Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 61-77 |
| Number of pages | 17 |
| Journal | Communications in Nonlinear Science and Numerical Simulation |
| Volume | 62 |
| DOIs | |
| Publication status | Published - 2018 Sep 1 |
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Keywords
- Hexagonal pattern
- Honeycomb
- Immersed boundary method
ASJC Scopus subject areas
- Numerical Analysis
- Modelling and Simulation
- Applied Mathematics
Cite this
Modeling and simulation of the hexagonal pattern formation of honeycombs by the immersed boundary method. / Jeong, Darae; Choi, Yongho; Kim, Junseok.
In: Communications in Nonlinear Science and Numerical Simulation, Vol. 62, 01.09.2018, p. 61-77.Research output: Contribution to journal › Article
}
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
PY - 2018/9/1
Y1 - 2018/9/1
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
UR - http://www.scopus.com/inward/record.url?scp=85042367100&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85042367100&partnerID=8YFLogxK
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 -