A fractional nonlinear differential system is studied to search for its periodic solution near the equilibrium. The release oscillation of silver ions from hollow fibers is used as an example to illustrate the importance of fractional order to the release frequency. The criterion for the periodic solution is obtained and it shows that the fractional order will greatly affect its periodic property.

Numerical study of NOx abatement in a photocatalytic reactor has been caught much attention recently. There are two ways for the numerical simulation, one is the CFD model, the other is the variational-based approach. The latter leads to a conservation algorithm with less requirement for the trial functions in the numerical study. In this paper we establish a variational principle for the problem, giving an alternative numerical method for NOx abatement.

The bubble electrospinningis a peerless technology for mass-production of various functional nanofibers. During the spinning process, multiple jets are ejected, which might be interacted with each other. The interaction might result in mass transfer, energy transfer and force in balance, all these factors will greatly affect the mechanical property and morphology of the resultant fibers. A theoretical model is established to study the two-jets combination during the spinning process, the mass conservation and momentum conservationare considered, and the combined fiber?s diameter and moving velocity are theoretically elucidated. The present theory analysis can be easily extended to multile jets interation.

This paper introduces an analytical method for the analysis and design of a dry-jet wet spinning system. The 1-D mass conservation equation is used, and velocity distribution is assumed to derive a simple relationship among various spinning parameters. The effect of spinneret mass flow rate, solution density, spinneret structure including velocity and air-gap length, and drawing velocity on the dry-jet wet spinning was simulated using the proposed analytical model. Theoretical prediction of fiber diameter is obtained, which depends upon spinning conditions, solution properties, and spinneret structure. The theoretical results were verified by comparing experimental data with the numerical solution. It was found obviously that the theoretical prediction has comparable accuracy as that by numerical computation. The analytical model can be useful for preliminary design of a spinning process for fabrication of fibers with controllable diameter by adjusting parameters in spinning conditions.