Narrow Results

This paper is devoted to analyzing the stability of charged anisotropic cylinder using the radial perturbation scheme. For this purpose, we consider the non-static cylindrically symmetric self-gravitating system and apply both Eulerian as well as Lagrangian approaches to establish a linearized perturbed form of dynamical equations. The conservation of baryon number is used to evaluate perturbed radial pressure in terms of an adiabatic index. A variational principle is developed to find a characteristic frequency which helps to examine the combined effect of charge and anisotropy on the stability of gaseous star. It is found that dynamical instability can be prevented until the radius of cylinder exceeds the limit $R\ge 18$ and anisotropy increases the instability up to the limiting value of $\beta =-1.5$. Finally, we conclude that the system becomes more stable by increasing the definite amount of charge gradually.

The problem of investigating the nonlinear acoustic waves in stepped acoustic resonators is treated theoretically. A perturbation scheme that combines the method of multi-scale expansion yields a set of coupled nonlinear ordinary differential equations for deriving an analytical model to describe the resonant oscillations. The nonlinear sound pressure in stepped resonator is predicted with accuracy up to the second-order terms of a small-amplitude parameter $𝜀$. The pressure amplitudes and waveforms at the closed end of stepped resonators with different size parameters are investigated by the derived analytical model and qualitatively compared with the measured results in experiment. The qualitative comparison of calculated and measured results shows good agreement. The results suggest that the sound pressure generated in stepped resonators with different size parameters may be very different. Not all stepped resonators can generate high-amplitude and low-distortion standing waves. The derived analytical model can be used to qualitatively study the nonlinear acoustic waves in stepped acoustic resonators and design suitable tube dimensions for resonant macrosonic synthesis.