Effects of layer number and initial pressure on continuum-based buckling analysis of multi-walled carbon nanotubes accounting for van der Waals interaction

The structural instability of multi-walled carbon nanotubes(MWCNTs) has captured extensive attention due to the unique characteristic of extremely thin hollow cylinder structure. The previous studies usually focus on the buckling behavior without considering the effects of the wall number and initial pressure. In this paper, the axial buckling behavior of MWCNTs with the length-to-outermost radius ratio less than 20 is investigated within the framework of the Donnell shell theory. The governing equations for the infinitesimal buckling of MWCNTs are established, accounting for the van der Waals(vd W) interaction between layers. The effects of the wall number, initial pressure prior to buckling, and aspect ratio on the critical buckling mode, buckling load, and buckling strain are discussed, respectively. Specially, the four-walled and twenty-walled CNTs are studied in detail, indicating the fact that the buckling instability may occur in other layers besides the outermost layer. The obtained results extend the buckling analysis of the continuum-based model, and provide theoretical support for the application of CNTs.

INSTABILITY OF THE OCEANIC WAVES IN THE TROPICAL REGION

In this paper, the effects of the large-scale mean sea temperature fields of the tropical ocean and the zonal current field (southern equatorial current) have been comprehensively entered in consideration on the basis of Chao and Ji (1985), and Ji and Chao (1986), the equatorial oceanic waves of the tropical ocean have been discussed by use of linearized primitive equations, then, the significant influence of the climatic back- ground fields of the tropical ocean upon the oceanic waves of this region has been further testified. When very cold water appears in the tropical region, and the southern equatorial current is also relatively strong, the effect of the Rossby wave weakens, as a consequence, there are substitutive slow waves (i.e. thermal waves) which travel in opposite direction (eastward) to the Rossby wave. The characteristics of the slow wave are similar to those of Rossby waves, only the travelling direction is opposite. Under a certain environ- mental background field, the slow wave and the modified Rossby wave may be instable. With this conclu- sion, the mechanism of the occurrence, development and propagation of El Nino events has been studied. It is pointed out that the opposite travelling direction of the thermal wave and Rossby wave will bring re- pectively into action under different marine environmental background fields. The physical causes for that the abnormal warm water inclines to occur along the South American coast have also been explored in this paper.

Qualitative analysis for a Wolbachia infection model with diffusion

We consider a reaction-diffusion model which describes the spatial Wolbachia spread dynamics for a mixed population of infected and uninfected mosquitoes. By using linearization method, comparison principle and Leray-Schauder degree theory, we investigate the influence of diffusion on the Wolbachia infection dynamics.After identifying the system parameter regions in which diffusion alters the local stability of constant steadystates, we find sufficient conditions under which the system possesses inhomogeneous steady-states. Surprisingly,our mathematical analysis, with the help of numerical simulations, indicates that diffusion is able to lower the threshold value of the infection frequency over which Wolbachia can invade the whole population.