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Resistance scaling and random walk dimensions for finitely ramified Sierpinski carpets

Authors:

Christian Schulzky,

Astrid Franz,

Karl Heinz HoffmannAuthors Info & Claims

ACM SIGSAM Bulletin, Volume 34, Issue 3

Pages 1 - 8

https://doi.org/10.1145/377604.377608

Published: 01 September 2000 Publication History

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Abstract

We present a new algorithm to calculate the random walk dimension of finitely ramified Sierpinski carpets. The fractal structure is interpreted as a resistor network for which the resistance scaling exponent is calculated using Mathematica. A fractal form of the Einstein relation, which connects diffusion with conductivity, is used to give a numerical value for the random walk dimension.

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Gašpar FKukal J(2024)Butterfly diffusion over sparse point setsPhysica A: Statistical Mechanics and its Applications10.1016/j.physa.2024.129893646(129893)Online publication date: Jul-2024
https://doi.org/10.1016/j.physa.2024.129893
Gašpar FKukal J(2022)Stochastic modelling of fractal diffusion and dimension estimationPhysica A: Statistical Mechanics and its Applications10.1016/j.physa.2022.127624602(127624)Online publication date: Sep-2022
https://doi.org/10.1016/j.physa.2022.127624
Wilson DBaker RWoodhouse F(2019)Displacement of Transport Processes on Networked TopologiesSIAM Journal on Applied Mathematics10.1137/19M124425179:5(1892-1915)Online publication date: 3-Oct-2019
https://doi.org/10.1137/19M1244251
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Index Terms

Resistance scaling and random walk dimensions for finitely ramified Sierpinski carpets
1. Mathematics of computing
  1. Discrete mathematics
  2. Probability and statistics

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Published In

ACM SIGSAM Bulletin Volume 34, Issue 3

Sept. 2000

31 pages

ISSN:0163-5824

DOI:10.1145/377604

Editor:
Mark Giesbrecht
Univ. of Western Ontario, London, Canada

Issue’s Table of Contents

Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 September 2000

Published in SIGSAM Volume 34, Issue 3

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Gašpar FKukal J(2024)Butterfly diffusion over sparse point setsPhysica A: Statistical Mechanics and its Applications10.1016/j.physa.2024.129893646(129893)Online publication date: Jul-2024
https://doi.org/10.1016/j.physa.2024.129893
Gašpar FKukal J(2022)Stochastic modelling of fractal diffusion and dimension estimationPhysica A: Statistical Mechanics and its Applications10.1016/j.physa.2022.127624602(127624)Online publication date: Sep-2022
https://doi.org/10.1016/j.physa.2022.127624
Wilson DBaker RWoodhouse F(2019)Displacement of Transport Processes on Networked TopologiesSIAM Journal on Applied Mathematics10.1137/19M124425179:5(1892-1915)Online publication date: 3-Oct-2019
https://doi.org/10.1137/19M1244251
Song LTang GXun ZHao DChen YZhang Z(2017)Influences of Fractal Substrate Structures on Dynamic Scaling Behaviors of Etching ModelCommunications in Theoretical Physics10.1088/0253-6102/68/4/47168:4(471)Online publication date: 19-Oct-2017
https://doi.org/10.1088/0253-6102/68/4/471
Haber RPrehl JHoffmann KHerrmann H(2014)Random walks of oriented particles on fractalsJournal of Physics A: Mathematical and Theoretical10.1088/1751-8113/47/15/15500147:15(155001)Online publication date: 28-Mar-2014
https://doi.org/10.1088/1751-8113/47/15/155001
Xun ZTang GSong LHan KXia HHao DYang Y(2014)Dynamic scaling behaviors of the Etching model on fractal substratesJournal of Statistical Mechanics: Theory and Experiment10.1088/1742-5468/2014/12/P120082014:12(P12008)Online publication date: 10-Dec-2014
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Zhu GYang HYin CLi B(2008)Localizations on complex networksPhysical Review E10.1103/PhysRevE.77.06611377:6Online publication date: 23-Jun-2008
https://doi.org/10.1103/PhysRevE.77.066113
Hoffmann KPrehl J(2008)Anomalous Transport on Disordered FractalsAnomalous Transport10.1002/9783527622979.ch14(397-427)Online publication date: 30-Sep-2008
https://doi.org/10.1002/9783527622979.ch14
Anh DHoffmann KSeeger STarafdar S(2007)Diffusion in disordered fractalsEurophysics Letters (EPL)10.1209/epl/i2005-10002-x70:1(109-115)Online publication date: 2-Jan-2007
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Anh DBlaudeck PHoffmann KPrehl JTarafdar S(2007)Anomalous diffusion on random fractal compositesJournal of Physics A: Mathematical and Theoretical10.1088/1751-8113/40/38/00240:38(11453-11465)Online publication date: 4-Sep-2007
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Using computer algebra methods to determine the chemical dimension of finitely ramified Sierpinski carpets

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