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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. doi:10.1209/0295-5075/87/20001 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, Engineering and Medicine > Research Centres > Centre for Complexity Science Faculty of Science, Engineering and Medicine > Science > Physics |
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| 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: |
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| Volume: | Vol.87 | ||||
| Number: | No.2 | ||||
| Number of Pages: | 5 | ||||
| Page Range: | p. 20001 | ||||
| DOI: | 10.1209/0295-5075/87/20001 | ||||
| Status: | Peer Reviewed | ||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||
| Funder: | National Science Foundation (U.S.) (NSF) | ||||
| Grant number: | DMS-0553487 (NSF) |
Data sourced from Thomson Reuters' Web of Knowledge
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