Thin film growth by single and multi-center DLA model: Fractal analysis

A modified Diffusion Limited Aggregation (DLA) model has been established for single and multi-center fractal growth. Number of particles [Formula: see text], size of one step [Formula: see text], deposition probability [Formula: see text], growth direction, and interaction effect are had been take into consideration for fractal analysis. In addition, the effect of internal interaction in multi-center growth have been taken into consideration. Fractal growth morphology shows strong boundary and interaction effects.

CONTACT PROCESS ON FRACTAL CLUSTERS SIMULATED BY GENERALIZED DIFFUSION-LIMITED AGGREGATION (g-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.

Study on fractal and island growth processes of thin films with a modified DLA model

A modified diffusion-limited aggregation (DLA) model for two-dimensional (2D), three-dimensional (3D) fractal growth and 3D island growth was established based on the DLA model in this paper. The number of particles [Formula: see text] and the size of the box size [Formula: see text] (related to side length [Formula: see text]), which are related to film thickness, are considered in the study. The simulation results are a good reflection of the actual experimental results. The results show that the particle number and simulation box size can affect the fractal morphology and fractal dimension of the film, and also the 2D to 3D transformation. In addition, the critical particle number [Formula: see text] and the critical box size [Formula: see text] during the transformation process are also given.

FRACTIONAL DIFFUSION-LIMITED AGGREGATION: ANISOTROPY ORIGINATING FROM MEMORY

This paper introduces a modified DLA model, based on a fractional diffusion mechanism, as a novel approach to modeling fractal growth. The specific memory performance of fractional operators can be reflected macroscopically in aggregated patterns eventually. The influence of the model’s order on the structure and behavior of its pattern is further quantitatively described by anisotropy index and fractal dimension. Some simulations are provided to illustrate the correctness and effectiveness of the main results.

Fractal Diffusion Limited Aggregation of Soot Particles Based on Fuzzy Membership Functions

In this paper, the membership function in fuzzy systems is used in the Diffusion Limited Aggregation (DLA) model to investigate the fractal diffusion of soot particles from diesel engine emissions. The transformation of the morphology of soot particle aggregates and the control of fractal diffusion of soot particles are investigated by analyzing the nonlinear relationship between the motion steps and angles of diffusing particles. The simulation results demonstrate that the morphology of the aggregates varies from loose to compact by changing the particles’ motion steps and angles in membership functions. Meanwhile, the Ballistic Aggregation (BA)-like aggregates are obtained. Furthermore, the control of the morphology of soot particle aggregates is realized, which makes the settlement of the aggregates become easier. This will provide a reference for further understanding the growth mechanism of soot particle diffusion and enhancing the purification technology of the soot particles.

A Numerical Study for the Relationship between Natural Manganese Dendrites and DLA Patterns

The formation mechanisms and the origin of manganese dendrites on the magnesite ore have been under discussion. The growth process of the manganese dendrites is statistically studied by comparing them to aggregations obtained according to the diffusion limited aggregation (DLA) model via Monte Carlo simulations. In this case, ten manganese dendrite patterns changing from the least dense to the densest aggregations on the surface are separately selected to determine the relationship between real and simulated patterns. The sticking parameter is ranged from 0.05≤t≤1. The density–density correlation functions C(r) (their critical exponent A), fractal dimension Df, critical exponent α, and critical exponent β pertaining to the root mean square (rms) thickness have been computed for both the ten manganese dendrites and the simulated aggregations representing them. The results indicate that manganese dendrites may be determined with the general DLA model. Analyses of manganese dendrites, both scaling and simulations, suggest the growth mechanism for the macroscopic expression of crystalline anisotropy for the dendritic patterns. These results are in good agreement with the values in other literature and can be helpful in comparing natural and simulated aggregations (both dendritic and compact deposits).

Topology change due to particle heterogeneity in DLAs

In the present paper, a variation of the widespread model of diffusion-limited aggregation (DLA) is presented. Unlike the traditional DLA model, where particles are attached to the aggregate whenever they touch it, we here restrict attachment by reducing the number of available bonds of the particles. This subtle change in the model changes the topological properties of the resulting aggregate. By using a binary mixture of particles, with different coordination number, the fractal dimension (df), the spectral dimension (ds) and the random walk dimension (dw) are studied as a function of particle-type ratio. The behavior of the system shows non-negligible deviation from the traditional model.

Durability Evolution of RC Bridge under Coupling Action of Chloride Corrosion and Carbonization Based on DLA Model

Chloride attack and carbonization are the main factors which affect the durability of concrete structures, and the respective theoretical models are systematically established. However, the quantitative analysis and models about the coupling effect of chloride attack and carbonization are less, so the precision and level of durability analysis of reinforced concrete are restricted. Diffusion-limited aggregation (DLA) model can finely simulate the process of gas diffusion and condensation with randomness and fractal characteristics, which is suitable for revealing the durability evolution process of the chloride attack, carbonization, and the coupling action in concrete. Based on the principle of DLA, considering the factors such as diffusion depth, concrete properties, and exposure conditions which influence the characteristics of chloride diffusion and carbonization, as well as the coupling effect, an integrated DLA model is established. The concentration of carbon dioxide and chloride at any time and any location can be obtained and dynamically displayed based on the DLA model. The performance predict method for concrete and steel bars considering fatigue effect is presented based on DLA, according to the demand for bridge durability analysis. Numerical examples show that the method can dynamically and intensively simulate the durability evolution process of reinforced concrete bridge.

Using Modified DLA Model Simulation of the Form of Copolymer Flower-Like Aggregation

In this papper, based on the study of basic algorithm of fractal DLA model, the standard DLA model was modified by setting the parameters, and the PS-b-PAA block copolymer representating a kind of flower-like aggregation was taken as the research object. Through observating the growth characteristics of this kind of flower-like aggregations formed in different external conditions, their fractal characteristics were determined by box-counting method. Then the modified DLA model combined with the image processing technology was used to simulate this kind of flower-like aggregations. Finally, the simulated results were evaluated through visual observation and fractal dimension.