Crossover scaling from multifractal theory: Dielectric breakdown with cutoffs

Eyal Arian*, Preben Alstrøm, Amnon Aharony, H. Eugene Stanley

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


The dielelctric breakdown model (DBM) is generalized to include lower cutoffs, which prevent growth at low fields. The new models may represent realistic situations in some DBM and some viscous fingering experiments. Multifractal theory is shown to provide quantitative predictions for the crossover from the usual DBM patterns (at small finger sizes) to a new, spiky, behavior (at large sizes). For one of the models, the theory also predicts when growth will stop. The predicted crossover scaling function is confirmed by numerical simulations.

Original languageEnglish
Pages (from-to)2005-2009
Number of pages5
JournalPhysical Review Letters
Issue number19
StatePublished - 1989


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