Truncation effects in superdiffusive front propagation with Lévy flights

Area of Science:

• Mathematical Physics
• Nonlinear Dynamics
• Statistical Mechanics

Background:

• Reaction-diffusion systems model phenomena from population dynamics to chemical reactions.
• Superdiffusion, driven by non-local transport, leads to faster-than-diffusive spread.
• Lévy flights are a key model for superdiffusive anomalous transport.

Purpose of the Study:

• Investigate the impact of exponentially truncated Lévy flights on reaction-diffusion fronts.
• Analyze the transition from superdiffusion to slower propagation regimes.
• Characterize the asymptotic behavior of front velocity and tail decay.

Main Methods:

• Numerical and analytical study of a modified Fisher-Kolmogorov equation.
• Incorporation of a lambda-truncated fractional derivative to model truncated Lévy flights.
• Analysis of front propagation dynamics under different truncation regimes.

Main Results:

• Truncated Lévy flights lead to tempered decay of front tails and transient acceleration.
• Front velocity approaches a terminal speed algebraically in the intermediate asymptotic regime.
• An overtruncated regime exhibits exponential tails and constant front velocity.

Conclusions:

• Exponential truncation fundamentally alters front propagation in reaction-diffusion systems.
• The transition from superdiffusion to tempered decay introduces novel dynamics.
• The study provides insights into anomalous transport effects in complex systems.