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Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials
Published on: September 26, 2014
Density and concentration field description of nonperiodic structures
1Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA. menzel@mpipmainz.mpg.de
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 21, 2011
Summary
We developed a new energy functional for modeling localized textures. This model captures stripe pattern evolution and has applications in polymer and vesicle dynamics.
Area of Science:
- Physics
- Materials Science
- Applied Mathematics
Background:
- Continuum field models are essential for describing complex material behaviors.
- Nonperiodic and localized textures present challenges for existing models.
- Understanding pattern formation and evolution is crucial in various scientific domains.
Purpose of the Study:
- To introduce a novel nonlocal energy functional for characterizing nonperiodic and localized textures.
- To investigate the kinetic evolution and scaling behavior of stripe patterns generated by this functional.
- To explore the functional's applicability to polymeric systems and vesicle dynamics.
Main Methods:
- Development of a phenomenological energy functional based on pairwise, direction-dependent interactions of field gradients.
- Numerical minimization of the proposed functional.
- Analysis of kinetic evolution, coarse-graining, and defect dynamics.
- Application and validation using simulations of polymeric systems and vesicle behavior.
Main Results:
- The functional successfully generates threadlike stripe patterns from disordered states.
- Observed coarse-graining exhibits scaling behavior consistent with the Cahn-Hilliard equation.
- A modified model allows for nonperiodic stripe phases and analysis of defect evolution.
- Simulations reproduce key behaviors of vesicles, such as tank treading and parachute folding.
Conclusions:
- The proposed nonlocal energy functional offers a versatile tool for continuum field characterization of localized textures.
- The model provides insights into pattern formation, scaling laws, and defect dynamics.
- Its demonstrated applicability to polymers and vesicles highlights its potential for diverse scientific investigations.
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