EXPERIMENTS ON LAPLACIAN GROWTH

1989 ◽  
pp. 296-333
Keyword(s):  
Laplacian Growth

scholarly journals Complexity and Criticality in Laplacian Growth Models

1993 ◽  
Vol 24 (9) ◽  
pp. 701-705
Author(s):  
F Guinea ◽  
O Pla ◽  
E Louis
Keyword(s):  
Growth Models ◽  
Laplacian Growth

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 Harmonic moment dynamics in Laplacian growth

2010 ◽  
Vol 81 (1) ◽  
Author(s):  
Alexander Leshchiner ◽  
Matthew Thrasher ◽  
Mark B. Mineev-Weinstein ◽  
Harry L. Swinney
Keyword(s):  
Laplacian Growth ◽  
Harmonic Moment

scholarly journals Evidence of Discrete Scale Invariance in DLA and Time-to-Failure by Canonical Averaging

1998 ◽  
Vol 09 (03) ◽  
pp. 433-447 ◽  
Author(s):  
A. Johansen ◽  
D. Sornette
Keyword(s):  
Scale Invariance ◽  
Time To Failure ◽  
Laplacian Growth ◽  
Ensemble Averaging ◽  
Diffusion Limited Aggregation ◽  
Discrete Scale Invariance ◽  
Diffusion Limited ◽  
Market Crashes ◽  
Discrete Scale

Discrete scale invariance, which corresponds to a partial breaking of the scaling symmetry, is reflected in the existence of a hierarchy of characteristic scales l0,l0λ,l0λ2,…, where λ is a preferred scaling ratio and l0 a microscopic cut-off. Signatures of discrete scale invariance have recently been found in a variety of systems ranging from rupture, earthquakes, Laplacian growth phenomena, "animals" in percolation to financial market crashes. We believe it to be a quite general, albeit subtle phenomenon. Indeed, the practical problem in uncovering an underlying discrete scale invariance is that standard ensemble averaging procedures destroy it as if it was pure noise. This is due to the fact, that while λ only depends on the underlying physics, l0 on the contrary is realization-dependent. Here, we adapt and implement a novel so-called "canonical" averaging scheme which re-sets the l0 of different realizations to approximately the same value. The method is based on the determination of a realization-dependent effective critical point obtained from, e.g., a maximum susceptibility criterion. We demonstrate the method on diffusion limited aggregation and a model of rupture.

scholarly journals Random matrices in 2D, Laplacian growth and operator theory

2008 ◽  
Vol 41 (26) ◽  
pp. 263001 ◽  
Author(s):  
Mark Mineev-Weinstein ◽  
Mihai Putinar ◽  
Razvan Teodorescu
Keyword(s):  
Random Matrices ◽  
Operator Theory ◽  
Laplacian Growth

Modified Laplacian Growth under Shear Flow

1991 ◽  
Vol 60 (8) ◽  
pp. 2700-2705 ◽  
Author(s):  
Takashi Nagatani
Keyword(s):  
Shear Flow ◽  
Laplacian Growth
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