Entropic transport: a test bed for the Fick–Jacobs approximation

Burada, P. S.; Schmid, Gerhard; Hänggi, Peter

doi:10.1098/rsta.2009.0068

Cited by 32 publications

(24 citation statements)

References 33 publications

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“…which maps the overall probability density P (x, t) onto one period of the pulse sequence [30,45,46]. That is, instead of considering the time-evolution of the swimmer's probability density along an infinite periodic pulse sequence, we focus on a single wave period and impose periodic boundary conditions to ensure the existence of a stationary state.…”

Section: Periodic Pulse Trainmentioning

confidence: 99%

Taxis of Artificial Swimmers in a Spatio-Temporally Modulated Activation Medium

Geiseler

Hänggi

Marchesoni

2017

Entropy

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Contrary to microbial taxis, where a tactic response to external stimuli is controlled by complex chemical pathways acting like sensor-actuator loops, taxis of artificial microswimmers is a purely stochastic effect associated with a non-uniform activation of the particles' self-propulsion. We study the tactic response of such swimmers in a spatio-temporally modulated activating medium by means of both numerical and analytical techniques. In the opposite limits of very fast and very slow rotational particle dynamics, we obtain analytic approximations that closely reproduce the numerical description. A swimmer drifts on average either parallel or anti-parallel to the propagation direction of the activating pulses, depending on their speed and width. The drift in line with the pulses is solely determined by the finite persistence length of the active Brownian motion performed by the swimmer, whereas the drift in the opposite direction results from the combination of the ballistic and diffusive properties of the swimmer's dynamics.

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Section: Periodic Pulse Trainmentioning

confidence: 99%

Taxis of Artificial Swimmers in a Spatio-Temporally Modulated Activation Medium

Geiseler

Hänggi

Marchesoni

2017

Entropy

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“…In the diffusion dominated regime, |f | ≪ 1, the Sutherland-Einstein relation emerges 47,48 and thus the dimensionless mobility equals the dimensionless effective diffusion coefficient:…”

Section: Transport Quantities For a Sinusoidally Shaped Tubementioning

confidence: 99%

“…In contrast to the 3D planar geometry, for biased transport in extreme corrugated tubes the corrections term to the particle velocity does not coincide with the expectation value of D(x, 0), see Eq. (47). Calculating the expectation value in Eq.…”

Section: B Corrections Based On Perturbation Series Expansionmentioning

confidence: 99%

Biased Brownian motion in extremely corrugated tubes

Martens

Schmid

Schimansky‐Geier

et al. 2011

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Biased Brownian motion of point-size particles in a three-dimensional tube with smoothly varying crosssection is investigated. In the fashion of our recent work 1 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. Particle transport in micro-and nanostructured channel structures exhibits peculiar characteristics which differs from other transport phenomena occurring for energetic systems. The theoretical modelling involves Fokker-Planck type dynamics in three dimensions which cannot be solved for arbitrary boundary conditions imposed by the geometrical restrictions. Recently, much effort is drawn on a reduction of the complexity of the problem resulting in the so-called FickJacobs approximation in which (infinitely) fast equilibration in certain spatial directions is assumed. Within the present manuscript we derive a reduction method which (i) corresponds in zeroth order in the expansion parameter, which describes the corrugation of the tube wall, to the celebrated Fick-Jacobs result and (ii) extends the validity of the Fick-Jacobs approximation towards extreme corrugated tube structures.

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“…One can find an interesting discussion of the reduction to the effective one-dimensional description in a series of papers by Kalinay and Percus [5–8]. Detailed analysis of entropic effects in drift and diffusion of non-interacting particles in two-dimensional systems has been carried out by Hanggi and colleagues [9–12]. The question of effective one-dimensional description of transport in such systems was also addressed in [13, 14].…”

Section: Introductionmentioning

confidence: 99%

Fluxes of non-interacting and strongly repelling particles through a single conical channel: Analytical results and their numerical tests

2010

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Using a diffusion model of particle dynamics in the channel, we study entropic effects in channelfacilitated transport. We derive general expressions for the fluxes of non-interacting particles and particles that strongly repel each other through the channel of varying cross section area, assuming that the transport is driven by the difference in particle concentrations on the two sides of the membrane. For a special case of a right truncated cone expanding in the left-to-right direction, we show how the fluxes depend on the geometric parameters of the channel and on the particle concentrations. For non-interacting particles the flux is direction-independent in the sense that inversion of the concentration difference leads to the inversion of the direction of the flux without changing its magnitude. This symmetry is broken for repelling particles: The flux in the left-toright direction exceeds its right-to-left counterpart. Our theoretical predictions are supported by three-dimensional Brownian dynamics simulations.

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Entropic transport: a test bed for the Fick–Jacobs approximation

Cited by 32 publications

References 33 publications

Taxis of Artificial Swimmers in a Spatio-Temporally Modulated Activation Medium

Taxis of Artificial Swimmers in a Spatio-Temporally Modulated Activation Medium

Biased Brownian motion in extremely corrugated tubes

Fluxes of non-interacting and strongly repelling particles through a single conical channel: Analytical results and their numerical tests

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