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The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
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Continuum percolation expressed in terms of density distributions
Fabian Coupette1, Andreas Härtel1, Tanja Schilling1
1Institute of Physics, University of Freiburg, Hermann-Herder-Straße 3, 79104 Freiburg, Germany.
Physical Review. E
|July 22, 2020
Summary
We developed a new method to calculate connectivity properties in interacting n-body systems. This approach links pair connectedness to nearest-neighbor distributions, simplifying analysis for various systems.
Area of Science:
- Statistical Mechanics
- Computational Physics
Background:
- Understanding connectivity properties in many-body systems is crucial for statistical mechanics.
- Existing methods often struggle with complex interactions and higher dimensions.
Purpose of the Study:
- To present a novel integral equation approach for deriving connectivity properties.
- To establish a relationship between pair connectedness and nearest-neighbor distributions.
Main Methods:
- Formulation of an integral equation connecting pair connectedness and nearest-neighbor distribution.
- Application to one-dimensional systems with nearest-neighbor interactions.
- Extension to include external fields, long-range interactions, and higher dimensions.
Main Results:
- An integral equation relating the pair-correlation function (g) to pair connectedness was derived for 1D systems.
- The method was successfully demonstrated for penetrable and impenetrable spheres.
- The formalism was illustrated for a 3D ideal gas, showing broad applicability.
Conclusions:
- The developed approach offers an efficient way to determine connectivity properties.
- This method is versatile and applicable to diverse systems and dimensions.
- It provides a pathway for analytical solutions when pair-correlation functions are known.
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