Exploring Mechanisms for Pattern Formation through Coupled Bulk-Surface PDEs in Case of Non-linear Reactions
Exploring Mechanisms for Pattern Formation through Coupled Bulk-Surface PDEs in Case of Non-linear Reactions
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DOI：
10.14569/ijacsa.2019.0100372
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发表时间：
2018-12
影响因子：
0.9
通讯作者：
M. Alhazmi
中科院分区：
文献类型：
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作者：
M. Alhazmi
本工作探讨机制图案形成通过耦合体表面偏微分方程的反应扩散型。反应扩散系统提出的体积和表面上的固定体积耦合通过线性罗宾型边界条件。本文分别研究了体相和表面非线性反应的情况。对于所研究的系统是无量纲化和严格的线性稳定性进行分析，以确定图案形成的必要和充分条件。生成适当的参数空间，从中选择模型参数。为了展示图案的形成，开发并实现了耦合体表面有限元方法。数值算法的实现使用一个开源软件包被称为交易。II和显示计算结果的球形和长方体域。此外，线性稳定性分析的理论预测进行了验证和支持的数值模拟。结果表明，在体和表面的非线性反应产生的图案无处不在。
This work explores mechanisms for pattern formation through coupled bulk-surface partial differential equations of reaction-diffusion type. Reaction-diffusion systems posed both in the bulk and on the surface on stationary volumes are coupled through linear Robin-type boundary conditions. The presented work in this paper studies the case of non-linear reactions in the bulk and surface respectively. For the investigated system is non-dimensionalised and rigorous linear stability analysis is carried out to determine the necessary and sufficient conditions for pattern formation. Appropriate parameter spaces are generated from which model parameters are selected. To exhibit pattern formation, a coupled bulk-surface nite element method is developed and implemented. The numerical algorithm is implemented using an open source software package known as a deal.II and show computational results on spherical and cuboid domains. Also, theoretical predictions of the linear stability analysis are verified and supported by numerical simulations. The results show that non-linear reactions in the bulk and surface generate patterns everywhere.