In this study, we demonstrate a self-excited oscillation induced in cholesteric liquid crystalline droplets under a temperature gradient. At equilibrium, a winding Maltese cross pattern with a point defect was observed via polarised microscopy in the droplets dispersed in an isotropic solvent. When the temperature gradient was applied, the pattern was deformed owing to the Marangoni convection induced by the gradient. Here, when both the droplet size and temperature gradient were sufficiently large, the periodic movement of the defect together with the pattern deformation was observed, which demonstrated the self-excited oscillation of the director field. To describe this phenomenon, we theoretically analysed the flow and director fields by using Onsager's variational principle. This principle enabled the simplified description of the phenomenon; consequently, the time evolution of the director field could be expressed by the phenomenological equations for the two parameters characterising the field. These equations represented the van der Pol equation, which well expressed the mechanism of the self-excited oscillation.

中文翻译：

---

温度梯度下胆甾型液晶液滴中指向矢场的自激振荡

在这项研究中，我们展示了在温度梯度下在胆甾型液晶液滴中诱导的自激振荡。在平衡状态下，通过偏光显微镜在分散在各向同性溶剂中的液滴中观察到具有点缺陷的缠绕马耳他十字图案。当施加温度梯度时，由于梯度引起的 Marangoni 对流，图案变形。在这里，当液滴尺寸和温度梯度都足够大时，观察到缺陷的周期性运动以及图案变形，这证明了导向场的自激振荡。为了描述这种现象，我们利用昂萨格变分原理从理论上分析了流场和导向场。这个原理使得对现象的描述变得简单；因此，指向场的时间演化可以用表征场的两个参数的现象学方程来表达。这些方程代表了van der Pol方程，很好地表达了自激振荡的机理。