Dynamic feedback in an aggregation-disaggregation model

We study an aggregation-disaggregation model which is relevant to biologica l processes such as the growth of senile plaques in Alzheimer disease. In t his model, during the aggregation each deposited particle has a probability of producing a new particle in its vicinity, while during disaggregation t he particles are anihilated randomly. The model is held in a dynamic equili brium by a feedback mechanism which changes the disaggregation probability in proportion to the change in the total number of particles. We also inclu de surface diffusion which influences the morphology of growing aggregates and colonies. A colony includes the descendents of a single particle. We in vestigate the statistical properties of the model in two dimensions. We fin d that unlike the colonies, individual aggregates are fractals with a fract al dimension of D-f=1.92+/-0.06 in the absence of surface diffusion. We sho w that the surface diffusion changes the fractal dimension of aggregates: a t a small aggregation-disaggregation rate, D-f is independent of the streng th of the surface diffusion, D-f=1.73+/-0.03. At larger aggregation-disaggr egation rates and different strengths of surface diffusion, aggregates with fractal dimensions between D-f=1.73 and 1.92 form, The steady-state distri bution of aggregate sizes is shown to be power law if the aggregation-disag gregation process dominates over We surface diffusion. In the limit of weak aggregation-disaggregation and strong surface diffusion the size distribut ion is log-normal. [S1063-651X(99)01008-9].