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Fractional telegrapher's equation from fractional persistent random walks.
1Departament de Física Fonamental, Universitat de Barcelona, Diagonal, 647, E-08028 Barcelona, Spain.
Physical Review. E
|June 15, 2016
Summary
This study generalizes the telegrapher's equation for anomalous transport using fractional calculus. The new model reveals distinct subdiffusive and superdiffusive behaviors over time, offering insights into complex particle movement.
Area of Science:
- Physics
- Mathematics
- Physical Chemistry
Background:
- The standard telegrapher's equation models particle transport with finite switching speeds.
- Anomalous transport phenomena deviate from standard Brownian motion, requiring more sophisticated models.
Purpose of the Study:
- To generalize the telegrapher's equation for anomalous transport.
- To introduce a space-time fractional telegrapher's equation.
- To analyze the characteristic function and behaviors of the fractional model.
Main Methods:
- Utilizing the persistent random walk in continuous time formalism.
- Deriving the space-time fractional telegrapher's equation.
- Obtaining and analyzing the characteristic function of the derived process.
Main Results:
- The space-time fractional telegrapher's equation was successfully derived.
- The characteristic function of the fractional process was obtained.
- Distinct behaviors across different time scales were identified, including transitions between subdiffusion and superdiffusion.
Conclusions:
- The generalized fractional telegrapher's equation accurately models anomalous transport.
- The model exhibits complex dynamics, transitioning between different transport regimes over time.
- This framework provides a valuable tool for understanding non-standard particle dynamics.
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