Determination of polarity parameters for liquid crystals using solvatochromic method in anisotropic and isotropic phases

The use of liquid crystals (LCs) as anisotropic solvents is desired for various potential applications and usually for other organic and inorganic compounds. In this work, solvent polarity parameters are obtained using a spectroscopic method for four LCs with a range of high and low dielectric anisotropy (?ε). Solvatochromic polarity parameters for these LCs were defined via Kamlet–Abboud–Taft polarity functions characterizing different temperatures and phases, isotropic and anisotropic, and using the Reichardt’s dye and 2,6-diphenyl-4-(2,4,6-triphenyl-1-pyridinio) phenolate standard probe. The investigated polarity parameters reveal the effects of LC media on the photo-physical behaviour of solute molecules in isotropic and anisotropic media. Subsequently, a new LC polarity parameter (Z_o) is introduced as an overall matrix anisotropy polarity parameter to characterize variation between isotropic and anisotropic phases. The values of Z_o are sorted from higher to lower dielectric anisotropies (?ε).     

矩阵代数收敛至球面与非交换度量几何

介绍了Rieffel定义的紧致量子度量空间与量子Gromov-Hausdorff距离和近来Latrémolière定义的量子Gromov-Hausdorff邻距,分别讨论了矩阵代数如何在这两种量子距离下收敛至球面.     

A fast discontinuous finite element discretization for the space‐time fractional diffusion‐wave equation

In this article, we study fast discontinuous Galerkin finite element methods to solve a space‐time fractional diffusion‐wave equation. We introduce a piecewise‐constant discontinuous finite element method for solving this problem and derive optimal error estimates. Importantly, a fast solution technique to accelerate Toeplitz matrix‐vector multiplications which arise from discontinuous Galerkin finite element discretization is developed. This fast solution technique is based on fast Fourier transform and it depends on the special structure of coefficient matrices. In each temporal step, it helps to reduce the computational work from required by the traditional methods to log , where is the size of the coefficient matrices (number of spatial grid points). Moreover, the applicability and accuracy of the method are verified by numerical experiments including both continuous and discontinuous examples to support our theoretical analysis.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 2043–2061, 2017     

椭圆PDE-约束优化问题的一个预条件子

针对由Galerkin有限元离散椭圆PDE-约束优化问题产生的具有特殊结构的3×3块线性鞍点系统,提出了一个预条件子并给出了预处理矩阵特征值及特征向量的具体表达形式.数值结果表明了该预条件子能够有效地加速Krylov子空间方法的收敛速率,同时也验证了理论结果.