Small-World Networks in Geophysics

TL;DR

This paper explores the application of small-world network theory to model geophysical processes like diffusion and transport in porous rocks, providing analytical and numerical insights into pollutant transport and percolation.

Contribution

It introduces a modified small-world network model tailored for geophysical processes and derives analytical expressions for saturation time and fractal dimension.

Findings

Analytical expression for system saturation time.

Fractal dimension characterization of small-world networks.

Validation through numerical simulations.

Abstract

Many geophysical processes can be modelled by using interconnected networks. The small-world network model has recently attracted much attention in physics and applied sciences. In this paper, we try to use and modify the small-world theory to model geophysical processes such as diffusion and transport in disordered porous rocks. We develop an analytical approach as well as numerical simulations to try to characterize the pollutant transport and percolation properties of small-world networks. The analytical expression of system saturation time and fractal dimension of small-world networks are given and thus compared with numerical simulations.