Thermodynamic formalism of the harmonic measure of diffusion limited aggregates: Phase transition

TY - JOUR

T1 - Thermodynamic formalism of the harmonic measure of diffusion limited aggregates

T2 - Phase transition

AU - Davidovitch, Benny

AU - Jensen, Mogens H.

AU - Levermann, Anders

AU - Mathiesen, Joachim

AU - Procaccia, Itamar

PY - 2001/10/2

Y1 - 2001/10/2

N2 - We study the nature of the phase transition in the multifractal formalism of the harmonic measure of diffusion limited aggregates. Contrary to previous work that relied on random walk simulations or ad hoc models to estimate the low probability events of deep fjord penetration, we employ the method of iterated conformal maps to obtain an accurate computation of the probability of the rarest events. We resolve probabilities as small as 10−35. We show that the generalized dimensions Dq are infinite for q max is finite. We present a converged f(α) curve.

AB - We study the nature of the phase transition in the multifractal formalism of the harmonic measure of diffusion limited aggregates. Contrary to previous work that relied on random walk simulations or ad hoc models to estimate the low probability events of deep fjord penetration, we employ the method of iterated conformal maps to obtain an accurate computation of the probability of the rarest events. We resolve probabilities as small as 10−35. We show that the generalized dimensions Dq are infinite for q max is finite. We present a converged f(α) curve.

UR - http://www.scopus.com/inward/record.url?scp=42749100903&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.87.164101

DO - 10.1103/PhysRevLett.87.164101

M3 - Journal article

AN - SCOPUS:42749100903

SN - 0031-9007

VL - 87

JO - Physical Review Letters

JF - Physical Review Letters

IS - 16

M1 - 164101

ER -