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Three-dimensional pattern formation, multiple homogeneous soft modes, and nonlinear dielectric electroconvection
1Department of Physics, Kyoto University, Kyoto 606-8502, Japan.
Summary
Three-dimensional patterns in dissipative systems excite more soft modes than 1D or 2D patterns due to fewer damping boundaries. This study compares analytic techniques for pattern dynamics, using dielectric electroconvection in liquid crystals as a model.
Area of Science:
- Soft matter physics
- Nonlinear dynamics
- Pattern formation
Background:
- Spontaneous pattern formation in extended dissipative systems is common.
- Homogeneous soft modes, or hydrodynamic modes, are often excited.
- Boundary conditions significantly influence pattern dynamics.
Purpose of the Study:
- To compare analytic techniques for deriving pattern dynamics from hydrodynamics.
- To investigate the role of multiple homogeneous soft modes in three-dimensional (3D) systems.
- To model 3D pattern formation using dielectric electroconvection in nematic liquid crystals.
Main Methods:
- Analysis of two analytic techniques for pattern dynamics.
- Application to dielectric electroconvection in nematic liquid crystals as a 3D model.
- Derivation of 3D pattern dynamics, including soft modes.
Main Results:
- Two analytic techniques yield different results for multiple soft modes.
- A 2D description is derived for finite thickness slabs, with limited validity above threshold.
- The transition from 2D to 3D pattern dynamics is analyzed.
Conclusions:
- The range of validity for 2D pattern descriptions is restricted.
- Experimentally testable predictions are made for pattern stability and electric Nusselt numbers.
- Analytic approximations in terms of material parameters are provided for most results.