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He's multiple scales method is a couple of the homotopy perturbation method and the multiple scales technology in the classic perturbation method. This method has been proved to be a powerful mathematical tool to various nonlinear equations, and it is extremely effective for forced nonlinear oscillators. This paper shows that the method can be further improved by incorporating some known technologies, e.g., the parameter-expanding technology, the enhanced perturbation method and the homotopy perturbation method with an auxiliary term. Due to the wide application of the homotopy perturbation method, He's multiple scales method cleans solutions of nonlinear equations while the classic perturbation method fails. [ABSTRACT FROM AUTHOR]

This paper studies a micro/nano scale capillary flow in a hollow fiber and its oscillation. The hollow fiber is immersed into a liquid (e.g. water), and the isolated air in the fiber plays as a spring-like oscillation. An oscillation model is established for the fluid vibration in the capillary tube, a simple estimation of its frequency is suggested for practical applications, and the silver ion release from hollow fibers is discussed. [ABSTRACT FROM AUTHOR]

A fractional model for the release oscillation of silver ions from hollow fibers was established recently, this paper gives an experimental verification of the release property, showing the concentration of the released ions increases exponentially at initial stage and it becomes stable when the time tends to a threshold, as predicted by the fractional oscillator. [ABSTRACT FROM AUTHOR]

A fast estimation of periodic properties of a nonlinear oscillator is much needed as pointed out by Tian and Liu in their review article (Tian D and Liu Z, Journal of Low Frequency Noise, Vibration & Active Control, https://doi.org/10.1177/1461348418756013). Although a relatively high accuracy can be achieved, there is no way to continue the solution process to obtain any accuracy of a solution. This paper suggests an effective modification so that any accurate frequency can be obtained. [ABSTRACT FROM AUTHOR]