Pore-structure-mediated hierarchical SAPO-34: Facile synthesis,tunable nanostructure,and catalysis applications for the conversion of dimethyl ether into olefins

Hierarchical cross-like SAPO-34 catalysts with different pore size distributions were obtained via hydrothermal synthesis with polyethylene glycol (PEG) as the mesopore-generating agent. The hierarchical SAPO-34 molecular sieves were characterized using X-ray diffraction, scanning electron microscopy, N₂ adsorption–desorption, thermogravimetric analysis, and temperature-programmed NH₃ desorption. The cross-like SAPO-34 catalysts exhibited enriched multi-porosity, and the sizes of their mesopores ranged from 10 to 50 nm. Both the mesoporous structures and morphologies of the hierarchical SAPO-34 could be further tuned through adjustments of the amount of PEG used. The as-obtained SAPO-34 showed dramatic catalytic performance in the conversion of dimethyl ether into olefins. A maximum selectivity of olefins of 96% was achieved, which was attributed to the rapid transport of the reactants and products in zeolitic micropores through mesopores.     

Changing the representation and improving stability in time-stepping analysis of structural non-linear dynamics

In the present paper, we propose a change in the representation of the discrete motion equations in structural non-linear dynamics to obtain an improvement in the stability of time numerical integrations. In particular, natural local state variables are indicated for a finite-element approach to beam problems. The results, relative to Newmark approximations for the variations in the displacement and velocity vectors, show a significant increase in the range of stability of the time-integration process and a reduction in the number of Newton iterations required in the time-integration steps. It is also shown that the proposed approach inherently obeys the law of conservation of energy.     

Persistence of Poincaré mappings in functional differential equations (with application to structural stability of complicated behavior)

A theorem on the dependence of Poincaré mappings for different functional differential equations (FDEs) on the right-hand side of the equation is proved. Together with recent results on hyperbolic sets for noninvertible mappings, this is used to describe how Poincaré mappings and their complicated behavior in the neighborhood of a transversal homoclinic orbit persist under FDE perturbations of the equation. The method is shown to apply to three example equations, where Poincaré mappings with such behavior are known to exist.