Banham Timothy, Li Bo, Zhao Yanxiang
West Virginia Wesleyan College, 59 College Ave, Buckhannon, West Virginia 26201, USA.
Department of Mathematics and Center for Theoretical Biological Physics, University of California, San Diego, 9500 Gilman Drive, MC 0112, La Jolla, California 92093-0112, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Sep;90(3):033308. doi: 10.1103/PhysRevE.90.033308. Epub 2014 Sep 17.
We explore a wide variety of patterns of closed surfaces that minimize the elastic bending energy with fixed surface area and volume. To avoid complicated discretization and numerical instabilities for sharp surfaces, we reformulate the underlying constrained minimization problem by constructing phase-field functionals of bending energy with penalty terms for the constraints and develop stable numerical methods to relax these functionals. We report our extensive computational results with different initial surfaces. These results are discussed in terms of the reduced volume and are compared with the known results obtained using the sharp-interface approach. Finally, we discuss the implications of our numerical findings.
我们探索了各种封闭曲面的模式，这些模式在固定表面积和体积的情况下使弹性弯曲能量最小化。为了避免尖锐曲面的复杂离散化和数值不稳定性，我们通过构建带有约束惩罚项的弯曲能量相场泛函来重新表述潜在的约束最小化问题，并开发稳定的数值方法来松弛这些泛函。我们报告了使用不同初始曲面的广泛计算结果。这些结果根据约化体积进行了讨论，并与使用尖锐界面方法获得的已知结果进行了比较。最后，我们讨论了数值研究结果的意义。
