A review on TiO2 nanotube arrays: Fabrication, properties, and sensing applications

Fabrication, properties, and sensing applications of TiO₂ nanotubes have been reviewed, and the highly ordered TiO₂ nanotube arrays made by anodic oxidation in fluoride-contained electrolytes highlighted. The effect of anodization parameters (electrolyte, pH, and voltage) on the titania nanotube size and shape were discussed. The excellent biocompatibility of TiO₂, the high orientation, the large surface area with tunable pore sizes, as well as the high electron transfer rate along with the nanotubes make TiO₂ nanotube array an ideal substrate for the sensor’s fabrication and application. The sensors based on the TiO₂ nanotube arrays for sensing hydrogen, oxygen, humidity, glucose and hydrogen peroxide all exhibited low detection limit, high stability, very good reproducibility and high sensitivity.     

Prescribing curvature problem of Bakry-Émery Ricci tensor

We consider the problem of deforming a metric in its conformal class on a closed manifold, such that the k-curvature defined by the Bakry-mery Ricci tensor is a constant. We show its solvability on the manifold, provided that the initial Bakry-mery Ricci tensor belongs to a negative cone. Moveover, the Monge-Ampère type equation with respect to the Bakry-mery Ricci tensor is also considered.     

Bifurcation and synchronization of synaptically coupled FHN models with time delay

This paper presents an investigation of dynamics of the coupled nonidentical FHN models with synaptic connection, which can exhibit rich bifurcation behavior with variation of the coupling strength. With the time delay being introduced, the coupled neurons may display a transition from the original chaotic motions to periodic ones, which is accompanied by complex bifurcation scenario. At the same time, synchronization of the coupled neurons is studied in terms of their mean frequencies. We also find that the small time delay can induce new period windows with the coupling strength increasing. Moreover, it is found that synchronization of the coupled neurons can be achieved in some parameter ranges and related to their bifurcation transition. Bifurcation diagrams are obtained numerically or analytically from the mathematical model and the parameter regions of different behavior are clarified.