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Growth by random walker sampling and scaling of the dielectric breakdown model
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Somfai, Ellák, Goold, Nicholas R., Ball, Robin, DeVita, Jason P. and Sander, Leonard M. (Leonard Michael) (2004) Growth by random walker sampling and scaling of the dielectric breakdown model. Physical Review E, Vol.70 (No.5). doi:10.1103/PhysRevE.70.051403 ISSN 1063-651X.
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Official URL: http://dx.doi.org/10.1103/PhysRevE.70.051403
Abstract
Random walkers absorbing on a boundary sample the harmonic measure linearly and independently: we discuss how the recurrence times between impacts enable nonlinear moments of the measure to be estimated. From this we derive a technique to simulate dielectric breakdown model growth, which is governed nonlinearly by the harmonic measure. For diffusion-limited aggregation, recurrence times are shown to be accurate and effective in probing the multifractal growth measure in its active region. For the dielectric breakdown model our technique grows large clusters efficiently and we are led to significantly revise earlier exponent estimates. Previous results by two conformal mapping techniques were less converged than expected, and in particular a recent theoretical suggestion of superuniversality is firmly refuted.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Physics | ||||
Library of Congress Subject Headings (LCSH): | Random walks (Mathematics), Breakdown (Electricity) -- Mathematical models, Particles -- Mathematical models | ||||
Journal or Publication Title: | Physical Review E | ||||
Publisher: | American Physical Society | ||||
ISSN: | 1063-651X | ||||
Official Date: | 17 November 2004 | ||||
Dates: |
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Volume: | Vol.70 | ||||
Number: | No.5 | ||||
Number of Pages: | 8 | ||||
DOI: | 10.1103/PhysRevE.70.051403 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Open Access (Creative Commons) | ||||
Date of first compliant deposit: | 4 December 2015 | ||||
Date of first compliant Open Access: | 4 December 2015 | ||||
Funder: | European Commission (EC), Higher Education Funding Council for England (HEFCE) | ||||
Grant number: | HPMF-CT-2000-00800 (EC) |
Data sourced from Thomson Reuters' Web of Knowledge
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