA
Riccardo Marchetti, Alessandro Taloni, Emanuele Caglioti, Vittorio, Loreto, Luciano Pietronero
TL;DR
This paper proves the harmonic measure's stationarity and uniqueness in cylindrical DLA growth, linking multiscaling, multifractality, and conformal invariance, supported by extensive simulations.
Contribution
It establishes the harmonic measure's stationarity and uniqueness on cylindrical DLA interfaces, connecting theoretical analysis with numerical validation.
Findings
Harmonic measure is stationary, unique, and invariant on DLA interfaces.
The DLA fractal dimension characterizes the stationary growth scaling.
Growth properties of active and frozen zones are elucidated.
Abstract
We prove that the harmonic measure is stationary, unique and invariant on the interface of DLA growing on a cylinder surface. We provide a detailed theoretical analysis puzzling together multiscaling, multifractality and conformal invariance, supported by extensive numerical simulations of clusters built using conformal mappings and on lattice. The growth properties of the active and frozen zones are clearly elucidated. We show that the unique scaling exponent characterizing the stationary growth is the DLA fractal dimension.
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