  Heat conduction in three-dimenisional nonlinear lattice models is studied
using nonequilibrium molecular dynamics simulations. We employ the FPU model,
in which there exists a nonlinearity in the interaction of biquadratic form. It
is confirmed that the thermal conductivity, the ratio of the energy flux to the
temperature gradient, diverges in systems up to 128x128x256 lattice sites. This
size corresponds to nanoscopic to mesoscopic scales of several tens of
nanometers. From these results, we conjecture that the energy transport in
insulators with perfect crystalline order exhibits anomalous behavior. The
effects of lattice structure, random impurities, and natural length in
interactions are also examined. We find that face-centered cubic (fcc) lattices
display stronger divergence than simple cubic lattices. When impurity sites of
infinitely large mass, which are hence fixed, are randomly distributed, such
divergence vanishes.
