# Homogeneous Cooling with Repulsive and Attractive Long-Range Potentials

Mathematical Modelling of Natural Phenomena (2011)

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

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topMüller, 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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