Graph-Theoretical Method to the Existence of Stationary Distribution of Stochastic Coupled Systems

In this paper, by linking Fokker–Planck equations with stochastic coupled systems, a new method is provided to investigate the existence of a stationary distribution of stochastic coupled systems. Based on the graph theory and the Lyapunov method, an appropriate Lyapunov function associated with stationary Fokker–Planck equations is constructed. Moreover, a Lyapunov-type theorem and a coefficients-type criterion are obtained to guarantee the existence of a stationary distribution. Furthermore, theoretical results are applied to explore the existence of a stationary distribution of stochastic predator–prey models with dispersal and a sufficient criterion is presented correspondingly. Finally, a numerical example is given to illustrate the effectiveness of our results.     

Controlled Variable Oxidative Doping of Individual Organometallic Nanoparticles

The charging and controlled oxidative doping of single organometallic ferrocene nanoparticles is reported in aqueous sodium tetrafluoroborate using the nano‐impacts method. It is shown that ferrocene nanoparticles of approximately 105 nm diameter are essentially quantitatively oxidatively doped with the uptake of one tetrafluoroborate anion per ferrocene molecule at suitably high overpotentials. By using lower potentials, it is possible to achieve low doping levels of single nanoparticles in a controlled manner.     

Single‐Walled Carbon Nanotubes in Highly Viscous Media: A Comparison between the Dispersive Agents [BMIM][BF4], L121, and Triton X‐100

Dispersions of single‐walled carbon nanotubes (SWNTs) have been prepared by using the room‐temperature ionic liquid [BMIM][BF₄] (1‐butyl‐3‐methylimidazolium tetrafluoroborate), the triblock copolymer Pluronic L121 [poly(ethylene oxide)₅‐poly(propylene oxide)₆₈‐poly(ethylene oxide)₅] and the non‐ionic surfactant Triton X‐100 (TX100) in the pure state. The size of the SWNTs aggregates and the dispersion degree in the three viscous systems depend on the sonication time, as highlighted by UV/Vis/NIR spectroscopy and optical microscopy analysis. A nonlinear increase in conductivity can be observed as a function of the SWNTs loading, as suggested by electrochemical impedance spectroscopy. The generation of a three‐dimensional network of SWNTs showing a viscoelastic gel‐like behavior above a critical percolation concentration has been found at 25 °C in all the investigated systems by oscillatory rheology measurements.     

Surface modulated hierarchical graphene film via sulfur and phosphorus dual-doping for high performance flexible supercapacitors

The steam-assistant heteroatoms of sulfur and phosphorus dual-doped graphene film fabricated via an ice-template and thermal-activation approach demonstrates an excellent pseudocapacitive behavior in flexible electrochemical capacitors.