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Somfai E, Goold NR, Ball RC, et al. Growth by random walker sampling and scaling of the dielectric breakdown model. Phys Rev E Stat Nonlin Soft Matter Phys. 2004;70(5):051403doi: 10.1103/PhysRevE.70.051403.
Somfai, E., Goold, N. R., Ball, R. C., DeVita, J. P., & Sander, L. M. (2004). Growth by random walker sampling and scaling of the dielectric breakdown model. Physical review. E, Statistical, nonlinear, and soft matter physics, 70(5), 051403. https://doi.org/10.1103/PhysRevE.70.051403
Somfai, Ellák, et al. "Growth by random walker sampling and scaling of the dielectric breakdown model." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 70,5 (2004): 051403. doi: https://doi.org/10.1103/PhysRevE.70.051403
Somfai E, Goold NR, Ball RC, DeVita JP, Sander LM. Growth by random walker sampling and scaling of the dielectric breakdown model. Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Nov;70(5):051403. doi: 10.1103/PhysRevE.70.051403. Epub 2004 Nov 17. PMID: 15600614.
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Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Nov;70(5):051403. doi: 10.1103/PhysRevE.70.051403. Epub 2004 Nov 17.

Growth by random walker sampling and scaling of the dielectric breakdown model.

Physical review. E, Statistical, nonlinear, and soft matter physics

Ellák Somfai, Nicholas R Goold, Robin C Ball, Jason P DeVita, Leonard M Sander

Affiliations

  1. Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom. [email protected]

PMID: 15600614 DOI: 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.

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