Tuning the total displacement of membranes
Tuning the total displacement of membranes
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DOI：
10.1016/j.cnsns.2021.105706
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
C. Kao;S. Mohammadi
中科院分区：
文献类型：
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作者：
C. Kao;S. Mohammadi
在本文中，我们研究了一个通过改变膜的脆弱性来调整膜的鲁棒性的设计问题。考虑一个能量泛函对应于具有Robin边界条件的Poisson方程的解.其目的是在重排类中找到函数，使得它们的能量是给定的特定值。我们证明了这个设计问题的解是存在的，并给出了一种求解方法，同时我们还得到了脆弱性结构的一些拓扑和几何性质。此外，当区域是一个N球时，还得到了一些显式解。对于一般区域，我们发展了一种基于重排的数值算法来求解。该算法在两个不同的重排类的最小化和最大化过程。我们的算法有效地适用于各种领域，得到的数值结果与我们的分析结果相吻合。
In this paper we study a design problem to tune the robustness of a membrane by changing its vulnerability. Consider an energy functional corresponding to solutions of Poisson’s equation with Robin boundary conditions. The aim is to find functions in a rearrangement class such that their energies would be a given specific value. We prove that this design problem has a solution and also we propose a way to find it. Furthermore, we derive some topological and geometrical properties of the configuration of the vulnerability. In addition, some explicit solutions are found analytically when the domain is an N-ball. For general domain we develop a numerical algorithm based on rearrangements to find the solution. The algorithm evolves both minimization and maximization processes over two different rearrangement classes. Our algorithm works efficiently for various domains and the numerical results obtained coincide with our analytical findings.