On the optimal parameters of GMSSOR method for saddle point problems

For solving saddle point problems, SOR-type methods are investigated by many researchers in the literature. In this short note, we study the GMSSOR method for solving saddle point problems and obtain the optimal parameters which minimize the spectral (or pseudo-spectral) radii of the iteration matrices.     

单入射波长及纤芯存在光致双折射的长周期光纤光栅的折射率传感分析

利用全矢量耦合模方程提出并分析了一种基于纤芯存在光致双折射的长周期光纤光栅的环境折射率传感测量方法.以波长为谐振波长的完全偏振光为入射波,通过分析不同环境折射率下输出光的偏振态在邦加球上与参考点间球面距离的变化测量环境折射率.分析表明,在环境折射率1～1.30范围内包层半径为20.75 μm的长周期光纤光栅传感器线性特性良好,灵敏度为0.356/RIU,可应用于湿度和气体的折射率测量;该分析方法适用于其他类型的双折射长周期光纤光栅传感器的设计.     

改进的孔隙模型评价流体性质与裂缝孔隙度

随着勘探开发的不断深入,渤海油田面临越来越多的疑难储层,这类储层流体性质识别与裂缝孔隙度评价成为测井评价的难点。本文依据Biot理论,描述了存在裂隙条件下的含裂隙Biot理论,形成改进的孔隙介质模型。根据该模型利用阵列声波测井数据进行反演得到裂缝孔隙度,同时通过流体置换,得到不同流体对应的岩石体积模量,对其进行交会判别流体性质,实现了阵列声波测井裂缝孔隙度定量评价与流体性质识别综合应用。利用该模型对渤海油田十几口井进行计算,结果表明该方法对于常规砂泥岩和复杂岩性储层均能取得较好效果,本文提出的储层流体性质识别与裂缝孔隙度评价方法,有助于扩展阵列声声波测井的应用范围。     

Effect of non-acoustic parameters on heterogeneous sonoporation mediated by single-pulse ultrasound and microbubbles

Sonoporation—transient plasma membrane perforation elicited by the interaction of ultrasound waves with microbubbles—has shown great potential for drug delivery and gene therapy. However, the heterogeneity of sonoporation introduces complexities and challenges in the realization of controllable and predictable drug delivery. The aim of this investigation was to understand how non-acoustic parameters (bubble related and bubble-cell interaction parameters) affect sonoporation. Using a customized ultrasound-exposure and fluorescence-imaging platform, we observed sonoporation dynamics at the single-cell level and quantified exogenous molecular uptake levels to characterize the degree of sonoporation. Sonovue microbubbles were introduced to passively regulate microbubble-to-cell distance and number, and bubble size. 1 MHz ultrasound with 10-cycle pulse duration and 0.6 MPa peak negative pressure were applied to trigger the inertial collapse of microbubbles. Our data revealed the impact of non-acoustic parameters on the heterogeneity of sonoporation. (i) The localized collapse of relatively small bubbles (diameter, D < 5.5 μm) led to predictable sonoporation, the degree of which depended on the bubble-to-cell distance (d). No sonoporation was observed when d/D > 1, whereas reversible sonoporation occurred when d/D < 1. (ii) Large bubbles (D > 5.5 μm) exhibited translational movement over large distances, resulting in unpredictable sonoporation. Translation towards the cell surface led to variable reversible sonoporation or irreversible sonoporation, and translation away from the cell caused either no or reversible sonoporation. (iii) The number of bubbles correlated positively with the degree of sonoporation when D < 5.5 μm and d/D < 1. Localized collapse of two to three bubbles mainly resulted in reversible sonoporation, whereas irreversible sonoporation was more likely following the collapse of four or more bubbles. These findings offer useful insight into the relationship between non-acoustic parameters and the degree of sonoporation.     

Positive solutions for a class of p-Laplacian systems with multiple parameters

Consider the system

     

A new estimate for the vertex number of an edge-regular graph

Given a connected edge-regular graph Γ with parameters (v, k, λ) and b ₁ = k ? λ ? 1, we prove that in the case k ≥ 3b ₁ ?2 either |Γ₂(u)|(k?2b ₁ + 2) < kb ₁ for every vertex u or Γ is a polygon, the edge graph of a trivalent graph without triangles that has diameter greater than 2, the icosahedral graph, the complete multipartite graph K _r×2, the 3 × 3-grid, the triangular graph T(m) with m ≤ 7, the Clebsch graph, or the Schläfli graph.     

Electrochemical behavior of kryptand 222 on a mercury electrode

The electrochemical behavior of kryptand 222 at the interface between a mercury electrode and an aqueous solution is studied by the impedance spectroscopy, polarography, and cyclic voltammetry methods. It is established that kryptand 222 possesses high surface activity at this interface. Adsorption parameters of kryptand 222 are found on the basis of the model of two parallel capacitors supplemented by the Frumkin isotherm by the regression analysis method. The potential dependences of the differential capacitance (C,E curves), calculated using these parameters satisfactorily agree with experiment. It is shown that the maximum in the C,E curves in the region of negative potentials is caused by catalytic process of hydrogen evolution.     

Conductivity and thermal expansion of the Ce<Subscript>0.8</Subscript>Gd<Subscript>0.2</Subscript>O<Subscript>1.9</Subscript> solid electrolyte in the oxidizing and reducing atmospheres

Highly compact (99%) solid electrolyte Ce_0.8Gd_0.2O_1.9 with submicron (0.3 μm) grains is synthesized. The dilatometric (20–850°C) and conductivity (180–350°C) measurements are performed on the electrolyte in air and as a function of the partial oxygen pressure \(p_{O_2 } \) (0.21?1×10^?25 atm) at 600, 700, and 800°C. An inflection is found in the temperature dependences of the thermal coefficient of linear expansion and conductivity (impedance measurements) at ～230°C, which is the evidence for a phase transition. The activation energies for conduction in the grain bulk and boundaries differ only slightly, indicating that the grain boundaries’ resistance is caused not by the precipitation of the second phase at the boundaries, but most probably by the presence of intergranular nanopores. The dilatometric measurements confirm a significant increase in the linear dimensions of Ce_0.8Gd_0.2O_1.9 in the reducing atmospheres with a parallel increase in its electron conductivity. The electron conductivity and specific elongation increase proportionally to \(p_{O_2 }^{ - 1/4} \) at all temperatures. The \(p_{O_2 } \) values, at which the transport numbers of ions t _i = 0.5, are determined. They are 10^?22.5, 10^?20, and 10^?18 atm at 600, 700, and 800°C, respectively.