分数阶布朗马达在闪烁棘齿势中的合作输运现象

Transport properties of fractional coupled Brownian motors in flash ratchet potential

引入分数阶微积分理论,建立耦合分数阶布朗马达在闪烁棘齿势中的合作输运模型,利用分数阶差分法求得模型数值解并分析了模型参数对合作定向输运性质的影响.发现在具有记忆性的分数阶棘齿系统中,系统阶数与粒子间耦合强度不仅可影响粒子链输运速度,还可使粒子链出现与整数阶方向相反的定向流;在阶数固定下,定向输运速度将随参数(噪声强度、耦合强度、棘齿势峰值高度)变化出现广义随机共振现象.

Based on the fractional calculus theory, the transport model of fractional coupled Brownian motors in flashing ratchet potential is established. Using the fractional difference, the numerical solution of the model is obtained, and the directional transport properties at various parameters are investigated. Numerical results show that in fractional ratchet system, the fractional order and spring constant not only affect the transport velocity of the particles, but also reverse the current direction. Moreover, when the fractional order is fixed, the generalized stochastic resonance phenomena are observed in the mean transport velocity as the noise density, spring constant or the depth of the ratchet potential varies.