Positive Recurrence of a One-Dimensional Variant of Diffusion Limited Aggregation

2008 ◽  
pp. 429-461 ◽  
Author(s):  
Harry Kesten ◽  
Vladas Sidoravicius
Keyword(s):  
Diffusion Limited Aggregation ◽  
Positive Recurrence ◽  
One Dimensional ◽  
Diffusion Limited

scholarly journals One-dimensional long-range diffusion-limited aggregation I

2016 ◽  
Vol 44 (5) ◽  
pp. 3546-3579 ◽  
Author(s):  
Gideon Amir ◽  
Omer Angel ◽  
Itai Benjamini ◽  
Gady Kozma
Keyword(s):  
Long Range ◽  
Diffusion Limited Aggregation ◽  
One Dimensional ◽  
Diffusion Limited

The Geometry of Dla: Different Aspects of the Departure from Self-Similarity

1994 ◽  
Vol 367 ◽  
Author(s):  
B.B. Mandelbrot ◽  
A. Vespignani ◽  
H. Kaufman
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Properties ◽  
Finite Size ◽  
Scaling Behavior ◽  
Self Similarity ◽  
Diffusion Limited Aggregation ◽  
One Dimensional ◽  
Diffusion Limited ◽  
Large Numbers ◽  
The One

AbstractIn order to understand better the morphology and the asymptotic behavior in Diffusion Limited Aggregation (DLA), we studied a large numbers of very large off-lattice circular clusters. We inspected both dynamical and geometric asymptotic properties, namely the moments of the particle's sticking distances and the scaling behavior of the transverse growth crosscuts, i.e., the one dimensional cuts by circles. The emerging picture for radial DLA departs from simple self-similarity for any finite size. It corresponds qualitatively to the scenario of infinite drift starting from the familiar five armed shape for small sizes and proceeding to an increasingly tight multi-armed shape. We show quantitatively how the lacunarity of circular clusters becomes increasingly “compact” with size. Finally, we find agreement among transverse cuts dimensions for clusters grown in different geometries, suggesting that the question of universality is best addressed on the crosscut.

DIFFUSION-LIMITED AGGREGATION DRIVEN BY OPTIMAL TRANSPORTATION

Fractals ◽  
2010 ◽  
Vol 18 (02) ◽  
pp. 247-253 ◽  
Author(s):  
QINGLAN XIA ◽  
DOUGLAS UNGER
Keyword(s):  
Transition Point ◽  
Full Range ◽  
Phase Transition Point ◽  
Optimal Transportation ◽  
Transport Cost ◽  
Diffusion Limited Aggregation ◽  
One Dimensional ◽  
Diffusion Limited ◽  
Final Cluster ◽  
Dla Model

In this article, we combine the DLA model of Witten and Sander with ideas from ramified optimal transportation. We propose a modification of the DLA model in which the probability of sticking is inversely proportional to the additional transport cost from the point to the root. We used a family of cost functions parameterized by a parameter α as studied in ramified optimal transportation. α < 0 promotes growth near the root whereas α > 0 promotes growth at the tips of the cluster. α = 0 is a phase transition point and corresponds to standard DLA. What makes this model interesting is that when α is negative enough (e.g. α < -2) the final cluster is an one-dimensional curve. On the other hand, when α is positive enough (e.g. α > 2) we get a nearly two dimensional disk. Thus our model encompasses the full range of fractal dimension from 1 to 2.

scholarly journals One-dimensional long-range diffusion limited aggregation II: The transient case

2017 ◽  
Vol 27 (3) ◽  
pp. 1886-1922 ◽  
Author(s):  
Gideon Amir ◽  
Omer Angel ◽  
Gady Kozma
Keyword(s):  
Long Range ◽  
Diffusion Limited Aggregation ◽  
One Dimensional ◽  
Diffusion Limited ◽  
Transient Case

Anisotropy and Cluster Growth by Diffusion-Limited Aggregation

1985 ◽  
Vol 55 (13) ◽  
pp. 1406-1409 ◽  
Author(s):  
Robin C. Ball ◽  
Robert M. Brady ◽  
Giuseppe Rossi ◽  
Bernard R. Thompson
Keyword(s):  
Cluster Growth ◽  
Diffusion Limited Aggregation ◽  
Diffusion Limited

Deterministic Growth of Diffusion-Limited Aggregation with Quenched Disorder

1990 ◽  
Vol 13 (4) ◽  
pp. 341-347 ◽  
Author(s):  
A Hansen ◽  
E. L Hinrichsen ◽  
S Roux ◽  
H. J Herrmann ◽  
L. de Arcangelis
Keyword(s):  
Quenched Disorder ◽  
Diffusion Limited Aggregation ◽  
Diffusion Limited
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