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Updated: Aug 6, 2026
08:01
The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
First-passage-time properties of diffusion with a broad class of stochastic diffusion coefficients
Go Uchida1,2, Hiromi Miyoshi1, Hitoshi Washizu2
1Tokyo Metropolitan University, Department of Mechanical Systems Engineering, Tokyo 1920397, Japan.
Physical Review. E
|July 24, 2026
Summary
Stochastic diffusion coefficients (DCs) enhance particle transport efficiency to boundaries. Fluctuations in DCs are crucial for efficient transport, especially in complex systems like single-molecule reactions.
Area of Science:
- Statistical Physics
- Physical Chemistry
- Biophysics
Background:
- Particle diffusion is fundamental across scientific disciplines.
- Understanding diffusion in heterogeneous environments is challenging.
- First-passage-time (FPT) properties quantify particle arrival times.
Purpose of the Study:
- Investigate FPT properties for particles with stochastic diffusion coefficients (DCs).
- Analyze the impact of DC fluctuations on transport efficiency.
- Compare FPT behavior in 1D and 3D diffusion scenarios.
Main Methods:
- Theoretical analysis of FPT properties for stochastic DCs.
- Mathematical modeling of diffusion in semi-infinite and spherical domains.
- Investigation of ergodic and non-ergodic DC properties.
Main Results:
- Particles with stochastic DCs exhibit enhanced early arrival efficiency compared to constant DCs.
- A larger supremum of stochastic DCs leads to more efficient transport.
- For ergodic DCs, mean FPT diverges, early-arrival enhancement diminishes over time, and FPT distribution converges to Lévy-Smirnov.
Conclusions:
- Fluctuations in diffusion coefficients are critical for efficient particle transport to distant targets.
- Non-Markovian or non-ergodic DCs may be necessary for optimal transport.
- Findings have implications for diffusion-limited reactions in physics, chemistry, and biology.
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