A simple rational model is proposed for discharge of batteries with aqueous electrolytes, based on Nernst equation. Details of electrode kinetics are not taken into account. Only a few overall parameters of the batter...A simple rational model is proposed for discharge of batteries with aqueous electrolytes, based on Nernst equation. Details of electrode kinetics are not taken into account. Only a few overall parameters of the battery are considered. A simple algorithm, with variable time step-length <span style="font-family:Verdana;">Δ</span><i><span style="font-family:Verdana;">t</span></i><span style="font-family:Verdana;">, is presented, for proposed model. The model is first applied to Daniel cell, in order to clar</span><span style="font-family:Verdana;">ify</span><span style="font-family:""><span style="font-family:Verdana;"> concepts and principles of battery operation. It is found that initial pinching, in time-history curve of voltage </span><i><span style="font-family:Verdana;">E-t</span></i><span style="font-family:Verdana;">, is due to initial under-concentration of product ion. Then, model is applied </span></span><span style="font-family:Verdana;">to</span><span> a lead-acid battery. In absence of an ion product, and in order to construct nominator of Nernst ratio, such an ion, with coefficient tending to zero, is assumed, thus yielding unity in nominator. Time-history curves of voltage, for various values of internal resistance, are compared with corresponding published experimental curves. Temperature effect on voltage-time curve is examined. Proposed model can be extended to other types of batteries, which can be considered as having aqueous electrolytes, too.</span>展开更多
The integrable nonlocal Lakshmanan–Porsezian–Daniel(LPD) equation which has the higher-order terms(dispersions and nonlinear effects) is first introduced. We demonstrate the integrability of the nonlocal LPD equatio...The integrable nonlocal Lakshmanan–Porsezian–Daniel(LPD) equation which has the higher-order terms(dispersions and nonlinear effects) is first introduced. We demonstrate the integrability of the nonlocal LPD equation,provide its Lax pair, and present its rational soliton solutions and self-potential function by using the degenerate Darboux transformation. From the numerical plots of solutions, the compression effects of the real refractive index profile and the gain-or-loss distribution produced by δ are discussed.展开更多
文摘A simple rational model is proposed for discharge of batteries with aqueous electrolytes, based on Nernst equation. Details of electrode kinetics are not taken into account. Only a few overall parameters of the battery are considered. A simple algorithm, with variable time step-length <span style="font-family:Verdana;">Δ</span><i><span style="font-family:Verdana;">t</span></i><span style="font-family:Verdana;">, is presented, for proposed model. The model is first applied to Daniel cell, in order to clar</span><span style="font-family:Verdana;">ify</span><span style="font-family:""><span style="font-family:Verdana;"> concepts and principles of battery operation. It is found that initial pinching, in time-history curve of voltage </span><i><span style="font-family:Verdana;">E-t</span></i><span style="font-family:Verdana;">, is due to initial under-concentration of product ion. Then, model is applied </span></span><span style="font-family:Verdana;">to</span><span> a lead-acid battery. In absence of an ion product, and in order to construct nominator of Nernst ratio, such an ion, with coefficient tending to zero, is assumed, thus yielding unity in nominator. Time-history curves of voltage, for various values of internal resistance, are compared with corresponding published experimental curves. Temperature effect on voltage-time curve is examined. Proposed model can be extended to other types of batteries, which can be considered as having aqueous electrolytes, too.</span>
基金Supported by the National Natural Science Foundation of China under Grant No.11271210the K.C.Wong Magna Fund in Ningbo University
文摘The integrable nonlocal Lakshmanan–Porsezian–Daniel(LPD) equation which has the higher-order terms(dispersions and nonlinear effects) is first introduced. We demonstrate the integrability of the nonlocal LPD equation,provide its Lax pair, and present its rational soliton solutions and self-potential function by using the degenerate Darboux transformation. From the numerical plots of solutions, the compression effects of the real refractive index profile and the gain-or-loss distribution produced by δ are discussed.
