Multifractal structure of the harmonic measure of diffusion-limited aggregates

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Standard

Multifractal structure of the harmonic measure of diffusion-limited aggregates. / Jensen, Mogens H.; Levermann, Anders; Mathiesen, Joachim; Procaccia, Itamar.

I: Physical Review E, Bind 65, Nr. 4, 046109, 01.01.2002.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Jensen, MH, Levermann, A, Mathiesen, J & Procaccia, I 2002, 'Multifractal structure of the harmonic measure of diffusion-limited aggregates', Physical Review E, bind 65, nr. 4, 046109. https://doi.org/10.1103/PhysRevE.65.046109

APA

Jensen, M. H., Levermann, A., Mathiesen, J., & Procaccia, I. (2002). Multifractal structure of the harmonic measure of diffusion-limited aggregates. Physical Review E, 65(4), [046109]. https://doi.org/10.1103/PhysRevE.65.046109

Vancouver

Jensen MH, Levermann A, Mathiesen J, Procaccia I. Multifractal structure of the harmonic measure of diffusion-limited aggregates. Physical Review E. 2002 jan. 1;65(4). 046109. https://doi.org/10.1103/PhysRevE.65.046109

Author

Jensen, Mogens H. ; Levermann, Anders ; Mathiesen, Joachim ; Procaccia, Itamar. / Multifractal structure of the harmonic measure of diffusion-limited aggregates. I: Physical Review E. 2002 ; Bind 65, Nr. 4.

Bibtex

@article{edf1848e152045f88fc9354d7b66c8ba,
title = "Multifractal structure of the harmonic measure of diffusion-limited aggregates",
abstract = "The method of iterated conformal maps allows one to study the harmonic measure of diffusion-limited aggregates with unprecedented accuracy. We employ this method to explore the multifractal properties of the measure, including the scaling of the measure in the deepest fjords that were hitherto screened away from any numerical probing. We resolve probabilities as small as [formula presented] and present an accurate determination of the generalized dimensions and the spectrum of singularities. We show that the generalized dimensions [formula presented] are infinite for [formula presented] where [formula presented] is of the order of [formula presented] In the language of [formula presented] this means that [formula presented] is finite. The [formula presented] curve loses analyticity (the phenomenon of “phase transition”) at [formula presented] and a finite value of [formula presented] We consider the geometric structure of the regions that support the lowest parts of the harmonic measure, and thus offer an explanation for the phase transition, rationalizing the value of [formula presented] and [formula presented] We thus offer a satisfactory physical picture of the scaling properties of this multifractal measure.",
author = "Jensen, {Mogens H.} and Anders Levermann and Joachim Mathiesen and Itamar Procaccia",
year = "2002",
month = jan,
day = "1",
doi = "10.1103/PhysRevE.65.046109",
language = "English",
volume = "65",
journal = "Physical Review E",
issn = "2470-0045",
publisher = "American Physical Society",
number = "4",

}

RIS

TY - JOUR

T1 - Multifractal structure of the harmonic measure of diffusion-limited aggregates

AU - Jensen, Mogens H.

AU - Levermann, Anders

AU - Mathiesen, Joachim

AU - Procaccia, Itamar

PY - 2002/1/1

Y1 - 2002/1/1

N2 - The method of iterated conformal maps allows one to study the harmonic measure of diffusion-limited aggregates with unprecedented accuracy. We employ this method to explore the multifractal properties of the measure, including the scaling of the measure in the deepest fjords that were hitherto screened away from any numerical probing. We resolve probabilities as small as [formula presented] and present an accurate determination of the generalized dimensions and the spectrum of singularities. We show that the generalized dimensions [formula presented] are infinite for [formula presented] where [formula presented] is of the order of [formula presented] In the language of [formula presented] this means that [formula presented] is finite. The [formula presented] curve loses analyticity (the phenomenon of “phase transition”) at [formula presented] and a finite value of [formula presented] We consider the geometric structure of the regions that support the lowest parts of the harmonic measure, and thus offer an explanation for the phase transition, rationalizing the value of [formula presented] and [formula presented] We thus offer a satisfactory physical picture of the scaling properties of this multifractal measure.

AB - The method of iterated conformal maps allows one to study the harmonic measure of diffusion-limited aggregates with unprecedented accuracy. We employ this method to explore the multifractal properties of the measure, including the scaling of the measure in the deepest fjords that were hitherto screened away from any numerical probing. We resolve probabilities as small as [formula presented] and present an accurate determination of the generalized dimensions and the spectrum of singularities. We show that the generalized dimensions [formula presented] are infinite for [formula presented] where [formula presented] is of the order of [formula presented] In the language of [formula presented] this means that [formula presented] is finite. The [formula presented] curve loses analyticity (the phenomenon of “phase transition”) at [formula presented] and a finite value of [formula presented] We consider the geometric structure of the regions that support the lowest parts of the harmonic measure, and thus offer an explanation for the phase transition, rationalizing the value of [formula presented] and [formula presented] We thus offer a satisfactory physical picture of the scaling properties of this multifractal measure.

UR - http://www.scopus.com/inward/record.url?scp=85035271848&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.65.046109

DO - 10.1103/PhysRevE.65.046109

M3 - Journal article

AN - SCOPUS:85035271848

VL - 65

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 4

M1 - 046109

ER -

ID: 203586663