A Kirchhoff‐type equation involving critical exponent and sign‐changing weight functions in dimension four

In the paper, we study the existence and multiplicity of positive solutions for the following Kirchhoff equation involving concave‐convex nonlinearities: (1) We obtain the existence and multiplicity of solutions of 1 by variational methods and concentration compactness principle.     

Third- and second-order optical nonlinearity of Ge-Ga-S-PbI2 chalcohalide glasses

Two series of metal iodide doped chalcohalide glasses (100−2x)GeS₂·xGa₂S₃·xPbI₂ (0?x?20) and (100−x)(0.8GeS₂·0.2Ga₂S₃)·xPbI₂ (0?x?15) were prepared and characterized. The microstructure of these glasses has been studied by Raman scattering spectra. Utilizing femtosecond time-resolved optical Kerr effect (OKE) technique at the wavelength of 820 nm, a largest third-order nonlinearity χ⁽³⁾ of 2.07×10⁻¹³ esu was obtained for the 90GeS₂·5Ga₂S₃·5PbI₂ glass, and it decreases with the addition of PbI₂ in both two series. After thermally poled, second-harmonic generation (SHG) has been observed in these glasses according to Maker fringe method and a large second-order nonlinearity χ⁽²⁾ as well as 4 pm/V was obtained for the 70GeS₂·15Ga₂S₃·15PbI₂ glass. The variations of χ⁽²⁾ and χ⁽³⁾ on glass composition are ascribed to the evolution of micro-structural units in glass. These novel chalcohalide glasses would be expected to be the promising candidate materials for nonlinear optical devices.     

General dynamic equation and dynamical characteristics of viscoelastic Timoshenko beams

In this paper, a governing differential equation of viscoelastic Timoshenko beam including both extension and shear viscosity is developed in the time domain by direct method. To measure the complex moduli and three parameters of standard linear solid, the forced vibration technique of beam is successfully used for PCL and PMMA specimens. The dynamical characteristics of viscoelastic Timoshenko beams, especially the damping properties, are derived from a considerable number of numerical computations. The analyses show that the viscosity of materials has great influence on dynamical characteristics of structures, especially on damping, and the standard linear solid model is the better one for describing the dynamic behavior of high viscous materials.     

Perron–Frobenius Theory and Symmetry of Solutions to Nonlinear PDE's

We suggest a simple but general method of establishing symmetry properties of stable solutions of nonlinear elliptic equations. The method relies on characterization of symmetry breaking with a help of zero modes and on a generalization of the Perron–Frobenius theory.     

聚苯胺/NMP溶液的激光诱导自衍射

实验观察到526um基模高斯先来通过聚苯按/N-甲基-2-吮咯烷酮(NMP)溶液时,在这场处产生了多个同心衍射圆环。该现象可以用高斯光束通过非线性介质时产生的空间自相位调制来解释。理论分析表明,对于薄样品,光束横截面上产生的非线性附加相移近似于高斯分布。通过测量衍射环个数,可以估算出聚苯胺/NMP溶液(对526um的吸收系数为0.56cm^-1)的克尔常数γ≈4.4x10^-10m²/W.     

Discontinuous reaction-diffusion equations under discontinuous and nonlocal flux conditions

In this paper, we consider a quasilinear parabolic equation with discontinuous source term in a bounded cylindrical domain under nonlocal and discontinuous flux conditions. Our main goal is to prove the existence of extremal solutions within a sector formed by appropriately defined upper and lower solutions. The main tools used in the proof of our result are recently obtained abstract results on nonlinear evolution equations, an abstract fixed-point result in partially ordered sets, compact embeddings, comparison, and truncation techniques.     

π-electron density dependence of third-order optical nonlinearities in poly(1,4-phenylene vinylene) derivatives

The third-order nonlinear optical properties of poly(1,4-phenylene vinylene) (PPV), poly(2-bromo-1,4-phenylene vinylene) (BrPPV) and poly(2-chloro-1,4-phenylene vinylene) (ClPPV) were studied by forward degenerate four-wave mixing (DFWM). They have large and ultrafast third-order optical nonlinear responses, which mainly arise from the distortion of the large π-conjugated electronic charge distribution in the backbone. It was found that there was a significant contribution to π-electron density and thus χ⁽³⁾ values from the substituents at the phenylene ring.     

Optical limiting action of 2-amino 5-nitro pyridinium chloride crystal for laser safety devices

ABSTRACT

The liquid crystal (LC) displays with narrow bezel design require excellent physical properties such as high adhesion, low moisture permeability, and low LC contamination. Among the adhesive components, the heat curing agent is an important component in the adhesive and plays a key role in the adhesion between the epoxy resins. In this study, new UV/heat dual-curable adhesives involving a multi-functional heat-curing agent of branched polyethylenimine have been prepared and evaluated by adhesive strength, moisture permeability, and LC contamination measurements. It is shown that the proposed adhesives offer excellent adhesive properties for narrow-bezel applications.     

基于ABCD矩阵的Z-扫描理论

基于光学系统对傍轴激光束的传输与变换技术—ABCD定理,以非线性相移为研究对象,采用表征高斯光束特征的q参量在光束无像散近似假设下,分析了Z-扫描测量方法的理论基础,得到了表达简单的解析理论公式.在非线性相移｜ΔΦ0｜<π rad时,所得模拟结果可以很好地与已知理论结果相吻合.对CS2和纳米碳管乙醇溶液的非线性测量及数据的拟合,证明了用此结论进行数据分析的简洁性和优越性.     

Ag:Bi2O3复合膜的线性和非线性光学性质

从实验和理论两个方面，探讨了金属Ag不同掺杂浓度对Ag:Bi₂O₃复合膜线性和非线性光学性质的影响. 用吸收光谱研究了Ag浓度与Ag:Bi₂O₃复合膜表面等离子体共振带之间的关系；用皮秒Z-扫描技术研究了共振和非共振情况下(激发光波长分别为532nm和1064nm)，金属Ag浓度与复合膜三阶非线性极化率的关系. 基于表面等离子体共振理论和局域场增强理论对复合膜进行了分析，得到了不同Ag浓度时Ag:Bi₂O₃复合膜的三阶非线性效应，研究了激发波长和金属浓度对复合膜线性和非线性光学性质的影响. 结果表明，等离子体共振增强和合适的金属掺杂浓度使得三阶极化率增强二个量级，在Ag浓度为35％左右和接近等离子体共振频率(相应吸收带位于560nm—622nm)的532nm激发时，χ⁽³⁾具有最大值2.4×10^-9esu. 关键词： 金属纳米颗粒 复合膜 三阶非线性 表面等离子体共振