The process of heat conduction in a chain with a periodic potential of nearest-neighbor interaction is investigated by means of molecular dynamics simulation. It is demonstrated that the periodic potential of nearest-neighbor interaction allows one to obtain normal heat conductivity in an isolated one-dimensional chain with conserved momentum. The system exhibits a transition from infinite to normal heat conductivity with the growth of its temperature. The physical reason for normal heat conductivity is the excitation of high-frequency stationary localized rotational modes. These modes absorb the momentum and facilitate locking of the heat flux.

We analyze numerically the thermal conductivity of carbon nanoribbons with ideal and rough edges. We demonstrate that edge disorder can lead to a suppression of thermal conductivity by several orders of magnitude. This effect is associated with the edge-induced Anderson localization and suppression of the phonon transport, and it becomes more pronounced for longer nanoribbons and low temperatures.

Dynamics of topological solitons describing open states in the DNA double helix are studied in the frameworks of the model which takes into account asymmetry of the helix. It is shown that three types of topological solitons can occur in the DNA double chain. Interaction between the solitons, their interactions with the chain inhomogeneities and stability of the solitons with respect to thermal oscillations are investigated.

We study the properties of heat conduction in chains of coupled particles subjected to different anharmonic on-site potentials. Particular emphasis is placed on the role of breathers in saturation of the thermal conductivity for chains with hard anharmonicity. When the chain particles are subject to on-site potentials with soft anharmonicity, we find a characteristic temperature, below which the conductivity decreases but while above which it increases.