Vesicles are membrane-bound structures commonly known for their roles in cellular transport and the shape of a vesicle is determined by its surrounding membrane (lipid bilayer). When the membrane is composed of different lipids, it is natural for the lipids of similar molecular structure to migrate towards one another (via spinodal decomposition), creating a multi-phase vesicle. In this article, we consider a two-phase vesicle model which is driven by nature's propensity to maintain a minimal state of elastic energy. The model assumes a continuum limit, thereby treating the membrane as a closed three-dimensional surface. The main purpose of this study is to reveal the complexity of the Helfrich two-phase vesicle model with non-zero spontaneous curvature and provide further evidence to support the relevance of spontaneous curvature as a modelling parameter. In this paper, we illustrate the complexity of the Helfrich two-phase model by providing multiple examples of undocumented solutions and energy hysteresis. We also investigate the influence of spontaneous curvature on morphological effects and membrane phenomena such as budding and fusion.

中文翻译：

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自发曲率对两相囊泡的影响

囊泡是膜结合结构，因其在细胞运输中的作用而闻名，囊泡的形状由其周围的膜（脂质双层）决定。当膜由不同的脂质组成时，分子结构相似的脂质自然会向彼此迁移（通过旋节线分解），形成多相囊泡。在本文中，我们考虑了一个两相囊泡模型，该模型是由保持弹性能量最小状态的自然倾向驱动的。该模型假设存在连续极限，从而将膜视为封闭的三维表面。本研究的主要目的是揭示具有非零自发曲率的 Helfrich 两相囊泡模型的复杂性，并提供进一步的证据来支持自发曲率作为建模参数的相关性。在本文中，我们通过提供多个未记录的解决方案和能量滞后的示例来说明 Helfrich 两相模型的复杂性。我们还研究了自发曲率对形态效应和膜现象（例如出芽和融合）的影响。