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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, R. C., 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). 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
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Divisions:	Faculty of 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
Date:	17 November 2004
Volume:	Vol.70
Number:	No.5
Number of Pages:	8
Identification Number:	10.1103/PhysRevE.70.051403
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access
Funder:	European Commission (EC), Higher Education Funding Council for England (HEFCE)
Grant number:	HPMF-CT-2000-00800 (EC)
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URI:	http://wrap.warwick.ac.uk/id/eprint/7508