Inelastic collapse and near-wall localization of randomly accelerated particles.
Inelastic collapse of stochastic trajectories of a randomly accelerated particle moving in half-space z>0 has been discovered by McKean [J. Math. Kyoto Univ. 2, 227 (1963)] and then independently rediscovered by Cornell et al. [Phys. Rev. Lett. 81, 1142 (1998)PRLTAO0031-900710.1103/PhysRevLett.81.1142]. The essence of this phenomenon is that the particle arrives at the wall at z=0 with zero velocity after an infinite number of inelastic collisions if the restitution coefficient β of particle velocity is smaller than the critical value β_{c}=exp(-π/sqrt[3]). We demonstrate that inelastic collapse takes place also in a wide class of models with spatially inhomogeneous random forcing and, what is more, that the critical value β_{c} is universal. That class includes an important case of inertial particles in wall-bounded random flows. To establish how inelastic collapse influences the particle distribution, we derive the exact equilibrium probability density function ρ(z,v) for the particle position and velocity. The equilibrium distribution exists only at β<β_{c} and indicates that inelastic collapse does not necessarily imply near-wall localization.
Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Russia.|Landau Institute for Theoretical Physics of the RAS, 142432 Chernogolovka, Russia.
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Belan
Institute of Automation and Electrometry SB of the RAS, 630090 Novosibirsk, Russia.|Novosibirsk State University, Novosibirsk 630073, Russia.
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Chernykh
Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Russia.|Landau Institute for Theoretical Physics of the RAS, 142432 Chernogolovka, Russia.
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Lebedev
Weizmann Institute of Science, Rehovot 76100, Israel.|Institute for Information Transmission Problems, 127994 Moscow, Russia.
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Falkovich