Emergence of pulled fronts in fermionic microscopic particle models.

Area of Science:

• Physics
• Chemistry
• Mathematical Biology

Background:

• Reaction-diffusion processes are fundamental to many natural phenomena.
• The Fisher-Kolmogorov-Petrovsky-Piscounov (FKPP) equation models these processes.
• Microscopic details and fluctuations can influence macroscopic behavior.

Purpose of the Study:

• To investigate the emergence and dynamics of pulled fronts in a microscopic reaction-diffusion model.
• To identify the key parameter controlling fluctuations in the lattice-based A+A<-->A reaction-diffusion system.
• To compare the microscopic model's behavior with the deterministic FKPP equation.

Main Methods:

• Simulating a microscopic reaction-diffusion process (A+A<-->A) on a lattice with a one-particle-per-site constraint.
• Identifying and manipulating the parameter representing particles per correlated volume to control internal fluctuations.
• Analyzing the conditions under which the microscopic model aligns with the FKPP equation.

Main Results:

• The number of particles per correlated volume was identified as the critical parameter for internal fluctuations.
• When internal fluctuations were suppressed, the microscopic model's front dynamics closely matched the FKPP equation.
• This confirms the FKPP equation's validity under specific microscopic conditions.

Conclusions:

• The FKPP equation accurately describes pulled fronts in microscopic reaction-diffusion systems when internal fluctuations are minimal.
• The study highlights the importance of considering fluctuation strength in reaction-diffusion modeling.
• This work bridges the gap between microscopic particle-based simulations and macroscopic continuum models.