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Related Experiment Video

Updated: May 23, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

Delayed uncoupled continuous-time random walks do not provide a model for the telegraph equation.

S A Rukolaine¹, A M Samsonov

¹The Ioffe Physical Technical Institute of the Russian Academy of Sciences, 26 Polytekhnicheskaya, St. Petersburg 194021, Russia. rukol@ammp.ioffe.ru

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|April 3, 2012

Summary

Delayed continuous-time random walks (DCTRWs) do not model the one-dimensional telegraph equation. The diffusion equation better approximates DCTRWs than the telegraph equation, challenging previous assumptions.

Related Experiment Videos

Last Updated: May 23, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

Area of Science:

Physics
Mathematical Modeling
Stochastic Processes

Background:

Delayed continuous-time random walks (DCTRWs) have been proposed as a microscopic model for the one-dimensional telegraph equation.
This proposition is questionable due to the infinite particle velocity in DCTRWs versus the finite propagation speed in the telegraph equation.

Purpose of the Study:

To investigate the accuracy of the telegraph equation as an approximation for DCTRWs.
To compare the approximation quality of the diffusion equation and the telegraph equation for DCTRWs.

Main Methods:

Analysis of the mathematical relationship between DCTRWs, the telegraph equation, and the diffusion equation.
Evaluation of approximation accuracy using the L(2) norm.

Main Results:

The diffusion equation provides a better L(2) norm approximation to DCTRWs compared to the telegraph equation.
The study demonstrates that the telegraph equation is not an accurate microscopic model for DCTRWs.

Conclusions:

Delayed continuous-time random walks (DCTRWs) do not offer a correct microscopic interpretation of the one-dimensional telegraph equation.
The kinetic model of the telegraph equation is distinct from models based on DCTRWs.