The nonlinear mechanical response of carbon nanotubes, referred to as their “buckling” behavior, is a major topic in the nanotube research community. Buckling means a deformation process in which a large strain beyond a threshold causes an abrupt change in the strain energy vs. deformation profile. Thus far, much effort has been devoted to analysis of the buckling of nanotubes under various loading conditions: compression, bending, torsion, and their certain combinations. Such extensive studies have been motivated by (i) the structural resilience of nanotubes against buckling, and (ii) the substantial influence of buckling on their physical properties. In this contribution, I review the dramatic progress in nanotube buckling research during the past few years.

We investigate localization properties of electron eigenstates in one-dimensional (1D) systems with long-range correlated diagonal disorder. Numerical studies on the localization length $\xi$ of eigenstates demonstrate the existence of the localization-delocalization transition in 1D systems and elucidate nontrivial behavior of $\xi$ as a function of the disorder strength. The critical exponent $\nu$ for localization length is extracted for various values of parameters characterizing the disorder, revealing that every $\nu$ disobeys the Harris criterion $\nu >2∕d$.

We demonstrate the effects of geometric perturbation on the Tomonaga-Luttinger liquid (TLL) states in a long, thin, and hollow cylinder whose radius varies periodically. The variation in the surface curvature inherent to the system gives rise to a significant increase in the power-law exponent of the single- particle density of states. The increase in the TLL exponent is caused by a curvature-induced potential that attracts low-energy electrons to region that has large curvature.

We investigate the critical behaviour of the two-dimensional Ising model defined on a curved surface with a constant negative curvature. Finite-size scaling analysis reveals that the critical exponents for the zero-field magnetic susceptibility and the correlation length deviate from those for the Ising lattice model on a flat plane. Furthermore, when reducing the effects of boundary spins, the values of the critical exponents tend to those derived from the mean field theory. These findings evidence that the underlying geometric character is responsible for the critical properties the Ising model when the lattice is embedded on negatively curved surfaces.

When two or more candle flames are fused by approaching them together, the resulting large flame often exhibits flickering, i.e., prolonged high-frequency oscillation in its size and luminance. In the present work, we investigate the collective behaviour of three-coupled candle flame oscillators in a triangular arrangement. The system showed four distinct types of syncronised modes as a consequence of spontaneous symmetry breaking. The modes obtained include the in-phase mode, the partial in-phase mode, the rotation mode, and an anomalous one called the “death” mode that causes a sudden stop of the flame oscillation followed by self-sustained stable combustion. We also clarified the correlation between the inter-flame distance and the frequency with which the modes occur.