Mathematical modeling and computer simulation of the three-dimensional pattern formation of honeycombs

Darae Jeong, Yibao Li, Sangkwon Kim, Yongho Choi, Chaeyoung Lee, Junseok Kim

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article number20364
JournalScientific reports
Volume9
Issue number1
DOIs
Publication statusPublished - 2019 Dec 1

ASJC Scopus subject areas

  • General

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