Biscari Paolo, Napoli Gaetano
Department of Mathematics, Politecnico di Milano, , Piazza Leonardo da Vinci 32, 20133 Milan, Italy.
Philos Trans A Math Phys Eng Sci. 2009 Sep 13;367(1902):3363-78. doi: 10.1098/rsta.2009.0118.
We study the equilibrium shapes of a lipid membrane, attached to a fixed circular substrate. We show how the weakening of the boundary conditions is able to break the axial symmetry of the optimal equilibrium configuration. We derive the critical threshold of the symmetry-breaking transition, and obtain the analytical expression of the free-energy minimizers in the quasi-planar approximation. Metastable states turn out to contain contributions only from the axisymmetric mode, and at most one single non-trivial Fourier mode.
我们研究了附着在固定圆形基底上的脂质膜的平衡形状。我们展示了边界条件的弱化如何能够打破最优平衡构型的轴对称性。我们推导出对称破缺转变的临界阈值，并在准平面近似下得到自由能极小值的解析表达式。结果表明，亚稳态仅包含轴对称模式的贡献，并且最多包含一个非平凡的傅里叶模式。
