TY - JOUR
T1 - Numerical simulation of the zebra pattern formation on a three-dimensional model
AU - Jeong, Darae
AU - Li, Yibao
AU - Choi, Yongho
AU - Yoo, Minhyun
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.
KW - Closest point method
KW - Lengyel–Epstein model
KW - Narrow band domain
KW - Turing pattern
KW - Zebra pattern formation
UR - http://www.scopus.com/inward/record.url?scp=85013128298&partnerID=8YFLogxK
U2 - 10.1016/j.physa.2017.02.014
DO - 10.1016/j.physa.2017.02.014
M3 - Article
AN - SCOPUS:85013128298
SN - 0378-4371
VL - 475
SP - 106
EP - 116
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
ER -