Fractal growth of copper electrodeposits

Brady, Robert M.; Ball, Robin C.

doi:10.1038/309225a0

Cited by 556 publications

(235 citation statements)

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“…Under diffusion-limited conditions, growth of copper by electrodeposition occurs preferentially on any protuberances, leading to dendritic and fractal growth. [12] In our experiments at lower currents globular rough surfaces were obtained. The deposited layers of copper were coated with a fluorocarbon hydrophobic layer; water drops on them then showed contact angles ranging from 115(±3)° to greater than 165°, depending upon the current density during deposition and therefore the degree of roughness of the surface.…”

Section: Table Of Contentsmentioning

confidence: 99%

Dual‐Scale Roughness Produces Unusually Water‐Repellent Surfaces

Shirtcliffe¹,

et al. 2004

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Section: Table Of Contentsmentioning

confidence: 99%

Dual‐Scale Roughness Produces Unusually Water‐Repellent Surfaces

Shirtcliffe¹,

et al. 2004

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“…[Exceptions exist, such as dielectric breakdown (Niemeyer, Pietronero & Wiesmann, 1984) and electrodeposition (Brady & Ball, 1984), in which monomer addition via DLA may be appropriate.] Early simulations of this cluster-cluster aggregation model (Meakin, 1983a;Kolb, Botet & Jullien, 1983) were relatively small simplified attempts in two dimensions (.--1000 particles) that left some doubt as to the validity of the results, but gradually more efficient and sophisticated algorithms became available (Botet, Jullien & Kolb, 1984) that reduced the uncertainties in the fractal dimension.…”

Section: Aggregates (A) Models Of Aggregationmentioning

confidence: 99%

Scattering from fractals

Martin¹,

Hurd²

1987

J Appl Crystallogr

573

376

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The concepts of dilation symmetry and the fractal dimension are introduced, and from these basic concepts scattering functions are computed for surface and mass fractals. It is then shown how the fractal structure of various random media has been elucidated from scattering measurements, and how these observations relate to specific models of fractal geometry. Examples include colloidal aggregates, gels, soot and the fractal porosity of rocks of various sorts.

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“…Indeed, in an incredible number of situations the objects of interest can be represented by self-similar structures over a large, even if finite, range of scales. Examples include commodity price fluctuations [9], the shape of coastlines [10], the discharge of electric fields [11], the branching of rivers [12], deposition processes [13], the growth of cities [14], fractures [15], and a variety of biological structures [16].…”

Section: Scale Invariance and Self-organizationmentioning

confidence: 99%

Self-Organization and Complex Networks

Caldarelli¹,

Garlaschelli

2009

Understanding Complex Systems

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In this chapter we discuss how the results developed within the theory of fractals and Self-Organized Criticality (SOC) can be fruitfully exploited as ingredients of adaptive network models. In order to maintain the presentation selfcontained, we first review the basic ideas behind fractal theory and SOC. We then briefly review some results in the field of complex networks, and some of the models that have been proposed. Finally, we present a self-organized model recently proposed by Garlaschelli et al. [Nat. Phys. 3, 813 (2007)] that couples the fitness network model defined by Caldarelli et al. [Phys. Rev. Lett. 89, 258702 (2002)] with the evolution model proposed by Bak and Sneppen [Phys. Rev. Lett. 71, 4083 (1993)] as a prototype of SOC. Remarkably, we show that the results obtained for the two models separately change dramatically when they are coupled together. This indicates that self-organized networks may represent an entirely novel class of complex systems, whose properties cannot be straightforwardly understood in terms of what we have learnt so far.

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Fractal growth of copper electrodeposits

Cited by 556 publications

References 5 publications

Dual‐Scale Roughness Produces Unusually Water‐Repellent Surfaces

Dual‐Scale Roughness Produces Unusually Water‐Repellent Surfaces

Scattering from fractals

Self-Organization and Complex Networks

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