Computer simulation of conductivity fluctuations in a dynamic percolation model based on resistive networks

Background and Objectives: Percolation models are widely used in the analysis of electrical, thermophysical and other properties of various systems with disordered structure, which causes their wide application in the theoretical consideration of near-critical behavior of such systems in various fields of modern science and technology. Studies of noise processes, in particular noise, in the context of percolation networks have significantly extended the understanding of how fluctuations can arise in this kind of systems. An important aspect that has often received less attention in classical approaches is the fact that local conductivity processes in a number of disordered materials occur in a dynamic environment. In this paper, we present results from computer simulations of fluctuations in the conductivity of a time-evolving random resistor network. The model calculates the conductance of a three-dimensional rectangular lattice in which about 70$\%$ of the total number of nodes is empty, corresponding to a percolation threshold. Materials and Methods: The modeled percolation network consists of 160000 nodes, connected in a three-dimensional rectangular lattice. A potential difference is applied to the opposite edges of the lattice along the long side containing each node, providing charge transfer in the system. The value of bond conductivity in the lattice could take either zero or finite value (two-phase system). The numerical value of the potential for each node and the current at each site are calculated by solving Kirchhoff's equations. Dynamics was introduced into the system by assuming that a small fraction of the whole nodes are able to diffuse through the lattice, thus changing the conduction paths, but keeping on the other hand the total fraction of the conducting phase unchanged. Results: The process of exchange between neighboring conducting and non-conducting nodes between each other in space has been simulated, after which the conductivity of the network has been recalculated. After repeating this process many times, temporal realizations of the conductivity fluctuations have been obtained, which allows a systematic analysis of the system dynamics. The characteristic lifetime $\tau$ reflects the reconfiguration time of the conductive part of the grid. In the limit of high exchange rate $\upsilon \rightarrow$ 1 it is expected that the power spectral density of the conductivity fluctuations will be white noise. Conclusion: The results are of particular interest for advancing fundamental understanding of charge transfer mechanisms in dispersed semiconductor materials, which are relevant to chemoresistive sensing and catalytic chemistry.