Numerical simulation of the zebra pattern formation on a three-dimensional model

Darae Jeong, Yibao Li, Yongho Choi, Minhyun Yoo, Dooyoung Kang, Junyoung Park, Jaewon Choi, Junseok Kim

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In this paper, we numerically investigate the zebra skin pattern formation on the surface of a zebra model in three-dimensional space. To model the pattern formation, we use the Lengyel–Epstein model which is a two component activator and inhibitor system. The concentration profiles of the Lengyel–Epstein model are obtained by solving the corresponding reaction–diffusion equation numerically using a finite difference method. We represent the zebra surface implicitly as the zero level set of a signed distance function and then solve the resulting system on a discrete narrow band domain containing the zebra skin. The values at boundary are dealt with an interpolation using the closet point method. We present the numerical method in detail and investigate the effect of the model parameters on the pattern formation on the surface of the zebra model.

Original languageEnglish
Pages (from-to)106-116
Number of pages11
JournalPhysica A: Statistical Mechanics and its Applications
Volume475
DOIs
Publication statusPublished - 2017 Jun 1

Fingerprint

three dimensional models
Pattern Formation
Numerical Simulation
Three-dimensional
simulation
Skin
Model
Zero set
Distance Function
Signed
Reaction-diffusion Equations
Level Set
inhibitors
Inhibitor
Difference Method
interpolation
narrowband
Finite Difference
Interpolate
Numerical Methods

Keywords

  • Closest point method
  • Lengyel–Epstein model
  • Narrow band domain
  • Turing pattern
  • Zebra pattern formation

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics

Cite this

Numerical simulation of the zebra pattern formation on a three-dimensional model. / Jeong, Darae; Li, Yibao; Choi, Yongho; Yoo, Minhyun; Kang, Dooyoung; Park, Junyoung; Choi, Jaewon; Kim, Junseok.

In: Physica A: Statistical Mechanics and its Applications, Vol. 475, 01.06.2017, p. 106-116.

Research output: Contribution to journalArticle

Jeong, Darae ; Li, Yibao ; Choi, Yongho ; Yoo, Minhyun ; Kang, Dooyoung ; Park, Junyoung ; Choi, Jaewon ; Kim, Junseok. / Numerical simulation of the zebra pattern formation on a three-dimensional model. In: Physica A: Statistical Mechanics and its Applications. 2017 ; Vol. 475. pp. 106-116.
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