Calculation of displacement correlation tensor indicating vortical cooperative motion in two-dimensional colloidal liquids.

@article{Ooshida2016CalculationOD,
  title={Calculation of displacement correlation tensor indicating vortical cooperative motion in two-dimensional colloidal liquids.},
  author={Takeshi Ooshida and Susumu Goto and Takeshi Matsumoto and Michio Otsuki},
  journal={Physical review. E},
  year={2016},
  volume={94 2-1},
  pages={
          022125
        }
}
As an indicator of cooperative motion in a system of Brownian particles that models two-dimensional colloidal liquids, a displacement correlation tensor is calculated analytically and compared with numerical results. The key idea for the analytical calculation is to relate the displacement correlation tensor, which is a kind of four-point space-time correlation, to the Lagrangian two-time correlation of the deformation gradient tensor. Tensorial treatment of the statistical quantities… 

Figures from this paper

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

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, which can be extended to the case of nonlinear fluctuations by means of closure approximation for the vacancy field.

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

Calculations of the two-particle displacement correlation in a system of repulsive Brownian particles confined in a (quasi-)one-dimensional channel describe nested space–time structure of cages, whereby smaller cages are enclosed in larger cages with longer lifetimes.

Insights from Single-File Diffusion into Cooperativity in Higher Dimensions

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.

Thermodynamic scaling of vibrational dynamics and relaxation.

An expression of the TS master curve of the structural relaxation with one adjustable parameter less than the available three-parameter alternatives is derived and fits well with the experimental TS master curves of thirty-four glassformers and, in particular, their slope at the glass transition, i.e., the isochoric fragility.

Thermodynamic scaling of relaxation: insights from anharmonic elasticity

This work proposes a method for evaluating both the characteristic exponent and the TS master curve that uses experimentally accessible quantities that characterise the anharmonic elasticity and does not use details about the microscopic interactions.

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

Collective motion of caged particles is studied by calculating correlations of elongations (i.e., excess distances between two tagged particles) in a one-dimensional colloidal system, with the focus

References

SHOWING 1-10 OF 143 REFERENCES

Analytical calculation of four-point correlations for a simple model of cages involving numerous particles.

The notorious difficulty in derivation of the mode-coupling theory concerning violation of the fluctuation-dissipation theorem is found to disappear by virtue of the Lagrangian description.

Displacement correlation as an indicator of collective motion in one-dimensional and quasi-one-dimensional systems of repulsive Brownian particles

While the slow dynamics in glassy liquids are known to be accompanied by collective motions undetectable with static structure factor and requiring four-point space-time correlations for their

Time-dependent, four-point density correlation function description of dynamical heterogeneity and decoupling in supercooled liquids

by neighboring particles. We evaluate these quantities for a cold Lennard-Jones ~LJ! liquid, and show that in this system x 4(t) is dominated by growing spatial correlations between localized

Insights from Single-File Diffusion into Cooperativity in Higher Dimensions

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.

Long-range spatial correlations of particle displacements and the emergence of elasticity.

It is argued that a four-point correlation length ξ_{4}(t) grows linearly in time in a glass and grows as sqrt[t] at long times in a fluid, and it is shown that in the glass the shear modulus can be obtained from the long-time, small-q limit of S_{4}.

Renormalized dynamics of the Dean-Kawasaki model.

We study the model of a supercooled liquid for which the equation of motion for the coarse-grained density ρ(x,t) is the nonlinear diffusion equation originally proposed by Dean and Kawasaki,

Equilibrium dynamics of the Dean-Kawasaki equation: mode-coupling theory and its extension.

This work extends a previously proposed field-theoretic self-consistent perturbation approach for the equilibrium dynamics of the Dean-Kawasaki equation to a set of three new equations for correlation functions of the system, which must carefully deal with the noninteracting Brownian gas theory.

Diffusion in concentrated lattice gases. III. Tracer diffusion on a one-dimensional lattice

The dynamical process of the diffusion of tagged particles in a one-dimensional concentrated lattice gas is investigated. The particles are noninteracting except that double occupancy is forbidden.

Thermal fluctuations, mechanical response, and hyperuniformity in jammed solids.

  • A. IkedaL. Berthier
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2015
This work uses computer simulations to analyze the effect of thermal fluctuations on several signatures of jamming criticality, and finds that fluctuations of particle displacements are spatially correlated, and define a transverse and a longitudinal correlation length scale which both diverge as the jamming transition is approached.

Cage effect in supercooled molecular liquids: Local anisotropies and collective solid-like response.

It is concluded that the cage rattling is largely affected by solid-like extended modes, in close resemblance with experimental findings on colloids.
...