Aging dynamics of d-dimensional locally activated random walks.

Area of Science:

• Physics
• Biophysics
• Mathematical Biology

Background:

• Random walks are fundamental models for diffusion and movement.
• Living systems exhibit complex movement patterns influenced by local environmental factors.
• Existing models often struggle to capture non-Markovian and aging dynamics.

Purpose of the Study:

• To develop a general analytical framework for locally activated random walks.
• To characterize statistical properties of these random walks on d-dimensional lattices.
• To identify experimental signatures of activated dynamics.

Main Methods:

• Definition of locally activated random walks with modified dynamics at activation sites.
• Analytical framework to determine statistical properties (position, dynamical parameters).
• Application to both passive (diffusive) and active (run and tumble) dynamics.

Main Results:

• Quantification of aging dynamics and potential trapping effects.
• Demonstration of strongly non-Markovian behavior.
• Identification of clear signatures characteristic of activated dynamics.

Conclusions:

• The proposed framework provides a robust method for analyzing complex biological movement.
• Activated random walks offer insights into cell migration and animal foraging behavior.
• The identified signatures can guide experimental data analysis in biophysical systems.