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Characterizing N-dimensional anisotropic Brownian motion by the distribution of diffusivities
Mario Heidernätsch1, Michael Bauer, Günter Radons
1Technische Universität Chemnitz, Faculty of Sciences, Institute of Physics, Complex Systems and Nonlinear Dynamics, D-09107 Chemnitz, Germany.
The Journal of Chemical Physics
|December 11, 2013
Summary
This study introduces a new method using the distribution of diffusivities to analyze anisotropic diffusion, crucial for understanding biological transport and liquid crystals. The approach effectively distinguishes between isotropic and anisotropic processes from experimental data.
Area of Science:
- Physics
- Biophysics
- Materials Science
Background:
- Anisotropic diffusion is prevalent in biological tissues and liquid crystals.
- The diffusion tensor describes motion in anisotropic systems.
- Mean squared displacement is often insufficient for characterizing multiple diffusion coefficients.
Purpose of the Study:
- To study diffusion in homogeneous anisotropic environments using the distribution of diffusivities.
- To develop analytical expressions for the distribution and its properties.
- To distinguish between isotropic and anisotropic diffusion processes.
Main Methods:
- Derivation of analytical expressions for the distribution of diffusivities.
- Relating distribution properties to an anisotropy measure (mean diffusivity and asymptotic decay).
- Analysis of projected trajectories for experimental relevance.
Main Results:
- Developed analytical expressions for the distribution of diffusivities in anisotropic environments.
- Introduced an anisotropy measure based on mean diffusivity and distribution decay.
- Demonstrated the ability to distinguish isotropic from anisotropic diffusion.
- Derived specific expressions for 2D and 3D anisotropic diffusion, including diffusion tensor determination.
Conclusions:
- The distribution of diffusivities provides a robust method for characterizing anisotropic diffusion.
- The proposed anisotropy measure is experimentally accessible and effective.
- The findings are applicable to real-world systems like biological tissue and liquid crystals.
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