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.

DIFFUSION LIMITED AGGREGATION FROM SHEAR STRESS AS A SIMPLE MODEL OF VASCULOGENESIS

Fractals ◽  
1999 ◽  
Vol 07 (01) ◽  
pp. 33-39 ◽  
Author(s):  
VINCENT FLEURY ◽  
LAURENT SCHWARTZ
Keyword(s):  
Shear Stress ◽  
Dendritic Growth ◽  
High Shear ◽  
Vascular Pattern ◽  
Laplacian Growth ◽  
High Shear Stress ◽  
Diffusion Limited Aggregation ◽  
Diffusion Limited ◽  
Capillary Bed ◽  
Arteries And Veins

A model is proposed by which the formation of the vascular network in animals proceeds via progressive penetration of the vessel ramification into a capillary mesh, by means of a laplacian growth mechanism of hydrodynamical origin. In this model, the growth of both arteries and veins follows the directions of high shear stress provoked by the blood flow on the endothelial wall of a pre-existing capillary mesh. This process is shown to be identical to the phenomenon of dendritic growth, which is responsible for the formation of such well-known patterns as dendritic crystals, lightning sparks or branching aggregates of bacteria. A number of straightforward consequences of potentially important medical and physiological interests are deduced. These include the natural and spontaneous organization of the arterial and venal trees, the spontaneous and unavoidable tropism of arteries towards veins and vice-versa, the hierarchical character of the vessels and the possibility of computerized prediction of the vascular pattern from the shape of the capillary bed.

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
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