中文摘要：

将基于离散变分原理的耗散动力学模拟方法应用到三维囊泡体系,通过优化囊泡的弯曲能求解其平衡态形状.该方法的优点之一是不需要预先假定对称性.针对特定约化自发曲率的囊泡体系,该方法模拟获得了一系列轴对称形状,模拟结果与文献中预先假定轴对称条件的计算方法所报道的结果一致,这验证了该模拟方法的可靠性及精确性.此外,使用该方法研究了两个差别巨大的平衡态形状之间的转变动力学,在转变过程中观察到了多个非轴对称的中间形状.研究结果表明该方法不仅可以模拟囊泡的非轴对称结构,而且具备模拟囊泡在剧烈形变下演化过程的能力.为研究更复杂的囊泡体系,特别是生物膜的形变提供了一个重要的理论模拟方法.

英文摘要：

In this article, the dissipative dynamical evolution method based on the discrete variational principle is applied to a three- dimensional（3D） vesicle system. The stationary shapes of vesicles are obtained through the minimization of membrane bending energy without any symmetric assumption, which is an outstanding merit of our method. Aiming at a 3D vesicle system with certain parameter settings, a series of axisymmetric shapes are achieved by our method. The simulation results are in good agreement with those obtained with axisymmetric assumption, which indicates that our method can describe the deformation of 3D vesicle with ex- tremely high precision. In addition, a shape transition between two stable states with great difference is studied, which further implies the capability of our proposed method in simulating large deformations regarding the 3D membrane. We believe that we have provided a very powerful simulation method for the future studies of bio-membrane deformations.