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Glass transition in driven granular fluids: a mode-coupling approach.

W T Kranz¹, M Sperl, A Zippelius

¹Georg-August-Universität Göttingen, Institut für Theoretische Physik, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany.

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

|March 19, 2013

Summary

Researchers studied inelastic hard spheres and disks, observing a glass transition at a critical packing fraction. This transition shows dynamics dependent on compression rate and dissipation, similar to thermal glasses.

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Area of Science:

Physics
Soft Matter Physics
Statistical Mechanics

Background:

Understanding the behavior of granular materials and dense fluids is crucial.
Inelastic hard sphere/disk systems exhibit complex dynamics under external forces.
Glass transitions in these systems are not fully understood, especially concerning dissipation.

Purpose of the Study:

To investigate the stationary state of inelastic hard spheres/disks under external forces.
To derive and analyze the equation of motion for the coherent scattering function.
To characterize the glass transition and its dependence on system parameters.

Main Methods:

Microscopic description of particle dynamics.
Derivation of a nonlinear equation of motion for the coherent scattering function.
Analysis of critical dynamics for coherent and tagged particle motion in 2D and 3D.

Main Results:

A glass transition was observed at a critical packing fraction (φ(c)(ε)) for all coefficients of restitution (ε).
Timescale divergence at the glass transition indicates compression-rate dependence, analogous to thermal glasses.
Critical dynamics were found to be nonuniversal, with exponents varying by space dimension and dissipation.

Conclusions:

The study reveals a dimension-dependent, nonuniversal glass transition in dissipative granular fluids.
The findings highlight similarities between granular and thermal glasses regarding rate dependence.
The derived nonlinear equation of motion provides a framework for understanding these complex systems.