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The Diffusion of Passive Tracers in Laminar Shear Flow

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Published on: May 1, 2018

Heterogeneous Mean First-Passage Time Scaling in Fractal Media.

Hyun-Myung Chun¹, Sungmin Hwang², Byungnam Kahng³

¹School of Physics, Korea Institute for Advanced Study, Seoul 02455, Korea.

Physical Review Letters

|December 15, 2023

Summary

This summary is machine-generated.

The mean first passage time (MFPT) in disordered media depends on site locations, not just distance. A central "hub" site influences paths, causing crossover scaling in MFPT.

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Area of Science:

Statistical Physics
Complex Systems
Network Science

Background:

The mean first passage time (MFPT) characterizes random walks on disordered media.
On random fractals, MFPT typically follows power-law scaling with distance.

Purpose of the Study:

To investigate the factors influencing MFPT scaling beyond simple distance.
To introduce and quantify the role of site centrality in first passage processes.

Main Methods:

Analysis of random walk dynamics on disordered media.
Introduction of random walk centrality to identify influential sites (hubs).
Numerical simulations on critical percolation clusters in 2D lattices.

Main Results:

MFPT scaling is influenced by site locations, not solely distance.
A high-centrality site (hub) significantly impacts first passage times.
MFPT exhibits crossover scaling, transitioning between direct and hub-detouring paths.

Conclusions:

The location and centrality of sites are crucial for understanding random walk dynamics.
MFPT scaling is a competition between direct and indirect paths via hubs.
Crossover scaling provides a more accurate model for MFPT on disordered media.