We studied the structural and electronic properties of carbon nanotubes under hydrostatic pressures based on molecular dynamics simulations and first principles band structure calculations. It is found that carbon nanotubes experience a hard-to-soft transition as external pressure increases. The bulk modulus of soft phase is two orders of magnitude smaller than that of hard phase. The band structure calculations show that band gap of （10, 0） nanotube increases with the increase of pressure at low pressures. Above a critical pressure （5.70GPa）, band gap of （10, 0） nanotube drops rapidly and becomes zero at 6.62GPa. Moreover, the calculated charge density shows that a large pressure can induce an sp^2-to-sp^3 bonding transition, which is confirmed by recent experiments on deformed carbon nanotubes.
Taking into account both gain/loss and time-dependent atomic scattering length, this paper analytically derives an exact bright solitary wave in a cigar-shaped attractive condensate in the presence of an expulsive parabolic potential. Due to the balance of the scattering length and gain/loss, the bright solitary wave is shown to have constant amplitude. Especially, it is found that the bright solitary wave is accelerated by expulsive force, whose velocity can be modulated by changing the axial and transverse angular frequencies. The results are in good agreement with the experimental observations by Khaykovich et al （2002 Science 296 1290）.
Taking into account both the intrinsic curvature and Zeeman effects, persistent currents in a multi-walled carbon nanotorus are explored by using a supercell method, within the tight-binding formalism. It is shown that in the absence of the Zeeman effect, the intrinsic curvature induces some dramatic changes in energy spectra and thus changes in the shape of the flux-dependent current. A paramagnetism diamagnetism transition is observed. With consideration of the Zeeman splitting energy, the period of persistent current is destroyed, and a diamagnetism-paramagnetism transition is obtained at high magnetic field. In addition, we further explore the effect of external electric field energy （Eef） on persistent current, indicating that it changes unmonotonously with Eef.
