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.     

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.     

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.     

Interface and defects engineering for multilayer laser coatings

High-reflective multilayer laser coatings are widely used in advanced optical systems from high power laser facilities to high precision metrology systems. However, the real interface quality and defects will significantly affect absorption/scattering losses and laser induced damage thresholds of multilayer coatings. With the recent advances in the control of coating design and deposition processes, these coating properties can be significantly improved when properly engineered the interface and defects. This paper reviews the recent progress in the physics of laser damage, optical losses and environmental stability involved in multilayer reflective coatings for high power nanosecond near-infrared lasers. We first provide an overview of the layer growth mechanisms, ways to control the microstructures and reduce layer roughness, as well as the nature of defects which are critical to the optical loss and laser induced damage. Then an overview of interface engineering based on the design of coating structure and the regulation of deposition materials reveals their ability to improve the laser induced damage threshold, reduce the backscattering, and realize the desirable properties of environmental stability and exceptional multifunctionality. Moreover, we describe the recent progress in the laser damage and scattering mechanism of nodule defects and give the approaches to suppress the defect-induced damage and scattering of the multilayer laser coatings. Finally, the present challenges and limitations of high-performance multilayer laser coatings are highlighted, along with the comments on likely trends in future.     

Self-oscillating gels based on novel catalyst for the Belousov–Zhabotinsky reaction

We report on the synthesis of new Ru(bpy)₂(phen) catalyst for the oscillatory Belousov–Zhabotinsky chemical reaction and on the preparation of novel Ru(bpy)₂(phen)-based self-oscillating gels. The synthesized gels exhibit high-amplitude autonomous mechanical oscillations when the Belousov–Zhabotinsky reaction proceeds inside these gels     

一类压缩型映射的不动点定理

在完备的度量空间中,讨论了一类新型的非线性压缩映射ρ(Tx,Ty)≤a(ρ(x,y))ρ(x,Tx)+b(ρ(x,y))ρ(y,Ty)+c(ρ(x,y))ρ(x,y)通过构造迭代序列,指出该映射的不动点的存在性和唯一性,并给出相应的误差估计式,拓展和改进了有关文献的范围.     

Application of advanced nuclear analytical techniques for the electrocatalyst's characterization: Paving the path for mechanistic investigations

As the application of electrocatalyst continues to expand, envisaging the hidden mechanisms occurring at various length scale affecting the catalytic efficiency became important. To enhance the stability of electrocatalyst and reduce the cost, it is of paramount importance to reveal the active site's dynamics (using in situ techniques for getting the real-time information) which directly affect the reactions such as oxygen evolution reaction, hydrogen evolution reaction, and so on. Since such reactions are crucial for many engineering and scientific applications, in situ characterization techniques are required, which could capture such reactions happening at a different length and time scale. This article analyzes the recent progress made in the field of electrocatalyst's characterization using in situ neutron techniques. The article also paves the future path and has delineated the future challenges involved in multiscale correlative techniques (e.g., neutron techniques in the combination of synchrotron or microscopic techniques) used for getting the multiscale (atomic to micrometer range) mechanistic information about the electrocatalyst's working and degradation.