Continuum Theory of Single-File Diffusion in Terms of Label Variable

Ooshida, Takeshi; Goto, Susumu; Matsumoto, Takeshi; Nakahara, Akio; Otsuki, Michio

doi:10.1143/jpsj.80.074007

Cited by 15 publications

(15 citation statements)

References 39 publications

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“…In this single-file diffusion (SFD), after an initial ballistic motion with a mean square displacement (MSD) scaling as t 2 , the particles undergo a subdiffusive motion characterized by a MSD increasing as t 1/2 . This non-Fickian t 1/2 scaling, which can be observed at long times, has also been predicted for particles with soft-core (or finite range) interactions [11][12][13][14].…”

Section: Introductionsupporting

confidence: 65%

Single-file diffusion of particles in a box: Transient behaviors

2012

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We consider a finite number of particles with soft-core interactions, subjected to thermal fluctuations and confined in a box with excluded mutual passage. Using numerical simulations, we focus on the influence of the longitudinal confinement on the transient behavior of the longitudinal mean squared displacement. We exhibit several power laws for its time evolution according to the confinement range and to the rank of the particle in the file. We model the fluctuations of the particles as those of a chain of springs and point masses in a thermal bath. Our main conclusion is that actual system dynamics can be described in terms of the normal oscillation modes of this chain. Moreover, we obtain complete expressions for the physical observables, in excellent agreement with our simulations. The correct power laws for the time dependency of the mean squared displacement in the various regimes are recovered, and analytical expressions of the prefactors according to the relevant parameters are given.

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Section: Introductionsupporting

confidence: 65%

Single-file diffusion of particles in a box: Transient behaviors

2012

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“…adoption of the Lagrangian description. 22,23 In the 1D case, Eq. (4.7) gives the MSD as a special case of the displacement correlation in Eq.…”

Section: Discussionmentioning

confidence: 99%

“…for n d = 2, and a trilinear equation in an analogous form for the 3D case. 22 It is then verified that ξ satisfies the convective equation can be constructed, where o is an arbitrary "initial" time.…”

Section: Ap Formula In Higher Dimensionsmentioning

confidence: 98%

“…Here we redevelop the AP formula, making it exact by changing the variables appropriately. 22,23 The key to this approach is the adoption of Lagrangian correlations, motivated by theories of the Navier-Stokes turbulence. [80][81][82] While the formula itself remains linear with regard to the correlation in the new variables, it can be combined with a nonlinear equation of the correlation, so that the result can be improved as we will see later in Subsec.…”

Section: Alexander-pincus Formula In Convected Coordinate Systemmentioning

confidence: 99%

“…A popular idea is to define four-point space-time correlations by analogy with spin glasses, 4,18,19 while there are different ideas that involve particle tracking, such as the bond breaking correlation. 7,20,21 Combining the idea of continuum-based particle tracking 22 with that of four-point space-time correlations, 23 we find that displacement correlation 14,24 can be quite useful. The present article aims to give some insights into space-time correlations characterizing cooperativity in glassy liquids, by studying a simpler model of caged dynamics.…”

Section: Introductionmentioning

confidence: 99%

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Insights from Single-File Diffusion into Cooperativity in Higher Dimensions

Ooshida

Goto

Matsumoto

et al. 2016

Biophys. Rev. Lett.

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Diffusion in colloidal suspensions can be very slow due to the cage effect, which confines each particle within a short radius on one hand, and involves large-scale cooperative motions on the other. In search of insight into this cooperativity, here the authors develop a formalism to calculate the displacement correlation in colloidal systems, mainly in the two-dimensional case. To clarify the idea for it, studies are reviewed on cooperativity among the particles in the one-dimensional case, i.e. the single-file diffusion (SFD). As an improvement over the celebrated formula by Alexander and Pincus on the mean-square displacement (MSD) in SFD, it is shown that the displacement correlation in SFD can be calculated from Lagrangian correlation of the particle interval in the one-dimensional case, and also that the formula can be extended to higher dimensions. The improved formula becomes exact for large systems. By combining the formula with a nonlinear theory for correlation, a correction to the asymptotic law for the MSD in SFD is obtained. In the two-dimensional case, the linear theory gives description of vortical cooperative motion. Special Issue Comments:This article presents methodological insights into mathematical treatment of particle cooperativity in colloidal liquids. This article is related to the Special Issue articles [in Biophys. Rev. Lett.] about mathematical approaches to single-file diffusion 1 and Fourier-based analysis of quasi-onedimensional systems.

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Basics of Single-File Diffusion

Ryabov

2015

Springer Theses

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Continuum Theory of Single-File Diffusion in Terms of Label Variable

Cited by 15 publications

References 39 publications

Single-file diffusion of particles in a box: Transient behaviors

Single-file diffusion of particles in a box: Transient behaviors

Insights from Single-File Diffusion into Cooperativity in Higher Dimensions

Basics of Single-File Diffusion

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