Asymptotic form of the spectral dimension of the Sierpinski gasket type of fractals
- 1 August 1987
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 20 (11) , L715-L719
- https://doi.org/10.1088/0305-4470/20/11/008
Abstract
The authors have studied the spectral dimension d48T of an infinite class of fractals. The first member (b=2) of the class is the two-dimensional Sierpinski gasket, while the last member (b= infinity ) appears to be a wedge of the ordinary triangular lattice. By studying the electric resistance of the fractals they have been able to calculate exact values of d for the first 200 members of the class. An analysis of the obtained data reveals that for large b the spectral dimension should approach the upper limit of 2 according to the formula d approximately=2-constant (ln b)beta , where beta is not larger than one. This result implies, among other things, that the scaling exponents of the resistivity and diffusion constant should logarithmically vanish at the fractal-lattice crossover.Keywords
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