Diffusion-limited aggregation on two-dimensional percolation clusters

1984 ◽  
Vol 29 (8) ◽  
pp. 4327-4330 ◽  
Author(s):  
Paul Meakin
Keyword(s):  
Two Dimensional ◽  
Diffusion Limited Aggregation ◽  
Percolation Clusters ◽  
Diffusion Limited

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

Concentration Influence on Diffusion Limited Cluster Aggregation

1994 ◽  
Vol 367 ◽  
Author(s):  
ST.C. Pencea ◽  
M. Dumitrascu
Keyword(s):  
Brownian Motion ◽  
Fractal Dimensions ◽  
Simple Random Walk ◽  
Two Dimensional ◽  
Diffusion Limited Aggregation ◽  
Dimensional Lattice ◽  
Cluster Aggregation ◽  
Box Counting ◽  
Diffusion Limited ◽  
Diffusion Limited Cluster Aggregation

AbstractDiffusion-limited cluster aggregation has been simulated on a square two dimensional lattice. In order to simulate the brownian motion, we used both the algorithm proposed initially by Kolb et all. and a new algorithm intermediary between a simple random walk and the ballistic model.The simulation was performed for many values of the concentration, from 1 to 50%. By using a box-counting algorithm one has calculated the fractal dimensions of the obtained clusters. Its increasing vs. concentration has been pointed out. The results were compared with those of the classical diffusion-limited aggregation (DLA).

Two-dimensional growth of germanium under a diffusion limited aggregation environment

2016 ◽  
Vol 13 (1) ◽  
pp. 91-96
Author(s):  
Jaejun Lee ◽  
Sung Wook Kim ◽  
Youn Ho Park ◽  
Jeong Min Park ◽  
Yeon Joo Kim ◽  
...  
Keyword(s):  
Two Dimensional ◽  
Diffusion Limited Aggregation ◽  
Diffusion Limited ◽  
Dimensional Growth

Simulation of Fractal-Like Crystal Growth

1991 ◽  
Vol 46 (1-2) ◽  
pp. 203-205
Author(s):  
Attila Felinger ◽  
Jänos Liszi
Keyword(s):  
Crystal Growth ◽  
Fractal Dimensions ◽  
Stochastic Method ◽  
Square Lattice ◽  
Two Dimensional ◽  
Diffusion Limited Aggregation ◽  
Equilibrium Crystallization ◽  
Diffusion Limited ◽  
Large Clusters ◽  
Small Clusters

AbstractNon-equilibrium crystallization was simulated on a two dimensional square lattice. Several clusters were grown simultaneously by using the model of diffusion limited aggregation. The growing process was reversible, i.e. dissolution of particles from the boundary of any cluster was made possible. The rate of growth and dissolution was determined by a stochastic method. The simulation resulted in an aggregate pattern having a few large and several small clusters. The fractal dimensions of the large clusters were found in the range of D = 1.62-1.72.

POWER LAW RELAXATION OF PERIMETER LENGTH OF FRACTAL AGGREGATES

Fractals ◽  
1996 ◽  
Vol 04 (03) ◽  
pp. 251-256 ◽  
Author(s):  
TOSHIHARU IRISAWA ◽  
MAKIO UWAHA ◽  
YUKIO SAITO
Keyword(s):  
Power Law ◽  
Dimensional Space ◽  
Thermal Relaxation ◽  
Diffusion Control ◽  
Two Dimensional ◽  
Diffusion Limited Aggregation ◽  
Diffusion Limited ◽  
Dimensional Diffusion ◽  
Dimensional Argument ◽  
Lower Cutoff

For a realistic aggregate grown under the diffusion control, the fractal scaling holds between two cutoff lengths. These cutoff lengths often control the dynamics of aggregation and relaxation. During thermal annealing, coarsening of the aggregate structure takes place, and the lower cutoff length increases. When the relaxation is limited by kinetics, we show by a simple dimensional argument that the perimeter length (or area) A of the aggregate shrinks in a power law with time t as A(t) ~ t(d–1–D)/2 in a d-dimensional space, where D is the fractal dimension of the aggregate. This prediction is tested by Monte Carlo simulation of the thermal relaxation of a two-dimensional diffusion-limited aggregation.

Diffusion-limited aggregation

1989 ◽  
Vol 423 (1864) ◽  
pp. 133-148 ◽  
Keyword(s):  
Lattice Model ◽  
Mean Field ◽  
Fractal Dimensionality ◽  
Lattice Diffusion ◽  
Field Theories ◽  
Two Dimensional ◽  
Diffusion Limited Aggregation ◽  
Diffusion Limited ◽  
Hypercubic Lattice ◽  
Mean Field Theories

Improved algorithms have been developed for both off-lattice and hypercubic lattice diffusion-limited aggregation (DLA) in dimensionalities ( d ) 3-8 and for two-dimensional off-lattice DLA. In two-dimensional off-lattice DLA a fractal dimensionality ( D ) of about 1.71 was obtained for clusters containing up to 10 6 particles. This is significantly larger than the value of ( d 2 + 1)/( d + 1) (5/3 for d = 2) predicted by mean field theories. For d > 2 the off-lattice simulations give results that are consistent with the mean field theories. For d = 3 and d = 4 the effects of lattice anisotropy can easily be seen for clusters containing 3 x 10 6 and 10 6 sites respectively and the effective fractal dimensionalities are slightly smaller for the lattice model clusters than for the off-lattice clusters. Results are also presented for two-, three- and four- dimensional lattice model clusters with noise reduction.

The Simulation of the Two-Dimensional Ising Model on the Creutz Cellular Automaton for the Fractals Obtained by Using the Model of Diffusion-Limited Aggregation

2010 ◽  
Vol 65 (8-9) ◽  
pp. 705-710 ◽  
Author(s):  
Ziya Merdan ◽  
Mehmet Bayirli ◽  
Mustafa Kemal Ozturk
Keyword(s):  
Cellular Automaton ◽  
Finite Size ◽  
Fractal Dimensions ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Diffusion Limited Aggregation ◽  
Diffusion Limited ◽  
Linear Dimensions ◽  
Creutz Cellular Automaton ◽  
Good Agreement

The fractals are obtained by using the model of diffusion-limited aggregation (DLA) for the lattice with L = 80, 120, and 160. The values of the fractal dimensions are compared with the results of former studies. As increasing the linear dimensions they are in good agreement with those. The fractals obtained by using the model of DLA are simulated on the Creutz cellular automaton by using a two-bit demon. The values computed for the critical temperature and the static critical exponents within the framework of the finite-size scaling theory are in agreement with the results of other simulations and theoretical values

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