Stationary Growth and Unique Invariant Harmonic Measure of Cylindrical Diffusion Limited Aggregation

Riccardo Marchetti, Alessandro Taloni, Emanuele Caglioti, Vittorio Loreto, and Luciano Pietronero

Phys. Rev. Lett. 109, 065501 – Published 8 August 2012

Abstract

We prove that the harmonic measure is stationary, unique, and invariant on the interface of diffusion limited aggregation (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 a 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.

Received 28 March 2012

DOI:https://doi.org/10.1103/PhysRevLett.109.065501

Authors & Affiliations

Riccardo Marchetti¹, Alessandro Taloni^1,2, Emanuele Caglioti³, Vittorio Loreto^1,4, and Luciano Pietronero^1,5

¹Dipartimento di Fisica, La Sapienza Università di Roma, P.le A. Moro 5, 00185 Rome, Italy
²CNR-IENI, Via R. Cozzi 53, 20125 Milano, Italy
³Dipartimento di Matematica, La Sapienza Università di Roma, P.le A. Moro 5, 00185 Rome, Italy
⁴ISI Foundation, Via Alassio 11/c 10126 Torino, Italy
⁵CNR-ISC, Via dei Taurini 19, 00185 Rome, Italy

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Issue

Vol. 109, Iss. 6 — 10 August 2012

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