中文摘要：

本文将细胞内环境假定为分数阶牛顿黏弹性体并建立了单位质量的一维线动分子马达的时间非对称分数阶类郎之万棘齿模型,其中的周期势函数是空间对称的,而用于刻画ATP水解反应引起的环境波动的则是无偏的时间非对称类郎之万噪声.然后本文将模型转化为离散映射以便进行计算机模拟.最后本文以Logistic映射所生成的类郎之万噪声为例简单模拟了模型的定向输运行为.各参数情形下的模拟结果均显示：无需势函数的空间对称破缺,时间非对称的类郎之万噪声已足以引起模型的定向输运.负向的输运行为应归因于Logistic映射的两个不稳定不动点的非对称分布.因此,尽管模拟结果同整数阶模型相比并无本质区别,但分数阶模型对于分子马达的噪声整流机理的刻画却无疑更接近实际情况.

英文摘要：

In this paper, a temporal-asymmetric fractional Langevin-like ratchet is constructed for the operation of a 1D linear molecular motor subjected to both spatial-symmetric periodic potential and temporal-asymmetric unbiased Langevin- like noise. In this ratchet, the Langevin-like noise is used to simulate the intracellular fluctuation induced by ATP hydrolysis. Then, for numerical study of this ratchet, the corresponding discrete mapping is derivated. Finally, as an example, the unidirectional transport of the ratchet driven by unbiased Langevin-like noise, generated by the Logistic mapping, is numerically studied. Negative transport of the ratchet indicates that without the spatial asymmetry of potential, the temporal asymmetry is enough for the presence of unidirectional transport. Since temporal asymmetry has to be regarded as a generic property of nonequilibrium system, this ratchet is expected to be resonably used for the operation of molecular motor.