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Related Experiment Video

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Self-Assembly of Microtubule Tactoids

Self-Assembly of Microtubule Tactoids

Published on: June 23, 2022

Random Walk on T-Fractal with Stochastic Resetting.

Xiaohan Sun¹, Anlin Li¹, Shaoxiang Zhu²

¹School of Mathematical Science, Jiangsu University, Zhenjiang 212013, China.

Entropy (Basel, Switzerland)

|January 8, 2025

Summary

Stochastic resetting enhances random walk search efficiency on T-fractal networks. Optimal resetting strategies significantly reduce mean first passage time, especially in larger networks.

Keywords:

T-fractal first passage time generating function random walk stochastic resetting

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Area of Science:

Physics
Complex Systems
Network Science

Background:

Random walks are fundamental models for transport and search processes.
Fractal networks exhibit complex topological properties influencing diffusion dynamics.
Stochastic resetting is a strategy to potentially enhance search efficiency.

Purpose of the Study:

To investigate the effect of stochastic resetting on random walks on a T-fractal network.
To determine the optimal resetting probability that minimizes mean first passage time.
To compare search efficiency with and without resetting.

Main Methods:

Utilized the generating function technique to analyze first passage time distributions.
Derived a recursive relation for the generating function of first passage time.
Calculated the mean first passage time (MFPT) with and without resetting.

Main Results:

Established a relationship between MFPT with resetting and the generating function of FPT without resetting.
Identified optimal resetting probabilities (γ*) for various scenarios.
Demonstrated that stochastic resetting significantly improves search efficiency, particularly for larger networks.

Conclusions:

Stochastic resetting is a powerful strategy for optimizing search processes in complex fractal networks.
The findings offer insights into improving search efficiency in diverse applications.
This study provides a theoretical framework for understanding resetting dynamics on fractal structures.