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     

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.     

Curvature investigation in tapered fibers and its application to sensing and mode conversion

Non-adiabatic tapered fibers are basic photonic components used in a wide range of applications. Here we investigate a way to increase their utility through the controllable bending of one of their tapered sections. The experiments carried out explain, for the first time, the mechanics of this approach showing how these tapers can be used to build more sensitive sensors. Their use as highly efficient mode converters is also discussed.     

Sobolev Stability of Plane Wave Solutions to the Nonlinear Schrödinger Equation

This article explores the questions of long time orbital stability in high order Sobolev norms of plane wave solutions to the NLSE in the defocusing case.     

Recent Progress in the $L_p$ Theory for Elliptic and Parabolic Equations with Discontinuous Coefficients

In this paper, we review some results over the last 10-15 years on elliptic and parabolic equations with discontinuous coefficients. We begin with an approach given by N. V. Krylov to parabolic equations in the whole space with $\rm{VMO}_x$ coefficients. We then discuss some subsequent development including elliptic and parabolic equations with coefficients which are allowed to be merely measurable in one or two space directions, weighted $L_p$estimates with Muckenhoupt ($A_p$) weights, non-local elliptic and parabolic equations, as well as fully nonlinear elliptic and parabolic equations.     

非线性互补问题的一种全局收敛的显式光滑Newton方法

本针对Po函数非线性互补问题，给出了一种显式光滑Newton方法，该方法将光滑参数μ进行显式迭代而不依赖于Newton方向的搜索过程，并在适当的假设条件下，证明了算法的全局收敛性。     

光束发散度对紫外写入光纤光栅的影响

用傅里叶衍射光学分析了准分子激光束发散度对于光纤光栅制备的影响，发现光束发散角使光纤光栅的布拉格波长发生改变，相位版后干涉场沿光纤轴向和径向不均匀，对制备30dB高反射率光纤光栅造成困难。实验结果与理论分析基本一致，相对于理想平行光束情况，会聚光束使得光纤光栅布拉格波长出现在短波一边，发射光束使得光纤光栅布拉格波长出现在长波一边。     

355nm Nd∶YAG激光在H_2中的高效一级斯托克斯转换

对脉冲Nd∶YAG激光(355 nm)在H2和H2∶He-Ar混合气体中的受激拉曼散射(SRS)进行了研究。在0.5 MPa的氢气中,同时测量到从二级反斯托克斯到三级斯托克斯的多波长输出,其总转化效率达88%;而高压下只剩下一级和二级斯托克斯输出,其中二级斯托克斯最大能量转化效率达44%(对应量子效率为63%)。由于高级斯托克斯的竞争,纯氢气中一级斯托克斯的最大能量转换效率不超过43%。通过向3 MPa氢气中掺入2 MPaAr气后,很好地抑制了二级斯托克斯的产生,从而获得了能量转换效率高达71%(对应量子效率为83%)的一级斯托克斯输出。对四波混频和级联受激拉曼散射在氢气多级斯托克斯产生中的作用以及惰性气体对它们的影响进行了讨论。