Range of applicability of modified Fick-Jacobs equation in two dimensions

Berezhkovskii, Alexander M.; Dagdug, Leonardo; Bezrukov, Sergey M.

doi:10.1063/1.4934223

Cited by 36 publications

(36 citation statements)

References 20 publications

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“…The staring point of our model is the Fick-Jacobs approximation [24][25][26] that has already been characterized [27][28][29][30][31][32][33] and exploited for diverse systems ranging from particle splitters [34,35], cooperative rectification [36][37][38] diffusion through porous media [39,40], electro-osmotic systems [41][42][43] and entropic stochastic resonance [44,45] just to mention a few cases among others. The Fick-Jacobs approximation allows us to project the convection-diffusion equation of a noninteracting particle, confined in a two-dimensional (2D) or three-dimensional (3D) corrugated channel, onto a one-dimensional (1D) equation in which the particle dynamics is controlled by an effective potential.…”

Section: Theoretical Framework a Fick-jacobs Approximationmentioning

confidence: 99%

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Non-monotonous polymer translocation time across corrugated channels: Comparison between Fick-Jacobs approximation and numerical simulations

Bianco

Malgaretti

2016

The Journal of Chemical Physics

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We study the translocation of polymers across varying-section channels. Using systematic approximations, we derive a simplified model that reduces the problem of polymer translocation through varying-section channels to that of a point-like particle under the action of an effective potential. Such a model allows us to identify the relevant parameters controlling the polymers dynamics and, in particular, their translocation time. By comparing our analytical results with numerical simulations we show that, under suitable conditions, our model provides reliable predictions of the dynamics of both Gaussian and self-avoiding polymers, in two-and three-dimensional confinement. Moreover, both theoretical predictions, as well Brownian dynamic results, show a non-monotonous dependence of polymer translocation velocity as a function of polymer size, a feature that can be exploited for polymer separation.

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Section: Theoretical Framework a Fick-jacobs Approximationmentioning

confidence: 99%

“…[24][25][26] for a derivation of the Fick-Jacobs approximation, Ref. [27][28][29][30][31][32] for a discussion of its limits and Ref. [33] for a review on recent applications).…”

Section: Theoretical Framework a Fick-jacobs Approximationmentioning

confidence: 99%

Non-monotonous polymer translocation time across corrugated channels: Comparison between Fick-Jacobs approximation and numerical simulations

Bianco

Malgaretti

2016

The Journal of Chemical Physics

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“…The applicability of the effective one-dimensional description of diffusion in two-dimensional channels of varying width in terms of the modified Fick-Jacobs equation is studied in detail in Ref. 4. As shown in this work, Eq.…”

Section: Theorymentioning

confidence: 93%

“…4, most of the particles do not collide with the walls while travelling the channel period if the condition that the period is longer than the doubled minimum width of the channel, l ≥ 4a, is not met. As a consequence, the modified Fick-Jackobs equation is not applicable in such a case.…”

Section: Comparison With the Simulation Resultsmentioning

confidence: 99%

Unbiased diffusion in two-dimensional channels with corrugated walls

Verdel

Dagdug

Berezhkovskii

et al. 2016

The Journal of Chemical Physics

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This paper deals with diffusion of point particles in linearly corrugated two-dimensional channels. Such geometry allows one to obtain an approximate analytical expression that gives the particle effective diffusivity as a function of the geometric parameters of the channel. To establish its accuracy and the range of applicability, the expression is tested against Brownian dynamics simulation results. The test shows that the expression works very well for long channel periods, but fails when the period is not long enough compared to the minimum width of the channel. To fix this deficiency, we propose a simple empirical correction to the analytical expression. The resulting corrected expression for the effective diffusivity is in excellent agreement with the simulation results for all values of the channel period. C 2016 AIP Publishing LLC. [http://dx

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“…We consider the periodic symmetric saw-tooth height profile h(x) = εζ(x) where ζ(x) = a + |x| for x ∈ [−1/2, 1/2] and shown in Fig. 3a, already studied by [46][47][48][49], as well as the ratchet-like height profile ζ(x) = a + x on [0, 1] shown in Fig. 3b.…”

Section: B Linear Channelmentioning

confidence: 99%

Dispersion in two dimensional channels—the Fick–Jacobs approximation revisited

Mangeat¹,

Guérin²,

Dean³

2017

J. Stat. Mech.

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We examine the dispersion of Brownian particles in a symmetric two dimensional channel, this classical problem has been widely studied in the literature using the so called Fick-Jacobs' approximation and its various improvements. Most studies rely on the reduction to an effective one dimensional diffusion equation, here we derive an explicit formula for the diffusion constant which avoids this reduction. Using this formula the effective diffusion constant can be evaluated numerically without resorting to Brownian simulations. In addition, a perturbation theory can be developed in ε = h0/L where h0 is the characteristic channel height and L the period. This perturbation theory confirms the results of Kalinay and Percus (Phys. Rev. E 74, 041203 (2006)), based on the reduction, to one dimensional diffusion are exact at least to O(ε 6 ). Furthermore, we show how the Kalinay and Percus pseudo-linear approximation can be straightforwardly recovered. The approach proposed here can also be exploited to yield exact results in the limit ε → ∞, we show that here the diffusion constant remains finite and show how the result can be obtained with a simple physical argument. Moreover, we show that the correction to the effective diffusion constant is of order 1/ε and remarkably has a some universal characteristics. Numerically we compare the analytic results obtained with exact numerical calculations for a number of interesting channel geometries.

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Range of applicability of modified Fick-Jacobs equation in two dimensions

Cited by 36 publications

References 20 publications

Non-monotonous polymer translocation time across corrugated channels: Comparison between Fick-Jacobs approximation and numerical simulations

Non-monotonous polymer translocation time across corrugated channels: Comparison between Fick-Jacobs approximation and numerical simulations

Unbiased diffusion in two-dimensional channels with corrugated walls

Dispersion in two dimensional channels—the Fick–Jacobs approximation revisited

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