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19
Moment inequalities and highenergy tails for Boltzmann equations wiht inelastic interactions
 J. Stat. Phys
, 2004
"... Abstract. We study the highenergy asymptotics of the steady velocity distributions for model systems of granular media in various regimes. The main results obtained are integral estimates of solutions of the hardsphere Boltzmann equations, which imply that the velocity distribution functions f(v) ..."
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Cited by 61 (9 self)
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Abstract. We study the highenergy asymptotics of the steady velocity distributions for model systems of granular media in various regimes. The main results obtained are integral estimates of solutions of the hardsphere Boltzmann equations, which imply that the velocity distribution functions f(v) behave in a certain sense as C exp(−rv  s) for v  large. The values of s, which we call the orders of tails, range from s = 1 to s = 2, depending on the model of external forcing. The method we use is based on the moment inequalities and careful estimating of constants in the integral form of the Povznertype inequalities.
LongTime Asymptotics of Kinetic Models of Granular Flows
 Arch. Rational Mech. Anal
, 2003
"... We analyze the longtime asymptotics of certain onedimensional kinetic models of granular flows, which have been recently introduced in [22] in connection with the quasi elastic limit of a model Boltzmann equation with dissipative collisions and variable coe#cient of restitution. These nonlinear ..."
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Cited by 46 (6 self)
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We analyze the longtime asymptotics of certain onedimensional kinetic models of granular flows, which have been recently introduced in [22] in connection with the quasi elastic limit of a model Boltzmann equation with dissipative collisions and variable coe#cient of restitution. These nonlinear equations, classified as nonlinear friction equations, split naturally into two classes, depending whether their similarity solutions (homogeneous cooling state) extinguish or not in finite time. For both classes, we show uniqueness of the solution by proving decay to zero in the Wasserstein metric of any two solutions with the same mass and mean velocity. Furthermore, if the similarity solution extinguishes in finite time, we prove that any other solution with initially bounded support extinguishes in finite time, by computing explicitly upper bounds for the lifetime of the solution in terms of the length of the support.
Breakdown of the Sonine expansion for the velocity distribution of Granular Gases
, 2005
"... PACS. 51.10.+y – Kinetic and transport theory of gases. ..."
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Cited by 3 (0 self)
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PACS. 51.10.+y – Kinetic and transport theory of gases.
Transient clusters in granular gases
 J. Phys.: Condens. Matter
"... Abstract The most striking phenomenon in the dynamics of granular gases is the formation of clusters and other structures. We investigate a gas of dissipatively colliding particles with a velocity dependent coefficient of restitution where cluster formation occurs as a transient phenomenon. Althoug ..."
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Abstract The most striking phenomenon in the dynamics of granular gases is the formation of clusters and other structures. We investigate a gas of dissipatively colliding particles with a velocity dependent coefficient of restitution where cluster formation occurs as a transient phenomenon. Although for small impact velocity the particles collide elastically, surprisingly the temperature converges to zero.
Kinetic Integrals in the Kinetic Theory of dissipative gases
, 2003
"... Summary. The kinetic theory of gases, including Granular Gases, is based on the Boltzmann equation. Many properties of the gas, from the characteristics of the velocity distribution function to the transport coefficients may be expressed in terms of functions of the collision integral which we call ..."
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Summary. The kinetic theory of gases, including Granular Gases, is based on the Boltzmann equation. Many properties of the gas, from the characteristics of the velocity distribution function to the transport coefficients may be expressed in terms of functions of the collision integral which we call kinetic integrals. Although the evaluation of these functions is conceptually straightforward, technically it is frequently rather cumbersome. We report here a method for the analytical evaluation of kinetic integrals using computer algebra. We apply this method for the computation of some properties of Granular Gases, ranging from the moments of the velocity distribution function to the transport coefficients. For their technical complexity most of these quantities cannot be computed manually. 1
Force Distribution and Comminution in Ball Mills
, 2002
"... The motion of granular material in a ball mill is investigated using molecular dynamics simulations in two dimensions. In agreement with experimental observations by Rothkegel 1 we find that local stresses – and hence the comminution efficiency – are maximal close to the bottom of the container. Thi ..."
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The motion of granular material in a ball mill is investigated using molecular dynamics simulations in two dimensions. In agreement with experimental observations by Rothkegel 1 we find that local stresses – and hence the comminution efficiency – are maximal close to the bottom of the container. This effect will be explained using analysis of statistics of force chains in the material. 1
LONGRANGE INTERACTIONS IN DILUTE GRANULAR SYSTEMS
"... ter verkrijging van de graad van doctor aan de Universiteit Twente, op gezag van de rector magnificus, prof. dr. W.H.M. Zijm, volgens besluit van het College voor Promoties in het openbaar te verdedigen op vrijdag 8 februari 2008 om 13.15 uur door ..."
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ter verkrijging van de graad van doctor aan de Universiteit Twente, op gezag van de rector magnificus, prof. dr. W.H.M. Zijm, volgens besluit van het College voor Promoties in het openbaar te verdedigen op vrijdag 8 februari 2008 om 13.15 uur door
Homogeneous Cooling with Repulsive and Attractive Longrange Interactions
"... Abstract. In granular matter, consisting of discrete particles, longrange interactions imply that each of the particles is interacting with all others. For many charged granular materials with Coulomb repulsion or largescale gravitationally attractive systems, a Molecular Dynamics environment is d ..."
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Abstract. In granular matter, consisting of discrete particles, longrange interactions imply that each of the particles is interacting with all others. For many charged granular materials with Coulomb repulsion or largescale gravitationally attractive systems, a Molecular Dynamics environment is developed. In granular systems with longrange interaction forces and dissipative collisions, both effects can lead to largescale structure formation, whereas already dissipation alone leads to ever growing clusters. For our threedimensional monocharged dissipative homogeneous systems we present the effect of both repulsive and attractive mutual longrange forces and make an attempt to predict the collision frequency and the temperature decay in the system by means of a modified pseudoLiouville operator formalism. The theoretical predictions are in perfect agreement with the simulations, but only in the limit of low density and for not too strong interaction potential enrgy.