The collapse phenomenon in one-dimensional inelastic point particle systems
1999; Elsevier BV; Volume: 132; Issue: 4 Linguagem: Inglês
10.1016/s0167-2789(99)00056-1
ISSN1872-8022
AutoresDario Benedetto, Emanuele Caglioti,
Tópico(s)Stochastic processes and statistical mechanics
ResumoWe consider a one-dimensional system of n inelastic particles on a line, with coefficient of restitution 1−2ε. We prove that if εn≲ln2 no collapses are possible for any initial datum, and we exhibit explicit collapsing solutions for εn≳π. For n=4 we construct a positive measure set of initial data which collapse in a finite time. For n=3 we also consider stochastic perturbations of the system and prove the occurrence of collapses with positive probability if ε is sufficiently close to 1/2. Finally, we consider the limit n→∞ of the exact collapse for n particles, obtaining a collapsing measure solution concentrated into two hydrodynamic profiles.
Referência(s)