Time delayed processes in physics, biophysics and archaeology

TL;DR

This paper introduces a hyperbolic partial differential equation framework for modeling transport processes with memory effects across physics, biophysics, and archaeology, unifying diffusion and wave phenomena.

Contribution

It formulates the master equation for transport as a time-delayed hyperbolic PDE, linking diffusion, waves, and memory effects in a unified approach.

Findings

The master equation becomes a generalized Klein-Gordon equation for short times.

The approach applies to particles in microtubules and migrating populations.

Provides a new mathematical framework for processes with memory effects.

Abstract

The motion of particles, where the particles: electrons, ions in microtubules or migrated peoples can be described as the superposition of diffusion and ordered waves. In this paper it is shown that the master equation for transport processes can be formulated as the time delayed hyperbolic partial equation. The equation describes the processes with memory. For characteristic times shorter than the relaxation time the master equation is the generalized Klein - Gordon equation. Key words: hyperbolic transport, microtubules, heat waves, Neolithic migration