@article{dba0eb4f09bc4d078b03044cc1f2a40a,
title = "Mathematical modeling and computer simulation of the three-dimensional pattern formation of honeycombs",
abstract = "We present a mathematical model, a numerical scheme, and computer simulations of the three-dimensional pattern formation of a honeycomb structure by using the immersed boundary method. In our model, we assume that initially the honeycomb cells have a hollow hemisphere mounted by a hollow circular cylinder shape at their birth and there is force acting upon the entire side of the cell. The net force from the individual cells is a key factor in their transformation from a hollow hemisphere mounted by a hollow circular cylinder shape to a rounded rhombohedral surfaces mounted by a hexagonal cylinder shape. Numerical simulations of the proposed mathematical model equation produce the rounded rhombohedral surfaces mounted by a hexagonal cylinder patterns observed in honeybee colonies.",
author = "Darae Jeong and Yibao Li and Sangkwon Kim and Yongho Choi and Chaeyoung Lee and Junseok Kim",
note = "Funding Information: The first author (D. Jeong) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2017R1E1A1A03070953). Y.B. Li was supported by National Natural Science Foundation of China (No. 11601416, No. 11631012) and National Key R & D Program of China (No. 2018YFB1105302). S.K. Kim and C. Lee were supported by the BK21 PLUS program. The corresponding author (J.S. Kim) was supported by Korea University Future Research Grant. The authors greatly appreciate the reviewers for their constructive comments and suggestions, which have improved the quality of this paper. Publisher Copyright: {\textcopyright} 2019, The Author(s).",
year = "2019",
month = dec,
day = "1",
doi = "10.1038/s41598-019-56942-6",
language = "English",
volume = "9",
journal = "Scientific reports",
issn = "2045-2322",
publisher = "Nature Publishing Group",
number = "1",
}