Sedimentation of particles acted upon by a vertical, time-oscillating force

We analyse a spatially restricted one-dimensional diffusion process occurring in a half-space under the influence of a harmonically oscillating and space-homogeneous driving force. The force possesses a dc component which points against the reflecting boundary. Our approach is based on an exact time-asymptotic solution of the underlying non-convolution integral equation. It yields the full time- and space-resolved density profile in the asymptotic non-equilibrium regime. We identify scaling laws for the complex amplitudes which control the nonlinear response. The time-averaged density profile exhibits surprising features. At the boundary, it equals the equilibrium value in the corresponding problem without modulation. However, farther from the boundary, it is first smaller and then bigger in comparison with its static counterpart. It can even develop a well-pronounced partially depleted region in the vicinity of the boundary which is then followed by a region of increased concentration. The time-averaged mean position always exceeds the equilibrium mean position. Their difference, viewed as a function of the temperature, displays a resonance-like maximum.