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The harmonic measure of diffusion-limited aggregates including rare events

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Adams, D. A., Sander, Leonard M. (Leonard Michael), Somfai, Ellák and Ziff, R. M.. (2009) The harmonic measure of diffusion-limited aggregates including rare events. Europhysics Letters, Vol.87 (No.2). p. 20001. ISSN 0295-5075

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Official URL: http://dx.doi.org/10.1209/0295-5075/87/20001

Abstract

We obtain the harmonic measure of diffusion-limited aggregate (DLA) clusters using a biased random-walk sampling technique which allows us to measure probabilities of random walkers hitting sections of clusters with unprecedented accuracy; our results include probabilities as small as 10- 80. We find the multifractal D(q) spectrum including regions of small and negative q. Our algorithm allows us to obtain the harmonic measure for clusters more than an order of magnitude larger than those achieved using the method of iterative conformal maps, which is the previous best method. We find a phase transition in the singularity spectrum f(α) at α≈14 and also find a minimum q of D(q), qmin=0.9±0.05.

Item Type:

Journal Article

Subjects:

Q Science > QC Physics

Divisions:

Faculty of Science > Centre for Complexity Science
Faculty of Science > Physics

Library of Congress Subject Headings (LCSH):

Fractals -- Research, Random walks (Mathematics), Condensed matter -- Research, Statistical physics

Journal or Publication Title:

Europhysics Letters

Publisher:

EDP Sciences

ISSN:

0295-5075

Official Date:

July 2009

Dates:

Date	Event
July 2009	Published

Volume:

Vol.87

Number:

No.2

Number of Pages:

Page Range:

p. 20001

Identification Number:

10.1209/0295-5075/87/20001

Status:

Peer Reviewed

Access rights to Published version:

Open Access

Funder:

National Science Foundation (U.S.) (NSF)

Grant number:

DMS-0553487 (NSF)

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