Structure of the active zone in diffusion-limited aggregation, cluster-cluster aggregation, and the screened-growth model

1985 ◽  
Vol 32 (1) ◽  
pp. 453-459 ◽  
Author(s):  
Paul Meakin
Keyword(s):  
Growth Model ◽  
Active Zone ◽  
Diffusion Limited Aggregation ◽  
Cluster Aggregation ◽  
Diffusion Limited

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.

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).

Diffusion Limited Aggregation of PMMA Stereocomplex in Thin Films

2001 ◽  
Vol 710 ◽  
Author(s):  
Yves Grohens ◽  
Gilles Castelein ◽  
Pascal Carriere ◽  
Jiri Spevacek
Keyword(s):  
Aggregation Process ◽  
Diffusion Limited Aggregation ◽  
Force Microscopy ◽  
Cluster Aggregation ◽  
Diffusion Limited ◽  
Atomic Force ◽  
Slow Aggregation ◽  
Nanoscale Patterns ◽  
Surface Nature ◽  
Aggregation Phenomena

ABSTRACTThe nanoscale patterns formed by poly(methyl methacrylate) (PMMA) stereocomplexes at the surface of silicon wafers, glass and mica, were investigated by tapping mode atomic force microscopy (TM-AFM). The effects of the solvent nature, PMMA concentration, i/s-ratio (stoechimetry) and surface nature on the morphology of the stereocomplex thin layer at a surface were addressed. The aggregation phenomena are well described by the diffusion limited cluster-cluster aggregation model (DLA) and the fractal exponent D calculated. The i/s-ratio strongly influences the fractal exponent D which is equal to 1.35 for the 1:2 ratio is lower than for the other i:s ratios which are 1.46, 1.61, 1.82 for 1:1, 2:1 and 4:1 ratios, respectively. The low values of the fractal dimension D are indicative of a fast aggregation process and higher values of D correspond to a slow aggregation process.

scholarly journals DIVISIBLE SANDPILE ON SIERPINSKI GASKET GRAPHS

Fractals ◽  
2019 ◽  
Vol 27 (03) ◽  
pp. 1950032
Author(s):  
WILFRIED HUSS ◽  
ECATERINA SAVA-HUSS
Keyword(s):  
Growth Model ◽  
Sierpinski Gasket ◽  
Internal Diffusion ◽  
Exact Representation ◽  
Sierpiński Gasket ◽  
Diffusion Limited Aggregation ◽  
Sandpile Model ◽  
Diffusion Limited ◽  
Graph Metric ◽  
Divisible Sandpile

The divisible sandpile model is a growth model on graphs that was introduced by Levine and Peres [Strong spherical asymptotics for rotor-router aggregation and the divisible sandpile, Potential Anal. 30(1) (2009) 1–27] as a tool to study internal diffusion limited aggregation. In this work, we investigate the shape of the divisible sandpile model on the graphical Sierpinski gasket [Formula: see text]. We show that the shape is a ball in the graph metric of [Formula: see text]. Moreover, we give an exact representation of the odometer function of the divisible sandpile.

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