Journal
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
Volume -, Issue -, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1742-5468/2007/08/P08021
Keywords
exact results; granular matter; kinetic theory of gases and liquids; rheology and transport properties
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The Boltzmann equation for inelastic Maxwell models is considered to determine the velocity moments through the fourth degree in the simple shear. flow state. First, the rheological properties ( which are related to the second-degree velocity moments) are exactly evaluated in terms of the coeff. cient of restitution a and the ( reduced) shear rate a*. For a given value of a, the above transport properties decrease with increasing shear rate. Moreover, as expected, the third- degree and the asymmetric fourth- degree moments vanish in the long time limit when they are scaled with the thermal speed. On the other hand, our results show that, for a given value of a, the scaled symmetric fourth- degree moments diverge in time for shear rates larger than a certain critical value a* c ( a) which decreases with increasing dissipation. The explicit shear- rate dependence of the fourth- degree moments below this critical value is also obtained.
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