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Approach to asymptotically diffusive behavior for Brownian particles in media with periodic diffusivities
1Université de Bordeaux and CNRS, Laboratoire Ondes et Matière d'Aquitaine (LOMA), UMR 5798, F-33400 Talence, France.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 24, 2015
Summary
We analyzed Brownian particle diffusion in a medium with periodic local diffusivity. Our findings reveal a linear relationship between mean squared displacement and time, offering insights into effective diffusion constants.
Area of Science:
- Physics
- Physical Chemistry
- Statistical Mechanics
Background:
- Brownian motion describes random particle movement.
- Diffusivity quantifies the rate of this movement.
- Spatially varying diffusivity affects particle dispersion.
Purpose of the Study:
- Analyze mean squared displacement (MSD) for Brownian particles.
- Investigate systems with periodic local diffusivity.
- Understand the asymptotic approach to the diffusive limit.
Main Methods:
- Analysis of mean squared displacement (MSD).
- Application of a Kubo-type formula.
- Modeling of periodic local diffusivity.
Main Results:
- MSD becomes a linear function of time at late times.
- A Kubo-type formula recovers known results for effective diffusion constant D(e).
- A formula for the y-axis intercept of the MSD linear fit is derived.
Conclusions:
- The study provides a framework for understanding diffusion in heterogeneous media.
- The derived formulas offer new insights into effective diffusion constants.
- This work aids in predicting particle dispersion in periodic environments.
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