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Front propagation in one-dimensional spatially periodic bistable media
Jakob Löber1, Markus Bär, Harald Engel
1Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 2, 2013
Summary
This study analyzes front propagation in heterogeneous media using the Schlögl model. Perturbative methods reveal how spatial modulations affect front speed, predicting phenomena like velocity overshoot and propagation failure.
Area of Science:
- Chemical kinetics
- Reaction-diffusion systems
- Nonlinear dynamics
Background:
- Front propagation in heterogeneous media is crucial in various scientific fields.
- The Schlögl model provides a framework for studying bistable systems.
- Understanding the impact of spatial parameter modulations is key.
Purpose of the Study:
- To investigate front propagation dynamics in heterogeneous bistable media.
- To develop an analytical model for predicting front behavior under periodic modulations.
- To compare analytical predictions with numerical simulations.
Main Methods:
- Utilized the Schlögl model for a representative bistable system.
- Applied singular perturbation techniques to derive an ordinary differential equation for front position.
- Analyzed the dependence of propagation speed on heterogeneity characteristics (L/l) and modulation amplitude.
Main Results:
- Derived an analytical equation for front propagation in heterogeneous media.
- Predicted phenomena such as velocity overshoot and propagation failure.
- Achieved quantitative agreement between analytical results and numerical simulations for large spatial periods.
Conclusions:
- The developed analytical model accurately describes front propagation in heterogeneous bistable media.
- Singular perturbation techniques are effective for this class of problems.
- The study provides insights into the complex behavior of reaction-diffusion fronts in modulated environments.
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