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Ekanayake, Dinesh B.; Ranpatidewage, Manjula Mahesh; LaFountain, Douglas J.

Optimal packings for filled rings of circles. (English) Zbl 07177869

Appl. Math., Praha 65, No. 1, 1-22 (2020).
A filled ring of circles is a finite family of congruent circles whose centres are placed on a larger core circle such that successive circles share a common tangent line. The authors study packings of circles of possibly different radii within a given circle that split into concentric filled rings of circles. The emphasis is on dense packings and their symmetry groups. Applications concern the construction of cables.
Reviewer: Christian Richter (Jena)

MSC:

52C26 Circle packings and discrete conformal geometry
52C15 Packing and covering in \(2\) dimensions (aspects of discrete geometry)

Keywords:

circle packing; dense packing; annulus; dihedral symmetry; optimization; minimal separation
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\textit{D. B. Ekanayake} et al., Appl. Math., Praha 65, No. 1, 1--22 (2020; Zbl 07177869)
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References:

[1] Cable, CME; Inc., Wire, \(AcuTech^TM\) ACSR, Aluminum Conductor, Steel Reinforced, Twisted Pair Conductors, (2019), Available at \brokenlink{http://www.cmewire.com/catalog/{sec03-bac/bac-08-acsrtp.php}}
[2] Fodor, F., The densest packing of 19 congruent circles in a circle, Geom. Dedicata 74 (1999), 139-145 · Zbl 0927.52024
[3] Graham, R. L.; Lubachevsky, B. D.; Nurmela, K. J.; ard, P. R. J. Österg\accent23, Dense packings of congruent circles in a circle, Discrete Math. 181 (1998), 139-154 · Zbl 0901.52017
[4] Li, Y.; Xu, S.; Yang, H., Design of circular signal constellations in the presence of phase noise, 4th International Conference on Wireless Communications, Networking and Mobile Computing IEEE, New York (2008), 2079-2086
[5] López, C. O.; Beasley, J. E., Packing a fixed number of identical circles in a circular container with circular prohibited areas, Optim. Lett. 13 (2019), 1449-1468 · Zbl 1430.90496
[6] Luenberger, D. G.; Ye, Y., Linear and Nonlinear Programming, International Series in Operations Research & Management Science 228, Springer, Cham (2016) · Zbl 1319.90001
[7] Mobasseri, B. G., Digital modulation classification using constellation shape, Signal Process. 80 (2000), 251-277 · Zbl 0939.94025
[8] Pedroso, J. P.; Cunha, S.; Tavares, J. N., Recursive circle packing problems, Int. Trans. Oper. Res. 23 (2016), 355-368 · Zbl 1338.90351
[9] Stoyan, Y.; Yaskov, G., Packing equal circles into a circle with circular prohibited areas, Int. J. Comput. Math. 89 (2012), 1355-1369 · Zbl 1255.52014
[10] F. R. Thrash, Jr., Transmission Conductors-A review of the design and selection criteria, Available at \brokenlink{https://hd-dev-ws11.mro4all.com/HagemeyerNA/media/Documents/{Southwire-Transmission-Conductors.pdf}} (2019), 11 pages
[11] Worzyk, T., Submarine Power Cables. Design, Installation, Repair, Environmental Aspects, Springer, Berlin (2009)
[12] Zoutendijk, G., Methods of Feasible Directions. A Study in Linear and Non-Linear Programming, Elsevier, Amsterdam (1960) · Zbl 0097.35408
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