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RBDT: A Computerized Task System based in Transposition for the Continuous Analysis of Relational Behavior Dynamics in Humans

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Published on: July 17, 2021

Two-dimensional telegraphic processes and their fractional generalizations.

Jaume Masoliver¹, Katja Lindenberg²

¹Department of Condensed Matter Physics and Institute of Complex Systems (UBICS), University of Barcelona, 08028 Catalonia, Spain.

Physical Review. E

|February 20, 2020

Summary

This summary is machine-generated.

This study derives the two-dimensional telegrapher's equation for planar motion using a random walk model. Fractional motions are also incorporated, highlighting the need for dimension-specific models.

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Area of Science:

Physics
Mathematical Physics

Background:

Telegrapher's equation describes random processes.
Previous work addressed 1D and 3D versions.

Purpose of the Study:

Derive the 2D telegrapher's equation for planar motion.
Generalize to include planar fractional motions.
Investigate dimensional independence of models.

Main Methods:

Utilized a 2D random walk model with a continuum of states.
Adapted multistate random walk for spatial directions.
Extended isotropic models and equations for fractional dynamics.

Main Results:

Successfully derived the 2D telegrapher's equation.
Incorporated planar fractional motions into the model.
Confirmed that 2D models cannot be derived from 1D or 3D counterparts.

Conclusions:

Each spatial dimension requires a unique random walk model.
The derived 2D telegrapher's equation is specific to planar motion.
The study advances understanding of fractional telegraphic processes in 2D.