Fractal dimension of the trunk of a diffusion limited aggregation cluster

1993 ◽  
Vol 196 (3) ◽  
pp. 317-319
Author(s):  
P. Pikhitsa
Keyword(s):  
Fractal Dimension ◽  
Diffusion Limited Aggregation ◽  
Diffusion Limited

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.

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

SCALING BEHAVIOR OF DIFFUSION LIMITED AGGREGATION IN PERCOLATION CLUSTER

2008 ◽  
Vol 22 (07) ◽  
pp. 507-513 ◽  
Author(s):  
QIANG TANG
Keyword(s):  
Fractal Dimension ◽  
Computer Model ◽  
Percolation Cluster ◽  
Multifractal Spectrum ◽  
Scaling Behavior ◽  
Diffusion Limited Aggregation ◽  
Occupancy Probability ◽  
Diffusion Limited ◽  
Multifractal Spectra ◽  
Simulation Results

This paper presents a computer model of diffusion limited aggregation (DLA) in percolation cluster. Simulation of the aggregation clusters in percolation cluster with varying occupancy probability is performed, and their fractal dimension and multifractal spectrum are obtained. The simulation results show that the percolation cluster has stronger effects on the aggregation clusters' pattern structure when occupancy probability is smaller. The dimension Df of aggregation clusters increases together with the increase of occupancy probability. Furthermore, the multifractal spectra f(α) curve becomes higher and the range of singularity α wilder. The bigger the occupancy probability is, the more irregular and non-uniform the aggregation clusters becomes.

Fractal simulation of thin film nucleation growth process using a diffusion-limited aggregation model

2018 ◽  
Vol 32 (33) ◽  
pp. 1850408 ◽  
Author(s):  
Min Zhang ◽  
Chaoyong Deng
Keyword(s):  
Fractal Dimension ◽  
Growth Process ◽  
Film Growth ◽  
Nucleation And Growth ◽  
Diffusion Limited Aggregation ◽  
Diffusion Limited ◽  
Initial Stage ◽  
Initial Nucleation ◽  
Fractal Simulation ◽  
Film Nucleation

In order to study the initial nucleation and growth process of the films, a two-dimensional (2D) DLA model was established, and fractal dimension was calculated by sandbox method. Compared with the experimental results, the model can well characterize the morphology of nucleation and growth in the initial stage of film growth. In addition to the number of particles and deposition probability involved in other studies, the size of substrate and the location of central particles are also considered in this work. The growth morphology, fractal dimension and the number of simulated steps are presented in this paper.

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