scholarly journals Automodel solutions for superdiffusive transport by Lévy walks

2019 ◽  
Vol 94 (11) ◽  
pp. 115009 ◽  
Author(s):  
A B Kukushkin ◽  
A A Kulichenko
Keyword(s):  
Lévy Walks ◽  
Superdiffusive Transport

scholarly journals Energetic Particle Superdiffusion in Solar System Plasmas: Which Fractional Transport Equation?

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2368
Author(s):  
Gaetano Zimbardo ◽  
Francesco Malara ◽  
Silvia Perri
Keyword(s):  
Solar System ◽  
Transport Equation ◽  
Pitch Angle ◽  
Energetic Particle ◽  
Time Derivative ◽  
Direction Parallel ◽  
Lévy Walks ◽  
Angle Scattering ◽  
Superdiffusive Transport ◽  
The Magnetic Field

Superdiffusive transport of energetic particles in the solar system and in other plasma environments is often inferred; while this can be described in terms of Lévy walks, a corresponding transport differential equation still calls for investigation. Here, we propose that superdiffusive transport can be described by means of a transport equation for pitch-angle scattering where the time derivative is fractional rather than integer. We show that this simply leads to superdiffusion in the direction parallel to the magnetic field, and we discuss some advantages with respect to approaches based on transport equations with symmetric spatial fractional derivates.

scholarly journals Search via Parallel Lévy Walks on Z2

2021 ◽  
Author(s):  
Andrea Clementi ◽  
Francesco d'Amore ◽  
George Giakkoupis ◽  
Emanuele Natale
Keyword(s):  
Lévy Walks

scholarly journals Experimental observation of superdiffusive transport in random dimer lattices

2013 ◽  
Vol 15 (1) ◽  
pp. 013045 ◽  
Author(s):  
U Naether ◽  
S Stützer ◽  
R A Vicencio ◽  
M I Molina ◽  
A Tünnermann ◽  
...  
Keyword(s):  
Experimental Observation ◽  
Superdiffusive Transport

Densities of scaling limits of coupled continuous time random walks

2016 ◽  
Vol 19 (6) ◽  
Author(s):  
Marcin Magdziarz ◽  
Tomasz Zorawik
Keyword(s):  
Fractional Differential Equations ◽  
Continuous Time ◽  
Stability Index ◽  
Scaling Limits ◽  
Explicit Formulas ◽  
Material Derivative ◽  
Lévy Walks ◽  
Continuous Time Random Walks ◽  
Fractional Differential ◽  
The Stability

AbstractIn this paper we derive explicit formulas for the densities of Lévy walks. Our results cover both jump-first and wait-first scenarios. The obtained densities solve certain fractional differential equations involving fractional material derivative operators. In the particular case, when the stability index is rational, the densities can be represented as an integral of Meijer

scholarly journals Response to Comment on "Levy Walks Evolve Through Interaction Between Movement and Environmental Complexity"

Science ◽  
2012 ◽  
Vol 335 (6071) ◽  
pp. 918-918 ◽  
Author(s):  
M. de Jager ◽  
F. J. Weissing ◽  
P. M. J. Herman ◽  
B. A. Nolet ◽  
J. van de Koppel
Keyword(s):  
Environmental Complexity ◽  
Lévy Walks
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