一类非线性发展方程的精确解

利用hirota双线性法,得到(3+1)维孤子方程、(3+1)维KP-Boussinesq方程、(2+1)维修正Caudrey-Dodd-Gibbon-Kotera-S awada方程、Hirota-Satsuma浅水波方程的精确解,并做出一部分解的图形,进一步研究解的结构和性质.     

Sc、Ce掺杂CrSi2的电子结构与光学性质的第一性原理

采用基于密度泛函理论的第一性原理赝势平面波方法对Sc、Ce单掺和共掺后CrSi₂的几何结构、电子结构、复介电函数、吸收系数和光电导率进行了计算。结果表明:Sc、Ce掺杂CrSi₂的晶格常数增大,带隙变小。本征CrSi₂的带隙为0.386 eV,Sc、Ce单掺及共掺CrSi₂的禁带宽度分别减小至0.245 eV、0.232 eV、0.198 eV,费米能级均向低能区移动进入价带。由于Sc的3d态电子和Ce的4f态电子的影响,Sc、Ce掺杂的CrSi₂在导带下方出现了杂质能级。掺杂后的CrSi₂介电函数虚部第一介电峰峰值增加且向低能方向移动,说明Sc、Ce掺杂使得CrSi₂在低能区的光跃迁强度增强,Sc-Ce共掺时更明显。Sc、Ce掺杂的CrSi₂吸收边在低能方向发生红移,在能量大于21.6 eV特别是在位于31.3 eV的较高能量附近,本征CrSi₂几乎不吸收光子,Sc单掺和Sc-Ce共掺CrSi₂吸收光子的能力有所增强,并在E=31.3 eV附近形成了第二吸收峰。说明掺杂Sc、Ce改善了CrSi₂对红外和较高能区光子的吸收。在小于3.91 eV的低能区掺杂后的CrSi₂光电导率增加。在20.01 eV<E<34.21 eV时,本征CrSi₂光电导率为零,但Sc、Ce掺杂后的体系不为零,掺杂拓宽了CrSi₂的光响应范围。研究结果为CrSi₂基光电器件的应用与设计提供了理论依据。     

密度泛函理论方法研究填料表面对聚合物摩擦化学的影响

采用超声分散法制备出氧化铝、高岭土、氧化硅/聚四氟乙烯复合材料, 使用线性往复摩擦磨损试验机对比三种复合材料的摩擦学性能. 结果表明 质量分数10%的氧化铝、高岭土能将聚四氟乙烯的磨损率降低约4个数量级, 而氧化硅仅能降低约3个数量级. 对金属对偶表面形成的转移膜的形貌和化学成分进行分析发现 氧化铝、高岭土/聚四氟乙烯在金属对偶面上形成了高度羧酸盐化的转移膜. 用密度泛函理论对三种填料表面上碳氟分子吸附过程进行模拟, 结果显示氧化铝、高岭土表面的路易斯酸性位点促进了碳氟分子的脱氟过程, 产生了更多的羧酸螯合物的中间产物; 氧化硅缺少路易斯酸性位点, 因此不能促进高度羧酸盐化的转移膜形成.     

Distribution dependent stochastic differential equations

Due to their intrinsic link with nonlinear Fokker-Planck equations and many other applications, distribution dependent stochastic differential equations (DDSDEs) have been intensively investigated. In this paper, we summarize some recent progresses in the study of DDSDEs, which include the correspondence of weak solutions and nonlinear Fokker-Planck equations, the well-posedness, regularity estimates, exponential ergodicity, long time large deviations, and comparison theorems.     

基于模糊神经元PID算法的注塑机注射速度控制算法研究

基于一款市场较为畅销的注塑机, 设计出一种能精确控制注射速度的模糊神经元PID控制器. 首先, 设计出具有自学能力的神经元PID控制器, 利用模糊算法对其进行优化; 其次, 在原有注射速度线性数学模型的基础上, 构建注塑机注射速度的非线性模型; 最后, 利用MATLAB在所建数学模型的基础上对模糊神经元PID控制器进行仿真实验. 实验结果表明, 所设计控制器具有响应迅速、无超调量、控制精度高、控制稳定等优点.     

Controlling thermomechanical behavior of semicrystalline hydrogenated polynorbornene through the cis- to trans-cyclopentylene ratio

Though polynorbornene synthesized by ring-opening metathesis polymerization has an intrinsically all-cis configuration of the cyclopentylene backbone rings, a fraction of these rings can be epimerized to the trans configuration during hydrogenation over suitable catalysts. By varying the method of hydrogenation, semicrystalline hydrogenated polynorbornenes (hPNs) with trans levels between 0 and 36% were obtained. With increasing trans content, the glass transition temperature, melting point, and enthalpy of melting decrease modestly. By contrast, the temperature at which the hPN crystal transitions into a rotationally disordered polymorph varies strongly with trans content, ranging from 126 °C (all-cis) to 71 °C at 27% trans; at trans contents of 34% and above, no rotationally-ordered phase is observed at any temperature. The room-temperature Young's modulus shows no dependence on trans content, while the yield stress drops by 20% at 1% trans content and slowly decreases further with additional epimerization. The temperature dependence of the Young's modulus differs for trans-containing versus all-cis polymers, while the temperature dependence of the yield stress is set by the polymorph type (rotationally ordered vs. disordered).     

A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

Monitoring the Thiol/Thiophenol Molecule-Modulated Plasmon-Mediated Silver Oxidation with Dark-Field Optical Microscopy

Surface plasmon can trigger or accelerate many photochemical reactions, especially useful in energy and environmental industries. Recently, molecular adsorption has proven effective in modulating plasmon-mediated photochemistry, however the realized chemical reactions are limited and the underlying mechanism is still unclear. Herein, by using in situ dark-field optical microscopy, the plasmon-mediated oxidative etching of silver nanoparticles (Ag NPs), a typical hot-hole-driven reaction, is monitored continuously and quantitatively. The presence of thiol or thiophenol molecules is found essential in the silver oxidation. In addition, the rate of silver oxidation is modulated by the choice of different thiol or thiophenol molecules. Compared with the molecules having electron donating groups, the ones having electron accepting groups accelerate the silver oxidation dramatically. The thiol/thiophenol modulation is attributed to the modulation of the charge separation between the Ag NPs and the adsorbed thiol or thiophenol molecules. This work demonstrates the great potential of molecular adsorption in modulating the plasmon-mediated photochemistry, which will pave a new way for developing highly efficient plasmonic photocatalysts.