# Stable algorithm for event detection in event-driven particle dynamics: logical states

## Abstract

Following the recent development of a stable event-detection algorithm for hard-sphere systems, the implications of more complex interaction models are examined. The relative location of particles leads to ambiguity when it is used to determine the interaction state of a particle in stepped potentials, such as the square-well model. To correctly predict the next event in these systems, the concept of an additional state that is tracked separately from the particle position is introduced and integrated into the stable algorithm for event detection.

## Keywords

DEM Event-driven Molecular dynamics Square well Stepped potential Collision detection## Notes

### Acknowledgments

The authors gratefully acknowledge the support of the German Research Foundation (DFG) through the Cluster of Excellence ‘Engineering of Advanced Materials’ at the University of Erlangen-Nuremberg and through Grant Po 472/25.

## References

- 1.Alder BJ, Wainwright TE (1959) Studies in molecular dynamics. 1. General method. J Chem Phys 31(2):459–466. doi: 10.1063/1.1730376 MathSciNetCrossRefGoogle Scholar
- 2.Bannerman MN, Lue L, Woodcock LV (2010) Thermodynamic pressures for hard spheres and closed-virial equation-of-state. J Chem Phys 132:084,507. doi: 10.1063/1.3328823 CrossRefGoogle Scholar
- 3.Bannerman MN, Sargant R, Lue L (2011) Dynamo: A free O(N) general event-driven simulator. J Comp Chem 32:3329–3338. doi: 10.1002/jcc.21915
- 4.Bannerman MN, Strobl S, Formella A, Pöschel T (2014) Stable algorithm for event detection in event-driven particle dynamics. Comp Part Mech 1:1–2. doi: 10.1007/s40571-014-0021-8 CrossRefGoogle Scholar
- 5.Frenkel D, Maguire JF (1983) Molecular dynamics study of the dynamical properties of an assembly of infinitely thin hard rods. Mol Phys 49(3):503–541. doi: 10.1080/00268978300101331 CrossRefGoogle Scholar
- 6.Marín M, Risso D, Cordero P (1993) Efficient algorithms for many-body hard particle molecular-dynamics. J Comput Phys 109(2):306–317. doi: 10.1006/jcph.1993.1219
- 7.Pöschel T, Schwager T (2005) Computational granular dynamics. Springer, Berlin. doi: 10.1007/3-540-27720-X Google Scholar
- 8.Rapaport DC (1980) Event scheduling problem in molecular dynamics simulation. J Comput Phys 34(2):184–201. doi: 10.1016/0021-9991(80)90104-7 MathSciNetCrossRefGoogle Scholar
- 9.Schultz AJ, Kofke DA (2015) Etomica: an object-oriented framework for molecular simulation. J Comput Chem 36(8):573–583. doi: 10.1002/jcc.23823 CrossRefGoogle Scholar
- 10.Thomson C, Lue L, Bannerman MN (2014) Mapping continuous potentials to discrete forms. J Chem Phys 140:034,105. doi: 10.1063/1.4861669 CrossRefGoogle Scholar