Homogeneous Cooling with Repulsive and Attractive Long-Range Potentials

M. K. Müller; S. Luding

Mathematical Modelling of Natural Phenomena (2011)

  • Volume: 6, Issue: 4, page 118-150
  • ISSN: 0973-5348

Abstract

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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.

How to cite

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Müller, M. K., and Luding, S.. "Homogeneous Cooling with Repulsive and Attractive Long-Range Potentials." Mathematical Modelling of Natural Phenomena 6.4 (2011): 118-150. <http://eudml.org/doc/222401>.

@article{Müller2011,
abstract = {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.},
author = {Müller, M. K., Luding, S.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {granular gas; hydrodynamics; long-range forces; numerical simulations},
language = {eng},
month = {7},
number = {4},
pages = {118-150},
publisher = {EDP Sciences},
title = {Homogeneous Cooling with Repulsive and Attractive Long-Range Potentials},
url = {http://eudml.org/doc/222401},
volume = {6},
year = {2011},
}

TY - JOUR
AU - Müller, M. K.
AU - Luding, S.
TI - Homogeneous Cooling with Repulsive and Attractive Long-Range Potentials
JO - Mathematical Modelling of Natural Phenomena
DA - 2011/7//
PB - EDP Sciences
VL - 6
IS - 4
SP - 118
EP - 150
AB - 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.
LA - eng
KW - granular gas; hydrodynamics; long-range forces; numerical simulations
UR - http://eudml.org/doc/222401
ER -

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