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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.
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关键词:
- 分数阶Brown马达 /
- 定向输运 /
- 反向定向流 /
- 随机共振
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.[1] Astumian R D 1997 Science 276 917
[2] Bao J D 2009 Stochastic Simulation Method of Classic and Quantum Dissipative Sysmtem (Beijing: Science Press) p160 (in Chinese) [包景东 2009 经典和量子耗散系统的随机模拟方法 (北京: 科学出版社) 第160页]
[3] Zheng Z G 2004 Spantiotemporal Dynamics and Collective Behaviors in Coupled Nonlinear Systems (Beijing: Higher Education Press) p286 (in Chinese) [郑志刚 2004 耦合非线性系统的时空动力学与合作行为 (北京: 高等教育出版社) 第286页]
[4] Guo H Y, Li W, Ji Q, Zhan Y, Zhao T J 204 Acta Phys. Sin. 53 3684 (in Chinese) [郭鸿涌, 李微, 纪青, 展永, 赵同军 2004 53 3684]
[5] Qian M, Wang Y, Zhang X J 2003 Chin. Phys. Lett. 20 810
[6] Cheng H T, He J Z, Xiao Y L 2012 Acta Phys. Sin. 61 010502 (in Chinese) [程海涛, 何济洲, 肖宇玲 2012 61 010502]
[7] Gitterman M 2005 Phys. Stat. Mech. Appl. 352 309
[8] de Andrade M F 2005 Phys. Lett. A 347 160
[9] Liu F, Anh V, Turner I, Zhuang P 2003 J. Appl. Math. Comput. 13 233
[10] Benson D A, Wheatcraft S W, Meerschaert M M 2000 Water Resour. Res. 36 1403
[11] Podlubny I 1998 Fractional Differential Equation (San Diego: Academic Press) 229
[12] Yang J H, Liu X B 2010 Chin. Phys. B 19 050504
[13] Reimann P 2002 Phys. Rep. 361 57
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[1] Astumian R D 1997 Science 276 917
[2] Bao J D 2009 Stochastic Simulation Method of Classic and Quantum Dissipative Sysmtem (Beijing: Science Press) p160 (in Chinese) [包景东 2009 经典和量子耗散系统的随机模拟方法 (北京: 科学出版社) 第160页]
[3] Zheng Z G 2004 Spantiotemporal Dynamics and Collective Behaviors in Coupled Nonlinear Systems (Beijing: Higher Education Press) p286 (in Chinese) [郑志刚 2004 耦合非线性系统的时空动力学与合作行为 (北京: 高等教育出版社) 第286页]
[4] Guo H Y, Li W, Ji Q, Zhan Y, Zhao T J 204 Acta Phys. Sin. 53 3684 (in Chinese) [郭鸿涌, 李微, 纪青, 展永, 赵同军 2004 53 3684]
[5] Qian M, Wang Y, Zhang X J 2003 Chin. Phys. Lett. 20 810
[6] Cheng H T, He J Z, Xiao Y L 2012 Acta Phys. Sin. 61 010502 (in Chinese) [程海涛, 何济洲, 肖宇玲 2012 61 010502]
[7] Gitterman M 2005 Phys. Stat. Mech. Appl. 352 309
[8] de Andrade M F 2005 Phys. Lett. A 347 160
[9] Liu F, Anh V, Turner I, Zhuang P 2003 J. Appl. Math. Comput. 13 233
[10] Benson D A, Wheatcraft S W, Meerschaert M M 2000 Water Resour. Res. 36 1403
[11] Podlubny I 1998 Fractional Differential Equation (San Diego: Academic Press) 229
[12] Yang J H, Liu X B 2010 Chin. Phys. B 19 050504
[13] Reimann P 2002 Phys. Rep. 361 57
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