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Updated: Aug 11, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
First-passage times for random walks in bounded domains
S Condamin1, O Bénichou, M Moreau
1Laboratoire de Physique Théorique de la Matière Condensée (UMR 7600), case courrier 121, Université Paris 6, France.
We developed a new computational method to calculate first-passage times in confined systems. This method accurately predicts diffusion times and is applicable to various confined media scenarios.
Area of Science:
- Computational physics
- Statistical mechanics
- Diffusion processes
Background:
- First-passage time problems are crucial in understanding diffusion.
- Existing methods often struggle with complex geometries or confined media.
- Accurate calculation of diffusion dynamics is essential in various scientific fields.
Purpose of the Study:
- To introduce a novel computational method for calculating first-passage times.
- To derive and validate accurate expressions for the moments of first-passage time.
- To extend the method to more complex scenarios, including continuous Brownian motion.
Main Methods:
- Development of a novel computational approach for first-passage time calculations.
- Derivation of analytical expressions for the moments of first-passage time.
- Validation through numerical simulations and discussion of the range of validity.
Main Results:
- Accurate expressions for first-passage time moments derived for regular bounded lattices.
- The method's validity and applicability were confirmed by numerical simulations.
- Extension to cases with multiple targets and continuous Brownian motion was achieved.
Conclusions:
- The presented computational method offers accurate predictions for first-passage times in confined media.
- The derived expressions and extensions enhance the understanding of diffusion dynamics.
- These findings are highly relevant for systems involving diffusion in confined environments.
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