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Nonequilibrium mode-coupling theory for uniformly sheared underdamped systems.

Koshiro Suzuki¹, Hisao Hayakawa

¹Analysis Technology Development Center, Canon Inc., 30-2 Shimomaruko 3-chome, Tokyo 146-8501, Japan. suzuki.koshiro@canon.co.jp

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

|February 16, 2013

Summary

This study develops nonequilibrium mode-coupling theory (MCT) for underdamped systems, revealing significant yield stress relaxation and inertia effects not seen in overdamped systems.

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Area of Science:

Physics
Soft Matter Physics
Theoretical Physics

Background:

Nonequilibrium mode-coupling theory (MCT) is crucial for understanding complex systems.
Existing MCT models often focus on overdamped systems, limiting applicability to underdamped scenarios.
Bridging the gap between simulations and theory for underdamped systems remains a challenge.

Purpose of the Study:

To develop a nonequilibrium mode-coupling theory (MCT) for uniformly sheared underdamped systems.
To incorporate translational invariance and isothermal conditions within the theoretical framework.
To resolve existing contradictions in MCT for sheared systems.

Main Methods:

Starting from microscopic Sllod and Liouville equations.
Defining transient time correlators for translational invariance in sheared frames.
Implementing isothermal conditions via current fluctuation in dissipative coupling.

Main Results:

Developed a translationally invariant MCT equation for underdamped systems.
Observed pronounced yield stress relaxation due to growing current fluctuations in the alpha relaxation regime.
Identified an inertia effect in response to shear rate perturbations, absent in overdamped cases.

Conclusions:

The new MCT provides a more accurate description of underdamped sheared systems.
This work resolves contradictions between previous theoretical approaches (Fuchs-Cates and Chong-Kim).
The theory bridges the gap between molecular dynamics simulations and existing MCT models.