A Complexity Research of Percolation and Permeation Behavior in Cluster Groups

In this study, a novel artificial potential-driven computational framework is proposed for studying macroscopic percolation and permeation phenomena in dynamic group systems. This framework extends the traditional static percolation theory to the analysis of dynamic porous media, thereby promoting the expansion of the former to the latter. The proposed model generates links between individuals of the groups through an adaptive interaction mechanism, where the individuals exhibit time-evolving equilibrium dimensions and heterogeneous spatial constraints. This dynamic coupling spontaneously generates self-organizing interference patterns, resulting in, for example, parceling or barrier effects in the groups. These effects fundamentally affect the permeation paths of the evolving group structure. In contrast to the traditional approach, which assumes a static structure, the study reveals how the individual time-varying equilibrium radius and the collective spatial organization dynamics dominate the percolation and permeation processes of the macroscopic group. This includes key factors such as porosity evolution, permeation dynamics, and critical percolation transitions. The experimental results demonstrate that groups of agents with time-varying equilibrium radius can significantly improve the percolation characteristics of the groups, and the different structures of tightly clustered groups can also directly affect the percolation and permeation of the groups.From the perspective of dynamic porous media mechanics, the method proposed in this paper provides an innovative theoretical framework for analyzing biological communities, active substance assemblages and group dynamics.