We show the existence and properties of an exact universal excitation waveform for optimal enhancement of directed ratchet transport (in the sense of the average velocity) by providing three alternative derivations. Specifically, it is deduced from the criticality scenario giving rise to ratchet universality as well as from an approach based on Fokker–Planck’s equation. Numerical experiments confirmed the existence of such exact universal excitation waveform in the context of a driven overdamped Brownian particle subjected to a periodic potential. While the universality scenario holds regardless of the waveform of the periodic vibratory excitations involved, it is shown that the enhancement of directed ratchet transport is optimal when the impulse transmitted by those excitations (time integral over a half-period) is maximum.

中文翻译：

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用于优化增强定向棘轮传输的精确通用激励波形

我们展示了一个存在和性质精确的通用激励波形通过提供三种替代推导来优化定向棘轮传输（在平均速度的意义上）。具体来说，它是从引起棘轮普遍性的临界情景以及基于 Fokker-Planck 方程的方法推导出来的。数值实验证实了在受到周期性电位的驱动过阻尼布朗粒子的背景下存在这种精确的通用激发波形。虽然普遍性场景与所涉及的周期性振动激励的波形无关，但表明当这些激励传输的脉冲（半周期内的时间积分）最大时，定向棘轮传输的增强是最佳的。