# Exact universal excitation waveform for optimal enhancement of directed ratchet transport

## TL;DR

This paper derives an exact universal excitation waveform that maximizes directed ratchet transport, confirmed through numerical experiments, highlighting the importance of impulse and frequency-dependent amplitude for optimal transport enhancement.

## Contribution

It introduces an exact universal excitation waveform for optimal ratchet transport, linking waveform properties to transport enhancement and confirming the theory with numerical simulations.

## Key findings

- Optimal transport occurs when the impulse transmitted by excitations is maximized.
- The universality holds regardless of the waveform shape of the periodic excitations.
- A frequency-dependent optimal amplitude ratio exists for harmonic excitations.

## Abstract

The existence and properties of an exact universal excitation waveform for optimal enhancement of directed ratchet transport are deduced from the criticality scenario giving rise to ratchet universality, and confirmed by numerical experiments in the context of a driven overdamped Brownian particle subjected to a vibrating 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. Additionally, the existence of a frequency-dependent optimal value of the relative amplitude of the two excitations involved is illustrated in the simple case of harmonic excitations.