Publisher's Note: Corrections to the Fick-Jacobs equation [Phys. Rev. E<b>74</b>, 041203 (2006)]

Kalinay, Pavol; Percus, J. K.

doi:10.1103/physreve.74.049904

Cited by 59 publications

(163 citation statements)

References 0 publications

Supporting

Mentioning

138

Contrasting

Unclassified

Order By: Relevance

“…The calculation of the expansion of D(x) (2.22) presented in the Section II also demonstrates how the mapping procedure [4,6] can be applied to diffusion bounded in a channel with hard walls and biased by a transverse force. Other possible extensions are straightforward: we can add also a force acting along the channel, or to go to 3D channels.…”

Section: Discussionmentioning

confidence: 95%

“…The effects of slower transverse relaxation are included in the effective diffusion coefficient D(x). We calculate this function within a recurrence procedure [4]- [6], mapping rigorously the 2D problem onto the longitudinal coordinate x in the limit of the stationary flow, i.e. when the net flux changes very slowly with respect to the relaxation in the transverse direction.…”

Section: Discussionmentioning

confidence: 99%

“…The higher order operatorsẐ n starting from n = 2 also contain the spatial derivatives ∂ x , what makes the equation (2.11) too difficult for direct use in practice. Alike the diffusion alone [6], this equation can be simplified by replacing the correction operator 1 − ǫẐ by the function D(x) in the limit of the stationary state, when the net flux changes very slowly.…”

Section: Mapping Proceduresmentioning

confidence: 99%

See 2 more Smart Citations

Effective one-dimensional description of confined diffusion biased by a transverse gravitational force

Kalinay

2011

Phys. Rev. E

View full text Add to dashboard Cite

Diffusion of point-like non interacting particles in a two-dimensional (2D) channel of varying cross section is considered. The particles are biased by a constant force in the transverse direction. We apply our recurrence mapping procedure, which enables us to derive an effective one-dimensional (1D) evolution equation, governing the 1D density of the particles in the channel. In the limit of stationary flow, we arrive at an extended Fick-Jacobs equation, corrected by an effective diffusion coefficient D(x), depending on the longitudinal coordinate x. Our result is an approximate formula for D(x), involving also influence of the transverse force. Our calculations are verified on the stationary diffusion in a linear cone, which is exactly solvable.

show abstract

Section: Discussionmentioning

confidence: 95%

Section: Discussionmentioning

confidence: 99%

Section: Mapping Proceduresmentioning

confidence: 99%

See 1 more Smart Citation

Effective one-dimensional description of confined diffusion biased by a transverse gravitational force

Kalinay

2011

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…In such examples, changes in the motion of a particle occur mainly in the axial direction along the channel, whereas local equilibrium is rapidly reached in the transverse directions. Thus transport is quasi onedimensional and the effects of the boundaries of the channel can be incorporated by introducing an entropic barrier into the dynamics of a Brownian particle, leading to the so-called Fick-Jacobs equation (Burada et al, 2009(Burada et al, , 2007Jacobs, 1967;Kalinay and Percus, 2006;Reguera and Rubi, 2001;Rubi and Reguera, 2010;Zwanzig, 1992). Typically a 3D narrow channel is represented by a cylinder that extends axially in the x-direction and has a periodically varying cross section that is rotationally symmetric about the x-axis, see Fig.…”

Section: Diffusion In Confined Geometriesmentioning

confidence: 99%

“…The Fick-Jacobs equation is valid provided that |w (x)| 1. However, it has been shown that the introduction of an x-dependent diffusion coefficient into the Fick-Jacobs equation can considerably increase the accuracy of the reduced FP equation and thus extend the domain of validity (Kalinay and Percus, 2006;Reguera and Rubi, 2001;Zwanzig, 1992):…”

mentioning

confidence: 99%

Stochastic models of intracellular transport

2013

View full text Add to dashboard Cite

The interior of a living cell is a crowded, heterogenuous, fluctuating environment. Hence, a major challenge in modeling intracellular transport is to analyze stochastic processes within complex environments. Broadly speaking, there are two basic mechanisms for intracellular transport: passive diffusion and motor-driven active transport. Diffusive transport can be formulated in terms of the motion of an over-damped Brownian particle. On the other hand, active transport requires chemical energy, usually in the form of ATP hydrolysis, and can be direction specific, allowing biomolecules to be transported long distances; this is particularly important in neurons due to their complex geometry. In this review we present a wide range of analytical methods and models of intracellular transport. In the case of diffusive transport, we consider narrow escape problems, diffusion to a small target, confined and single-file diffusion, homogenization theory, and fractional diffusion. In the case of active transport, we consider Brownian ratchets, random walk models, exclusion processes, random intermittent search processes, quasisteady-state reduction methods, and mean field approximations. Applications include receptor trafficking, axonal transport, membrane diffusion, nuclear transport, protein-DNA interactions, virus trafficking, and the self-organization of subcellular structures.

show abstract

Phase Space Reduction of the One-Dimensional Fokker-Planck (Kramers) Equation

Kalinay

Percus

2012

J Stat Phys

View full text Add to dashboard Cite

A pointlike particle of finite mass m, moving in a one-dimensional viscous environment and biased by a spatially dependent force, is considered. We present a rigorous mapping of the FokkerPlanck equation, which determines evolution of the particle density in phase space, onto the spatial coordinate x. The result is the Smoluchowski equation, valid in the overdamped limit, m → 0, with a series of corrections expanded in powers of m. They are determined unambiguously within the recurrence mapping procedure. The method and the results are interpreted on the simplest model with no field and on the damped harmonic oscillator.

show abstract

Publisher's Note: Corrections to the Fick-Jacobs equation [Phys. Rev. E74, 041203 (2006)]

Cited by 59 publications

References 0 publications

Effective one-dimensional description of confined diffusion biased by a transverse gravitational force

Effective one-dimensional description of confined diffusion biased by a transverse gravitational force

Stochastic models of intracellular transport

Phase Space Reduction of the One-Dimensional Fokker-Planck (Kramers) Equation

Contact Info

Product

Resources

About