The European Physical Journal Special Topics

, Volume 223, Issue 11, pp 2205–2225 | Cite as

Free cooling phase-diagram of hard-spheres with short- and long-range interactions

  • S. Gonzalez
  • A.R. Thornton
  • S. Luding
Part of the following topical collections:
  1. Dynamic Systems: From Statistical Mechanics to Engineering Applications


We study the stability, the clustering and the phase-diagram of free cooling granular gases. The systems consist of mono-disperse particles with additional non-contact (long-range) interactions, and are simulated here by the event-driven molecular dynamics algorithm with discrete (short-range shoulders or wells) potentials (in both 2D and 3D). Astonishingly good agreement is found with a mean field theory, where only the energy dissipation term is modified to account for both repulsive or attractive non-contact interactions. Attractive potentials enhance cooling and structure formation (clustering), whereas repulsive potentials reduce it, as intuition suggests. The system evolution is controlled by a single parameter: the non-contact potential strength scaled by the fluctuation kinetic energy (granular temperature). When this is small, as expected, the classical homogeneous cooling state is found. However, if the effective dissipation is strong enough, structure formation proceeds, before (in the repulsive case) non-contact forces get strong enough to undo the clustering (due to the ongoing dissipation of granular temperature). For both repulsive and attractive potentials, in the homogeneous regime, the cooling shows a universal behaviour when the (inverse) control parameter is used as evolution variable instead of time. The transition to a non-homogeneous regime, as predicted by stability analysis, is affected by both dissipation and potential strength. This can be cast into a phase diagram where the system changes with time, which leaves open many challenges for future research.


Dissipation Rate European Physical Journal Special Topic Granular System Attractive Potential Repulsive Potential 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© EDP Sciences and Springer 2014

Authors and Affiliations

  1. 1.Multiscale Mechanics (MSM), CTW, MESA+, University of TwenteAE EnschedeThe Netherlands
  2. 2.Mathematics of Computational Science, Dept. of Appl. Math., University of TwenteEnschedeThe Netherlands

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