Effects of Cage-Breaking Events in Single-File Diffusion on Elongation Correlation

Ooshida, Takeshi; Otsuki, Michio

doi:10.7566/jpsj.86.113002

Cited by 3 publications

(10 citation statements)

References 30 publications

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“…The Lagrangian correlation of the field ψ links R i R j to the Dean-Kawasaki equation (12) that describes the fluctuating density field, while overtaking is taken into account through δΞ i (t). The main analytical result is represented by Equations (43) and (44). This result is reasonably consistent with the numerical behavior of R i R j in Figure 6.…”

Section: Discussion and Concluding Remarkssupporting

confidence: 77%

“…Overtaking is incorporated into the theory though temporal changes of Ξ i (t) [44]. The kinematics of overtaking were discussed in Subsection 2.5: as is illustrated in Figure 3, two particles exchange their labels according to Equation (21).…”

Section: Theory Of Displacement Correlation In Sfd With Overtakingmentioning

confidence: 99%

“…A crucial step is found in Equation (27) where R i is obtained on the assumption that Ξ i is independent of t. This is the point at which the "no overtaking" rule was enforced [30,44].…”

Section: Theory Of Displacement Correlation In Sfd With Overtakingmentioning

confidence: 99%

“…[25] that can be fitted with a straight line, whose slope gives ν α . The values of ν α , collected in this way as a function of (ρ 0 , V max ), are fitted with an Arrhenius-like expression, with a prefactor that depends both on V max and ρ 0 [44]:…”

Section: Appendix B Numerical Evaluation Of the Hopping Ratementioning

confidence: 99%

“…as a function of the particle number i and the time t, and consider its t-derivative [30,44]. Provided that the conventional chain rule is valid, the time-derivative of…”

Section: Label Variablementioning

confidence: 99%

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Collective Motion of Repulsive Brownian Particles in Single-File Diffusion with and without Overtaking

Ooshida

Goto

Otsuki

2018

Entropy

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Subdiffusion is commonly observed in liquids with high density or in restricted geometries, as the particles are constantly pushed back by their neighbors. Since this "cage effect" emerges from many-body dynamics involving spatiotemporally correlated motions, the slow diffusion should be understood not simply as a one-body problem but as a part of collective dynamics, described in terms of space-time correlations. Such collective dynamics are illustrated here by calculations of the two-particle displacement correlation in a system of repulsive Brownian particles confined in a (quasi-)one-dimensional channel, whose subdiffusive behavior is known as the single-file diffusion (SFD). The analytical calculation is formulated in terms of the Lagrangian correlation of density fluctuations. In addition, numerical solutions to the Langevin equation with large but finite interaction potential are studied to clarify the effect of overtaking. In the limiting case of the ideal SFD without overtaking, correlated motion with a diffusively growing length scale is observed. By allowing the particles to overtake each other, the short-range correlation is destroyed, but the long-range weak correlation remains almost intact. These results describe nested space-time structure of cages, whereby smaller cages are enclosed in larger cages with longer lifetimes.

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Section: Discussion and Concluding Remarkssupporting

confidence: 77%

Section: Theory Of Displacement Correlation In Sfd With Overtakingmentioning

confidence: 99%

“…A crucial step is found in Equation (27) where R i is obtained on the assumption that Ξ i is independent of t. This is the point at which the "no overtaking" rule was enforced [30,44].…”

Section: Theory Of Displacement Correlation In Sfd With Overtakingmentioning

confidence: 99%

Section: Appendix B Numerical Evaluation Of the Hopping Ratementioning

confidence: 99%

“…as a function of the particle number i and the time t, and consider its t-derivative [30,44]. Provided that the conventional chain rule is valid, the time-derivative of…”

Section: Label Variablementioning

confidence: 99%

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Collective Motion of Repulsive Brownian Particles in Single-File Diffusion with and without Overtaking

Ooshida

Goto

Otsuki

2018

Entropy

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Two-tag correlations and nonequilibrium fluctuation–response relation in ageing single-file diffusion

Ooshida

Otsuki

2018

J. Phys.: Condens. Matter

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Spatiotemporally correlated motions of interacting Brownian particles, confined in a narrow channel of infinite length, are studied in terms of statistical quantities involving two particles. A theoretical framework that allows analytical calculation of two-tag correlations is presented on the basis of the Dean-Kawasaki equation describing density fluctuations in colloidal systems. In the equilibrium case, the time-dependent Einstein relation holds between the two-tag displacement correlation and the response function corresponding to it, which is a manifestation of the fluctuation-dissipation theorem for the correlation of density fluctuations. While the standard procedure of closure approximation for nonlinear density fluctuations is known to be obstructed by inconsistency with the fluctuation-dissipation theorem, this difficulty is naturally avoided by switching from the standard Fourier representation of the density field to the label-based Fourier representation of the vacancy field. In the case of ageing dynamics started from equidistant lattice configuration, the time-dependent Einstein relation is violated, as the two-tag correlation depends on the waiting time for equilibration while the response function is not sensitive to it. Within linear approximation, however, there is a simple relation between the density (or vacancy) fluctuations and the corresponding response function, which is valid even if the system is out of equilibrium. This non-equilibrium fluctuation-response relation can be extended to the case of nonlinear fluctuations by means of closure approximation for the vacancy field.

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Shaking-induced stress anisotropy in the memory effect of paste

Kitsunezaki¹,

Nakahara²,

Matsuo³

2016

EPL

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When paste of fine granular particles and water is shaken in one direction and then left undisturbed, memory of the direction of shaking is retained for a sufficiently long time to result in a directional crack pattern that appears after drying. Although it has been conjectured that anisotropy in residual stresses caused by plastic deformation is responsible for this memory effect, to this time, no evidence of such anisotropy has been found. We experimentally investigated the stress in drying paste by measuring the bending of elastic plates supporting the paste sample and found stress anisotropy developing in paste. Additional bending tests suggested that paste retains plasticity during the drying process and that plastic deformation is not always frozen in place after initial shaking.

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Effects of Cage-Breaking Events in Single-File Diffusion on Elongation Correlation

Cited by 3 publications

References 30 publications

Collective Motion of Repulsive Brownian Particles in Single-File Diffusion with and without Overtaking

Collective Motion of Repulsive Brownian Particles in Single-File Diffusion with and without Overtaking

Two-tag correlations and nonequilibrium fluctuation–response relation in ageing single-file diffusion

Shaking-induced stress anisotropy in the memory effect of paste

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