Optimal packings for filled rings of circles
Dinesh B. Ekanayake; Manjula Mahesh Ranpatidewage; Douglas J. LaFountain
Applications of Mathematics (2020)
- Volume: 65, Issue: 1, page 1-22
- ISSN: 0862-7940
Access Full Article
top
Abstract
topHow to cite
topEkanayake, Dinesh B., Ranpatidewage, Manjula Mahesh, and LaFountain, Douglas J.. "Optimal packings for filled rings of circles." Applications of Mathematics 65.1 (2020): 1-22. <http://eudml.org/doc/295022>.
@article{Ekanayake2020,
abstract = {General circle packings are arrangements of circles on a given surface such that no two circles overlap except at tangent points. In this paper, we examine the optimal arrangement of circles centered on concentric annuli, in what we term rings. Our motivation for this is two-fold: first, certain industrial applications of circle packing naturally allow for filled rings of circles; second, any packing of circles within a circle admits a ring structure if one allows for irregular spacing of circles along each ring. As a result, the optimization problem discussed herein will be extended in a subsequent paper to a more general setting. With this framework in mind, we present properties of concentric rings that have common points of tangency, the exact solution for the optimal arrangement of filled rings along with its symmetry group, and applications to construction of aluminum-conductor steel reinforced cables.},
author = {Ekanayake, Dinesh B., Ranpatidewage, Manjula Mahesh, LaFountain, Douglas J.},
journal = {Applications of Mathematics},
language = {eng},
number = {1},
pages = {1-22},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Optimal packings for filled rings of circles},
url = {http://eudml.org/doc/295022},
volume = {65},
year = {2020},
}
TY - JOUR
AU - Ekanayake, Dinesh B.
AU - Ranpatidewage, Manjula Mahesh
AU - LaFountain, Douglas J.
TI - Optimal packings for filled rings of circles
JO - Applications of Mathematics
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 1
SP - 1
EP - 22
AB - General circle packings are arrangements of circles on a given surface such that no two circles overlap except at tangent points. In this paper, we examine the optimal arrangement of circles centered on concentric annuli, in what we term rings. Our motivation for this is two-fold: first, certain industrial applications of circle packing naturally allow for filled rings of circles; second, any packing of circles within a circle admits a ring structure if one allows for irregular spacing of circles along each ring. As a result, the optimization problem discussed herein will be extended in a subsequent paper to a more general setting. With this framework in mind, we present properties of concentric rings that have common points of tangency, the exact solution for the optimal arrangement of filled rings along with its symmetry group, and applications to construction of aluminum-conductor steel reinforced cables.
LA - eng
UR - http://eudml.org/doc/295022
ER -
References
top- 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}}. (2019)
- Fodor, F., 10.1023/A:1005091317243, Geom. Dedicata 74 (1999), 139-145. (1999) Zbl0927.52024MR1674049DOI10.1023/A:1005091317243
- Graham, R. L., Lubachevsky, B. D., Nurmela, K. J., ard, P. R. J. Österg\accent23, 10.1016/S0012-365X(97)00050-2, Discrete Math. 181 (1998), 139-154. (1998) Zbl0901.52017MR1600759DOI10.1016/S0012-365X(97)00050-2
- Li, Y., Xu, S., Yang, H., 10.1109/wicom.2008.498, 4th International Conference on Wireless Communications, Networking and Mobile Computing IEEE, New York (2008), 2079-2086. (2008) DOI10.1109/wicom.2008.498
- López, C. O., Beasley, J. E., 10.1007/s11590-018-1351-x, Optim. Lett. 13 (2019), 1449-1468. (2019) Zbl07119195MR4002309DOI10.1007/s11590-018-1351-x
- Luenberger, D. G., Ye, Y., 10.1007/978-3-319-18842-3, International Series in Operations Research & Management Science 228, Springer, Cham (2016). (2016) Zbl1319.90001MR3363684DOI10.1007/978-3-319-18842-3
- Mobasseri, B. G., 10.1016/S0165-1684(99)00127-9, Signal Process. 80 (2000), 251-277. (2000) Zbl0939.94025DOI10.1016/S0165-1684(99)00127-9
- Pedroso, J. P., Cunha, S., Tavares, J. N., 10.1111/itor.12107, Int. Trans. Oper. Res. 23 (2016), 355-368. (2016) Zbl1338.90351MR3423777DOI10.1111/itor.12107
- Stoyan, Y., Yaskov, G., 10.1080/00207160.2012.685468, Int. J. Comput. Math. 89 (2012), 1355-1369. (2012) Zbl1255.52014MR2946545DOI10.1080/00207160.2012.685468
- 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.
- Worzyk, T., 10.1007/978-3-642-01270-9, Springer, Berlin (2009). (2009) DOI10.1007/978-3-642-01270-9
- Zoutendijk, G., Methods of Feasible Directions. A Study in Linear and Non-Linear Programming, Elsevier, Amsterdam (1960). (1960) Zbl0097.35408MR0129119
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.