Physics and Fractal Structures

Gouyet, J. F.; Bug, A. L. R.

doi:10.1119/1.18629

Cited by 163 publications

(267 citation statements)

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“…However, recent studies have proposed [6] that the complex spatial phenomena associated with actual urban systems is rather better described using fractal geometry consistent with growth dynamics in disordered media [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Modeling urban growth patterns with correlated percolation

et al. 1998

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We propose and test a model that describes the morphology of cities, the scaling of the urban perimeter of individual cities, and the area distribution of systems of cities. The model is also consistent with observable urban growth dynamics, our results agreeing both qualitatively and quantitatively with urban data. The resulting growth morphology can be understood from interactions among the constituent units forming an urban region, and can be modeled using a correlated percolation model in the presence of a gradient.

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Section: Introductionmentioning

confidence: 99%

Modeling urban growth patterns with correlated percolation

et al. 1998

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“…Self similarity and space filling are two common important properties of fractal geometry. Self similarity leads to wide band while space filling increases the electrical length [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. In [26], a super wide band fractal antenna had been modeled and simulated for super wideband application.…”

mentioning

confidence: 99%

Design of a Novel Super Wide Band Circular-Hexagonal Fractal Antenna

Ali¹,

Islam²,

Azim³

2013

PIER

100

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Abstract-In this paper, a novel circular-hexagonal Fractal antenna is investigated for super wide band applications. The proposed antenna is made of iterations of a hexagonal slot inside a circular metallic patch with a transmission line. A partial ground plane and asymmetrical patch toward the substrate are used for designing the antenna to achieve a super wide bandwidth ranging from 2.18 GHz to 44.5 GHz with a bandwidth ratio of 20.4 : 1. The impedance bandwidth and gain of the proposed antenna are much better than the recently reported super wideband antennas which make it appropriate for many wireless communications systems such as ISM, Wi-Fi, GPS, Bluetooth, WLAN and UWB. Details of the proposed antenna design are presented and discussed.

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“…Using the box-counting method (for more details on the fractal measurement procedure see Ref [33]), the fractal dimension D2d was measured to be 1.62, in accordance with the value obtained for the same preform infiltrated with pure copper (D2d between 1.6 and 1.7) in Ref [33]. Since D3d = D2d + 1, this means that the cluster of invaded pores is a fractal of dimension near 2.5, as predicted by percolation theory [40][41][42]. The present results thus extend to Cu-Sn alloys and (as concerns only the scaling law) to mercury the findings documented in Ref.…”

Section: Initial Stage Of Infiltration: Percolationmentioning

confidence: 51%

Infiltration of tin bronze into alumina particle beds: influence of alloy chemistry on drainage curves

2014

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The wetting of angular alumina particle preforms by Cu-Sn alloys is investigated by means of pressure infiltration experiments conducted at 1150°C, using a system enabling dynamic and precise measurements of the metal volume injected into the preform. Wetting is quantified in terms of drainage curves, which plot the volume fraction of molten metal in the packed powder preform (also called saturation) versus the applied pressure. The shape of the curves confirms earlier findings, namely (i) the initial stage of infiltration is dominated by percolation and obeys a universal scaling relation while the metal shape is fractal and (ii) at higher saturation incremental pore-filling is dictated by local pore geometrical characteristics, saturation curves obeying then the Brooks-Corey correlation. According to sessile drop data in the literature, the Cu-Sn system is characterized by relatively small changes in the contact angle with alloy composition (128 to 122°), while the metal surface tension changes by more than a factor two over the whole composition range. One would therefore expect that the drainage curves be indifferently proportional to the molten metal surface tension or the work of immersion: the present data show that this is indeed verified.

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Physics and Fractal Structures

Cited by 163 publications

References 0 publications

Modeling urban growth patterns with correlated percolation

Modeling urban growth patterns with correlated percolation

Design of a Novel Super Wide Band Circular-Hexagonal Fractal Antenna

Infiltration of tin bronze into alumina particle beds: influence of alloy chemistry on drainage curves

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