本文讨论了二维时间分数阶Caputo-Hadamard慢扩散方程的交替方向隐式(Alternating Direction Implicit,ADI)紧致差分格式。首先,在指数型网格上对Caputo-Hadamard型分数阶导数进行离散;其次,利用紧致ADI方法将高维问题转化为2个一维问题...本文讨论了二维时间分数阶Caputo-Hadamard慢扩散方程的交替方向隐式(Alternating Direction Implicit,ADI)紧致差分格式。首先,在指数型网格上对Caputo-Hadamard型分数阶导数进行离散;其次,利用紧致ADI方法将高维问题转化为2个一维问题;根据离散系数的性质,利用数学归纳法证明了差分格式的稳定性和收敛性;最后,对具体模型进行数值求解。算例验证了上述理论分析的有效性。展开更多
Improving zinc metal(Zn^(0))reversibility and minimizing the N/P ratio are critical to boosting the energy density of Zn^(0) batteries.However,in reality,an excess Zn source is usually adopted to offset the irreversib...Improving zinc metal(Zn^(0))reversibility and minimizing the N/P ratio are critical to boosting the energy density of Zn^(0) batteries.However,in reality,an excess Zn source is usually adopted to offset the irreversible zinc loss and guarantee sufficient zinc cycling,which sacrifices the energy density and leads to poor practicability of Zn^(0) batteries.To address the above conundrum,here,we report a lean-Zn and hierarchical anode based on metal-organic framework(MOF)-derived carbon,where trace Zn^(0) is pre-reserved within the anode structure to make up for any irreversible zinc source loss.This allows us to construct low N/P ratio Zn^(0) full cells when coupling the lean-Zn anode with Zn-containing cathodes.Impressively,high Zn^(0) reversibility(average Coulombic efficiency of 99.4% for 3000 cycles)and long full-cell lifetime(92% capacity retention after 900 cycles)were realized even under the harsh lean-Zn condition(N/P ratio:1.34).The excellent Zn reversibility is attributed to the hierarchy structure that homogenizes zinc ion flux and electric field distribution,as confirmed by theoretical simulations,which therefore stabilizes Zn^(0) evolution.The lean-Zn anode design strategy will provide new insights into construction of high-energy Zn^(0) batteries for practical applications.展开更多
文摘本文讨论了二维时间分数阶Caputo-Hadamard慢扩散方程的交替方向隐式(Alternating Direction Implicit,ADI)紧致差分格式。首先,在指数型网格上对Caputo-Hadamard型分数阶导数进行离散;其次,利用紧致ADI方法将高维问题转化为2个一维问题;根据离散系数的性质,利用数学归纳法证明了差分格式的稳定性和收敛性;最后,对具体模型进行数值求解。算例验证了上述理论分析的有效性。
基金State Key Laboratory of Heavy Oil Processing,Grant/Award Number:SKLHOP202101006National Natural Science Foundation of China,Grant/Award Numbers:21905304,52073305Natural Science Foundation of Shandong Province,Grant/Award Number:ZR2020QE048。
文摘Improving zinc metal(Zn^(0))reversibility and minimizing the N/P ratio are critical to boosting the energy density of Zn^(0) batteries.However,in reality,an excess Zn source is usually adopted to offset the irreversible zinc loss and guarantee sufficient zinc cycling,which sacrifices the energy density and leads to poor practicability of Zn^(0) batteries.To address the above conundrum,here,we report a lean-Zn and hierarchical anode based on metal-organic framework(MOF)-derived carbon,where trace Zn^(0) is pre-reserved within the anode structure to make up for any irreversible zinc source loss.This allows us to construct low N/P ratio Zn^(0) full cells when coupling the lean-Zn anode with Zn-containing cathodes.Impressively,high Zn^(0) reversibility(average Coulombic efficiency of 99.4% for 3000 cycles)and long full-cell lifetime(92% capacity retention after 900 cycles)were realized even under the harsh lean-Zn condition(N/P ratio:1.34).The excellent Zn reversibility is attributed to the hierarchy structure that homogenizes zinc ion flux and electric field distribution,as confirmed by theoretical simulations,which therefore stabilizes Zn^(0) evolution.The lean-Zn anode design strategy will provide new insights into construction of high-energy Zn^(0) batteries for practical applications.
