点涡的内在动力学阴影与有限时间奇点
Intrinsic dynamical shadowing of point vortices and finite time singularities
- Aix Marseille Univ, Univ Toulon, CNRS, CPT, Marseille, France（艾克斯-马赛大学，土伦大学）
- Univ Toulon, Aix Marseille Univ, CNRS, CPT, Marseille, France（土伦大学，艾克斯-马赛大学）
- Instituto de Física, Universidad Autónoma de San Luis Potosí, México（圣路易斯波托西自治大学物理研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究揭示点涡分裂后轨迹的阴影现象，源于尺度不变性，可推广至更多涡旋及高阶奇点，引发对涡旋测量本质的思考。
AI中文摘要：
研究了通过逆坍缩路径分裂后点涡的轨迹。在此设定中，出现了一个意想不到的奇特现象，对应于涡旋分裂的阴影效应。当系统在分裂后从三个涡旋演化为五个涡旋时，这种现象至少在一段有限时间内发生。分析研究表明，这一观测到的数值现象与尺度不变性条件相关，而该条件是有限时间奇点出现的必要条件。进一步的模拟与我们的分析结果一致，并表明阴影效应可以发生在超过五个涡旋的情况下，也可与更高阶的奇点一同出现。这一现象引发了对涡旋实际上在测量什么的疑问，并引发了关于此阴影特性是否能推广到其他具有有限时间奇点的哈密顿系统的猜想。
英文摘要：
The trajectories of point vortices after a division using reverse collapse route are studied. In this setting, an unexpected peculiar phenomenon appears, corresponding to the shadowing of the vortex breakup. This occurs at least for a finite time, when the system evolves from three to five vortices after a breakup. An analytical study reveals that this observed numerical phenomenon is related to the condition of scale invariance, a condition necessary for the finite time singularity. Further simulations agree with our analytical findings and indicate that shadowing can occur with more than five vortices, and as well with higher order singularities. This phenomenon leads to question what a vortex is actually measuring, triggering speculations if this shadowing property could be generalized to other Hamiltonian systems with finite-time singularities.
