Is the Alexander–Orbach Conjecture Suitable for Treating Diffusion in Correlated Percolation Clusters?

• Main Authors: Ommar Cruz, Ricardo Hidalgo, Salomón Alas, Salomón Cordero, Laura Meraz, Raúl Lopez, Armando Dominguez
• Format: Article
• Language: English
• Published: Hindawi - SAGE Publishing 2011-07-01
• Series: Adsorption Science & Technology
• Online Access: https://doi.org/10.1260/0263-6174.29.7.663

How does a particle diffuse inside a percolation cluster? This question is of both scientific and practical importance, e.g. in drug-controlled release and vapour adsorption. Diffusion in fractal media is characterized by the fracton dimension, d s . The Alexander and Orbach conjecture indicates that d s = 4/3 for diffusion in classical percolation clusters and, after much research on the subject, it is still provides a very good approximation for d s in the case of uncorrelated percolation cluster structures. However, what happens to the value of d s when a particle is moving inside a correlated percolation cluster? In this work, this problem is studied via Monte Carlo computer simulation. Our results show that the Alexander and Orbach conjecture is not always fulfilled.