Dynamics of swollen fractal networks

TL;DR

This paper investigates the dynamics of swollen fractal networks using computer simulations, revealing anomalous diffusion characterized by a power-law decay of the diffusion coefficient related to the network's spectral dimension.

Contribution

It introduces a simulation-based analysis of swollen fractal networks' dynamics using the fluctuation-relaxation theorem, providing new insights into their diffusion behavior.

Findings

Observed anomalous diffusion with power-law decay of D

Diffusion exponent proportional to spectral dimension

Analyzed Sierpinski and percolation networks

Abstract

The dynamics of swollen fractal networks (Rouse model) has been studied through computer simulations. The fluctuation-relaxation theorem was used instead of the usual Langevin approach to Brownian dynamics. We measured the equivalent of the mean square displacement $\langle \vec r^{\,2} \rangle$ and the coefficient of self-diffusion $D$ of two-and three-dimensional Sierpinski networks and of the two-dimensional percolation network. The results showed an anomalous diffusion, i. e., a power law for $D$, decreasing with time with an exponent proportional to the spectral dimension of the network.