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Updated: Jan 9, 2026
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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
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Dimensional study of the dynamical arrest in a random Lorentz gas
Yuliang Jin1,2,3, Patrick Charbonneau1,4
1Department of Chemistry, Duke University, Durham, North Carolina 27708, USA.
Summary
This study investigates dynamical arrest in the random Lorentz gas (RLG) across multiple dimensions. Results show standard mode-coupling theory predictions worsen with increasing dimensions, suggesting new approaches are needed.
Area of Science:
- Physics
- Statistical Mechanics
- Complex Systems
Background:
- The random Lorentz gas (RLG) models transport in heterogeneous media.
- RLG exhibits subdiffusion and dynamical arrest as obstacle density increases.
- Dynamical arrest in RLG relates to void percolation and glass transitions.
Purpose of the Study:
- To investigate the dimensional dependence of dynamical arrest in the random Lorentz gas.
- To compare numerical results with standard mode-coupling theory predictions.
- To clarify discrepancies and improve theoretical understanding of dynamical arrest.
Main Methods:
- Numerical determination of dynamical arrest in dimensions d=2-6.
- Mapping RLG arrest to void percolation for Poisson-distributed obstacles.
- Relating RLG arrest to the dynamic glass transition of the Mari-Kurchan model.
Main Results:
- Dynamical arrest was numerically determined for dimensions 2 through 6.
- Mode-coupling theory predictions for dynamical arrest become less accurate with increasing dimensionality.
- An improved dimensional scaling form and geometrical upper bound for arrest were extracted.
Conclusions:
- Standard mode-coupling theory faces increasing challenges with higher dimensions in RLG.
- Understanding RLG asymptotic behavior is crucial for addressing limitations in mode-coupling theory of glasses.
- The study provides a refined understanding of dynamical arrest and its theoretical underpinnings.
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