  The paper is concerned with the problem of toppling propagation velocity in
elastic, domino-like mechanical systems. We build on the work of Efthimiou and
Johnson, who developed the theory of perfectly elastic collisions of thin rigid
dominoes on a frictional foundation. This theory has been criticised for the
lack of correspondence with the experimental observations, in particular,
prediction of infinite propagation velocity for zero spacing between dominoes,
as well as the inability to represent the collective nature of collisions in
real domino systems. In our work we consider a more realistic scenario of
dominoes of finite stiffness and obtain a theory of fast elastic domino waves,
taking into account a limit velocity of the perturbation propagation in the
system of dominoes. Moreover, finite collision time allows to extract dynamic
quantities of collisions and establish upper and lower borders for domino
separations where the theory could still be applied. Our discrete element
simulations support our theoretical findings and shed light on the nature of
collective interactions in the nearly-elastic domino chains.
