On mesh restrictions to satisfy comparison principles,maximum principles,and the non-negative constraint: Recent developments and new results

This article concerns mesh restrictions that are needed to satisfy several important mathematical properties—maximum principles, comparison principles, and the nonnegative constraint—for a general linear second-order elliptic partial differential equation. We critically review some recent developments in the field of discrete maximum principles, derive new results, and discuss some possible future research directions in this area. In particular, we derive restrictions for a three-node triangular (T3) element and a four-node quadrilateral (Q4) element to satisfy comparison principles, maximum principles, and the nonnegative constraint under the standard single-field Galerkin formulation. Analysis is restricted to uniformly elliptic linear differential operators in divergence form with Dirichlet boundary conditions specified on the entire boundary of the domain. Various versions of maximum principles and comparison principles are discussed in both continuous and discrete settings. In the literature, it is well-known that an acute-angled triangle is sufficient to satisfy the discrete weak maximum principle for pure isotropic diffusion. Herein, we show that this condition can be either too restrictive or not sufficient to satisfy various discrete principles when one considers anisotropic diffusivity, advection velocity field, or linear reaction coefficient. Subsequently, we derive appropriate restrictions on the mesh for simplicial (e.g., T3 element) and nonsimplicial (e.g., Q4 element) elements. Based on these conditions, an iterative algorithm is developed to construct simplicial meshes that preserve discrete maximum principles using existing open source mesh generators. Various numerical examples based on different types of triangulations are presented to show the pros and cons of placing restrictions on a computational mesh. We also quantify local and global mass conservation errors using representative numerical examples and illustrate the performance of metric.     

In Situ Observation of Crystallization of Methylammonium Lead Iodide Perovskite from Microdroplets

It is of great importance to investigate the crystallization of organometallic perovskite from solution for enhancing performance of perovskite solar cells. Here, this study develops a facile method for in situ observation of crystallization and growth of the methylammonium lead iodide (MAPbI₃) perovskite from microdroplets ejected by an alternating viscous and inertial force jetting method. It is found that there are two crystallization modes when MAPbI₃ grows from the CH₃NH₃I (MAI)/PbI₂/N,N‐dimethylformamide (DMF) solution: needle precursors and granular perovskites. Generally, needle Lewis adduct of MAPbI₃·DMF tends to nucleate and grow from the solution due to low solubility of PbI₂. The growth of MAPbI₃·DMF depends on both the concentration of MAI and temperature. It tends to form large perovskite domains on substrates at high temperature. The MAPbI₃·DMF coverts to nanocrystalline perovskite due to lattice shrinkage when DMF molecules escape from the Lewis adduct. Granular perovskite can also directly nucleate from the solution at high concentration of MAI due to compositional segregation.     

Elemental partitioning,lattice misfit and creep behaviour of Cr containing γ′ strengthened Co base superalloys

Novel Cr containing Co-Al-W base superalloys were studied by atom probe tomography and neutron diffraction. Cr is found to predominantly partition to the γ matrix and decrease partitioning of W to γ′. Furthermore, Cr significantly enhances the γ′ volume fraction, decreases the γ/γ′ lattice misfit and deteriorates the creep resistance. Addition of Ni to the Cr containing alloys affects partitioning of W and Al, further decreases the lattice misfit and results in the formation of irregularly shaped precipitates. Al, W and Cr tend to occupy the ‘B'sublattice in the γ′-A₃B phase (L1₂ type), while Co and Ni reside in the ‘A' sublattice.     

高效单晶硅太阳电池基区结构设计与参数优化

首先利用TCAD半导体器件仿真软件全面系统地分析了在不同少子寿命的情况下,基区电阻率对常规P型单晶硅太阳电池输出特性的影响。然后基于对仿真结果的分析,提出一种具有非均匀基区的单晶硅太阳电池结构,并对其输出特性进行了仿真研究。结果表明:当少子寿命一定时,存在最优的基区电阻率,使得常规电池的转换效率最大;随着少子寿命的减小,电池最优的基区电阻率减小;提高基区电阻率有利于常规电池长波段量子效率和短路电流的提高,但同时会降低电池的开路电压和填充因子;当少子寿命较低时,非均匀基区结构不具有提高常规电池转换效率的作用。但当少子寿命增大到一定值时,通过优化非均匀基区的表面浓度,非均匀基区结构可有效改善常规电池的电学性能。     

基于海量数据分析的煤矿生产辅助决策支持系统的设计

以某煤矿自动化系统的建设为例,提出了一种基于海量数据分析的煤矿生产辅助决策支持系统的设计方案。该系统通过融合全矿井各传感器采集的数据,进行分系统的汇聚统计分析以及全系统的集成统计分析,可对煤矿生产过程中各机电设备的健康状况、故障、运行能耗作出判断,从而实现对煤矿生产的辅助决策支持。实际应用表明,该系统运行良好,提高了煤矿生产效率和管理水平。     

数据库技术的研究现状及发展趋势

介绍了数据库系统设计过程的六个阶段,即需求分析阶段、概念结构设计阶段、逻辑结构设计阶段、物理结构设计阶段、实施阶段、运行与维护阶段;以分布式数据库系统、知识库系统和主动数据库系统为例,阐述了当前数据库系统研究的现状;结合数据仓库、工程数据库、统计数据库、空间数据库等多种数据库,指出了当前数据库技术的研究热点和发展趋势。     

职业学校课程项目化教学改革

项目化教学是一种面向就业市场的新型教学模式,正逐步走进职业学校的课堂。在获得师生认可的同时,该教学方式在教学改革中体现出的矛盾也十分突出。本文对当前职业学校课程项目化教学改革中的诸多问题进行系统分析,提出比较现实的解决对策及具体的实施过程。     

MATLAB仿真在基带传输教学中的应用

根据基带传输相关课程内容的特点,提出采用MATLAB/Simulink仿真来进行演示和实验以解决相关的问题。同时阐述了使用MATLAB/Simulink对基带传输系统仿真的过程。