  We propose a revision of the classic mean-field approach of diffusion-limited
aggregation (DLA) model originally introduced by Witten and Sander [Phys. Rev.
Lett. 47, 1400 (1981)]. The derived nonlinear mean-field equations providing
lattice anisotropy are used to model diffusional growth on square lattice in
linear and circular source geometries. The overall cluster shapes obtained from
the mean-field calculations are found to satisfy the known scaling behavior
experimentally observed for DLA simulations.
