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A discrete, space variation model for studying the kinetics of shape deformation of vesicles coupled with phase separation

机译：离散的空间变化模型，用于研究囊泡形状变形与相分离的动力学

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摘要

The evolution dynamics of phase separation, coupled with shape deformation of vesicles is described by using dissipative dynamic equations, specifically the time-dependent Ginzburg-Landau (TDGL) equations. In order to improve the numerical stability and thus to efficiently deal with a large deformation of vesicles, a new algorithm, namely the discrete space variation model (DSVM) has been developed for the first time. The algorithm is based on the variation of the discretized free-energy functional, which is constructed in discrete membrane space, in contrast to the commonly used continuous free-energy functional. For the sake of numerical tractability, only the cylindrical vesicles (2D), with two components, are taken into consideration to illustrate the efficiency and validity of new algorithm. The simulation results, based on the DSVM algorithm have been compared with those from both linear analysis and strong segregation theory using the continuous space free-energy functional. It is found that the DSVM algorithm can correctly describe the coupling between the lateral phase-separation on the vesicle membrane and the vesicle shape deformation, both for early and late stages.
机译：通过使用耗散动力学方程，特别是时间相关的金兹堡-朗道（TDGL）方程，描述了相分离的演化动力学以及囊的形状变形。为了提高数值稳定性，从而有效地处理大的囊泡变形，首次开发了一种新的算法，即离散空间变异模型（DSVM）。该算法基于离散的自由能泛函的变化，与通常使用的连续自由能泛函相比，离散函数在离散的膜空间中构建。为了数值上的可处理性，仅考虑具有两个成分的圆柱囊泡（2D）来说明新算法的效率和有效性。将基于DSVM算法的仿真结果与使用连续空间自由能函数的线性分析和强分离理论的仿真结果进行了比较。发现DSVM算法可以正确地描述早期和晚期囊泡膜上的横向相分离与囊泡形状变形之间的耦合。

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