An improvement to the deterministic fractal interpretation of biological materials is proposed. The deterministic self- similar structure of electric circuits representing the hierarchical cellular organization in the fractal interpretation is replaced by an electric circuit of parallel R-C subcircuits with randomly distributed R and C values. We show that the so-called heavy-tailed distribution of the variate 1/(R_iC_i), representing the relaxation rate of the i-th subcircuit, is the necessary and sufficient condition for the power law behavior of the electric impedance of such a system in the high frequency range. The equivalence of the results obtained in two differently rooted approaches indicates that the variations in the local environment can provide a basis for self-similar relaxation dynamics without the need for hierarchically constrained fractal models.

Date Published: 13 June 1997
PDF: 8 pages
Proc. SPIE 3181, Dielectric and Related Phenomena: Materials Physico-Chemistry, Spectrometric Investigations, and Applications, (13 June 1997); doi: 10.1117/12.276261

Published in SPIE Proceedings Vol. 3181:
Dielectric and Related Phenomena: Materials Physico-Chemistry, Spectrometric Investigations, and Applications
Andrzej Wlochowicz, Editor(s)