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.

We provide molecular-dynamics simulation of heat transport in one-dimensional molecular chains with different interparticle pair potentials. We show that the thermal conductivity is finite in the thermodynamic limit in chains with the potentials that allow for bond dissociation. The Lennard-Jones, Morse, and Coulomb potentials are such potentials. The convergence of the thermal conductivity is provided by phonon scattering on the locally strongly stretched loose interatomic bonds at low temperature and by the many-particle scattering at high temperature. On the other hand, chains with a confining pair potential, which does not allow for bond dissociation, possess anomalous thermal conductivity, diverging with the chain length. We emphasize that chains with a symmetric or asymmetric Fermi-Pasta-Ulam potential or with combined potentials, containing a parabolic and/or a quartic confining potential, all exhibit anomalous heat transport.

We study moving topological solitons (kinks and antikinks) in the nonlinear Klein-Gordon chain. These solitons are shown to exist with both monotonic (non-oscillating) and oscillating asymptotics (tails). Using the pseudo-spectral method, the (anti)kink solutions with oscillating background (so-called nanopterons) are found as travelling waves of permanent profile propagating with constant velocity. Each of these solutions may be considered as a bound state of an (anti)kink with a background nonlinear periodic wave, so that the wave "pushes" the (anti)kink over the Peierls-Nabarro barrier. The stability of these bound states is confirmed numerically. Travelling-wave solutions of permanent profile are shown to exist depending on the convexity of the on-site (substrate) potential. The set of velocities at which the (anti)kinks with monotonic asymptotics propagate freely is calculated. We also find moving non-oscillating (anti)kink profiles with higher topological charges, each of which appears to be the bound state of (anti)kinks with lower topological charge (|Q| = 1).

We study numerically the thermal conductivity of single-walled carbon nanotubes for the cases of an isolated nanotube and a nanotube interacting with a substrate. We employ two different numerical methods: ͑i͒ direct modeling of the heat transfer by molecular-dynamics simulations and ͑ii͒ analysis of the equilibrium dynamics by means of the Green-Kubo formalism. For the numerical modeling of the effective interatomic interactions, we employ both the Brenner potentials and the intermolecular potentials used in the study of the dynamics of large macromolecules. We demonstrate that, quite independently of the methods employed and the potentials used, the character of the thermal conductivity depends crucially on the interaction between a nanotube and a substrate. While an isolated nanotube demonstrates anomalous thermal conductivity due to ballistic transport of long-wave acoustic phonons, the nanotube interacting with a flat substrate displays normal thermal conductivity due to both the appearance of a gap in the frequency spectrum of acoustic phonons and the absorption of long-wave acoustic phonons by the substrate. We study the dependence of the thermal conductivity on chirality, radius, and temperature of the single-walled carbon nanotubes in both the regimes and compare our findings with experimental data and earlier theoretical results for the thermal conductivity.

Carbon nanoscroll is a unique topologically open configuration of graphene nanoribbon possessing outstanding properties and application perspectives due to its morphology. However molecular dynamics study of nanoscrolls with more than a few coils is limited by computational power. Here, we propose a simple model of the molecular chain moving in the plane, allowing to describe the folded and rolled packaging of long graphene nanoribbons. The model is used to describe a set of possible stationary states and the low-frequency oscillation modes of isolated single-layer nanoribbon scrolls as the function of the nanoribbon length. Possible conformational changes of scrolls due to thermal fluctuations are analyzed and their thermal stability is examined. Using the full-atomic model, frequency spectrum of thermal vibrations is calculated for the scroll and compared to that of the flat nanoribbon. It is shown that the density of phonon states of the scroll differs from the one of the flat nanoribbon only in the low (ω < 100 cm −1 ) and high (ω > 1450 cm −1 ) frequency ranges. Finally, the linear thermal expansion coefficient for the scroll outer radius is calculated from the long-term dynamics with the help of the developed planar chain model. The scrolls demonstrate anomalously high coefficient of thermal expansion and this property can find new applications.