Effective medium approach for heterogeneous reaction-diffusion media.

Area of Science:

• Physical Chemistry
• Chemical Physics
• Complex Systems

Background:

• Reaction-diffusion systems are fundamental to many natural phenomena.
• Modeling heterogeneity in these systems is crucial for accurate predictions.
• Existing theories may struggle with diverse heterogeneity types and scales.

Purpose of the Study:

• To develop and validate an effective medium theory for random heterogeneous reaction-diffusion systems.
• To assess the theory's accuracy across various heterogeneity types and diffusion lengths.
• To compare theoretical predictions with computational simulations.

Main Methods:

• Development of an effective medium theory for diffusion and reaction rates.
• Spatially distributed simulations of reaction-diffusion systems with varying heterogeneity.
• Comparison of theoretical predictions with simulation results, focusing on front velocity in bistable media.

Main Results:

• The theory shows quantitative agreement with simulations when diffusion lengths in heterogeneities are large compared to the front width.
• Agreement is dependent on the specific type of heterogeneity when diffusion lengths are small.
• The theory's predictions were also compared against systems with regular and temporal disorder.

Conclusions:

• The effective medium theory provides a valuable tool for analyzing heterogeneous reaction-diffusion systems.
• The theory's predictive power is strongly influenced by the scale of diffusion within heterogeneities relative to system dynamics.
• Further investigation is needed for systems with complex or small-scale heterogeneities.