Tip Splittings and Phase Transitions in the Dielectric Breakdown Model: Mapping to the Diffusion-Limited Aggregation Model

TY - JOUR

T1 - Tip Splittings and Phase Transitions in the Dielectric Breakdown Model

T2 - Mapping to the Diffusion-Limited Aggregation Model

AU - Mathiesen, Joachim

AU - Jensen, Mogens H.

PY - 2002/1/1

Y1 - 2002/1/1

N2 - We show that the fractal growth described by the dielectric breakdown model exhibits a phase transition in the multifractal spectrum of the growth measure. The transition takes place because the tip splitting of branches forms a fixed angle. This angle is [Formula presented] dependent but it can be rescaled onto an “effectively” universal angle of the diffusion-limited aggregation branching process. We derive an analytic rescaling relation which is in agreement with numerical simulations. The dimension of the clusters decreases linearly with the angle and the growth becomes non-ractal at an angle close to [Formula presented] (which corresponds to [Formula presented]).

AB - We show that the fractal growth described by the dielectric breakdown model exhibits a phase transition in the multifractal spectrum of the growth measure. The transition takes place because the tip splitting of branches forms a fixed angle. This angle is [Formula presented] dependent but it can be rescaled onto an “effectively” universal angle of the diffusion-limited aggregation branching process. We derive an analytic rescaling relation which is in agreement with numerical simulations. The dimension of the clusters decreases linearly with the angle and the growth becomes non-ractal at an angle close to [Formula presented] (which corresponds to [Formula presented]).

UR - http://www.scopus.com/inward/record.url?scp=85038277556&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.88.235505

DO - 10.1103/PhysRevLett.88.235505

M3 - Journal article

AN - SCOPUS:85038277556

SN - 0031-9007

VL - 88

JO - Physical Review Letters

JF - Physical Review Letters

IS - 23

M1 - 235505

ER -