论文标题
时间棘轮的多定时分析
A multiple-timing analysis of temporal ratcheting
论文作者
论文摘要
我们开发了两种计时的扰动分析，以研究粒子在流体罐中移动的粒子的示例性系统中的存在，以响应储罐的外部振动。我们考虑具有角频率$ω$和$αΩ$的两种模式振动，其中$α$是一个合理的数字。 It has been established, in other physical systems, that if $α$ is a ratio of odd and even integers (e.g., $\tfrac{2}{1}$, $\tfrac{3}{2}$, $\tfrac{4}{3}$), the system yields a net response: here, a nonzero time-average particle velocity.我们的一阶和三阶两态扰动方案分别预测了$α= 2 $和$α= \ tfrac {3} {2} {2} $，$ \ tfrac {4} {3} $。更重要的是，我们发现了这些$α$值的诱导净速度的幅度和方向的封闭式公式。
We develop a two-timing perturbation analysis to investigate the existence of temporal ratchets in an exemplary system of a particle moving in a tank of fluid in response to an external vibration of the tank. We consider two-mode vibrations with angular frequencies $ω$ and $αω$, where $α$ is a rational number. It has been established, in other physical systems, that if $α$ is a ratio of odd and even integers (e.g., $\tfrac{2}{1}$, $\tfrac{3}{2}$, $\tfrac{4}{3}$), the system yields a net response: here, a nonzero time-average particle velocity. Our first-order and third-order two-timing perturbation schemes predict the existence of temporal ratchets for, respectively, $α=2$ and $α=\tfrac{3}{2}$, $\tfrac{4}{3}$. More importantly, we find closed form formula for the magnitude and direction of the induced net velocities for these $α$ values.
