New bifurcations of basin boundaries involving Wada and a smooth Wada basin boundary

This paper demonstrates and analyses double heteroclinic tangency in a three-well potential model, which can produce three new types of bifurcations of basin boundaries including from smooth to Wada basin boundaries, from fractal to Wada basin boundaries in which no changes of accessible periodic orbits happen, and from Wada to Wada basin boundaries. In a model of mechanical oscillator, it shows that a Wada basin boundary can be smooth.     

纯Cr2O3包覆Li4Ti5O12微球的制备及其储锂性能研究

The pure Cr₂O₃ coated Li₄Ti₅O₁₂ microspheres were prepared by a facile and cheap solutionbased method with basic chromium(III) nitrate solution (pH=11.9). And their Li-storage properties were investigated as anode materials for lithium rechargeable batteries. The pure Cr₂O₃ works as an adhesive interface to strengthen the connections between Li₄Ti₅O₁₂ particles, providing more electric conduction channels, and reduce the inter-particle resistance. Moreover, LixCr₂O₃, formed by the lithiation of Cr₂O₃, can further stabilize Li₇Ti₅O₁₂ with high electric conductivity on the surface of particles. While in the acid chromium solution (pH=3.2) modification, besides Cr₂O₃, Li₂CrO₄ and TiO₂ phases were also found in the final product. Li₂CrO₄ is toxic and the presence of TiO₂ is not welcome to improve the electrochemical performance of Li₄Ti₅O₁₂ microspheres. The reversible capacity of 1% Cr₂O₃-coated sample with the basic chromium solution modification was 180 mAh/g at 0.1 C, and 134 mAh/g at 10 C. Moreover, it was even as high as 127 mAh/g at 5 C after 600 cycles. At-20℃, its reversible specific capacity was still as high as 118 mAh/g.     

New bifurcations of basin boundaries involving Wada and a smooth Wada basin boundary

This paper demonstrates and analyses double heteroclinic tangency in a three-well potential model, which can produce three new types of bifurcations of basin boundaries including from smooth to Wada basin boundaries, from fractal to Wada basin boundaries in which no changes of accessible periodic orbits happen, and from Wada to Wada basin boundaries. In a model of mechanical oscillator, it shows that a Wada basin boundary can be smooth.