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Viscosity in molecular dynamics with periodic boundary conditions
1Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Campus Plaine, Code Postal 231, B-1050 Brussels, Belgium.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 20, 2003
Summary
This study introduces a refined Helfand moment method for calculating viscosity in systems with periodic boundary conditions. The new approach accurately determines viscosity, even for simple systems like hard disks, aligning with established theories.
Area of Science:
- Physics
- Physical Chemistry
- Computational Science
Background:
- Calculating viscosity in systems with periodic boundary conditions presents challenges due to the minimum image convention.
- Existing methods may be affected by ambiguities arising from these boundary conditions.
Purpose of the Study:
- To propose a new definition of the Helfand moment suitable for molecular dynamics simulations with periodic boundary conditions.
- To develop a robust method for viscosity calculation that is unambiguous and accurate.
Main Methods:
- The study employs the Helfand moment method, introducing a novel definition to account for the minimum image convention.
- The proposed method is validated against the Green-Kubo formula and the Alder, Gass, and Wainwright method for hard-ball systems.
Main Results:
- The new Helfand-moment method provides viscosity calculations equivalent to the Green-Kubo formula, free from periodic boundary condition ambiguities.
- For systems of hard disks undergoing elastic collisions, the method yields viscosity coefficients in good agreement with Enskog's theory, even for N=2 disks in hexagonal geometry.
Conclusions:
- The refined Helfand moment method offers a reliable approach for determining viscosity in simulations with periodic boundary conditions.
- This method is particularly effective for simple fluid systems and provides accurate results comparable to established theories.