Growth of adaptive networks in a modified diffusion-limited-aggregation model

Adaptive-network growth has been obtained by a diffusion-limited-aggregation model in which particles of the cluster that do not connect active regions (regions in which deposition is occurring) to the seed or origin of the cluster are removed from the cluster. In the computer simulation of this model, the accumulated ‘‘score’’ associated with each of the ${\mathit{N}}_{\mathit{b}}$ particles connecting a deposited particle to the seed is increased by 1/${\mathit{N}}_{\mathit{b}}$ when the particle is added. At the same time, the scores of all particles in the cluster are decreased by an amount 1/${\mathit{N}}_{\mathit{m}}$, which is a parameter of the model. Particles with scores less than zero are then removed from the cluster. This model leads to the formation of clusters that reach a stationary state in which the cluster size s(t) fluctuates about a constant value controlled by the parameter ${\mathit{N}}_{\mathit{m}}$. The number of particles N(r) within a distance r from the seed is given by N(r)∼${\mathit{r}}^{\gamma }$, where the exponent (fractal dimensionality) γ≃1.25. The scaling of the cluster size with ${\mathit{N}}_{\mathit{m}}$ is described by s¯(t)=${\mathit{N}}_{\mathit{m}}^{\nu }$f(t/${\mathit{N}}_{\mathit{m}}^{\nu }$), where t is the time (number of particles that have contacted the cluster). The exponent ν has a value of about 0.75. The score of each surviving particle is a measure μ(r) that also exhibits interesting scaling behavior.