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Towards deterministic equations for Lévy walks: the fractional material derivative
1Institut für Physik, Humboldt-Universität zu Berlin, Invalidenstrasse 110, 10115 Berlin, Germany. igor.sokolov@physik.hu-berlin.de
Summary
Lévy walks, a type of particle motion, are described by a new dynamical formulation. This method accounts for spatiotemporal coupling and is useful for complex systems.
Area of Science:
- Physics
- Stochastic Processes
- Physical Chemistry
Background:
- Lévy walks describe particle motion with broad jump length distributions.
- Spatiotemporal coupling in Lévy walks penalizes long jumps.
Purpose of the Study:
- To derive a generalized dynamical formulation for Lévy walks.
- To provide a framework for describing Lévy walks in external fields.
Main Methods:
- Developed a generalized dynamical formulation for Lévy walks.
- Introduced the fractional equivalent of the material derivative.
Main Results:
- The new formulation offers a robust description of Lévy walks.
- It addresses limitations of continuous time random walk models.
Conclusions:
- The generalized dynamical formulation is a powerful tool for studying Lévy walks.
- This approach is particularly useful for systems with external forces or in phase space.