Asymptotic structure of diffusion-limited aggregation clusters in two dimensions

1987 ◽  
Vol 83 ◽  
pp. 139 ◽  
Author(s):  
Fereydoon Family ◽  
H. George E. Hentschel
Keyword(s):  
Two Dimensions ◽  
Asymptotic Structure ◽  
Diffusion Limited Aggregation ◽  
Diffusion Limited

scholarly journals Fractal and Dendritic Growth of Surface Aggregates

1995 ◽  
Vol 407 ◽  
Author(s):  
H. Brune ◽  
K. Bromann ◽  
K. Kern ◽  
J. Jacobsen ◽  
P. Stoltze ◽  
...  
Keyword(s):  
Dendritic Growth ◽  
Kinetic Monte Carlo ◽  
Variable Temperature ◽  
Two Dimensions ◽  
Present System ◽  
Diffusion Limited Aggregation ◽  
Microscopic Mechanism ◽  
Diffusion Limited ◽  
Kinetic Monte Carlo Simulations ◽  
Equilibrium Growth

ABSTRACTThe similarity of patterns formed in non-equilibrium growth processes in physics, chemistry and biology is conspicuous and many attempts have been made to discover common mechanisms underlying their growth. The central question in this context is what causes some patterns to be dendritic, as e.g. snowflakes, while others grow fractal (randomly ramified). Here we report a crossover from fractal to dendritic patterns for growth in two dimensions: the diffusion limited aggregation of Ag atoms on a Pt(111) surface as observed by means of variable temperature STM. The microscopic mechanism of dendritic growth can be analyzed for the present system. It originates from the anisotropy of the diffusion of adatoms at corner sites which is linked to the trigonal symmetry of the substrate. This corner diffusion is observed to be active as soon as islands form, therefore, the classical DLA clusters with the hit and stick mechanism do not form. The ideas on the mechanism for dendritic growth have been verified by kinetic Monte-Carlo simulations which are in excellent agreement with experiment.

scholarly journals Integrability-preserving regularizations of Laplacian Growth

2020 ◽  
Vol 15 ◽  
pp. 9
Author(s):  
Razvan Teodorescu
Keyword(s):  
Universality Class ◽  
Two Dimensions ◽  
Laplacian Growth ◽  
Boundary Singularity ◽  
Diffusion Limited Aggregation ◽  
Scaling Properties ◽  
Scale Free ◽  
Diffusion Limited ◽  
Long Time ◽  
Discrete Counterpart

The Laplacian Growth (LG) model is known as a universality class of scale-free aggregation models in two dimensions, characterized by classical integrability and featuring finite-time boundary singularity formation. A discrete counterpart, Diffusion-Limited Aggregation (or DLA), has a similar local growth law, but significantly different global behavior. For both LG and DLA, a proper description for the scaling properties of long-time solutions is not available yet. In this note, we outline a possible approach towards finding the correct theory yielding a regularized LG and its relation to DLA.

scholarly journals Diffusion-Limited Aggregation as Branched Growth

1994 ◽  
Vol 367 ◽  
Author(s):  
Thomas C. Halsey
Keyword(s):  
Unstable Manifold ◽  
First Principles ◽  
Scaling Law ◽  
Mean Field ◽  
Field Approximation ◽  
Two Dimensions ◽  
Mean Field Approximation ◽  
Diffusion Limited Aggregation ◽  
Diffusion Limited

AbstractI present a first-principles theory of diffusion-limited aggregation in two dimensions. A renormalized mean-field approximation gives the form of the unstable manifold for branch competition, following the method of Halsey and Leibig [Phys. Rev. A 46, 7793 (1992)]. This leads to a result for the cluster dimensionality, D ≍ 1.66, which is close to numerically obtained values. Quenched and annealed multifractal dimensions can also be computed in this theory; the multifractal dimension τ(3) = D, in agreement with a proposed “electro- static” scaling law.

Diffusion-Limited Aggregation in Two Dimensions

1985 ◽  
Vol 54 (10) ◽  
pp. 1043-1046 ◽  
Author(s):  
Alan J. Hurd ◽  
Dale W. Schaefer
Keyword(s):  
Two Dimensions ◽  
Diffusion Limited Aggregation ◽  
Diffusion Limited

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
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