  The paper considers heat conduction in a model chain of composite particles
with hard core and elastic external shell. Such model mimics three main
features of realistic interatomic potentials - hard repulsive core, quasilinear
behavior in a ground state and possibility of dissociation. It has become clear
recently, that this latter feature has crucial effect on convergence of the
heat conduction coefficient in thermodynamic limit. We demonstrate that in
one-dimensional chain of elastic particles with hard core the heat conduction
coefficient also converges, as one could expect. Then we explore effect of
dimensionality on the heat transport in this model. For this sake, longitudinal
and transversal motions of the particles are allowed in a long narrow channel.
With varying width of the channel, we observe sharp transition from
"one-dimensional" to "two-dimensional" behavior. Namely, the heat conduction
coefficient drops by about order of magnitude for relatively small widening of
the channel. This transition is not unique for the considered system. Similar
phenomenon of transition to quasi-1D behavior with growth of aspect ratio of
the channel is observed also in a gas of densely packed hard (billiard)
particles, both for two- and three-dimensional cases. It is the case despite
the fact that the character of transition in these two systems is not similar,
due to different convergence properties of the heat conductivity. In the
billiard model, the divergence of the heat conduction coefficient smoothly
changes from logarithmic to power-like law with increase of the length.
