Asymptotic front behavior in an A + B → 2A reaction under subdiffusion.

Area of Science:

• Chemical kinetics
• Reaction-diffusion systems
• Subdiffusion phenomena

Background:

• Front propagation is crucial in reaction-diffusion systems.
• Subdiffusion, characterized by heavy-tailed waiting times, alters standard diffusion behavior.
• Understanding reaction dynamics under anomalous diffusion is key.

Purpose of the Study:

• To investigate front propagation in the A + B → 2A reaction under subdiffusion conditions.
• To identify and characterize different scaling regimes of front propagation.
• To compare subdiffusive front behavior with continuous models.

Main Methods:

• Modeling subdiffusion using continuous-time random walks (CTRWs) with power-law waiting times.
• Employing a crossover argument to analyze scaling regimes.
• Solving the continuous reaction-subdiffusion equation.

Main Results:

• Two distinct scaling regimes for front propagation were identified.
• An intermediate regime matches the continuous equation solution, while the final regime is fluctuation-dominated.
• The continuous description breaks down at later times, showing atomically sharp fronts.
• Subdiffusive front velocities decay faster than predicted by continuous models.

Conclusions:

• Subdiffusion significantly impacts front propagation dynamics.
• Continuous models fail to capture late-stage front behavior under subdiffusion.
• Fluctuations play a dominant role in the final asymptotic regime of front propagation.