Fractal Dimension, Walk Dimension and Conductivity Exponent of Karst Networks around Tulum

Frontiers in Physics

Hendrick, Martin¹  Renard, Philippe² 

[1] Center For Hydrogeology and Geothermics, University of Neuchâtel, Neuchâtel, Switzerland

关键词: Karst network;    fractal;    renormalization;    Einstein relation;    Critical Phenomena;   

DOI  :  10.3389/fphy.2016.00027

学科分类：物理（综合）

来源: Frontiers

【 摘 要 】

Understanding the complex structure of karst networks is a challenge. In this work, we characterize the fractal properties of some of the largest coastal karst network systems in the world. They are located near the town of Tulum (Quintana Roo, Mexico). Their fractal dimension $d_f$, conductivity exponent $\tilde{\mu}$ and walk dimension $d_w$ are estimated using real space renormalization and numerical simulations. We obtain the following values for these exponents: $d_f\approx 1.5$, $d_w\approx 2.4$, $\tilde{\mu}\approx 0.9$. We observe that the Einstein relation holds for these structures $\tilde{\mu} \approx -d_f + d_w$. These results indicate that coastal karst networks can be considered as critical systems and this provides some foundations to model them within this framework.

【 授权许可】

CC BY