Scaling exponent of the maximum growth probability in diffusion-limited aggregation

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

SN - 2470-0045

VL - 67

JO - Physical Review E

JF - Physical Review E

IS - 4

M1 - 042402

ER -