Dealloying Ag–Al Alloy to Prepare Nanoporous Silver as a Substrate for Surface‐Enhanced Raman Scattering: Effects of Structural Evolution and Surface Modification

Sensitive detection of molecules by using the surface‐enhanced Raman scattering (SERS) technique depends on the nanostructured metallic substrate and many efforts have been devoted to the preparation of SERS substrates with high sensitivity, stability, and reproducibility. Herein, we report on the fabrication of stable monolithic nanoporous silver (NPS) by chemical dealloying of Ag–Al precursor alloys with an emphasis on the effect of structural evolution on SERS signals. It was found that the dealloying conditions had great influence on the morphology (the ligament/pore size) and the crystallization status, which determined the SERS signal of rhodamine 6G on the NPS. NPS with small pores, low residual Al, and perfect crystallization gave high SERS signals. A high enhancement factor of 7.5×10⁵ was observed on bare NPS obtained by dealloying Ag₃₀Al₇₀ in 2.5 wt % HCl at room temperature followed by 15 min aging at around 85 °C. After coating Ag nanoparticles on the NPS surface, the enhancement factor increased to 1.6×10⁸ owing to strong near‐field coupling between the ligaments and nanoparticles.     

On a novel expression of the field scattered by an arbitrary constant impedance plane

The electromagnetic field scattered by an impedance plane is generally given by its plane wave expansion (Fourier representation). Here we derive an alternative expression which is more suitable for point source illumination. For this, we consider an original expression of the Hertz potentials for the incident field and express the scattered potentials in a novel form. A special function then involved can be expressed in an integral which is in turn expanded in a convergent series. The expression presented also permits us to express complete asymptotics. Our development considers an arbitrary impedance, passive or active.     

Surface wave scattering by a material filled rectangular impedance groove in a reactive plane

The problem of TE-polarized surface wave scattering from a rectangular impedance groove located on an infinite reactive plane which is filled with dielectric material is considered for a rather general case where the impedances of the horizontal and vertical sides of the groove have different values. The multiple interactions up to the second order between the edges of the groove are obtained to yield diffracted field. The diffraction problem is first reduced into a modified Wiener-Hopf equation and then solved approximately. The solution contains branch-cut integrals and two infinite sets of constants satisfying two infinite systems of linear algebraic equations. The approximate analytical evaluations of the corresponding integrals as well as the numerical solutions of the linear algebraic equation systems are obtained for various values of the parameters such as the surface reactance of the guiding plane, the vertical and horizontal wall impedances of the groove, the permittivity of the material loading, the width and the height of the groove which permit one to study the effect of these parameters on the diffraction phenomenon.     

平面P波在充满流体的任意形状孔洞上的散射

采用复变函数的保角映射方法和波函数展开法,根据孔洞与内部流体在界面上的应力和位移连续的边界条件,得到了充满流体的任意形状的孔洞对入射平面P波的散射问题的理论解,以椭圆形孔洞为例,着重分析了椭圆的长短轴之比、流体的存在与否以及入射频率对散射幅值的影响,结果表明:(1)圆形孔洞的分波波谱的峰值分布均匀,而椭圆形孔洞则不均匀;(2)散射P波的波谱主要集中于前进方向和背向一侧,而散射S波的波谱主要集中于与传播方向垂直的一侧;(3)入射波与孔洞的作用面积越大,散射P波的波谱也越大,而散射S波的波谱也越小;(4)当孔洞为圆形时,流体对散射P波和S波的波谱影响最小,即此时流体与孔壁的动力相互作用最小.     

扭转变形平面假设的讨论

在对圆轴扭转平面假设的内涵进行分析的基础上, 关联其在应力分析中 的应用, 并讨论了平面假设成立的条件以解释矩形截面翘曲现象, 可作为该部分课堂教学的 参考材料.     

损伤因素对单层平面索网静力性能影响研究：有限元分析与试验验证

运用通用有限元软件ANSYS建立三维有限元模型,对横索与竖索连接节点失效、索预应力损失和锚固端失效这三种损伤因素的不同损伤工况下,单层平面索网结构的受力性能进行了非线性有限元分析,并与相应的试验结果进行了全面对比分析。结果表明：本文的有限元模型能够准确地分析计算上述三种损伤因素对单层平面索网结构受力性能的影响,包括结构...     

Structural stability analysis of gene regulatory networks modeled by Boolean networks

This paper studies the structural monostability and structural cycle‐stability of Boolean networks (BNs). Firstly, the structural‐equivalent Boolean networks are converted to the algebraic forms by using the semitensor product of matrices. Secondly, the concepts of structural monostability and structural cycle‐stability for Boolean networks are proposed. On the basis of the algebraic forms of structural‐equivalent Boolean networks, some necessary and sufficient conditions are presented for the structural monostability and structural cycle‐stability of Boolean networks. Finally, an illustrative example is worked out to show the effectiveness of the obtained results.     

Schwarz problem for higher‐order complex partial differential equations in the upper half plane

Linear and nonlinear elliptic complex partial differential equations of higher‐order are considered under Schwarz conditions in the upper‐half plane. Firstly, using the integral representations for the solutions of the inhomogeneous polyanalytic equation with Schwarz conditions, a class of integral operators is introduced together with some of their properties. Then, these operators are used to transform the problem for linear equations into singular integral equations. In the case of nonlinear equations such a transformation yields a system of integro‐differential equations. Existence of the solutions of the relevant boundary value problems for linear and nonlinear equations are discussed via Fredholm theory and fixed point theorems, respectively.     

单轴压缩条件下溶蚀礁灰岩细观变形破坏特征研究

礁灰岩的溶蚀对海洋工程和岛礁工程的稳定性有明显的影响.孔隙型溶蚀是礁灰岩常见的溶蚀方式.本文通过构建随机溶蚀孔洞的离散元模型,模拟孔洞型溶蚀礁灰岩的细观变形破坏特征,分析其变形破坏规律与裂隙演化特征.结果 表明,基于随机聚类算法构建的溶蚀礁灰岩离散元模型能够很好地模拟孔洞型溶蚀作用,且其变形破坏特征具有明显的规律;随着溶蚀率的增加,溶蚀礁灰岩单轴应力应变曲线由单峰型逐渐转变为双峰型或多峰型,破坏特征由脆性破坏逐渐转变为塑性破坏;随着溶蚀率的增加,礁灰岩单轴抗压强度和弹性模量都逐渐减小,抗压强度呈指数函数下降,弹性模量呈线性函数下降,而泊松比则表现为先增后降,说明试样在高溶蚀率时主要发生结构性破坏;随着溶蚀率增加,礁灰岩的宏观破裂面逐渐消失,由于溶蚀孔洞的相互作用,导致了起源于孔洞周围的裂隙开始萌生,并逐渐贯通,最终导致试样发生整体宏观破坏.本研究成果可为深入认识海洋工程和岛礁工程中溶蚀礁灰岩的变形破坏特征提供理论参考.