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Published on: September 26, 2016
Diffusion of two particles with a finite interaction potential in one dimension
Tobias Ambjörnsson1, Robert J Silbey
1Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA. ambjorn@mit.edu
We solved the Fokker-Planck equation for two interacting diffusing particles. This provides exact results for their dynamics, including overtake and trapping probabilities, validated by simulations.
Area of Science:
- Statistical physics
- Soft matter physics
- Chemical kinetics
Background:
- Understanding particle interactions is crucial in various fields.
- Diffusing particle dynamics are complex, especially with interactions.
- Analytical solutions for multi-particle systems are often challenging.
Purpose of the Study:
- To investigate the dynamics of two interacting diffusing particles.
- To derive exact analytical solutions for their behavior.
- To calculate key probabilities like overtaking and trapping.
Main Methods:
- Solving a 2+1-variate Fokker-Planck equation.
- Obtaining the two-particle conditional probability density function (PDF).
- Utilizing the Gillespie algorithm for stochastic simulations.
Main Results:
- Exact results for the two-particle PDF derived.
- Overtake probability calculated for exchanged particle positions.
- Trapping probability determined for particles near each other.
- Tagged particle PDF investigated for single-particle dynamics.
Conclusions:
- Analytical results show excellent agreement with simulations.
- The study provides a comprehensive framework for two-interacting-particle dynamics.
- This work offers insights into particle behavior in one-dimensional systems.
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