The directed transport of inertial Lévy flights resulting from the superimposed roughness in a corrugated potential is investigated in this paper. The influence of the roughness on the transport is studied by calculating the mean velocity (MV) and the mean first escape time (MFET), with respect to the Lévy index [Formula: see text] and the asymmetry parameter [Formula: see text] which determines the asymmetry of the potential. The results indicate that the particles’ directed transport caused by the asymmetry of the potential will be counteracted by the roughness, which behaves as the absolute value of the MV decreases with roughness [Formula: see text] increasing, and the MFET increases with [Formula: see text] increasing, correspondingly. Though smaller Lévy index [Formula: see text] can produce more large jumps, which yield the enhancement of the directed transport, since the roughness superimposed on the corrugated potential supplies the hinder effect, the directed transport is also weakened after the appearance of the roughness.

中文翻译：

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具有粗糙波纹势的惯性 Lévy 飞行的弱定向传输

本文研究了由波纹势中的叠加粗糙度引起的惯性 Lévy 飞行的定向传输。通过计算平均速度 (MV) 和平均第一次逃逸时间 (MFET) 来研究粗糙度对传输的影响，其中涉及 Lévy 指数 [公式：参见文本] 和不对称参数 [公式：参见文本]这决定了电位的不对称性。结果表明，由电位不对称引起的粒子定向输运会被粗糙度抵消，表现为MV的绝对值随着粗糙度[公式：见正文]的增加而减小，MFET随着[公式]的增加而增加: 见正文] 相应地增加。虽然较小的 Lévy 指数 [公式：见正文] 可以产生更大的跳跃，