非线性玻尔兹曼方程的傅里叶谱方法

玻尔兹曼方程作为空气动理学中最基本的方程之一,是连接微观牛顿力学和宏观连续介质力学的重要桥梁.该方程描述了一个由大量粒子组成的复杂系统的非平衡态时间演化:除了基本的输运项,其最重要的特性是粒子间的相互碰撞由一个高维,非局部且非线性的积分算子来描述,从而给玻尔兹曼方程的数值求解带来非常大的挑战.在过去的二十年间,基于傅里叶级数的谱方法成为了数值求解玻尔兹曼方程的一种很受欢迎且有效的确定性算法.这主要归功于谱方法的高精度及它可以被快速傅里叶变换加速的特质.本文将回顾玻尔兹曼方程的傅里叶谱方法,具体包括方法的导出,稳定性和收敛性分析,快速算法,以及在一大类基于碰撞的空气动理学方程中的推广.     

基于NiCo2O4纳米片电极的非对称混合电容器

The looming global energy crisis and ever-increasing energy demands have catalyzed the development of renewable energy storage systems. In this regard, supercapacitors (SCs) have attracted widespread attention because of their advantageous attributes such as high power density, excellent cycle stability, and environmental friendliness. However, SCs exhibit low energy density and it is important to optimize electrode materials to improve the overall performance of these devices. Among the various electrode materials available, spinel nickel cobaltate (NiCo₂O₄) is particularly interesting because of its excellent theoretical capacitance. Based on the understanding that the performances of the electrode materials strongly depend on their morphologies and structures, in this study, we successfully synthesized NiCo₂O₄ nanosheets on Ni foam via a simple hydrothermal route followed by calcination. The structures and morphologies of the as-synthesized products were characterized by X-ray diffraction, scanning electron microscopy, and Brunauer-Emmett-Teller (BET) surface area analysis, and the results showed that they were uniformly distributed on the Ni foam support. The surface chemical states of the elements in the samples were identified by X-ray photoelectron spectroscopy. The as-synthesized NiCo₂O₄ products were then tested as cathode materials for supercapacitors in a traditional three-electrode system. The electrochemical performances of the NiCo₂O₄ electrode materials were studied and the area capacitance was found to be 1.26 C·cm^-2 at a current density of 1 mA·cm^-2. Furthermore, outstanding cycling stability with 97.6% retention of the initial discharge capacitance after 10000 cycles and excellent rate performance (67.5% capacitance retention with the current density from 1 to 14 mA·cm^-2) were achieved. It was found that the Ni foam supporting the NiCo₂O₄ nanosheets increased the conductivity of the electrode materials. However, it is worth noting that the contribution of nickel foam to the areal capacitance of the electrode materials was almost zero during the charge and discharge processes. To further investigate the practical application of the as-synthesized NiCo₂O₄ nanosheets-based electrode, a device was assembled with the as-prepared samples as the positive electrode and active carbon (AC) as the negative electrode. The assembled supercapacitor showed energy densities of 0.14 and 0.09 Wh·cm^-3 at 1.56 and 4.5 W·cm^-3, respectively. Furthermore, it was able to maintain 95% of its initial specific capacitance after 10000 cycles. The excellent electrochemical performance of the NiCo₂O₄ nanosheets could be ascribed to their unique spatial structure composed of interconnected ultrathin nanosheets, which facilitated electron transportation and ion penetration, suggesting their potential applications as electrode materials for high performance supercapacitors. The present synthetic route can be extended to other ternary transition metal oxides/sulfides for future energy storage devices and systems.     

四方体MgO的制备及对有机染料的吸附

以六水氯化镁和六次甲基四胺为原料,采用水热法合成四方体MgO,考察其对有机染料甲基橙和亚甲基蓝的吸附行为.通过TGA-DTA、SEM、XRD、N2-sorption和FT-IR等手段表征样品.结果表明,原料浓度、温度和表面活性剂对四方体MgO结构的形成影响较小,而反应时间的延长有助于有序结构的组装.温度170℃、时间24h、MgCl2·6H2O与C6H12N4浓度比为1∶2和表面活性剂PVP是制备四方体MgO的最佳条件.在溶液浓度10mg · L-1的单一吸附实验过程中,四方体MgO对甲基橙和亚甲基蓝的去除率分别为91.3;和22.3;,吸附过程均为单层吸附且符合Langmuir等温吸附模型和伪二级吸附动力学方程.在溶液浓度40 mg·L-1、甲基橙和亚甲基蓝浓度比3∶1的混合溶液吸附过程中,四方体MgO对甲基橙和亚甲基蓝的去除率分别为80.1;和97.9;.     

含分布时滞的时滞微分系统多步龙格-库塔方法的时滞相关稳定性

本文研究了一类含分布时滞的时滞微分系统的多步龙格-库塔方法的稳定性.基于辐角原理，本文给出了多步龙格-库塔方法弱时滞相关稳定性的充分条件，并通过数值算例验证了理论结果的有效性.     

Ostrowski-Taussky不等式的推广

行列式的概念是矩阵分析中的一个很基本的概念,其中一个非常重要的应用就是解线性方程组.由于行列式的概念是和矩阵特征值紧密相关的,研究行列式的一些性质可以从侧面反映出该矩阵特征值的一些性质.Ostrowski-Taussky不等式是一个关于行列式的不等式,利用矩阵极分解的概念,给出了不等式的一个新的证明,并且推广了不等式.     

冷冻法硝酸磷肥工艺中酸不溶物提纯研究

采用酸浸、磁选酸浸、水淬/研磨酸浸等不同工艺对冷冻法硝酸磷肥生产工艺中的废渣-酸不溶物进行了提纯处理,利用X射线荧光光谱仪(XRF测试)对酸不溶物提纯前后各成分含量的变化进行了分析,从中得出了不同工艺流程对酸不溶物纯度的影响,最终确定了最佳的酸不溶物处理工艺.结果表明:在酸浸实验中,盐酸酸浸效果最佳,可将酸不溶物中SiO2纯度达到82.43;;在酸浸工艺前加入磁选、水淬、研磨的工序均可有效提升酸不溶物的提纯效果;冷冻法硝酸磷肥工艺中酸不溶物最佳的提纯工艺路线为:干燥、筛分、水洗、磁选、研磨、盐酸酸浸,处理后酸不溶物中SiO2纯度达到88.92;,符合微硅粉的生产要求.     

CoP纳米片制备及其电催化产氢性能的研究

高稳定性的催化剂对于规模化电催化产氢起着关键的作用.因此,采用简单的方法合成CoP纳米片,其表现出优越电催化活性和稳定性. CoP纳米片采用水热法和在氩气中磷化法制备的,纳米片的厚度为100～300 nm.CoP纳米片在0.5 M H2SO4的电解质中,表现出良好的电化学产氢性能,起始过电为～75 mV,塔菲尔斜率为～39. 67 mV/decade,当电流密度为10 mA· cm-2,过电压为～125 mV,经过1000次的循环后,保持良好的稳定性能.