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Diffusion and velocity autocorrelation at the jamming transition.

¹Department of Physics, Umeå University, 901 87 Umeå, Sweden.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|May 21, 2010

Summary

Particle diffusion in soft-disk models near jamming density shows distinct behaviors. Below jamming, diffusion scales with shear rate; at the transition, it exhibits a slower, power-law dependence related to velocity correlations.

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Area of Science:

Soft matter physics
Computational physics
Statistical mechanics

Background:

Understanding particle dynamics is crucial in soft matter systems.
Jamming transition in granular materials and colloids is a key phenomenon.
Shear flow significantly alters particle motion and system properties.

Purpose of the Study:

To investigate particle diffusion in a 2D soft-disk model under steady shear.
To analyze the behavior of diffusion constants around the jamming density.
To connect diffusion properties to the velocity autocorrelation function.

Main Methods:

Numerical simulations of a two-dimensional soft-disk model.
Analysis of particle diffusion constants at zero temperature.
Examination of the velocity autocorrelation function and its time scales.

Main Results:

Diffusion constant (D) scales with shear rate (gamma) as D ~ gamma below jamming.
At the jamming transition, diffusion scales as D ~ gamma^qD with qD < 1.
Velocity autocorrelation function exhibits two decay processes: exponential and algebraic.

Conclusions:

The observed scaling of diffusion constants is linked to the dual time scales of velocity correlations.
The transition in diffusion behavior is governed by the interplay of shear rate and shear stress.
This study provides insights into the fundamental mechanisms of particle transport in sheared soft materials.