15,173 research outputs found
Steering the potential barriers: entropic to energetic
We propose a new mechanism to alter the nature of the potential barriers when
a biased Brownian particle under goes a constrained motion in narrow, periodic
channel. By changing the angle of the external bias, the nature of the
potential barriers changes from purely entropic to energetic which in turn
effects the diffusion process in the system. At an optimum angle of the bias,
the nonlinear mobility exhibits a striking bell-shaped behavior. Moreover, the
enhancement of the scaled effective diffusion coefficient can be efficiently
controlled by the angle of the bias. This mechanism enables the proper design
of channel structures for transport of molecules and small particles. The
approximative analytical predictions have been verified by precise Brownian
dynamic simulations.Comment: (6 pages, 7 figures) Submitted to PR
Controlling diffusive transport in confined geometries
We analyze the diffusive transport of Brownian particles in narrow channels
with periodically varying cross-section. The geometrical confinements lead to
entropic barriers, the particle has to overcome in order to proceed in
transport direction. The transport characteristics exhibit peculiar behaviors
which are in contrast to what is observed for the transport in potentials with
purely energetic barriers. By adjusting the geometric parameters of the channel
one can effectively tune the transport and diffusion properties. A prominent
example is the maximized enhancement of diffusion for particular channel
parameters. The understanding of the role of channel-shape provides the
possibility for a design of stylized channels wherein the quality of the
transport can be efficiently optimized.Comment: accepted for publication in Acta Physica Polonica
Double Entropic Stochastic Resonance
We demonstrate the appearance of a purely entropic stochastic resonance (ESR)
occurring in a geometrically confined system, where the irregular boundaries
cause entropic barriers. The interplay between a periodic input signal, a
constant bias and intrinsic thermal noise leads to a resonant ESR-phenomenon in
which feeble signals become amplified. This new phenomenon is characterized by
the presence of two peaks in the spectral amplification at corresponding
optimal values of the noise strength. The main peak is associated with the
manifest stochastic resonance synchronization mechanism involving the
inter-well noise-activated dynamics while a second peak relates to a regime of
optimal sensitivity for intra-well dynamics. The nature of ESR, occurring when
the origin of the barrier is entropic rather than energetic, offers new
perspectives for novel investigations and potential applications. ESR by itself
presents yet another case where one constructively can harvest noise in driven
nonequilibrium systems.Comment: 6 pages, 7 figures ; Europhys. Lett., in press (2009
Detectable inertial effects on Brownian transport through narrow pores
We investigate the transport of suspended Brownian particles dc driven along
corrugated narrow channels in a regime of finite damping. We demonstrate that
inertial corrections cannot be neglected as long as the width of the channel
bottlenecks is smaller than an appropriate particle diffusion length, which
depends on both, the temperature and the strength of the dc drive. Therefore,
transport through sufficiently narrow constrictions turns out to be sensitive
to the viscosity of the suspension fluid. Applications to colloidal systems are
discussed
Entropic stochastic resonance: the constructive role of the unevenness
We demonstrate the existence of stochastic resonance (SR) in confined systems
arising from entropy variations associated to the presence of irregular
boundaries. When the motion of a Brownian particle is constrained to a region
with uneven boundaries, the presence of a periodic input may give rise to a
peak in the spectral amplification factor and therefore to the appearance of
the SR phenomenon. We have proved that the amplification factor depends on the
shape of the region through which the particle moves and that by adjusting its
characteristic geometric parameters one may optimize the response of the
system. The situation in which the appearance of such entropic stochastic
resonance (ESR) occurs is common for small-scale systems in which confinement
and noise play an prominent role. The novel mechanism found could thus
constitute an important tool for the characterization of these systems and can
put to use for controlling their basic properties.Comment: 8 pages, 8 figure
Biased diffusion in confined media: Test of the Fick-Jacobs approximation and validity criteria
We study biased, diffusive transport of Brownian particles through narrow,
spatially periodic structures in which the motion is constrained in lateral
directions. The problem is analyzed under the perspective of the Fick-Jacobs
equation which accounts for the effect of the lateral confinement by
introducing an entropic barrier in a one dimensional diffusion. The validity of
this approximation, being based on the assumption of an instantaneous
equilibration of the particle distribution in the cross-section of the
structure, is analyzed by comparing the different time scales that characterize
the problem. A validity criterion is established in terms of the shape of the
structure and of the applied force. It is analytically corroborated and
verified by numerical simulations that the critical value of the force up to
which this description holds true scales as the square of the periodicity of
the structure. The criterion can be visualized by means of a diagram
representing the regions where the Fick-Jacobs description becomes inaccurate
in terms of the scaled force versus the periodicity of the structure.Comment: 20 pages, 7 figure
A variational framework for flow optimization using semi-norm constraints
When considering a general system of equations describing the space-time
evolution (flow) of one or several variables, the problem of the optimization
over a finite period of time of a measure of the state variable at the final
time is a problem of great interest in many fields. Methods already exist in
order to solve this kind of optimization problem, but sometimes fail when the
constraint bounding the state vector at the initial time is not a norm, meaning
that some part of the state vector remains unbounded and might cause the
optimization procedure to diverge. In order to regularize this problem, we
propose a general method which extends the existing optimization framework in a
self-consistent manner. We first derive this framework extension, and then
apply it to a problem of interest. Our demonstration problem considers the
transient stability properties of a one-dimensional (in space) averaged
turbulent model with a space- and time-dependent model "turbulent viscosity".
We believe this work has a lot of potential applications in the fluid
dynamics domain for problems in which we want to control the influence of
separate components of the state vector in the optimization process.Comment: 30 page
Giant enhancement of hydrodynamically enforced entropic trapping in thin channels
Using our generalized Fick-Jacobs approach [Martens et al., PRL 110, 010601
(2013); Martens et al., Eur. Phys. J. Spec. Topics 222, 2453-2463 (2013)] and
extensive Brownian dynamics simulations, we study particle transport through
three-dimensional periodic channels of different height. Directed motion is
caused by the interplay of constant bias acting along the channel axis and a
pressure-driven flow. The tremendous change of the flow profile shape in
channel direction with the channel height is reflected in a crucial dependence
of the mean particle velocity and the effective diffusion coefficient on the
channel height. In particular, we observe a giant suppression of the effective
diffusivity in thin channels; four orders of magnitude compared to the bulk
value.Comment: 16 pages, 8 figure
Hydrodynamically enforced entropic trapping of Brownian particles
We study the transport of Brownian particles through a corrugated channel
caused by a force field containing curl-free (scalar potential) and
divergence-free (vector potential) parts. We develop a generalized Fick-Jacobs
approach leading to an effective one-dimensional description involving the
potential of mean force. As an application, the interplay of a pressure-driven
flow and an oppositely oriented constant bias is considered. We show that for
certain parameters, the particle diffusion is significantly suppressed via the
property of hyrodynamically enforced entropic particle trapping.Comment: 5 pages, 4 figures, in press with Physical Review Letter
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