Transport and reaction on diffusion-limited aggregates

Using large two-dimensional diffusion-limited aggregates, we obtain very accurate estimates for the fractal and chemical dimensions of these aggregates, the spectral and random-walk dimensions, the resistivity exponent, and investigate the trapping phenomenon on these fractals both at short and long times. Our results indicate that neither the Alexander-Orbach conjecture nor that of Aharony and Stauffer for the random-walk dimension holds for these aggregates, although the latter one appears to be a very accurate approximation. We propose that the chemical and fractal dimensions of these aggregates are equal at all dimensions. Our results also indicate that the theoretically predicted asymptotic (long-time) behavior of trapping on these aggregates may be well outside of the experimental range.