TY - JOUR
T1 - Modeling and simulation of the hexagonal pattern formation of honeycombs by the immersed boundary method
AU - Jeong, Darae
AU - Choi, Yongho
AU - Kim, Junseok
N1 - Funding Information:
The authors thank the reviewers for the constructive and helpful comments on the revision of this article. The first author (D. Jeong) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) ( NRF-2017R1E1A1A03070953 ). The corresponding author (J.S. Kim) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( NRF-2016R1D1A1B03933243 ).
PY - 2018/9
Y1 - 2018/9
N2 - We present a simple mathematical model and numerical simulations of the hexagonal pattern formation of a honeycomb using the immersed boundary method. In our model, we assume that the cells have a circular shape at their inception and that there is a force acting upon the entire circumference of the cell. The net force from the individual cells is a key factor in their transformation from a circular shape to a rounded hexagonal shape. Numerical experiments using the proposed mathematical model confirm the hexagonal patterns observed in honeybee colonies.
AB - We present a simple mathematical model and numerical simulations of the hexagonal pattern formation of a honeycomb using the immersed boundary method. In our model, we assume that the cells have a circular shape at their inception and that there is a force acting upon the entire circumference of the cell. The net force from the individual cells is a key factor in their transformation from a circular shape to a rounded hexagonal shape. Numerical experiments using the proposed mathematical model confirm the hexagonal patterns observed in honeybee colonies.
KW - Hexagonal pattern
KW - Honeycomb
KW - Immersed boundary method
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U2 - 10.1016/j.cnsns.2018.02.024
DO - 10.1016/j.cnsns.2018.02.024
M3 - Article
AN - SCOPUS:85042367100
VL - 62
SP - 61
EP - 77
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
SN - 1007-5704
ER -