Topology change due to particle heterogeneity in DLAs

2015 ◽  
Vol 26 (12) ◽  
pp. 1550136
Author(s):  
Lucas Ismael Candia ◽  
Julio Carbonetti ◽  
Guillermo Daniel Garcia ◽  
Fabricio Orlando Sanchez-Varretti
Keyword(s):  
Fractal Dimension ◽  
Random Walk ◽  
Traditional Model ◽  
Topological Properties ◽  
Particle Type ◽  
Topology Change ◽  
Diffusion Limited Aggregation ◽  
Subtle Change ◽  
Diffusion Limited ◽  
Dla Model

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.

scholarly journals Diamond aggregation

2010 ◽  
Vol 149 (2) ◽  
pp. 351-372
Author(s):  
WOUTER KAGER ◽  
LIONEL LEVINE
Keyword(s):  
Random Walk ◽  
Growth Model ◽  
Power Law ◽  
Simple Random Walk ◽  
Internal Diffusion ◽  
Diffusion Limited Aggregation ◽  
Directional Bias ◽  
Model Based ◽  
Diffusion Limited ◽  
Logarithmic Fluctuations

AbstractInternal diffusion-limited aggregation is a growth model based on random walk in ℤd. We study how the shape of the aggregate depends on the law of the underlying walk, focusing on a family of walks in ℤ2 for which the limiting shape is a diamond. Certain of these walks—those with a directional bias toward the origin—have at most logarithmic fluctuations around the limiting shape. This contrasts with the simple random walk, where the limiting shape is a disk and the best known bound on the fluctuations, due to Lawler, is a power law. Our walks enjoy a uniform layering property which simplifies many of the proofs.

Characterizing Fractal and Hierarchical Morphologies Beyond the Fractal Dimension

1994 ◽  
Vol 367 ◽  
Author(s):  
Raphael Blumenfeld ◽  
Robin C. Ball
Keyword(s):  
Asymptotic Behavior ◽  
Fractal Dimension ◽  
Finite Size ◽  
Size Analysis ◽  
Corrections To Scaling ◽  
Diffusion Limited Aggregation ◽  
Diffusion Limited ◽  
Markovian Processes ◽  
Branching Patterns ◽  
Admissible Solutions

AbstractWe present a novel correlation scheme to characterize the morphology of fractal and hierarchical patterns beyond traditional scaling. The method consists of analysing correlations between more than two-points in logarithmic coordinates. This technique has several advantages: i) It can be used to quantify the currently vague concept of morphology; ii) It allows to distinguish between different signatures of structures with similar fractal dimension but different morphologies already for relatively small systems; iii) The method is sensitive to oscillations in logarithmic coordinates, which are both admissible solutions for renormalization equations and which appear in many branching patterns (e.g., noise-reduced diffusion-limited-aggregation and bronchial structures); iv) The methods yields information on corrections to scaling from the asymptotic behavior, which is very useful in finite size analysis. Markovian processes are calculated exactly and several structures are analyzed by this method to demonstrate its advantages.

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 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.

Observation of fractal patterns in C60-polymer thin films

1994 ◽  
Vol 9 (9) ◽  
pp. 2216-2218 ◽  
Author(s):  
H.J. Gao ◽  
Z.Q. Xue ◽  
Q.D. Wu ◽  
S. Pang
Keyword(s):  
Thin Films ◽  
Fractal Dimension ◽  
Long Range ◽  
Diffusion Limited Aggregation ◽  
Aggregation Model ◽  
Diffusion Limited ◽  
Range Correlation ◽  
Microscopic Features ◽  
Fractal Patterns ◽  
Cluster Diffusion

We report the observation of fractal patterns in C60-tetracyanoquinodimethane thin films. The fractal patterns and their microscopic features are described and characterized. The fractal dimension was determined to be 1.69 ± 0.07. According to the characterization results, the observed fractals are compared to the cluster-diffusion-limited-aggregation model. The growth of the fractal patterns in the thin films is also in terms of the existing long-range correlation.

Fractal dimension of the accessible perimeter of diffusion-limited aggregation

1989 ◽  
Vol 40 (3) ◽  
pp. 1713-1716 ◽  
Author(s):  
Cettina Amitrano ◽  
Paul Meakin ◽  
H. Eugene Stanley
Keyword(s):  
Fractal Dimension ◽  
Diffusion Limited Aggregation ◽  
Diffusion Limited

scholarly journals SCREENING BEHAVIOR OF THE DIFFUSION-LIMITED AGGREGATION FOR SOME RANDOM WALK PARTICLES

1990 ◽  
Vol 39 (7) ◽  
pp. 19
Author(s):  
WENG JIA-QIANG ◽  
KONG LING-JIANG ◽  
CHEN GUANG-ZHI
Keyword(s):  
Random Walk ◽  
Diffusion Limited Aggregation ◽  
Screening Behavior ◽  
Diffusion Limited

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.

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.

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