作为阻尼驱动系统的行走液滴
Walking droplets as a damped-driven system
摘要：
我们考虑液滴在振动液浴上的动力学。这种流体动力学量子模拟系统所示的阻尼驱动系统，包括一个周期加倍的路线，以引起规范的行为混乱。通过将系统近似为增益和损失动态之间的组成图，可以证明潜在的非线性动态是由系统中的能量平衡驱动的。增益-损失迭代映射类似于在这种空间扩展系统中产生的图案形成不稳定性的范式编码。类似于锁模激光器和旋转爆震发动机，基本的分叉持续的一般形式的损失和增益，这两者都承认明确表示在我们的近似。此外，粒子-波相互作用的几何描述完全表征了实验中观察到的不稳定性。
英文摘要：
We consider the dynamics of a droplet on a vibrating fluid bath. This hydrodynamic quantum analog system is shown to elicit the canonical behavior of damped-driven systems, including a period doubling route to chaos. By approximating the system as a compositional map between the gain and loss dynamics, the underlying nonlinear dynamics can be shown to be driven by energy balances in the systems. The gain-loss iterative mapping is similar to a normal form encoding for the pattern forming instabilities generated in such spatially-extended system. Similar to mode-locked lasers and rotating detonation engines, the underlying bifurcations persist for general forms of the loss and gain, both of which admit explicit representations in our approximation. Moreover, the resulting geometrical description of the particle-wave interaction completely characterizes the instabilities observed in experiments.
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