Front propagation in an A→2A, A→3A process in one dimension: velocity, diffusion, and velocity correlations

Area of Science:

• Physics
• Chemical Kinetics
• Statistical Mechanics

Background:

• Reaction-diffusion systems are fundamental to modeling various spatio-temporal phenomena.
• Front propagation in such systems is crucial for understanding pattern formation and dynamics.
• Hard-core interactions introduce complexity not present in simpler models.

Purpose of the Study:

• To investigate front propagation dynamics in a 1D reaction-diffusion model with hard-core interactions.
• To analyze the role of temporal velocity correlations on front dynamics and diffusion coefficients.
• To explore the transition to uncorrelated random walker behavior.

Main Methods:

• Utilizing the leading particle picture to approximate front velocity.
• Employing various approximate analytical methods.
• Comparing analytical results with numerical simulations.
• Investigating the influence of reaction rates (ε, ε(t)) and bare diffusion (D).

Main Results:

• Approximate methods accurately predict front velocity, aligning well with simulations.
• Temporal velocity correlations are identified as critical for accurate diffusion coefficient estimation.
• The sign of ε(t)-D dictates the nature of these temporal correlations.
• Analytical and numerical evidence shows uncorrelated random walker behavior when ε(t)=D.

Conclusions:

• The leading particle picture provides a robust framework for studying front propagation in this system.
• Accurate modeling of front diffusion requires accounting for temporal velocity correlations.
• The system exhibits a transition to simple random walk behavior under specific reaction-diffusion parameter regimes.