Spatially restricted Double Z-Simplified Box Orbital basis sets: Optimization and comparison with some standard basis sets

As part of previous studies, we introduced a new type of basis function named Simplified Box Orbitals (SBOs) that belong to a class of spatially restricted functions which allow the zero differential overlap (ZDO) approximation to be applied with complete accuracy. The original SBOs and their Gaussian expansions SBO-3G form a minimal basis set, which was compared to the standard Slater-type orbital basis set (STO-3G). In the present paper, we have developed the SBO basis functions at double-zeta (DZ) level, and we have assessed the option of expanding the SBO-DZ as a combination of Gaussian functions. Finally, we have determined the quality of the new basis set by comparing the molecular properties calculated with SBO-nG with those achieved with some standard basis sets.     

Accurate theoretical prediction of optical properties of BODIPY dyes

Boron-dipyrromethene dyes (BODIPY) are of great interest nowadays mostly due to their valuable optical properties. Nevertheless, no systematic research of the optical property dependence on the structure of dyes has been performed yet. In this work, analysis of the available quantum-chemical methods for BODIPY optical property calculations has been carried out. The accuracy of eight DFT functionals has been studied. The solvation effects upon excitation have been considered within two schemes. The methods that predict the absorption and emission spectra of BODIPY derivatives with high accuracy have been proposed. Using the suggested methods, the influence of nature of substituents and their position in the BODIPY core on the optical spectra of the dyes has been studied. A complex pattern of red- and blue-shifts in optical spectra in dependence of nature and position of substituents has been revealed. The results of this work provide the way for efficient design of BODIPY derivatives with desired optical properties.     

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.     

An Insight into the Diffusion of Unsaturated Polyester (UP) Resin into Expanded Graphite (EG) to Improve the Mechanical Properties of the UP/EG Composites

Abstract

Polymer/expanded graphite (EG) nanocomposites have great importance in many industrial applications mainly due to their high electrical/thermal conductivity or flame retardancy. However, to fully employ the benefits of polymer/EG nanocomposites one must consider the high degree of porosity of EG. The high degree of porosity of EG can deteriorate the composites’ mechanical properties if the polymer chains cannot diffuse completely into the EG pores. In this article, an insight is given into the diffusion of unsaturated isophthalic polyester (UP) resin, consisting of a combination of maleic anhydride and isophthalic anhydride in the resin backbone, with two viscosities, into the pores of the EG particles of various degrees of porosity. The diffusion experiments were carried out on compressed EG tablets with the same density but different porosity due to the different porosity of the EG particles. The results showed that the diffusion rate of the UP resin with higher viscosity slightly decreased when the EG porosity decreased but, in the opposite way, it strongly increased for the low viscosity UP resin. The EG nanocomposites samples were molded at varying pressures. The micrographs of the fractured surfaces of the EG nanocomposites showed that the EG pores were not filled with resin, thus the EG nanocomposites had residual pores. It was found that composites containing EGs with higher expansion ratio and larger particles and pores showed larger residual pores. Furthermore, the composites prepared with the more viscous UP resin showed more residual pores. By applying a pressure of 10?bar instead of 1?bar, a reduction of 7–20% in the residual pores of the nanocomposites was observed which led to improved mechanical properties by up to 20% in flexural strength for the EG with the highest expansion ratio.     

一种非正交对称条带束流位置监测器设计

介绍了一种条带束流位置监测器(BPM)的设计与仿真方法。在国家同步辐射实验室"太赫兹近场高通量材料物性测试系统"工程项目中,针对波荡器出口处真空室非正交对称性的问题,设计了矩形真空室和跑道形真空室下的两种非正交对称性条带BPM,并与传统的圆形真空室下条带BPM进行对比。基于边界元法,利用MATLAB软件分别对三种真空室下的条带BPM进行建模和仿真。仿真结果表明:相对于传统的圆形真空室下条带BPM,矩形和跑道形真空室下条带BPM灵敏度提高了30%,阻抗匹配误差相对降低了20%,束流位置拟合误差降低了80%。考虑加工精度,矩形真空室下的条带BPM更适用于该工程。     

均匀磁场下碳离子笔形束的剂量变化分析及位置修正方法

分析外加均匀磁场对于碳离子笔形束剂量分布的影响,并考虑修正这种影响,为磁共振成像引导碳离子放射治疗的临床应用提供指导。本文利用蒙特卡罗方法模拟计算了不同能量碳离子笔形束在不同强度磁场下的剂量分布情况,发现垂直于碳离子束入射方向的均匀磁场对于碳离子笔形束射程缩短的影响很小,磁场对碳离子束的主要影响是引起束流横向偏转,特别是碳离子束布拉格峰位置的横向侧移。横向侧移程度与碳离子束的能量和磁场强度相关,根据模拟结果,得到了一个计算碳离子束布拉格峰在磁场中相对横向偏转的方程,并提出一种校正外加磁场引起的碳离子束布拉格峰横移的角度修正方法。这些结果可用于指导磁共振图像引导碳离子放射治疗计划系统的研发。     

变角度纤维复合材料层合斜板的颤振分析

假设纤维方向角沿层合板的长度方向线性变化，研究了变角度纤维复合材料层合斜板的颤振．通过坐标变换将斜板变换为正方形板，采用层合板表面连续变化的速度环量来模拟空气对其的作用，速度环量分布利用Cauchy积分公式计算．建立了系统的Lagrange方程并采用Ritz法得到了层合板的自振频率和颤振/不稳定性分离临界速度．通过数值算例验证了本文模型和方法的正确性和收敛性，分析了各个铺层内纤维方向角的变化对自振频率和颤振/不稳定性分离临界速度的影响．研究结果表明，通过纤维的变角度铺设，可有效地提高层合板的基频和颤振/不稳定性分离临界速度．经合理设计的变角度复合材料层合板具有抑制颤振的作用．     

L1-type smoothness indicators based weighted essentially nonoscillatory scheme for Hamilton-Jacobi equations

This article presents an improved fifth-order finite difference weighted essentially nonoscillatory (WENO) scheme to solve Hamilton-Jacobi equations. A new type of nonlinear weights is introduced with the construction of local smoothness indicators on each local stencil that are measured with the help of generalized undivided differences in L¹-norm. A novel global smoothness measurement is also constructed with the help of local measurements from its linear combination. Numerical experiments are conducted in one- and two-dimensions to demonstrate the performance enhancement, resolution power, numerical accuracy for the proposed scheme, and compared it with the classical WENO scheme.