Modification of the RLA model for presenting a cluster system of a composite material with a fractal filler structure

The paper proposes a modification of the diffusion-limited aggregation model to study the properties of a cluster system. A computational experiment to determine the mutual influence of the sticking probability and the volume concentration of particles on the formation of fractal clusters in a cluster system was carried out in accordance with the second-order orthogonal central compositional plan (OCCP). As a result of a computational experiment in accordance with the OCCP, an equation was obtained for the dependence of the mass fractal dimension of clusters on the volume of particle concentration and the probability of adhesion of diffusing particles and cluster particles in the adhesion zone. This dependence was obtained in a range of volume concentration of particles from 2 to 5 % and the probability of adhesion of diffusing particles and particles of clusters in the adhesion zone from 0.2 to 1.

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Formation of Fractal Clusters and Networks by Irreversible Diffusion-Limited Aggregation

Physical Review Letters ◽

10.1103/physrevlett.51.1119 ◽

1983 ◽

Vol 51 (13) ◽

pp. 1119-1122 ◽

Cited By ~ 1324

Author(s):

Paul Meakin

Keyword(s):

Diffusion Limited Aggregation ◽

Fractal Clusters ◽

Diffusion Limited

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CONTACT PROCESS ON FRACTAL CLUSTERS SIMULATED BY GENERALIZED DIFFUSION-LIMITED AGGREGATION (g-DLA) MODEL

Fractals ◽

10.1142/s0218348x20501376 ◽

2020 ◽

Vol 28 (07) ◽

pp. 2050137

Author(s):

ASHWINI V. MAHAJAN ◽

ABHAY V. LIMAYE ◽

ARUN G. BANPURKAR ◽

PRASHANT M. GADE

Keyword(s):

Nearest Neighbor ◽

Local Density ◽

Contact Process ◽

Universality Class ◽

Active Phase ◽

Diffusion Limited Aggregation ◽

Remote Areas ◽

Fractal Clusters ◽

Diffusion Limited ◽

Dla Model

The spread of infectious disease, virus epidemic, fashion, religion and rumors is strongly affected by the nearest neighbor hence underlying morphologies of the colonies are crucial. Likewise, the morphology of naturally grown patterns ranges from fractal to compact with lacunarity. We analyze the contact process on the fractal clusters simulated by generalized Diffusion-limited Aggregation (g-DLA) model. In g-DLA model, randomly walking particle is added to the cluster with sticking probability [Formula: see text] depending on the local density of occupied sites in the neighborhood of radius [Formula: see text] from the center of active site. It takes values [Formula: see text], [Formula: see text] and [Formula: see text] ([Formula: see text]) for highly dense, moderately dense and sparsely occupied regions, respectively. The corresponding morphology varies from fractal to compact as [Formula: see text] varies from [Formula: see text] to [Formula: see text]. Interestingly, the contact process on the g-DLA clusters shows clear transition from active phase to absorbing phase and the exponent values fall between 1-d and 2-d in directed percolation (DP) universality class. The local persistence exponents at transition are studied and are found to be much smaller than that for 1-d and 2-d DP cases. We conjecture that infection in the fractal cluster does not easily reach far-flung or remote areas at the periphery of the cluster.

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