Scaling exponent of the maximum growth probability in diffusion-limited aggregation
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Scaling exponent of the maximum growth probability in diffusion-limited aggregation. / Jensen, Mogens H.; Mathiesen, Joachim; Procaccia, Itamar.
I: Physical Review E, Bind 67, Nr. 4, 042402, 01.01.2003.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Scaling exponent of the maximum growth probability in diffusion-limited aggregation
AU - Jensen, Mogens H.
AU - Mathiesen, Joachim
AU - Procaccia, Itamar
PY - 2003/1/1
Y1 - 2003/1/1
N2 - An early (and influential) scaling relation in the multifractal theory of diffusion limited aggregation (DLA) is the Turkevich-Scher conjecture that relates the exponent [Formula presented] that characterizes the “hottest” region of the harmonic measure and the fractal dimension D of the cluster, i.e., [Formula presented] Due to lack of accurate direct measurements of both D and [Formula presented] this conjecture could never be put to a serious test. Using the method of iterated conformal maps, D was recently determined as [Formula presented] In this paper, we determine [Formula presented] accurately with the result [Formula presented] We thus conclude that the Turkevich-Scher conjecture is incorrect for DLA.
AB - An early (and influential) scaling relation in the multifractal theory of diffusion limited aggregation (DLA) is the Turkevich-Scher conjecture that relates the exponent [Formula presented] that characterizes the “hottest” region of the harmonic measure and the fractal dimension D of the cluster, i.e., [Formula presented] Due to lack of accurate direct measurements of both D and [Formula presented] this conjecture could never be put to a serious test. Using the method of iterated conformal maps, D was recently determined as [Formula presented] In this paper, we determine [Formula presented] accurately with the result [Formula presented] We thus conclude that the Turkevich-Scher conjecture is incorrect for DLA.
UR - http://www.scopus.com/inward/record.url?scp=85037241513&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.67.042402
DO - 10.1103/PhysRevE.67.042402
M3 - Journal article
AN - SCOPUS:85037241513
VL - 67
JO - Physical Review E
JF - Physical Review E
SN - 2470-0045
IS - 4
M1 - 042402
ER -
ID: 203586516