Lukasz Machura
Performance of Brownian Motors
Supervisor: Prof. Dr. Peter Hänggi [Theoretical physics I]
Date of oral examination: 03/15/2006
67 pages, english , Opus On-line
The transport properties of Brownian motors have attracted many attention in the last years. The vast majority of works focused on this topic is concentrated on the behavior of the overdamped regime and the control of the emerging directed transport as a function of control parameters such as temperature, external load, or some other control variable. In this thesis we will study transport of an inertial Brownian particle in a periodic ratchet-type potential additionally subjected to an external, time periodic force, i.e. rocked ratchet. We focus here in more detail on the fluctuating behavior of the Brownian motor position and current. The average drift motion together with its fluctuation statistics are salient features when characterizing the performance of a Brownian motor. The goal of this work is to constitute the most significant characteristics relevant for optimization of the Brownian motors modus operandi. We identify the operating conditions that both maximize the motor current and minimize its dispersion. Extensive numerical simulation of an inertial rocked ratchet displays that two quantifiers, namely the energetic efficiency and the Peclet number (or equivalently the Fano factor), suffice to determine the regimes of optimal transport. We demonstrate also that the velocity-load characteristics is distinctly non-monotonic, possessing regimes with a negative differential mobility or even absolute negative mobility.