The arrangement of cells in a net. II

Aboav, D.A.

doi:10.1016/0026-0800(83)90012-5

Cited by 29 publications

(11 citation statements)

References 6 publications

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“…On the basis of experimental studies, β ≈ 1.2 was found to be conserved for several natural physical and biological structures(Aboav, 1983; Aboav, 1980; Mombach, Vasconcellos & De Almeida, 1990; Mombach, De Almeida & Iglesias, 1993). This number was very close to the average ratio of a ∕ b of cells of several kinds of 2D structures (Tables 1–2, Fig.…”

Section: Resultsmentioning

confidence: 99%

Ellipse packing in two-dimensional cell tessellation: a theoretical explanation for Lewis’s law and Aboav-Weaire’s law

Xu¹

2019

PeerJ

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Background Lewis’s law and Aboav-Weaire’s law are two fundamental laws used to describe the topology of two-dimensional (2D) structures; however, their theoretical bases remain unclear. Methods We used R software with the Conicfit package to fit ellipses based on the geometric parameters of polygonal cells of ten different kinds of natural and artificial 2D structures. Results Our results indicated that the cells could be classified as an ellipse’s inscribed polygon (EIP) and that they tended to form the ellipse’s maximal inscribed polygon (EMIP). This phenomenon was named as ellipse packing. On the basis of the number of cell edges, cell area, and semi-axes of fitted ellipses, we derived and verified new relations of Lewis’s law and Aboav-Weaire’s law. Conclusions Ellipse packing is a short-range order that places restrictions on the cell topology and growth pattern. Lewis’s law and Aboav-Weaire’s law mainly reflect the effect of deformation from circle to ellipse on cell area and the edge number of neighboring cells, respectively. The results of this study could be used to simulate the dynamics of cell topology during growth.

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Section: Resultsmentioning

confidence: 99%

Ellipse packing in two-dimensional cell tessellation: a theoretical explanation for Lewis’s law and Aboav-Weaire’s law

Xu¹

2019

PeerJ

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“…To estimate how many funnels would be sampled by a spacecraft trajectory through the solar wind plasma, two‐dimensional cellularization patterns (magnetic cells, soap froth, etc.) can be examined [e.g., Aboav , ; Weaire and Hutzler , ; Durand , ]. In Figure one such cellularization is shown.…”

Section: Discussion: Expectations For Structure Scalesmentioning

confidence: 99%

The plasma structure of coronal hole solar wind: Origins and evolution

Borovsky

2016

JGR Space Physics

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Whereas slow solar wind is known to be highly structured, the fast (coronal hole origin) wind is usually considered to be homogeneous. Using measurements from Helios 1 + 2, ACE, Wind, and Ulysses, structure in the coronal hole origin solar wind is examined from 0.3 AU to 2.3 AU. Care is taken to collect and analyze intervals of “unperturbed coronal hole plasma.” In these intervals, solar wind structure is seen in the proton number density, proton temperature, proton specific entropy, magnetic field strength, magnetic field to density ratio, electron heat flux, helium abundance, heavy‐ion charge‐state ratios, and Alfvenicity. Typical structure amplitudes are factors of 2, far from homogeneous. Variations are also seen in the solar wind radial velocity. Using estimates of the motion of the solar wind origin footpoint on the Sun for the various spacecraft, the satellite time series measurements are converted to distance along the photosphere. Typical variation scale lengths for the solar wind structure are several variations per supergranule. The structure amplitude and structure scale sizes do not evolve with distance from the Sun from 0.3 to 2.3 AU. An argument is quantified that these variations are the scale expected for solar wind production in open magnetic flux funnels in coronal holes. Additionally, a population of magnetic field foldings (switchbacks, reversals) in the coronal hole plasma is examined: this population evolves with distance from the Sun such that the magnetic field is mostly Parker spiral aligned at 0.3 AU and becomes more misaligned with distance outward.

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“…Therefore, the area of a cell with more than six sides increases, of a cell with less than six sides decreases, and of cells with exactly six sides remains the same. The Aboav law [4,5] relating the number of edges of neighboring clusters is…”

Section: Introductionmentioning

confidence: 99%