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Three-dimensional telegrapher's equation and its fractional generalization.

Jaume Masoliver1

  • 1Department of Condensed Matter Physics and Institute of Complex Systems (UBICS), University of Barcelona, Catalonia, Spain.

Physical Review. E
|September 28, 2017
PubMed
Summary

This study introduces a new three-dimensional random walk model to derive the telegrapher

Area of Science:

  • Physics
  • Mathematical Physics
  • Statistical Mechanics

Background:

  • The telegrapher's equation describes signal propagation.
  • Random walk models are used to simulate particle movement.
  • Multistate random walks offer complex movement patterns.

Purpose of the Study:

  • To derive the three-dimensional telegrapher's equation from a random walk model.
  • To generalize the model for fractional anomalous transport.

Main Methods:

  • Developing a three-dimensional multistate random walk with a continuum of spatial directions.
  • Solving general equations for isotropic and uniform walks.
  • Generalizing the model to include fractional anomalous transport.

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Main Results:

  • Successfully derived the three-dimensional telegrapher's equation.
  • Established a framework for fractional anomalous transport in three dimensions.

Conclusions:

  • The random walk model provides a foundation for the three-dimensional telegrapher's equation.
  • The generalized model accommodates complex transport phenomena.