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arXiv · 1209.0904

Feedback-induced oscillations in one-dimensional colloidal transport

Ken Lichtner·Andrey Pototsky·Sabine H. L. Klapp
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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).

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Ken Lichtner, Andrey Pototsky, Sabine H. L. Klapp. 2012-09-05. Feedback-induced oscillations in one-dimensional colloidal transport. https://doi.org/10.1103/physreve.86.051405

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