Resistance scaling factor of the pillow and fractalina fractals

Michael J. Ignatowich; Daniel J. Kelleher; Catherine E. Maloney; David J. Miller; Khrystyna Serhiyenko

doi:10.1142/S0218348X15500188

Resistance scaling factor of the pillow and fractalina fractals

Michael J. Ignatowich
, Daniel J. Kelleher
, Catherine E. Maloney
, David J. Miller
, Khrystyna Serhiyenko

Mathematics

Producción científica: Article › revisión exhaustiva

3 Citas (Scopus)

Resumen

Much is known in the analysis of a finitely ramified self-similar fractal when the fractal has a harmonic structure: a Dirichlet form which respects the self-similarity of a fractal. What is still an open question is when such a structure exists in general. In this paper, we introduce two fractals, the fractalina and the pillow, and compute their resistance scaling factor. This is the factor which dictates how the Dirichlet form scales with the self-similarity of the fractal. By knowing this factor one can compute the harmonic structure on the fractal. The fractalina has scaling factor (3+41)/16, and the pillow fractal has scaling factor 1/[3]{2}.

Idioma original	English
Número de artículo	1550018
Publicación	Fractals
Volumen	23
N.º	2
DOI	https://doi.org/10.1142/S0218348X15500188
Estado	Published - jun 1 2015

Nota bibliográfica

Publisher Copyright:
© 2015 World Scientific Publishing Company.

Financiación

Research supported in part by NSF Grant DMS 0505622. The authors would like to thank Alexander Teplyaev for his insight and guidance.

Financiadores	Número del financiador
National Science Foundation Arctic Social Science Program	1106982, DMS 0505622

ASJC Scopus subject areas

General Computer Science
Modeling and Simulation
General Engineering
Geometry and Topology
Applied Mathematics

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abstract = "Much is known in the analysis of a finitely ramified self-similar fractal when the fractal has a harmonic structure: a Dirichlet form which respects the self-similarity of a fractal. What is still an open question is when such a structure exists in general. In this paper, we introduce two fractals, the fractalina and the pillow, and compute their resistance scaling factor. This is the factor which dictates how the Dirichlet form scales with the self-similarity of the fractal. By knowing this factor one can compute the harmonic structure on the fractal. The fractalina has scaling factor (3+41)/16, and the pillow fractal has scaling factor 1/[3]\{2\}.",

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AU - Ignatowich, Michael J.

AU - Kelleher, Daniel J.

AU - Maloney, Catherine E.

AU - Miller, David J.

AU - Serhiyenko, Khrystyna

PY - 2015/6/1

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AB - Much is known in the analysis of a finitely ramified self-similar fractal when the fractal has a harmonic structure: a Dirichlet form which respects the self-similarity of a fractal. What is still an open question is when such a structure exists in general. In this paper, we introduce two fractals, the fractalina and the pillow, and compute their resistance scaling factor. This is the factor which dictates how the Dirichlet form scales with the self-similarity of the fractal. By knowing this factor one can compute the harmonic structure on the fractal. The fractalina has scaling factor (3+41)/16, and the pillow fractal has scaling factor 1/[3]{2}.

KW - Analysis on Fractals

KW - Dirichlet Forms

KW - Electric Networks

KW - Resistance Forms

KW - Self-Similar Fractals

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Resistance scaling factor of the pillow and fractalina fractals

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ASJC Scopus subject areas

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