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

doi:10.1016/j.physa.2017.02.014

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

Department of Mathematics

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

21 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 language	English
Pages (from-to)	106-116
Number of pages	11
Journal	Physica A: Statistical Mechanics and its Applications
Volume	475
DOIs	https://doi.org/10.1016/j.physa.2017.02.014
Publication status	Published - 2017 Jun 1

Bibliographical note

Funding Information:
The author (D. Jeong) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2014R1A6A3A01009812). Y.B. Li is supported by National Natural Science Foundation of China (No. 11601416, No. 11631012). The corresponding author (J.S. Kim) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2014R1A2A2A01003683). The authors greatly appreciate the reviewers for their constructive comments and suggestions, which have improved the quality of this paper.

Publisher Copyright:
© 2017 Elsevier B.V.

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

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10.1016/j.physa.2017.02.014

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title = "Numerical simulation of the zebra pattern formation on a three-dimensional model",

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.",

keywords = "Closest point method, Lengyel–Epstein model, Narrow band domain, Turing pattern, Zebra pattern formation",

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

note = "Funding Information: The author (D. Jeong) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2014R1A6A3A01009812). Y.B. Li is supported by National Natural Science Foundation of China (No. 11601416, No. 11631012). The corresponding author (J.S. Kim) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2014R1A2A2A01003683). The authors greatly appreciate the reviewers for their constructive comments and suggestions, which have improved the quality of this paper. Publisher Copyright: {\textcopyright} 2017 Elsevier B.V.",

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AU - Jeong, Darae

AU - Li, Yibao

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AU - Kang, Dooyoung

AU - Park, Junyoung

AU - Choi, Jaewon

AU - Kim, Junseok

N1 - Funding Information: The author (D. Jeong) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2014R1A6A3A01009812). Y.B. Li is supported by National Natural Science Foundation of China (No. 11601416, No. 11631012). The corresponding author (J.S. Kim) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2014R1A2A2A01003683). The authors greatly appreciate the reviewers for their constructive comments and suggestions, which have improved the quality of this paper. Publisher Copyright: © 2017 Elsevier B.V.

PY - 2017/6/1

Y1 - 2017/6/1

N2 - 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.

AB - 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.

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JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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