Modeling and simulation of the hexagonal pattern formation of honeycombs by the immersed boundary method

Darae Jeong; Yongho Choi; Junseok Kim

doi:10.1016/j.cnsns.2018.02.024

Modeling and simulation of the hexagonal pattern formation of honeycombs by the immersed boundary method

Darae Jeong, Yongho Choi, Junseok Kim

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

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	https://doi.org/10.1016/j.cnsns.2018.02.024
Publication status	Published - 2018 Sep

Keywords

Hexagonal pattern
Honeycomb
Immersed boundary method

ASJC Scopus subject areas

Numerical Analysis
Modelling and Simulation
Applied Mathematics

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10.1016/j.cnsns.2018.02.024

Cite this

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title = "Modeling and simulation of the hexagonal pattern formation of honeycombs by the immersed boundary method",

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.",

keywords = "Hexagonal pattern, Honeycomb, Immersed boundary method",

author = "Darae Jeong and Yongho Choi and Junseok Kim",

note = "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). Publisher Copyright: {\textcopyright} 2018 Elsevier B.V.",

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doi = "10.1016/j.cnsns.2018.02.024",

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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). Publisher Copyright: © 2018 Elsevier B.V.

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.

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KW - Honeycomb

KW - Immersed boundary method

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JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

SN - 1007-5704

ER -

Modeling and simulation of the hexagonal pattern formation of honeycombs by the immersed boundary method

Abstract

Keywords

ASJC Scopus subject areas

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