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Advective-diffusive motion on large scales from small-scale dynamics with an internal symmetry
Raffaele Marino1, Erik Aurell2
1NORDITA, Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden.
Physical Review. E
|July 15, 2016
Summary
This study analyzes coupled diffusions on manifolds, revealing effective advective-diffusive motion. The research determines effective drift and diffusion using multiscale analysis and solvability conditions.
Area of Science:
- Mathematical Physics
- Statistical Mechanics
- Differential Geometry
Background:
- Coupled diffusions are fundamental in modeling transport phenomena.
- Understanding large-scale effective motion from microscopic dynamics is crucial.
- Manifold-based diffusions present unique analytical challenges.
Purpose of the Study:
- To analyze coupled diffusions in n-dimensional spaces and on compact manifolds.
- To derive the effective advective-diffusive motion on large scales.
- To generalize and extend existing results for specific group manifolds.
Main Methods:
- Multiscale analysis to determine effective drift and diffusion.
- Application of solvability conditions.
- Utilizing local charts and invariance arguments for detailed analysis.
Main Results:
- Effective drift and diffusion are determined via solvability conditions.
- Examples on SO(3) and SU(2) group manifolds illustrate the framework.
- Diffusion on SU(2) is shown to be generally more isotropic due to global solvability conditions.
Conclusions:
- The multiscale analysis provides a robust method for characterizing effective diffusion on manifolds.
- Global properties of solvability conditions significantly influence diffusion behavior.
- The framework offers a generalized approach to advective-diffusive motion in complex spaces.
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