This article proposes a high-order numerical method for a space distributed-order time-fractional diffusion equation.First,we use the mid-point quadrature rule to transform the space distributed-order term into multi-...This article proposes a high-order numerical method for a space distributed-order time-fractional diffusion equation.First,we use the mid-point quadrature rule to transform the space distributed-order term into multi-term fractional derivatives.Second,based on the piecewise-quadratic polynomials,we construct the nodal basis functions,and then discretize the multi-term fractional equation by the finite volume method.For the time-fractional derivative,the finite difference method is used.Finally,the iterative scheme is proved to be unconditionally stable and convergent with the accuracy O(σ^(2)+τ^(2-β)+h^(3)),whereτand h are the time step size and the space step size,respectively.A numerical example is presented to verify the effectiveness of the proposed method.展开更多
Owing to sluggish ionic mobility at low temperatures, supercapacitors, as well as other energy-storage devices, always suffer from severe capacity decay and even failure under extreme low-temperature circumstances. So...Owing to sluggish ionic mobility at low temperatures, supercapacitors, as well as other energy-storage devices, always suffer from severe capacity decay and even failure under extreme low-temperature circumstances. Solar-thermal-enabled self-heating promises an attractive approach to overcome this issue.Here, we report a unique H-bonding charge-transfer complex with a high photothermal conversion efficiency of 79.5% at 405 nm based on chloranilic acid and albendazole. Integrated with a microsupercapacitor, the chloranilic acid-albendazole complex(CAC) film prompts an apparent temperature increase of 22.7 °C under 1 sun illumination at-32.6 °C, effectively elevating the working temperature of devices.As a result, the rate capability of the microsupercapacitor has been significantly improved with a 17-fold increase in capacitance at a current density of 60 μA cm^(-2), leading to outstanding low-temperature performances. Importantly, the integrated device is capable of working at a low temperature of-30 °C in the open air, which demonstrates the potential of CAC in practical applications for low-temperature ultracapacitive energy-storage devices.展开更多
基金supported by the Natural and Science Foundation Council of China(11771059)Hunan Provincial Natural Science Foundation of China(2018JJ3519)Scientific Research Project of Hunan Provincial office of Education(20A022)。
文摘This article proposes a high-order numerical method for a space distributed-order time-fractional diffusion equation.First,we use the mid-point quadrature rule to transform the space distributed-order term into multi-term fractional derivatives.Second,based on the piecewise-quadratic polynomials,we construct the nodal basis functions,and then discretize the multi-term fractional equation by the finite volume method.For the time-fractional derivative,the finite difference method is used.Finally,the iterative scheme is proved to be unconditionally stable and convergent with the accuracy O(σ^(2)+τ^(2-β)+h^(3)),whereτand h are the time step size and the space step size,respectively.A numerical example is presented to verify the effectiveness of the proposed method.
基金supported by the National Natural Science Foundation of China (Nos. 51772116 and 51972132)Program for HUST Academic Frontier Youth Team (2016QYTD04)。
文摘Owing to sluggish ionic mobility at low temperatures, supercapacitors, as well as other energy-storage devices, always suffer from severe capacity decay and even failure under extreme low-temperature circumstances. Solar-thermal-enabled self-heating promises an attractive approach to overcome this issue.Here, we report a unique H-bonding charge-transfer complex with a high photothermal conversion efficiency of 79.5% at 405 nm based on chloranilic acid and albendazole. Integrated with a microsupercapacitor, the chloranilic acid-albendazole complex(CAC) film prompts an apparent temperature increase of 22.7 °C under 1 sun illumination at-32.6 °C, effectively elevating the working temperature of devices.As a result, the rate capability of the microsupercapacitor has been significantly improved with a 17-fold increase in capacitance at a current density of 60 μA cm^(-2), leading to outstanding low-temperature performances. Importantly, the integrated device is capable of working at a low temperature of-30 °C in the open air, which demonstrates the potential of CAC in practical applications for low-temperature ultracapacitive energy-storage devices.
