标题： 模拟受固定樟脑源扰动的樟脑转子的时间演化模型 显示英文标题

标题： Modeling the time evolution of a camphor rotor perturbed by a stationary camphor source

摘要： 从樟脑分子在水面上的耗散产生的自推进运动已经吸引了超过200年的科学关注。现象的一个普遍接受的描述包括物体运动与马拉高尼流体动力学以及樟脑表面浓度时间演化的耦合方程。这类方程的解是一个数值上复杂的问题。在最近的出版物中，一种基于哈密顿量的方法被应用于模拟樟脑转子的时间演化，该方法包括表示马拉高尼相互作用的势能项。与标准描述相比，这种模型代表了显著的数值简化。在这里，我们通过将哈密顿量方法应用于一个被固定在水面上的樟脑盘扰动的单个樟脑转子来评论其适用性。我们证明在这种情况下，该方法导致的结果在定性上与实验结果不同。因此，我们怀疑它适用于描述相互作用的樟脑转子的时间演化。我们还表明，如果与包含流体动力摩擦的运动方程一起使用，将马拉高尼力近似为势能可以得到更现实的结果。然而，通过考虑樟脑表面浓度的时间演化的一个附加方程，可以更好地与实验结果一致。 显示英文摘要

摘要： A self-propelled motion resulting from the dissipation of camphor molecules on the water surface has been attracting scientific attention for more than 200 years. A generally accepted description of the phenomenon includes equations for the object motion coupled with the hydrodynamics of Marangoni flows and the time evolution of camphor surface concentration. The solution of such equations is a numerically complex problem. In recent publications, an alternative approach based on Hamiltonian including the potential term representing Marangoni interactions has been applied to simulate the time evolution of camphor rotors. Such a model represents a significant numerical simplification if compared to the standard description. Here, we comment on the applicability of Hamiltonian approach by applying it to a single camphor rotor perturbed by a camphor disk fixed on the water surface. We demonstrate that in such a case, the approach leads to the results qualitatively different from the experimental ones. Therefore, we doubt in its applicability to describe the time evolution of interacting camphor rotors. We also show that the approximation of the Marangoni forces by a potential gives more realistic results if used together with the equation of motion that includes the hydrodynamic friction. Still, a better agreement with experiments can be obtained by considering an additional equation for the time evolution of camphor surface concentration.