Interface fluctuations, Burgers equations, and coarsening under shear

Area of Science:

• Physics
• Materials Science
• Complex Systems

Background:

• Coarsening dynamics describe how systems with multiple domains evolve over time to reduce surface area.
• Shear flow and thermal fluctuations significantly influence the behavior of these domain surfaces.
• Understanding these effects is crucial for various physical and materials science applications.

Purpose of the Study:

• To investigate the combined effects of thermal fluctuations and shear flow on domain surface coarsening.
• To analyze systems with both nonconserved and conserved dynamics, including fluid-advected conserved order parameters.
• To derive and solve the governing equations for interface height dynamics.

Main Methods:

• Formulating equations of motion for interface height under shear flow.
• Reducing these equations to an anisotropic Burgers equation for various system types.
• Calculating scaling exponents for interface growth and coarsening in arbitrary dimensions.

Main Results:

• The equation of motion for interface height consistently reduces to an anisotropic Burgers equation.
• Exact scaling exponents for coarsening were determined for both conserved and nonconserved dynamics.
• Exponents for fluid-advected conserved order parameters were found, though perturbative support was lacking.

Conclusions:

• The anisotropic Burgers equation provides a unified framework for understanding shear-influenced coarsening.
• Exact scaling exponents offer quantitative predictions for system evolution.
• Further theoretical development is needed to fully support findings for fluid-advected systems.