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The Diffusion of Passive Tracers in Laminar Shear Flow

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Truncation effects in superdiffusive front propagation with Lévy flights.

D Del-Castillo-Negrete¹

¹Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-8071, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|April 28, 2009

Summary

This summary is machine-generated.

Exponentially truncated Lévy flights modify reaction-diffusion fronts, leading to tempered decay and transient acceleration. Front velocity approaches a terminal speed algebraically, unlike the exponential convergence in the diffusive case.

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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.