Tip Splittings and Phase Transitions in the Dielectric Breakdown Model: Mapping to the Diffusion-Limited Aggregation Model
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Tip Splittings and Phase Transitions in the Dielectric Breakdown Model : Mapping to the Diffusion-Limited Aggregation Model. / Mathiesen, Joachim; Jensen, Mogens H.
I: Physical Review Letters, Bind 88, Nr. 23, 235505, 01.01.2002.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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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
VL - 88
JO - Physical Review Letters
JF - Physical Review Letters
SN - 0031-9007
IS - 23
M1 - 235505
ER -
ID: 203586595