In many real-world oscillator systems, the phase response curves are highly heterogeneous. However, the dynamics of heterogeneous oscillator networks has not been seriously addressed. We propose a theoretical framework to analyze such a system by dealing explicitly with the heterogeneous phase response curves. We develop a method to solve the self-consistent equations for order parameters by us...

Phase transformations such as freezing typically start with heterogeneous nucleation. Heterogeneous nucleation near a wetting transition, of a crystalline phase is studied. The wetting transition occurs at or near a vapour-liquid transition which occurs in a metastable fluid. The fluid is metastable with respect to crystallisation, and it is the crystallisation of this fluid phase that we are i...

vanadium phosphorus oxides (vpo) has been applied as a heterogeneous catalyst in gas phase oxidation reactions and its application is very limited in liquid phase. in this study a series of cobalt-doped vanadium phosphorus oxides (vpo-co) catalysts with different loading of co (0.01-1.0 mol ratio of co/v) were prepared. oxidation of benzyl alcohol was studied in the liquid phase over vpo and vp...

polyethylene glycol was easily grafted to silica gel and used as a solid–liquid phase transfer catalyst in the reduction of aromatic nitro compounds. this silica-grafted polyethylene glycol is proved to be an efficient heterogeneous catalyst in the reduction of nitroarenes to the corresponding aromatic amines with zinc powder in water. the reduction reactions proceeded efficiently with excellen...