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

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.

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The Screening Behavior in Diffusion-Limited Aggregation

Communications in Theoretical Physics ◽

10.1088/0253-6102/8/1/113 ◽

1987 ◽

Vol 8 (1) ◽

pp. 113-117

Author(s):

Weng Jia-qiang

Keyword(s):

Diffusion Limited Aggregation ◽

Screening Behavior ◽

Diffusion Limited

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Study on Laplace Growth and Diffusion Limited Aggregation with Material Properties

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.703.71 ◽

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.

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Topology change due to particle heterogeneity in DLAs

International Journal of Modern Physics C ◽

10.1142/s0129183115501363 ◽

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.

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