分数阶Brown马达及其定向输运现象

Fractional Brownian motor and its directed transport

选取幂函数作为广义Langevin方程的阻尼核函数,采用闪烁棘轮势,建立了过阻尼分数阶Brown马达模型.结合分数阶微积分的记忆性,分析了粒子在过阻尼分数阶Brown马达作用下的运动特性.研究发现,较之整数阶情形,过阻尼分数阶Brown马达也会产生定向输运现象,并且在某些阶数下会产生整数阶情形所不具有的反向定向流.此外,还讨论了阶数和噪声强度对系统输运速度的影响,发现当阶数固定时,其平均输运速度会随噪声变化出现随机共振;当噪声强度固定时,其输运速度会随阶数变化而振荡,即出现多峰的广义随机共振现象.

Adopting power function as a damping kernel function of generalized Langevin equation, flash ratchet potential as a potential field, the model of fractional Brownian motor is derived in the case of overdamped condition. With the memory effect of fractional derivatives, the motion characteristics of the particle in overdamped fractional Brownian motor are discussed. Inverse transport which is not seen in conventional Brownian motor, is found in an overdamped fractional Brownian motor. The influences of fractional order and noise density on transport speed are discussed separately. For a fixed fractional order, stochastic resonance appears in transport speed as noise density varies. For a fixed noise density, transport speed will oscillate as the fractional order varies, that is, multipeak generalized stochastic resonance takes place.