TY - JOUR
T1 - Pattern formation in reaction–diffusion systems on evolving surfaces
AU - Kim, Hyundong
AU - Yun, Ana
AU - Yoon, Sungha
AU - Lee, Chaeyoung
AU - Park, Jintae
AU - Kim, Junseok
N1 - Funding Information:
The first author (Hyundong Kim) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2020R1A6A3A13077105). C. Lee was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2019R1A6A3A13094308). The corresponding author (Junseok Kim) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2016R1D1A1B03933243). The authors appreciate the reviewers for their constructive comments, which have improved the quality of this paper.
Funding Information:
The first author (Hyundong Kim) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( NRF-2020R1A6A3A13077105 ). C. Lee was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( 2019R1A6A3A13094308 ). The corresponding author (Junseok Kim) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( NRF-2016R1D1A1B03933243 ). The authors appreciate the reviewers for their constructive comments, which have improved the quality of this paper.
Publisher Copyright:
© 2020 Elsevier Ltd
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2020/11/1
Y1 - 2020/11/1
N2 - In this paper, we propose an explicit time-stepping scheme for the pattern formation in reaction–diffusion systems on evolving surfaces. The proposed numerical method is based on a simple discretization scheme of Laplace–Beltrami operator over triangulated surface. On the static and evolving domains, we perform various numerical experiments for effect of domain growth and pattern formations. The computational results demonstrate that our proposed method can simulate pattern formation in reaction–diffusion systems on evolving surfaces. The actual zebra skin pattern and computational results are compared. In the computational results, we can observe different pattern formations on the evolving surface with specific rotation speed.
AB - In this paper, we propose an explicit time-stepping scheme for the pattern formation in reaction–diffusion systems on evolving surfaces. The proposed numerical method is based on a simple discretization scheme of Laplace–Beltrami operator over triangulated surface. On the static and evolving domains, we perform various numerical experiments for effect of domain growth and pattern formations. The computational results demonstrate that our proposed method can simulate pattern formation in reaction–diffusion systems on evolving surfaces. The actual zebra skin pattern and computational results are compared. In the computational results, we can observe different pattern formations on the evolving surface with specific rotation speed.
KW - Evolving surface
KW - Laplace–Beltrami operator
KW - Pattern formation
KW - Reaction–diffusion system
KW - Triangle surface mesh
UR - http://www.scopus.com/inward/record.url?scp=85090918815&partnerID=8YFLogxK
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U2 - 10.1016/j.camwa.2020.08.026
DO - 10.1016/j.camwa.2020.08.026
M3 - Article
AN - SCOPUS:85090918815
VL - 80
SP - 2019
EP - 2028
JO - Computers and Mathematics with Applications
JF - Computers and Mathematics with Applications
SN - 0898-1221
IS - 9
ER -