  Heat conduction in 1-dimensional anharmonic systems is anomalous in the sense
that the conductivity \kappa scales with a positive power of the system size,
\kappa ~ L^\alpha. In two dimensions, previous simulations and theoretical
arguments gave a logarithmic divergence. For rectangular systems of size L_\| x
L_\perp there should be a cross-over from the 2-d to the 1-d behaviour as the
aspect ratio r = L_\| / L_\perp increases from r=1 to r >> 1. When taking
periodic boundary conditions in the transverse direction, this should be of
direct relevance for the heat conduction in single-walled carbon nanotubes. In
particular, one expects that k nanotubes of diameter R should conduct heat
better than a single nanotube of the same length and of radius kR. We study
this cross-over numerically by simulating the Fermi-Pasta-Ulam model. Apart
from giving a precise estimate of the exponent \alpha, our most intriguing
results are that the divergence does not seem to be logarithmic in d=2 but also
power-like, and that the cross-over does not happen at a fixed aspect ratio.
Instead, it happens at r=r^* with r^* -> \infty for L -> \infty.
