Imposing accurate wall boundary conditions in corrective‐matrix‐based moving particle semi‐implicit method for free surface flow

Corrective matrix that is derived to restore consistency of discretization schemes can significantly enhance accuracy for the inside particles in the Moving Particle Semi‐implicit method. In this situation, the error due to free surface and wall boundaries becomes dominant. Based on the recent study on Neumann boundary condition (Matsunaga et al, CMAME, 2020), the corrective matrix schemes in MPS are generalized to straightforwardly and accurately impose Neumann boundary condition. However, the new schemes can still easily trigger instability at free surface because of the biased error caused by the incomplete/biased neighbor support. Therefore, the existing stable schemes based on virtual particles and conservative gradient models are applied to free surface and nearby particles to produce a stable transitional layer at free surface. The new corrective matrix schemes are only applied to the particles under the stable transitional layer for improving the wall boundary conditions. Three numerical examples of free surface flows demonstrate that the proposed method can help to reduce the pressure/velocity fluctuations and hence enhance accuracy further.     

Cycloparaphenylene and their radicals anchored to a metal−organic framework

Cycloparaphenylene (CPP) shows modulated photophysical and electronic properties due to its strained structure and radially oriented π-electron system. Incorporation of CPP into metal-organic frameworks (MOFs) could transfer its extensive properties in solution to porous solids. Moreover, with the unique arrangement of the macrocycles and their interactions with the framework, emerging characteristics are anticipated. As an example of “robust dynamics”, we synthesized the first MOF structure (FDM-1001) with CPP precisely anchored to the ordered framework by employing a [8]CPP-containing linear dicarboxylate linker. Metric relationship between the dynamic macrocycles and the robust backbone creates ideal π-π interactions between them, which leads to an essentially directional arrangement of [8]CPP in the three-dimensional space. Furthermore, the MOF with [8]CPP could be successfully oxidized to generate an infinite array of radicals that show enhanced air stability compared to its molecular analogue.     

改进的PNC方法及其在非线性偏微分方程多解问题中的应用

2017年，李昭祥等提出了一种偏牛顿-校正法（Partial Newton-Correction Method，简记为PNC方法），并利用它成功地计算出了三类非线性偏微分方程的多重不稳定解.本文在PNC方法的基础上，提出并发展了一种改进的PNC方法.首先，利用Nehari流形$\mathcal{N}$与零平凡解的可分离性，建立并证明了$\mathcal{N}$的某特殊子流形$\mathcal{M}$上的全局分离定理及其推广（即局部分离定理）.全局分离定理只跟非线性偏微分算子或相应的非线性泛函本身有关，而与具体的计算方法无关.对一些典型的非线性偏微分方程多解问题（比如，Henon方程问题），该全局分离定理的分离条件，经验证是成立的.另一个方面，通过修改或补充原辅助变换的定义，去掉了原辅助变换的奇异性；接着建立并证明了某些非线性偏微分方程问题的新未知解与该非线性偏微分算子零核空间的密切关系；在证明中，去掉了在原奇异变换下所需的标准收敛（standard convergence）假设.最后，计算实例与数值结果验证了改进的PNC方法的可行性和有效性；同时表明子流形$\mathcal{M}$与已知解的可分离性是PNC方法和本文新方法能成功找到多解的关键.     

Comparative analysis of the main active components and hypoglycemic effects after the compatibility of Scutellariae Radix and Coptidis Rhizoma

In this study, a rapid and highly sensitive ultra high performance liquid chromatography with triple quadrupole mass spectrometry method with the mobile phase of acetonitrile and 0.1% aqueous formic acid was established and successfully applied to comparatively analyze main active components after their compatibility. Besides, the effects of Scutellariae Radix, Coptidis Rhizoma and combined extracts on type 2 diabetic rats induced by high‐fat diet along with low dose of streptozocin were investigated. Under the optimized chromatographic conditions, good separation of seven target components was achieved within 12 min. All calibration curves exhibited good linearity (R² ≥ 0.999). The relative standard deviation of precision, repeatability and stability varied from 0.69 to 2.23, 0.98 to 2.56, and 0.92 to 2.57%, respectively. The recovery ranged from 91.11 to 105.35%. The contents of seven active components were notably reduced after compatibility; however, the hypoglycemic effect of combined extracts was stronger than single drug by decreasing the activities of fructose‐1,6‐bisphosphatase, glucose 6‐phosphatase, phosphoenolpyruvate carboxykinase and increasing the activities of glucokinase, phosphofructokinase, pyruvate kinase. Accordingly, the established analytical method was accurate and sensitive enough for quantitative evaluation of seven investigated compounds. Moreover, the combined extract had definite effects on type 2 diabetes through multiple components against multiple targets.     

Shape morphing and topology optimization of fluid channels by explicit boundary tracking

An integrated shape morphing and topology optimization approach based on the deformable simplicial complex methodology is developed to address Stokes and Navier‐Stokes flow problems. The optimized geometry is interpreted by a set of piecewise linear curves embedded in a well‐formed triangular mesh, resulting in a physically well‐defined interface between fluid and impermeable regions. The shape evolution is realized by deforming the curves while maintaining a high‐quality mesh through adaption of the mesh near the structural boundary, rather than performing global remeshing. Topological changes are allowed through hole merging or splitting of islands. The finite element discretization used provides smooth and stable optimized boundaries for simple energy dissipation objectives. However, for more advanced problems, boundary oscillations are observed due to conflicts between the objective function and the minimum length scale imposed by the meshing algorithm. A surface regularization scheme is introduced to circumvent this issue, which is specifically tailored for the deformable simplicial complex approach. In contrast to other filter‐based regularization techniques, the scheme does not introduce additional control variables, and at the same time, it is based on a rigorous sensitivity analysis. Several numerical examples are presented to demonstrate the applicability of the approach.     

Metal-free phthalocyanine single crystal: Solvothermal synthesis and near-infrared electroluminescence

A metal-free purple H₂Pc single crystal was synthesized by a facile solvothermal method, and its solubility and near-infrared (NIR) optical properties were also investigated due to its potential applications as a light-emitting layer for OLEDs. The H₂Pc single crystal is insoluble in 1-chlorine naphthalene and other organic solvents. It gives a wide absorption in the range from 620 nm to 679 nm and a wide emission in near 922 nm. As an active light-emitting layer, H₂Pc was employed to fabricate electroluminescent (EL) devices with a structure of ITO/NPB (30 nm)/Alq₃:H₂Pc (30 nm)/BCP (20 nm)/Alq₃ (20 nm)/Al. The emission center is at 936 nm when the H₂Pc doping concentration is 20 wt%. The doping concentration strongly governs the emission intensity. When doping concentration decreases from 10 wt% to 1 wt%, the emission intensity remarkably fades, and simultaneously the emission center undergoes a blue shift.