Homogeneous Cooling with Repulsive and Attractive Long-Range Potentials

M. K. Müller¹ ; S. Luding¹

¹ Multi Scale Mechanics, CTW, UTwente, P. O. Box 217, 7500 AE Enschede, Netherlands

Mathematical modelling of natural phenomena, Tome 6 (2011) no. 4, pp. 118-150.

Résumé

The interplay between dissipation and long-range repulsive/attractive forces in homogeneous, dilute, mono-disperse particle systems is studied. The pseudo-Liouville operator formalism, originally introduced for hard-sphere interactions, is modified such that it provides very good predictions for systems with weak long-range forces at low densities, with the ratio of potential to fluctuation kinetic energy as control parameter. By numerical simulations, the theoretical results are generalized with empirical, density dependent correction-functions up to moderate densities.The main result of this study on dissipative cooling is an analytical prediction for the reduced cooling rate due to repulsive forces and for the increased rate due to attractive forces. In the latter case, surprisingly, for intermediate densities, similar cooling behavior is observed as in systems without long-range interactions. In the attractive case, in general, dissipation leads to inhomogeneities earlier and faster than in the repulsive case.

Détail

DOI : 10.1051/mmnp/20116406

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