Mean squared displacement in a generalized Lévy walk model

Area of Science:

• Stochastic processes
• Statistical physics
• Turbulence modeling

Background:

• Lévy walks are stochastic models with diverse applications.
• The Richardson law describes turbulent dispersion.
• Previous work challenged the Richardson regime in original Lévy walk models due to MSD divergence.

Purpose of the Study:

• Investigate a generalized Lévy walk model.
• Analyze the mean squared displacement (MSD) behavior.
• Determine conditions for MSD existence or divergence.

Main Methods:

• Detailed investigation of ensemble MSD.
• Comparison with the original Lévy walk model.
• Analysis of ordinary and aged situations.

Main Results:

• The generalized model's MSD behavior matches the original model where it exists.
• Identified conditions under which the MSD exists or diverges.
• The generalized model interpolates between original and Drude-like models.

Conclusions:

• The generalized Lévy walk model provides a more robust framework for studying phenomena like turbulent dispersion.
• Understanding MSD behavior is crucial for accurate modeling of physical processes.
• This work resolves ambiguities regarding the Richardson regime in Lévy walk models.