Feedback-induced oscillations in one-dimensional colloidal transport

TL;DR

This paper explores how time-delayed feedback control can induce oscillations in a one-dimensional colloidal system, analyzing stability and nonlinear dynamics through numerical methods and DDFT.

Contribution

It introduces a combined approach using Fokker-Planck, numerical continuation, and DDFT to study feedback-induced oscillations in colloidal transport.

Findings

Identification of conditions for oscillatory states

Bifurcation diagram of system stability

Impact of particle interactions on dynamics

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).