Aggregation with fractal trajectories of changing dimensionality

The fractal dimension of a particle-cluster aggregate depends on the space dimensionality, the geometric characteristic of the particle trajectory and on the progress of the process. The asymptotic values of fractal dimension are characteristic for large aggregates. The influence is analyzed of the step size of random walk on the structure of aggregates built by the successive addition of monomers to a growing cluster. Increasing the step size it is possible to obtain more and more compact structures [Phys. Rev. A 36 (1987) 4518] changing from that characteristic for diffusion-limited process to that observed for ballistic particle-cluster aggregation. Moreover, the trajectory fractal dimension increases as the aggregation proceeds due to the aggregate growth and the constancy of the step size of random walk. It is shown that aggregation act equation models such aggregation processes well.