Parametric instabilities in single-walled carbon nanotubes

Abstract

Parametric instabilities induced by the coupling excitation between the high frequency quantum Langmuir waves and the low frequency quantum ion-acoustic waves in single-walled carbon nanotubes are studied with a quantum Zakharov model. By linearizing the quantum hydrodynamic equations, we get the dispersion relations for the high frequency quantum Langmuir wave and the low frequency quantum ion-acoustic wave. Using two-time scale method, we obtain the quantum Zaharov model in the cylindrical coordinates. Decay instability and four-wave instability are discussed in detail. It is shown that the carbon nanotube's radius, the equilibrium discrete azimuthal quantum number, the perturbed discrete azimuthal quantum number, and the quantum parameter all play a crucial role in the instabilities.

Vibration and buckling analyses of nanobeams embedded in an elastic medium

“…Recently, nanomaterials have aroused interest among the scientific communities in the fields of physics, chemistry, and engineering. Some of these materials are nanoparticles, nanowires, [1][2][3][4] nanotubes, [5][6][7][8][9][10][11][12][13][14][15] and nanotube resonators. Among them, beam type structures play a vital role in the field of nanotechnology.…”