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

Darae Jeong, Yongho Choi, Junseok Kim

Research output: Contribution to journalArticle

5 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 languageEnglish
Pages (from-to)61-77
Number of pages17
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume62
DOIs
Publication statusPublished - 2018 Sep 1

Fingerprint

Immersed Boundary Method
Honeycomb
Pattern Formation
Hexagon
Modeling and Simulation
Mathematical models
Cell
Mathematical Model
Circumference
Computer simulation
Numerical Experiment
Entire
Numerical Simulation
Experiments
Model

Keywords

  • Hexagonal pattern
  • Honeycomb
  • Immersed boundary method

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

Cite this

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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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