A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

Response surface methodology toward the optimization of high-energy carotenoid extraction from Aristeus antennatus shrimp

High-energy assisted extraction techniques, like ultrasound assisted extraction (UAE) and microwave assisted extraction (MAE), are widely applied over the last years for the recovery of bioactive compounds such as carotenoids, antioxidants and phenols from foods, animals and herbal natural sources. Especially for the case of xanthophylls, the main carotenoid group of crustaceans, they can be extracted in a rapid and quantitative way with the use of UAE and MAE.     

基于电化学老化衰退模型的锂离子动力电池外特性

当前锂离子动力电池电化学模型存在模型复杂、建模难度大、计算效率低、老化评估效果差的问题,本文提出一种考虑电池衰退老化的机理模型(ADME).本文首先通过有限差分法对伪二维(P2D)电化学模型进行离散降阶处理,得到简化伪二维(SP2D)模型.在SP2D模型的基础上,基于阴阳两极发生的副反应导致的衰退老化现象,提出一种考虑电池衰退老化的机理模型.其次,使用多变量偏差补偿最小二乘法实现模型参数辨识.最后通过动力电池衰退老化性能循环实验,对比分析了恒流、脉冲工况下SP2D模型和ADME模型的终端电压输出.结果表明:ADME模型较为简单、计算效率和估算精度高,可以有效评估电池容量老化衰退,得到理想的锂离子动力电池外特性曲线.     

13C NMR investigations of molecular order of rod-like,bent-core,and thiophene mesogens

In this review, methods to obtain the orientational order of topologically variant molecular mesogens using by one- and two-dimensional (2D) solid-state ¹³C nuclear magnetic resonance (NMR) spectroscopy are described. Besides ¹³C chemical shifts, the ¹³C─¹H dipolar couplings measured from 2D-separated local field (SLF) technique are used for computing the order parameters of a variety of mesogens. The investigated molecules are composed of a variable number of rings in the core, that is, core ranging from simply one ring to five rings. Among the mesogens investigated, a special focus has been placed on mesogens with thiophene rings, which are gaining popularity as liquid crystalline organic semiconductors. The replacement of a phenyl ring by thiophene in the core has a dramatic influence on molecular topology, as observed from the measured order parameters. The review highlights the advantages of the 2D SLF method for understanding the local dynamics and for mapping the topology of mesogens through the measured order parameters. SLF NMR studies of as many as 24 molecular mesogens that vary in terms of the molecular structure as well as topology are covered in the review. Order parameters of the rings have been estimated from the ¹³C─¹H dipolar couplings in the nematic, smectic A, smectic C, and tilted hexatic phases as well as in B₁ and B₂ mesophases of various mesogens. It is anticipated that, in the years to come, the 2D SLF method would provide advanced molecular information on structurally complex mesogens that are emerging in liquid crystal science through the incessant efforts of synthetic chemists. The mini review covers the orientational order of topologically variant molecular mesogens determined by 1D and 2D solid-state ¹³C NMR spectroscopy. Accordingly, rod-like, bent-core, and thiophene mesogens were subjected to 2D SLF measurements to get the order parameters from which the topology was established. The replacement of phenyl ring by thiophene and its influence on order parameters as well as on molecular topology is also discussed.     

Time-dependent Ginzburg–Landau equations for multi-gap superconductors

We numerically solve the time-dependent Ginzburg–Landau equations for two-gap superconductors using the finite-element technique. The real-time simulation shows that at low magnetic field, the vortices in small-size samples tend to form clusters or other disorder structures. When the sample size is large, stripes appear in the pattern. These results are in good agreement with the previous experimental observations of the intriguing anomalous vortex pattern, providing a reliable theoretical basis for the future applications of multi-gap superconductors.     

Azobenzene‐Functionalized Cage Silsesquioxanes as Inorganic–Organic Hybrid,Photoresponsive, Nanoscale,Building Blocks

Mono‐ and octa‐azobenzene‐functionalized cage silsesquioxanes were easily synthesized by the reaction of 4‐bromoazobenzene with monovinyl‐substituted octasilsesquioxane and cubic octavinylsilsesquioxane through the Heck coupling reaction. Excited‐state energies obtained from time‐dependent density functional theory (TDDFT) and the CAM‐B3LYP functional correlate very well with experimental trans–cis photoisomerization results from UV/Vis spectroscopy. These azobenzene‐functionalized cages exhibit good thermal stability and are fluorescent with maximum emission at approximately 400 nm, making them potential materials for blue‐light emission.     

Efficient Collocation Schemes for Singular Boundary Value Problems

We discuss an error estimation procedure for the global error of collocation schemes applied to solve singular boundary value problems with a singularity of the first kind. This a posteriori estimate of the global error was proposed by Stetter in 1978 and is based on the idea of Defect Correction, originally due to Zadunaisky. Here, we present a new, carefully designed modification of this error estimate which not only results in less computational work but also appears to perform satisfactorily for singular problems. We give a full analytical justification for the asymptotical correctness of the error estimate when it is applied to a general nonlinear regular problem. For the singular case, we are presently only able to provide computational evidence for the full convergence order, the related analysis is still work in progress. This global estimate is the basis for a grid selection routine in which the grid is modified with the aim to equidistribute the global error. This procedure yields meshes suitable for an efficient numerical solution. Most importantly, we observe that the grid is refined in a way reflecting only the behavior of the solution and remains unaffected by the unsmooth direction field close to the singular point.     

Effect of absorbed pump power on the quality of output beam from monolithic microchip lasers

The dependence of the beam propagation factor (M ² parameter) with the absorbed pump power in the case of monolithic microchip laser under face-cooled configuration is extensively studied. Our investigations show that the M ₂ parameter is related to the absorbed pump power through two parameters (α and β) whose values depend on the laser material properties and laser configuration. We have shown that one parameter arises due to the oscillation of higher order modes in the microchip cavity and the other parameter accounts for the spherical aberration associated with the thermal lens induced by the pump beam. Such dependency of M ² parameter with the absorbed pump power is experimentally verified for a face-cooled monolithic microchip laser based on Nd³⁺ -doped GdVO₄ crystal and the values of α and β parameters were estimated from the experimentally measured data points.     

A likelihood-based method for haplotype association studies of case-control data with genotyping uncertainty

This paper discusses the associations between traits and haplotypes based on Fl (fluorescent intensity) data sets. We consider a clustering algorithm based on mixtures of t distributions to obtain all possible genotypes of each individual (i.e. "GenoSpec-trum"). We then propose a likelihood-based approach that incorporates the genotyping uncertainty to assessing the associations between traits and haplotypes through a haplotype-based logistic regression model. Simulation studies show that our likelihood-based method can reduce the impact induced by genotyping errors.     

93W合金有关力学参量的综合选评

 对93W合金材料进行了超声测量实验，并结合原有的超声测量结果进行了分析比较，提出了可以直接用冲击波速度关系式的三个系数c₀ 、λ和λ′来对钨合金的有关力学参量，如G₀、K₀、G₀′、K₀′等进行综合选评的方法。得到了一组对93W合金较为合理的力学参量推荐值。