Ratchet transport of overdamped particles in superimposed driven lattices
Huang Shu-Na, Zhu Wei-Jing, Huang Xiao-Qun, Ai Bao-Quan, Li Feng-Guo
       

Average velocity V as a function of oscillation frequency ω for different ϕ. (a) Without white noise. (b) With white noise. The other parameters are D0 = 0.1 and d = π.