3,444 research outputs found
Entropic transport - A test bed for the Fick-Jacobs approximation
Biased diffusive transport of Brownian particles through irregularly shaped,
narrow confining quasi-one-dimensional structures is investigated. The
complexity of the higher dimensional diffusive dynamics is reduced by means of
the so-called Fick-Jacobs approximation, yielding an effective one-dimensional
stochastic dynamics. Accordingly, the elimination of transverse, equilibrated
degrees of freedom stemming from geometrical confinements and/or bottlenecks
cause entropic potential barriers which the particles have to overcome when
moving forward noisily. The applicability and the validity of the reduced
kinetic description is tested by comparing the approximation with Brownian
dynamics simulations in full configuration space. This non-equilibrium
transport in such quasi-one-dimensional irregular structures implies for
moderate-to-strong bias a characteristic violation of the Sutherland-Einstein
fluctuation-dissipation relation.Comment: 15 pages, 6 figures ; Phil. Trans. R. Soc. A (2009), in pres
Diffusion of multiple species with excluded-volume effects
Stochastic models of diffusion with excluded-volume effects are used to model
many biological and physical systems at a discrete level. The average
properties of the population may be described by a continuum model based on
partial differential equations. In this paper we consider multiple interacting
subpopulations/species and study how the inter-species competition emerges at
the population level. Each individual is described as a finite-size hard core
interacting particle undergoing Brownian motion. The link between the discrete
stochastic equations of motion and the continuum model is considered
systematically using the method of matched asymptotic expansions. The system
for two species leads to a nonlinear cross-diffusion system for each
subpopulation, which captures the enhancement of the effective diffusion rate
due to excluded-volume interactions between particles of the same species, and
the diminishment due to particles of the other species. This model can explain
two alternative notions of the diffusion coefficient that are often confounded,
namely collective diffusion and self-diffusion. Simulations of the discrete
system show good agreement with the analytic results
Kinetics and mechanism of proton transport across membrane nanopores
We use computer simulations to study the kinetics and mechanism of proton
passage through a narrow-pore carbon-nanotube membrane separating reservoirs of
liquid water. Free energy and rate constant calculations show that protons move
across the membrane diffusively in single-file chains of hydrogen-bonded water
molecules. Proton passage through the membrane is opposed by a high barrier
along the effective potential, reflecting the large electrostatic penalty for
desolvation and reminiscent of charge exclusion in biological water channels.
At neutral pH, we estimate a translocation rate of about 1 proton per hour and
tube.Comment: 4 pages, 4 figure
Entropic Stochastic Resonance
We present a novel scheme for the appearance of Stochastic Resonance when the
dynamics of a Brownian particle takes place in a confined medium. The presence
of uneven boundaries, giving rise to an entropic contribution to the potential,
may upon application of a periodic driving force result in an increase of the
spectral amplification at an optimum value of the ambient noise level. This
Entropic Stochastic Resonance (ESR), characteristic of small-scale systems, may
constitute a useful mechanism for the manipulation and control of
single-molecules and nano-devices.Comment: 4 pages, 3 figure
Non-Markovian Stochastic Resonance
The phenomenological linear response theory of non-Markovian Stochastic
Resonance (SR) is put forward for stationary two-state renewal processes. In
terms of a derivation of a non-Markov regression theorem we evaluate the
characteristic SR-quantifiers; i.e. the spectral power amplification (SPA) and
the signal-to-noise ratio (SNR), respectively. In clear contrast to Markovian
SR, a characteristic benchmark of genuine non-Markovian SR is its distinctive
dependence of the SPA and SNR on small (adiabatic) driving frequencies;
particularly, the adiabatic SNR becomes strongly suppressed over its Markovian
counterpart. This non-Markovian SR theory is elucidated for a fractal gating
dynamics of a potassium ion channel possessing an infinite variance of closed
sojourn times.Comment: 4 pages, 1 figur
Non-Markovian Stochastic Resonance: three state model of ion channel gating
Stochastic Resonance in single voltage-dependent ion channels is investigated
within a three state non-Markovian modeling of the ion channel conformational
dynamics. In contrast to a two-state description one assumes the presence of an
additional closed state for the ion channel which mimics the manifold of
voltage-independent closed subconformations (inactivated ``state''). The
conformational transition into the open state occurs through a domain of
voltage-dependent closed subconformations (closed ``state''). At distinct
variance with a standard two-state or also three-state Markovian approach, the
inactivated state is characterized by a broad, non-exponential probability
distribution of corresponding residence times. The linear response to a
periodic voltage signal is determined for arbitrary distributions of the
channel's recovery times. Analytical results are obtained for the spectral
amplification of the applied signal and the corresponding signal-to-noise
ratio. Alternatively, these results are also derived by use of a corresponding
two-state non-Markovian theory which is based on driven integral renewal
equations [I. Goychuk and P. Hanggi, Phys. Rev. E 69, 021104 (2004)]. The
non-Markovian features of stochastic resonance are studied for a power law
distribution of the residence time-intervals in the inactivated state which
exhibits a large variance. A comparison with the case of bi-exponentially
distributed residence times possessing the same mean value, i.e. a simplest
non-Markovian two-state description, is also presented
Psi-series solutions of the cubic H\'{e}non-Heiles system and their convergence
The cubic H\'enon-Heiles system contains parameters, for most values of
which, the system is not integrable. In such parameter regimes, the general
solution is expressible in formal expansions about arbitrary movable branch
points, the so-called psi-series expansions. In this paper, the convergence of
known, as well as new, psi-series solutions on real time intervals is proved,
thereby establishing that the formal solutions are actual solutions
Biased Brownian motion in extreme corrugated tubes
Biased Brownian motion of point-size particles in a three-dimensional tube
with smoothly varying cross-section is investigated. In the fashion of our
recent work [Martens et al., PRE 83,051135] we employ an asymptotic analysis to
the stationary probability density in a geometric parameter of the tube
geometry. We demonstrate that the leading order term is equivalent to the
Fick-Jacobs approximation. Expression for the higher order corrections to the
probability density are derived. Using this expansion orders we obtain that in
the diffusion dominated regime the average particle current equals the
zeroth-order Fick-Jacobs result corrected by a factor including the corrugation
of the tube geometry. In particular we demonstrate that this estimate is more
accurate for extreme corrugated geometries compared to the common applied
method using the spatially dependent diffusion coefficient D(x,f). The analytic
findings are corroborated with the finite element calculation of a
sinusoidal-shaped tube.Comment: 10 pages, 4 figure
Collective shuttling of attracting particles in asymmetric narrow channels
The rectification of a single file of attracting particles subjected to a low
frequency ac drive is proposed as a working mechanism for particle shuttling in
an asymmetric narrow channel. Increasing the particle attraction results in the
file condensing, as signalled by the dramatic enhancement of the net particle
current. Magnitude and direction of the current become extremely sensitive to
the actual size of the condensate, which can then be made to shuttle between
two docking stations, transporting particles in one direction, with an
efficiency much larger than conventional diffusive models predict
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