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Fabrication, Operation and Flow Visualization in Surface-acoustic-wave-driven Acoustic-counterflow Microfluidics
Published on: August 27, 2013
Front propagation and pattern formation in anisotropic bistable media
1Max-Planck-Institut fur Physik komplexer Systeme, Nothnitzer Strasse 38, 01187 Dresden, Germany and The Blaustein Institute for Desert Research and the Physics Department, Ben-Gurion University, Sede Boker Campus 84990, Israel.
Summary
Diffusion anisotropy significantly impacts pattern formation in bistable media. It can lead to ordered stripes or a unique state of one-dimensional spatiotemporal chaos, termed stratified chaos.
Area of Science:
- Complex Systems
- Nonlinear Dynamics
- Mathematical Biology
Background:
- Reaction-diffusion systems are fundamental to modeling pattern formation in various scientific fields.
- Diffusion anisotropy, where diffusion rates differ along different directions, can introduce complex behaviors not seen in isotropic systems.
- Understanding these effects is crucial for predicting pattern evolution in anisotropic media.
Purpose of the Study:
- To investigate the influence of diffusion anisotropy on pattern formation within bistable media.
- To identify and characterize novel spatiotemporal patterns arising from anisotropic diffusion.
- To explore the relationship between front velocity, curvature, and anisotropy.
Main Methods:
- Utilized the FitzHugh-Nagumo reaction-diffusion model to simulate pattern dynamics.
- Derived a mathematical relation connecting front normal velocity and curvature.
- Analyzed the resulting spatiotemporal patterns across a range of parameters.
Main Results:
- Diffusion anisotropy was found to induce an ordering effect, promoting stationary or breathing periodic stripes aligned with principal axes.
- In specific parameter regimes, anisotropy led to the emergence of spatiotemporal chaos confined to one dimension, termed 'stratified chaos'.
- Distinct spatiotemporal patterns were identified and characterized based on the derived velocity-curvature relation.
Conclusions:
- Diffusion anisotropy plays a critical role in shaping pattern formation in bistable reaction-diffusion systems.
- Anisotropy can stabilize patterns into ordered states or destabilize them into complex chaotic dynamics.
- The study introduces 'stratified chaos' as a novel phenomenon driven by diffusion anisotropy in one spatial dimension.
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