In the interactive percolation model we introduced, the occupation of a lattice site is dependent on the presence or absence of neighboring particles, which is a more realistic description of physical systems such as adsorption of gas atoms on metallic surfaces. This is the situation shown in the picture at the right. In recent years, however, there have been several studies which indicate that the short-range details of a percolating cluster may have some effect on the ability of a particle to diffuse through the percolating cluster. I am currently investigating how this diffusion exponent might depend on the strength of the interactions introduced into the percolation model. The fractal dimension and the diffusion exponent are not the only exponents which characterize a percolation cluster.
Diffusion is simply related to the ability of a current to pass through the cluster.
It has recently been shown that the distribution of currents in the different branches of the cluster can be used to define an infinite number of independent dimensions which provide detailed information about its structure. In future research, therefore, I am interested in examining the multifractal characteristics of interactive percolation clusters. These pages may be freely distributed if unmodified.