21 research outputs found
Transport reversal in a delayed feedback ratchet
Feedback flashing ratchets are thermal rectifiers that use information on the
state of the system to operate the switching on and off of a periodic
potential. They can induce directed transport even with symmetric potentials
thanks to the asymmetry of the feedback protocol. We investigate here the
dynamics of a feedback flashing ratchet when the asymmetry of the ratchet
potential and of the feedback protocol favor transport in opposite directions.
The introduction of a time delay in the control strategy allows one to
nontrivially tune the relative relevance of the competing asymmetries leading
to an interesting dynamics. We show that the competition between the
asymmetries leads to a current reversal for large delays. For small ensembles
of particles current reversal appears as the consequence of the emergence of an
open-loop like dynamical regime, while for large ensembles of particles it can
be understood as a consequence of the stabilization of quasiperiodic solutions.
We also comment on the experimental feasibility of these feedback ratchets and
their potential applications.Comment: LaTeX, 7 pages, 6 figure
Information and flux in a feedback controlled Brownian ratchet
We study a feedback control version of the flashing Brownian ratchet, in
which the application of the flashing potential depends on the state of the
particles to be controlled. Taking the view that the ratchet acts as a
Maxwell's demon, we study the relationship that exists between the performance
of the demon as a rectifier of random motion and the amount of information
gathered by the demon through measurements. In the context of a simple
measurement model, we derive analytic expressions for the flux induced by the
feedback ratchet when acting on one particle and a few particles, and compare
these results with those obtained with its open-loop version, which operates
without information. Our main finding is that the flux in the feedback case has
an upper bound proportional to the square-root of the information. Our results
provide a quantitative analysis of the value of information in feedback
ratchets, as well as an effective description of imperfect or noisy feedback
ratchets that are relevant for experimental applications.Comment: LaTeX, 13 pages, 2 figure
Closed-loop control strategy with improved current for a flashing ratchet
We show how to switch on and off the ratchet potential of a collective
Brownian motor, depending only on the position of the particles, in order to
attain a current higher than or at least equal to that induced by any periodic
flashing. Maximization of instant velocity turns out to be the optimal protocol
for one particle but is nevertheless defeated by a periodic switching when a
sufficiently large ensemble of particles is considered. The protocol presented
in this article, although not the optimal one, yields approximately the same
current as the optimal protocol for one particle and as the optimal periodic
switching for an infinite number of them.Comment: 4 pages, 4 figure
Reliability of rectified transport: Coherence and reproducibility of transport by open-loop and feedback-controlled Brownian ratchets
Brownian ratchets are small-scale systems which rectify thermal fluctuations to produce a net current of particles. They have inspired many models of molecular motors that perform transport in the noisy environment of living cells. For the most common ratchet systems, this rectification is achieved by means of the switching of a periodic and spatially asymmetric potential (flashing ratchets) or by means of a rocking force (rocking ratchets). The rectification mechanism can be applied without information on the state of the system (open-loop ratchets) or using information on the state of the system (feedback or closed-loop ratchets). In order to characterize the transport, the most used quantity is the mean velocity of the center of mass of the system. However, another important transport attribute that has not received much attention is its quality. Here we analyze the quality of transport by studying the coherence and reproducibility of the transport induced by several representative open-and closed-loop rectification protocols under the maximum mean velocity conditions. We find that for few-particle systems, the best protocol is the rocked feedback protocol, producing the transport of particles with the highest coherence and reproducibility per distance traveled at the maximum mean velocity, while for larger systems it is overtaken by its open-loop counterpart. Our results also show that protocols with similar maximum mean velocities can have quite different coherences and reproducibilities. This highlights the importance of studying the reliability of rectified transport to develop performant synthetic rectification devices. These contributions to the emerging field of reliable transport in noisy environments are expected also to provide insight into the performance of natural molecular motors
Information in feedback ratchets
Feedback control uses the state information of the system to actuate on it.
The information used implies an effective entropy reduction of the controlled
system, potentially increasing its performance. How to compute this entropy
reduction has been formally shown for a general system, and has been explicitly
computed for spatially discrete systems. Here, we address a relevant example of
how to compute the entropy reduction by information in a spatially continuous
feedback-controlled system. Specifically, we consider a feedback flashing
ratchet, which constitutes a paradigmatic example for the role of information
and feedback in the dynamics and thermodynamics of transport induced by the
rectification of Brownian motion. A Brownian particle moves in a periodic
potential that is switched on and off by a controller, with the latter
performing the switching depending on the system state. We show how the entropy
reduction can be computed from the entropy of a sequence of control actions,
and also discuss the required sampling effort for its accurate computation.
Moreover, the output power developed by the particle against an external force
is investigated, which -- for some values of the system parameters -- is shown
to become larger than the input power due to the switching of the potential:
the apparent efficiency of the ratchet thus becomes higher than one, if the
entropy reduction contribution is not considered. This result highlights the
relevance of including the entropy reduction by information in the
thermodynamic balance of feedback controlled devices, specifically when writing
the second principle: the inclusion of the entropy reduction by information
leads to a well-behaved efficiency over all the range of parameters
investigated.Comment: 17 pages, 13 figure
Artificial Brownian motors: Controlling transport on the nanoscale
In systems possessing spatial or dynamical symmetry breaking, Brownian motion
combined with symmetric external input signals, deterministic or random, alike,
can assist directed motion of particles at the submicron scales. In such cases,
one speaks of "Brownian motors". In this review the constructive role of
Brownian motion is exemplified for various one-dimensional setups, mostly
inspired by the cell molecular machinery: working principles and
characteristics of stylized devices are discussed to show how fluctuations,
either thermal or extrinsic, can be used to control diffusive particle
transport. Recent experimental demonstrations of this concept are reviewed with
particular attention to transport in artificial nanopores and optical traps,
where single particle currents have been first measured. Much emphasis is given
to two- and three-dimensional devices containing many interacting particles of
one or more species; for this class of artificial motors, noise rectification
results also from the interplay of particle Brownian motion and geometric
constraints. Recently, selective control and optimization of the transport of
interacting colloidal particles and magnetic vortices have been successfully
achieved, thus leading to the new generation of microfluidic and
superconducting devices presented hereby. Another area with promising potential
for realization of artificial Brownian motors are microfluidic or granular
set-ups.....Comment: 57 pages, 39 figures; submitted to Reviews Modern Physics, revised
versio
Separation and collective phenomena of colloidal particles in Brownian ratchets
Ph.DDOCTOR OF PHILOSOPH