Diffusion-limited cluster aggregation example

This structure is generated via the modified diffusion-limited aggregation (DLA) algorithm of [205] using the law p = a (m/N). Here, N = 2, 000 (the number of particles of the DLA clusters), a = 10 and ft = 0.5 are constants that determine the shape of the cluster, p is the radius of the circle in which the cluster is embedded, pc = 0.1 is the lower limit of p (always pc < p), and to is the number of particles sticking to the downstream portion of the cluster. This example corresponds to a radial Hele-Shaw cell where water has been injected radially from the central hole. Due to heterogeneity a sample cannot be used to calculate the dissolved amount at any time, i.e., an average value for the percent dissolved amount at any time does not exist. This property is characteristic of fractal objects and processes. 

Diffusion-Limited Aggregation (DLA) Clustering of particles in random due to Brownian motion. DLA is prevalent in diffusion systems. Lich-tenberg figures (or electric trees) are a common example of DLA. 

The authors of Ref [19] used the stated above treatment of polymers cold flow with application of Witten-Sander model of diffusion-limited aggregation [20] on the example of PC. As it has been shown in Refs. [21, 22], PC structure can be simulated as totality of Witten-Sander clusters (WS clusters) large number. These clusters have compact central part, which in the model [18, 23] is associated with notion cluster. Further to prevent misunderstandings the term cluster will be understood exactly as a compact local order region. At translational motion of such compact region in viscous medium molecular friction coefficient of each cluster, a particle, having radius a, is determined as follows [24] ... 

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