论文标题
飞行员波动力学：使用动态模式分解来表征分叉，混乱的路线和新兴统计
Pilot-Wave Dynamics: Using Dynamic Mode Decomposition to characterize Bifurcations, Routes to Chaos and Emergent Statistics
论文作者
论文摘要
我们开发了针对飞行波水动力学系统的数据驱动表征，其中沿振动浴的表面弹跳的液滴自我弹跳。我们考虑在限制的一维几何形状中进行下降运动，并应用{\ em动态模式分解}（DMD），以表征波场的演变，因为浴缸的振动加速度逐渐增加。 DMD提供了一个回归框架，用于自适应地学习比时空数据快照的最佳拟合线性动力学模型。波场的DMD表征对蹦蹦跳跳的垃圾问题产生了新的视角，该问题通过量子力学的数学机制构建了有价值的新链接。此外，它提供了对试验波物理的分叉结构的低级别表征。具体而言，分析表明，随着振动加速度的增加，飞行员波场经历了一系列的HOPF分叉，最终导致了混乱的波场。平均飞行器波场和液滴统计数据之间建立的关系使我们能够表征出紧急统计的演变，而从飞行员波场的演变中增加了振动强迫。因此，我们开发了一个与量子力学相同的基本结构的数值框架，特别是预测粒子统计的波浪理论。
We develop a data-driven characterization of the pilot-wave hydrodynamic system in which a bouncing droplet self-propels along the surface of a vibrating bath. We consider drop motion in a confined one-dimensional geometry, and apply the {\em Dynamic mode decomposition} (DMD) in order to characterize the evolution of the wave field as the bath's vibrational acceleration is increased progressively. DMD provides a regression framework for adaptively learning a best-fit linear dynamics model over snapshots of spatio-temporal data. The DMD characterization of the wave field yields a fresh perspective on the bouncing-droplet problem that forges valuable new links with the mathematical machinery of quantum mechanics. Moreover, it provides a low-rank characterization of the bifurcation structure of the pilot wave physics. Specifically, the analysis shows that as the vibrational acceleration is increased, the pilot-wave field undergoes a series of Hopf bifurcations that ultimately lead to a chaotic wave field. The established relation between the mean pilot-wave field and the droplet statistics allows us to characterize the evolution of the emergent statistics with increased vibrational forcing from the evolution of the pilot-wave field. We thus develop a numerical framework with the same basic structure as quantum mechanics, specifically a wave theory that predicts particle statistics.
