Feedback-induced oscillations in one-dimensional colloidal transport

Abstract

We investigate a driven, one-dimensional system of colloidal particles in a periodically currogated narrow channel subject to a time-delayed feedback control. Our goal is to identify conditions under which the control induces oscillatory, time-periodic states. The investigations are based on the Fokker-Planck equation involving the density distribution of the system. First, by using the numerical continuation technique, we determine the linear stability of a stationary density. Second, the nonlinear regimes are analyzed by studying numerically the temporal evolution of the first moment of the density distribution. In this way we construct a bifurcation diagram revealing the nature of the instability. Apart from the case of a system with periodic boundary conditions, we also consider a microchannel of finite length. Finally, we study the influence of (repulsive) particle interactions based on Dynamical Density Functional Theory (DDFT).

12 pages, 10 figures

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• Uncertainty relations for time-delayed Langevin systems
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• Force-linearization closure for non-Markovian Langevin systems with time delay
• Enhancement of mobility in an interacting colloidal system under feedback control
• On the waiting time distribution for continuous stochastic systems
• Dynamic mode locking in a driven colloidal system: experiments and theory
• Novel structure formation of a phase separating colloidal fluid in a ratchet potential