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

2021 ◽  
pp. 2150162
Author(s):  
Xun Zhou ◽  
Min Zhang ◽  
Chaoyong Deng
Keyword(s):  
Fractal Analysis ◽  
Film Growth ◽  
Growth Direction ◽  
Diffusion Limited Aggregation ◽  
Fractal Growth ◽  
Diffusion Limited ◽  
Internal Interaction ◽  
One Step ◽  
Dla Model ◽  
Number Of Particles

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.

Insights into the Formation Process of the Retinal Vasculature

Fractals ◽  
1997 ◽  
Vol 05 (04) ◽  
pp. 615-624 ◽  
Author(s):  
S. Kyriacos ◽  
F. Nekka ◽  
L. Cartilier ◽  
P. Vico
Keyword(s):  
Structural Characteristic ◽  
Fractal Analysis ◽  
Formation Process ◽  
Natural Sciences ◽  
Retinal Vasculature ◽  
Formation Processes ◽  
Diffusion Limited Aggregation ◽  
Theoretical Approaches ◽  
Diffusion Limited ◽  
Dla Model

Growth phenomena have been studied extensively in natural sciences. This interest has been renewed since the introduction of the fractal concept. In an attempt to understand the origin of irregular phenomena, several computer models and theoretical approaches have recently been developed. Studies using fractal analysis of the retinovasculature have proposed diffusion-limited aggregation (DLA) one of the most popular models to explain the formation of the retina. A deeper investigation of the physiological laws ruling the development of the retinovasculature has, however, revealed static and dynamic discrepancies with DLA, leading to rejection of the DLA model, and reopening the debate. In light of comparison of the two formation processes and of the absence of a DLA structural characteristic in retinovasculature, we discuss the validity of some previously proposed models.

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

2019 ◽  
Vol 33 (35) ◽  
pp. 1950441
Author(s):  
Min Zhang ◽  
Xun Zhou ◽  
Chaoyong Deng
Keyword(s):  
Particle Number ◽  
Three Dimensional ◽  
Transformation Process ◽  
Island Growth ◽  
Diffusion Limited Aggregation ◽  
Diffusion Limited ◽  
Number Formula ◽  
Dla Model ◽  
2D To 3D ◽  
Number Of Particles

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.

Two-dimensional fractal growth by diffusion limited aggregation of copper

1989 ◽  
Vol 140 (4) ◽  
pp. 193-196 ◽  
Author(s):  
A.S. Paranjpe ◽  
Sandhya Bhakay-Tamhane ◽  
M.B. Vasan
Keyword(s):  
Two Dimensional ◽  
Diffusion Limited Aggregation ◽  
Fractal Growth ◽  
Diffusion Limited

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

2016 ◽  
Vol 71 (3) ◽  
pp. 225-234
Author(s):  
Tugba Ozbey ◽  
Mehmet Bayirli
Keyword(s):  
Critical Exponent ◽  
Numerical Study ◽  
Formation Mechanisms ◽  
Diffusion Limited Aggregation ◽  
Density Correlation ◽  
Diffusion Limited ◽  
Crystalline Anisotropy ◽  
The Relationship ◽  
Good Agreement ◽  
Dla Model

AbstractThe 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).

Diffusion-Limited Aggregation with a Restriction on the Growth Direction

1986 ◽  
Vol 55 (1) ◽  
pp. 61-64 ◽  
Author(s):  
Mitsugu Matsushita ◽  
Hiroshi Kondo ◽  
Shuhei Ohnishi ◽  
Yasuji Sawada
Keyword(s):  
Growth Direction ◽  
Diffusion Limited Aggregation ◽  
Diffusion Limited

DIFFUSION-LIMITED AGGREGATION IN LAMINAR FLOWS

2003 ◽  
Vol 14 (09) ◽  
pp. 1171-1182 ◽  
Author(s):  
R. M. H. MERKS ◽  
A. G. HOEKSTRA ◽  
J. A. KAANDORP ◽  
P. M. A. SLOOT
Keyword(s):  
Flow Direction ◽  
Cluster Structure ◽  
Three Dimensional ◽  
Laminar Flows ◽  
Diffusion Field ◽  
Diffusion Limited Aggregation ◽  
Diffusion Limited ◽  
Advection Diffusion ◽  
Multiple Particles ◽  
Dla Model

In the diffusion-limited aggregation (DLA) model, pioneered by Witten and Sander (Phys. Rev. Lett.47, 1400 (1981)), diffusing particles irreversibly attach to a growing cluster which is initiated with a single solid seed. This process generates clusters with a branched morphology. Advection–diffusion-limited aggregation (ADLA) is a straightforward extension to this model, where the transport of the aggregating particles not only depends on diffusion, but also on a fluid flow. The authors studying two-dimensional and three-dimensional ADLA in laminar flows reported that clusters grow preferentially against the flow direction. The internal structure of the clusters was mostly reported to remain unaffected, except by Kaandorp et al. (Phys. Rev. Lett.77, 2328 (1996)) who found compact clusters "as the flow becomes more important". In the present paper we present three-dimensional simulations of ADLA. We did not find significant effects of low Reynolds-number advection on the cluster structure. The contradicting results by Kaandorp et al. (1996) were recovered only when the relaxation into equilibrium of the advection–diffusion field was too slow, in combination with the synchronous addition of multiple particles.

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

2019 ◽  
Vol 29 (05) ◽  
pp. 1950073 ◽  
Author(s):  
Jie Sun ◽  
Wei Qiao ◽  
Shuai Liu
Keyword(s):  
Fuzzy Systems ◽  
Soot Particle ◽  
Membership Functions ◽  
Engine Emissions ◽  
Diffusion Limited Aggregation ◽  
Soot Particles ◽  
Fuzzy Membership Functions ◽  
Diffusion Limited ◽  
Particle Aggregates ◽  
Dla Model

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.

Study on Laplace Growth and Diffusion Limited Aggregation with Material Properties

2013 ◽  
Vol 703 ◽  
pp. 71-74
Author(s):  
Shou Gang Sui ◽  
Shu Lan Gong ◽  
Tao Wang
Keyword(s):  
Computer Simulation ◽  
Random Walk ◽  
Material Properties ◽  
Material Science ◽  
Diffusion Limited Aggregation ◽  
Fractal Growth ◽  
Diffusion Limited ◽  
Wide Range ◽  
And Diffusion ◽  
Important Significance

The diffused fractal growth has a wide range of applications in material fields, especially the diffusion limited aggregation. As a result, the research of fractal growth has important significance in material science. In this paper, iterative steps are introduced in Laplace's equation based on the meaning of random walk, and computer simulation is used to analysis the influence of steps' change on fractal growth.

Sign in / Sign up

Export Citation Format

Share Document