Wavelet analysis of the self-similarity of diffusion-limited aggregates and electrodeposition clusters

Argoul, Françoise; Arnéodo, A.; Elezgaray, Juan; Grasseau, G.; Murenzi, Romain

doi:10.1103/physreva.41.5537

Cited by 81 publications

(46 citation statements)

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“…As we have pointed out in our previous study of Laplacian growth processes [23,24,30], the application of the wavelet transform [39,41,42] may eventually result in a more complete understanding of the local scaling properties of fractal aggregates. In fact, as seen through the « wavelet microscope », the self-similarity of the branched geometry of DLA clusters and electrochemical deposits is likely to be the expression of a nonlinear chaotic recursive construction process which accounts for the proliferation of tip-splitting and side-branching instabilities observed during the growth [24].…”

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confidence: 99%

“…In fact, as seen through the « wavelet microscope », the self-similarity of the branched geometry of DLA clusters and electrochemical deposits is likely to be the expression of a nonlinear chaotic recursive construction process which accounts for the proliferation of tip-splitting and side-branching instabilities observed during the growth [24]. But thus far, no computer simulation of the DLA model (image processing of electrodeposition clusters) has achieved the necessary size (resolution) to make definite conclusions about the deterministic character of the fractal patterns observed in diffusion-controlled growth.…”

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confidence: 99%

“…Because the complexity of the geometry is intricately connected with the dynamical evolution, most attention has been initially focused on the fractal structure of Laplacian aggregates [1][2][3][17][18][19][20][21][22]. But only very recently [23,24], DLA clusters were shown to be statistically self-similar as generally believed. Moreover, it has been realized that this geometrical self-similarity is intimately related to the nonhomogeneous distribution of the velocity field along the cluster boundary.…”

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confidence: 99%

“…Thus, the multifractal properties [31] of the growth probability distribution were investigated through the measurement of the generalized fractal dimensions Dq and the f ( a )-spectrum of singularities [30,[32][33][34][35][36][37][38]. But the Dq and f ( a )-spectra are, in effect, statistical averages [24,39,40] that do not provide all the information we need to understand the growth of fractal aggregates. What is essentially missing is the local information concerning the spatial distribution of the scaling exponents along the cluster boundary.…”

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confidence: 99%

“…Extensive computer investigations [1][2][3] [lc, 3-7] or to mimic anisotropic growth [3, [8][9][10][11][12][13][14][15][16]. The fractal geometry of these aggregates has been analyzed by computational [2,3,11,[17][18][19][20][21][22][23][24] and analytical methods [15,[25][26][27][28]. But [3] or the result of a proliferation of deterministic tip-splitting instabilities [29].…”

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Experimental evidence for deterministic chaos in electrochemical deposition

Argoul

Arnéodo

1990

J. Phys. France

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We report an experimental study of the statics and dynamics of electrodeposition of zinc in an aqueous medium, in the intermediate regime between dendritic and DLA-like metallic clusters. During the growth process, periodic and nonperiodic oscillations of the voltage are recorded under constant applied current intensity. Period-doubling bifurcations are identified. Analysis of the data in terms of phase portraits, Poincaré maps and 1-D maps shows that the fractal geometry of these electrochemical deposits is the signature of a low-dimensional deterministic chaotic dynamics which displays sensitivity to initial conditions. The study of the apparently more complex dynamics recorded in the DLA limit is a very promising experimental challenge

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confidence: 99%

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confidence: 99%

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Experimental evidence for deterministic chaos in electrochemical deposition

Argoul

Arnéodo

1990

J. Phys. France

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The Effect of Boundaries on the Aggregation Process

Korneta

1993

Physica Status Solidi (b)

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The aggregation process in which basic units (atoms, particles, small agglomerates, etc.) stick together has been intensively studied in recent years [l to 31. Special attention received the kinetic growth processes such as diffusion-limited aggregation in which the structural rearrangements of growing aggregates are not allowed, because they lead to unusual morphologies of aggregates. This process dominates in the earliest stages of the phase separation and it eventually is replaced by the nucleation or spinodal decomposition processes [4, 51. Moreover the formation of aggregates by the kinetic growth process is observed in systems being far from equilibrium, e.g. for deep quenches. The understanding of the kinetic growth of aggregates is thus important from a scientific point of view. The intensive study of this process is also motivated by the need to develop new materials [6]. The unusual morphologies of materials with non-equilibrium structures are connected with unexpected combinations of their chemical and physical properties. Recently properties of rather small metallic aggregates embedded in a matrix or in porous media attracted considerable attention. They exhibit characteristic features that are not found in pure materials, e.g. they show a pronounced peak in the light absorption spectrum, what found applications in selective absorbers of solar energy [7]. The observed optical absorption is due to excitations of surface plasmon modes of conduction electrons, what strongly depends on the morphology and the size of an aggregate. In order to determine the relation between the morphology and properties of an aggregate, it is necessary to define quantities well describing the morphology. The quantification of the morphology of aggregates attracted considerable attention in recent years. Nowadays the morphology of small aggregates can be observed directly by using electron microscopes [ 1, 71. In order to characterize complex morphologies the concept of the fractal dimension was introduced. In [ 11 different methods of calculation of the fractal dimension of small aggregates by analyzing their digitized images are given. However, during the growth process the fractal dimension of an aggregate increases [8], although the growth process remains the same. This is due to the decreasing contribution of the surface part of the growing aggregate in its overall structure. In recent years the non-orthogonal wavelet transform [9] has been used for the characterization of the geometrical complexity of numerical and experimental aggregates [lo, 111. In this note we characterize the morphology of an aggregate during the growth by quantities obtained from decomposition coefficients of the digitized image of an aggregate into an orthogonal wavelet basis. The orthogonal wavelet basis is constructed from the analyzing wavelet ') E-15706 Santiago de Compostela, Spain. ' ) Permanent address:

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Directional Wavelets Revisited: Cauchy Wavelets and Symmetry Detection in Patterns

Antoine

Murenzi

Vandergheynst

1999

Applied and Computational Harmonic Analysis

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The analysis of oriented features in images requires two-dimensional directional wavelets. Among these, we study in detail the class of Cauchy wavelets, which are strictly supported in a (narrow) convex cone in spatial frequency space. They have excellent angular selectivity, as shown by a standard calibration test, and they have minimal uncertainty. In addition, we present a new application of directional wavelets, namely a technique for determining the symmetries of a given pattern with respect to rotations and dilation.

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Wavelet analysis of the self-similarity of diffusion-limited aggregates and electrodeposition clusters

Cited by 81 publications

References 106 publications

Experimental evidence for deterministic chaos in electrochemical deposition

Experimental evidence for deterministic chaos in electrochemical deposition

The Effect of Boundaries on the Aggregation Process

Directional Wavelets Revisited: Cauchy Wavelets and Symmetry Detection in Patterns

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