Diffusion-limited aggregation in which cluster sites have a distribution of reaction times.

Abstract

Studies of the growth of aggregates have been limited so far to those cases where the aggregate particles can react with incoming Brownian particles for infinite time. Recently, Miyazima et al. have investigated the effect of a fixed reaction time \ensuremath{\tau} and have found that the long-time aggregates in two dimensions have a fractal dimension ${d}_{f}$\ensuremath{\simeq}1.04\ifmmode\pm\else\textpm\fi{}0.03 for all finite \ensuremath{\tau} values. Here we study square lattices, in which, in the more general case, each aggregate site is randomly assigned an infinite reaction time (with probability q) or a finite reaction time (with probability 1-q). We find a dynamical phase transition at q=${q}_{c}$=0.5 and three different values for ${\mathit{d}}_{\mathit{f}}$: ${\mathit{d}}_{\mathit{f}}$\ensuremath{\simeq}1.04(q${<}_{\mathit{c}}$), ${\mathit{d}}_{\mathit{f}}$\ensuremath{\simeq}1.5 (q=${\mathit{q}}_{\mathit{c}}$), and ${\mathit{d}}_{\mathit{f}}$\ensuremath{\simeq}1.7 (q\ensuremath{\gtrsim}${\mathit{q}}_{\mathit{c}}$), irrespective of the magnitude of \ensuremath{\tau}.