Dissertation/Thesis Abstract

Feedback Controlled Collective Transport in One-Dimensional Periodic Potentials
by Gernert, Robert, Ph.D., Technische Universitaet Berlin (Germany), 2015, 150; 10703770
Abstract (Summary)

In this thesis, we investigate the transport of colloids in one spatial dimension by numerical computations and theoretical considerations. We consider the Brownian motion of the colloids in the presence of spatially periodic strong external fields, which we model with a tilted washboard potential. We are interested in the time-dependent evolution of non-equilibrium processes in this potential. We focus on the time and length scales which span from the motion inside one valley of the periodic potential to the motion among the valleys. The theoretical description of the continuous stochastic thermal fluctuations in the particles’ positions is achieved via the overdamped Langevin equation and its Fokker-Planck equation, the Smoluchowski equation (SE). Further, we employ the Dynamical density functional theory (DDFT) to predict the motion of interacting colloids on large time and length scales. In the first two content chapters we consider the transport of a single Brownian particle in a tilted washboard potential. We are interested in the short time diffusion, in particular in the mean squared displacement (MSD). We propose a simple model which yields analytic expressions for the time dependence of diffusional properties such as the MSD. Then we turn to the question: How long does a stochastic process take? To answer this question for our asymmetric continuous system, we propose a generalisation for the waiting time distribution (WTD), which was previously available only for discrete systems. Our definition of the WTD and our recipe to calculate the WTD via a SE facilitates a detailed characterisation of nearly discrete stochastic processes. In the middle of this thesis we present a time delayed feedback control protocol for the motion of a single Brownian particle in an asymmetric periodic potential. Feedback control means that the systems is steered towards a certain behaviour by using information from the system itself. We show that an ensemble averaged modelling of feedback control via a Fokker-Planck equation makes sense for a dilute colloidal suspension. We apply the modelling to a ratchet system where the time delay in the feedback protocol creates the ratchet effect. By varying the parameters of the control protocol we show that the generated current can be higher than that of a corresponding standard ratchet system. Further, we address stochastic thermodynamics and examine the entropy production entwined with this non-equilibrium process. In the last two chapters, we consider the effect of particle interactions on diffusion and transport in a tilted washboard potential. We consider ultra-soft particle interaction and attractive hard spheres. We find that ultra-soft repulsive interaction between particles results in a much stronger diffusion compared to the single particle case. We calculate the MSD and the diffusion coefficient and show the influence of particle interaction to the giant diffusion effect. Finally, we propose a feedback control protocol for the collective transport of several particles. We impose a trapping potential onto the colloids which mimics moving optical tweezers. The particles agglomerate to clusters. We show that the combined influence of the feedback controlled trap and the repulsive particle interactions leads to an enhancement of the mobility of the particle cluster of several orders of magnitude.

Indexing (document details)
Advisor: Klapp, Sabine H.L.
School: Technische Universitaet Berlin (Germany)
School Location: Germany
Source: DAI-C 81/1(E), Dissertation Abstracts International
Subjects: Theoretical physics, Computational physics
Keywords: Colloid transport
Publication Number: 10703770
ISBN: 9781392546567
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