Inelastic Collapse of Three Particles

Details Inelastic Collapse of Three Particles Inelastic Collapse of Three Particles

1996-04-10

arxiv.org/abs/mtrl-th/9604003v1

Physics

Condensed Matter

Materials Science

6 pages, figures on request, accepted by PRE

Scientific paper

10.1103/PhysRevE.54.623

A system of three particles undergoing inelastic collisions in arbitrary spatial dimensions is studied with the aim of establishing the domain of ``inelastic collapse''---an infinite number of collisions which take place in a finite time. Analytic and simulation results show that for a sufficiently small restitution coefficient, $0\leq r<7-4\sqrt{3}\approx 0.072$, collapse can occur. In one dimension, such a collapse is stable against small perturbations within this entire range. In higher dimensions, the collapse can be stable against small variations of initial conditions, within a smaller $r$ range, $0\leq r<9-4\sqrt{5}\approx 0.056$.

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