Evolution equation for tagged-particle density and correlations in single-file diffusion

Suárez, Gonzalo; Hoyuelos, Miguel; Mártin, H. O.

doi:10.1103/physreve.88.022131

Cited by 5 publications

(9 citation statements)

References 25 publications

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“…(Of course, it does have an effect in the single particle diffusion coefficient [29,30].) This result is obtained from the expression for the diffusion coefficient (16) using (29) for the mean field potential and γ = 1.…”

Section: Hard Core Interactionmentioning

confidence: 99%

Mean-field approach for diffusion of interacting particles

2015

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A nonlinear Fokker-Planck equation is obtained in the continuous limit of a one-dimensional lattice with an energy landscape of wells and barriers. Interaction is possible among particles in the same energy well. A parameter γ, related to the barrier's heights, is introduced. Its value is determinant for the functional dependence of the mobility and diffusion coefficient on particle concentration, but has no influence on the equilibrium solution. A relation between the mean field potential and the microscopic interaction energy is derived. The results are illustrated with classical particles with interactions that reproduce fermion and boson statistics.

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Section: Hard Core Interactionmentioning

confidence: 99%

Mean-field approach for diffusion of interacting particles

2015

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“…This expression is a generalization of the crossover time t s = 1/D 0 c 2 that corresponds to a homogeneous substrate (ν = 1/2) [25]. In the right panel of figure 2, we plot in a scaled form the same data shown in left panel, i. e., ∆ 2 x HC (t)/∆ 2 x HC (t s ) against t/t s .…”

Section: Short Times: the Effect Of Particle Concentrationmentioning

confidence: 99%

“…For short enough times, every particle behaves almost as in the non-interacting case. At these early stages of time evolution, the correlations between particle motions are negligible, and we can use a mean-field theory [25]. Within this approximation, the mean-square displacement of a tagged particle in a hard-core interacting system ∆ 2 x HC satisfies…”

Section: Short Times: the Effect Of Particle Concentrationmentioning

confidence: 99%

“…In the case of single-file diffusion on an infinite homogeneous line, a representative tagged particle always starts diffusing normally, provided that interactions are of short range. However, after a finite time, the dynamics become subdiffusive, and the taggedparticle MSD behaves as ∼ t 1/2 as a function of time t, because of the correlations between neighbor particles [25]. The tagged-particle MSD recovers the normal behavior (∼ t) at long times if single-file diffusion occurs on a homogeneous segment of finite size with periodic boundary conditions.…”

Section: Introductionmentioning

confidence: 96%

“…This is, for instance, the situation of a set of particles diffusing on a one-dimensional medium, in such a way that the interactions prevent for particles to jump over one another. The sequence of particles is then preserved, and the phenomenon is commonly called single-file diffusion [19][20][21][22][23][24][25]. In the case of single-file diffusion on an infinite homogeneous line, a representative tagged particle always starts diffusing normally, provided that interactions are of short range.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Universal behavior for single-file diffusion on a disordered fractal

2017

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We study single-file diffusion on a one-dimensional lattice with a random fractal distribution of hopping rates. For finite lattices, this problem shows three clearly different regimes, namely, nearly independent particles, highly interacting particles, and saturation. The mean-square displacement of a tagged particle as a function of time follows a power law in each regime. The first crossover time t s , between the first and the second regime, depends on the particle density. The other crossover time t l , between the second and the third regime, depends on the lattice length. We find analytic expressions for these dependencies and show how the general behavior can be characterized by an universal form. We also show that the mean-square displacement of the center of mass presents two regimes; anomalous diffusion for times shorter than t l , and normal diffusion for times longer than t l . arXiv:1611.00640v1 [cond-mat.stat-mech] 2 Nov 2016Universal behavior for single-file diffusion on a disordered fractal

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Single file diffusion into a semi-infinite tube

Farrell

Brown²,

Rutenberg³

2015

Phys. Biol.

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We investigate single file diffusion (SFD) of large particles entering a semi-infinite tube, such as luminal diffusion of proteins into microtubules or flagella. While single-file effects have no impact on the evolution of particle density, we report significant single-file effects for individually tracked tracer particle motion. Both exact and approximate ordering statistics of particles entering semi-infinite tubes agree well with our stochastic simulations. Considering initially empty semi-infinite tubes, with particles entering at one end starting from an initial time t = 0, tracked particles are initially super-diffusive after entering the system, but asymptotically diffusive at later times. For finite time intervals, the ratio of the net displacement of individual single-file particles to the average displacement of untracked particles is reduced at early times and enhanced at later times. When each particle is numbered, from the first to enter (n = 1) to the most recent (n = N), we find good scaling collapse of this distance ratio for all n. Experimental techniques that track individual particles, or local groups of particles, such as photo-activation or photobleaching of fluorescently tagged proteins, should be able to observe these single-file effects. However, biological phenomena that depend on local concentration, such as flagellar extension or luminal enzymatic activity, should not exhibit single-file effects.

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Evolution equation for tagged-particle density and correlations in single-file diffusion

Cited by 5 publications

References 25 publications

Mean-field approach for diffusion of interacting particles

Mean-field approach for diffusion of interacting particles

Universal behavior for single-file diffusion on a disordered fractal

Single file diffusion into a semi-infinite tube

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