TY - JOUR
T1 - Crossover scaling from multifractal theory
T2 - Dielectric breakdown with cutoffs
AU - Arian, Eyal
AU - Alstrøm, Preben
AU - Aharony, Amnon
AU - Stanley, H. Eugene
PY - 1989
Y1 - 1989
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=33645062366&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.63.2005
DO - 10.1103/PhysRevLett.63.2005
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C2 - 10040738
AN - SCOPUS:33645062366
SN - 0031-9007
VL - 63
SP - 2005
EP - 2009
JO - Physical Review Letters
JF - Physical Review Letters
IS - 19
ER -