Distribution dependent stochastic differential equations

Due to their intrinsic link with nonlinear Fokker-Planck equations and many other applications, distribution dependent stochastic differential equations (DDSDEs) have been intensively investigated. In this paper, we summarize some recent progresses in the study of DDSDEs, which include the correspondence of weak solutions and nonlinear Fokker-Planck equations, the well-posedness, regularity estimates, exponential ergodicity, long time large deviations, and comparison theorems.     

一类压缩型映射的不动点定理

在完备的度量空间中,讨论了一类新型的非线性压缩映射ρ(Tx,Ty)≤a(ρ(x,y))ρ(x,Tx)+b(ρ(x,y))ρ(y,Ty)+c(ρ(x,y))ρ(x,y)通过构造迭代序列,指出该映射的不动点的存在性和唯一性,并给出相应的误差估计式,拓展和改进了有关文献的范围.     

Shedding vortex simulation method based on viscous compensation technology research

Owing to the influence of the viscosity of the flow field, the strength of the shedding vortex decreases gradually in the process of backward propagation. Large-scale vortexes constantly break up, forming smaller vortexes. In engineering, when numerical simulation of vortex evolution process is carried out, a large grid is needed to be arranged in the area of outflow field far from the boundary layer in order to ensure the calculation efficiency. As a result, small scale vortexes at the far end of the flow field cannot be captured by the sparse grid in this region, resulting in the dissipation or even disappearance of vortexes. In this paper, the effect of grid scale is quantified and compared with the viscous effect through theoretical derivation. The theoretical relationship between the mesh viscosity and the original viscosity of the flow field is established, and the viscosity term in the turbulence model is modified. This method proves to be able to effectively improve the intensity of small-scale shedding vortexes at the far end of the flow field under the condition of sparse grid. The error between the simulation results and the results obtained by using fine mesh is greatly reduced, the calculation time is shortened, and the high-precision and efficient simulation of the flow field is realized.     

高居里温度铁电单晶PIN-PT的机电性能

弛豫铁电单晶Pb(In_1/2Nb_1/2)O₃-PbTiO₃(PIN-PT)相较于常用的Pb(Mg_1/3Nb_2/3)O₃-PbTiO₃(PMN-PT)具有更高的居里温度,在高稳定性、高性能的传感器、换能器方面具有应用前景。本工作采用谐振法研究了[001]方向极化的0.66PIN-0.34PT铁电单晶的全矩阵机电性能参数。0.66PIN-0.34PT 单晶的三方-四方相变温度(T_RT)约为160 ℃,居里温度(T_C)约为260 ℃,室温压电系数d₃₃、d₃₁、d₁₅分别为1 340 pC/N、-780 pC/N、321 pC/N,介电常数ε^T₃₃、ε^S₃₃、ε^T₁₁、ε^S₁₁分别为2 700、905、2 210、1 927,机电耦合系数 k₃₃、k₃₁、k₁₅、k_t分别为 87%、58%、38%、61%。其纵向压电常数(d₃₃)和纵向机电耦合系数(k₃₃)小于 PMN-PT 单晶,但是横向压电性能(d₃₁)和剪切压电性能(d₁₅)都略高于PMN-PT单晶。另外,研究了机电耦合性能随温度的变化趋势,发现0.66PIN-0.34PT单晶在150 ℃以下有较好的温度稳定性。     

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.     

Effect of quality control on the proliferation of the extract from Taraxacum mongolicum Hand.‐Mazz. in Lactobacillus plantarum

In recent years, the fingerprint of high‐performance liquid chromatography has been extensively applied in the identification and quality control of traditional Chinese medicine. It can be a potential protocol for assessing the authenticity, stability and consistency of traditional Chinese medicine and guaranteeing the expected biological activity. In this paper, a method using high‐performance liquid chromatography to identify and control the quality of the extract of Taraxacum mongolicum Hand.‐Mazz. (TME) was established. With this method, the correlation coefficients of the similarity of 10 batches were ≥0.994. The TME displayed a steady proliferative effect in Lactobacillus plantarum. In brief, this study successfully built a reliable, simple and efficient method to control and confirm the quality and the stability of biological activity of the TME.     

RAFM钢TIG焊和电子束焊疲劳性能实验和分析模拟

利用ANSYS 对低活化铁素体马氏体(RAFM)钢进行非熔化极气体保护焊(TIG 焊)与电子束焊的抗疲劳模拟分析，再利用SDS200 电液伺服疲劳试验机对TIG 焊和电子束焊的两种RAFM 钢试件进行实验。通过施加相同梯度负荷对TIG 焊和电子束焊试件进行焊缝的疲劳性能实验。与实验结果对比分析，结果显示电子束焊优于 TIG 焊，但在一定负载下可以用TIG 焊代替电子束焊。     

Analysis of F-53B,Gen-X,ADONA, and emerging fluoroalkylether substances in environmental and biomonitoring samples: A review

The persistent, bioaccumulative, and toxic properties of certain per- and polyfluoroalkyl substances (PFAS) raise concerns for environmental and human health. This has led to the gradual phase-out from production and commerce of some legacy PFAS. Fluoroalkylether compounds (ether-PFAS) are among the fluorinated alternative chemicals that are beginning to be reported in impacted and background environments. Extensive monitoring activities were conducted since 2015–2019 to bridge knowledge gaps on the environmental fate and effects of ether-PFAS including F-53B (6:2 chlorinated polyfluoroalkyl ether sulfonate [6:2 Cl-PFAES] and 8:2 Cl-PFAES), Gen-X (hexafluoropropylene oxide dimer acid [HFPO-DA]), and ADONA (dodecafluoro-3H-4,8-dioxanonanoate). In recent years, advances in nontarget screening using high-resolution mass spectrometry have revealed the identities of other infrequently monitored ether-PFAS. In this critical review, we provide an up-to-date inventory of the structures of ether-PFAS discovered in the recent literature. Their environmental occurrence, fate, and effects are discussed on a comparative perspective with some legacy PFAS such as perfluorooctanoic acid (PFOA) and perfluorooctane sulfonic acid (PFOS). Information on the methods employed for the quantitative and semi-quantitative analysis of ether-PFAS is also provided, including sample preparation and mass spectrometry analysis, analytical performance, and limitations. In particular, the compiled database of MS/MS fragment ions (n = 111) can be useful in spectrum interpretation of novel ether-PFAS. The concluding remarks open on possible research avenues and the challenges that remain to be addressed.