竖直恒温面自然对流边界层不稳定性研究

在无扰动、随机式扰动以及正弦式扰动下,通过对竖直恒温面处状态Ra为1.328×10^9、Pr为6.24的自然对流进行模拟,探索了热边界层的不稳定性和共振强化自然对流换热。结果表明:(1)竖直自然对流边界层上游位置的随机式扰动对热边界层的影响主要体现在稳定阶段;(2)该状态下的竖直自然对流边界层的特征频率为15 067,且相比于无扰动状态,频率为15 067的正弦式扰动能在竖直恒温面处提高5.15%的换热量;(3)在竖直自然对流边界层上游位置加入特征频率的正弦式扰动,竖直恒温面处的局部努塞尔数Nu均出现明显波动,且波动随着边界层高度的增加而增大。     

Two-dimensional vortex sheets for the nonisentropic Euler equations: Nonlinear stability

We show the short-time existence and nonlinear stability of vortex sheets for the nonisentropic compressible Euler equations in two spatial dimensions, based on the weakly linear stability result of Morando and Trebeschi (2008) [20]. The missing normal derivatives are compensated through the equations of the linearized vorticity and entropy when deriving higher-order energy estimates. The proof of the resolution for this nonlinear problem follows from certain a priori tame estimates on the effective linear problem in the usual Sobolev spaces and a suitable Nash–Moser iteration scheme.     

Hermitian adjacency matrix of the second kind for mixed graphs

This contribution gives an extensive study on spectra of mixed graphs via its Hermitian adjacency matrix of the second kind (N-matrix for short) introduced by Mohar [25]. This matrix is indexed by the vertices of the mixed graph, and the entry corresponding to an arc from u to v is equal to the sixth root of unity $\omega =\frac{1+\mathbf{i}\sqrt{3}}{2}$ (and its symmetric entry is $\overline{\omega }=\frac{1?\mathbf{i}\sqrt{3}}{2}$); the entry corresponding to an undirected edge is equal to 1, and 0 otherwise. The main results of this paper include the following: equivalent conditions for a mixed graph that shares the same spectrum of its N-matrix with its underlying graph are given. A sharp upper bound on the spectral radius is established and the corresponding extremal mixed graphs are identified. Operations which are called two-way and three-way switchings are discussed–they give rise to some cospectral mixed graphs. We extract all the mixed graphs whose rank of its N-matrix is 2 (resp. 3). Furthermore, we show that if $M_G$ is a connected mixed graph with rank 2, then $M_G$ is switching equivalent to each connected mixed graph to which it is cospectral. However, this does not hold for some connected mixed graphs with rank 3. We identify all mixed graphs whose eigenvalues of its N-matrix lie in the range $(?\alpha ,\alpha )$ for $\alpha \in \{\sqrt{2},\sqrt{3},2\}$.     

Chemometrics‐assisted chromatographic fingerprinting: An illicit methamphetamine case study

The volatile chemical constituents in complex mixtures can be analyzed using gas chromatography with mass spectrometry. This analysis allows the tentative identification of diverse impurities of an illicit methamphetamine sample. The acquired two‐dimensional data of liquid–liquid extraction was resolved by multivariate curve resolution alternating curve resolution to elucidate the embedded peaks effectively. This is the first report on the application of a curve resolution approach for chromatogram fingerprinting to identify particularly the embedded impurities of a drug of abuse. Indeed, the strong and broad peak of methamphetamine makes identifying the underlying peaks problematic and even impossible. Mathematical separation instead of conventional chromatographic approaches was performed in a way that trace components embedded in methamphetamine peak were successfully resolved. Comprehensive analysis of the chromatogram, using multivariate curve resolution, resulted in elution profiles and mass spectra for each pure compound. Impurities such as benzaldehyde, benzyl alcohol, benzene, propenyl methyl ketone, benzyl methyl ketone, amphetamine, N‐benzyl‐2‐methylaziridine, phenethylamine, N ,N ,α‐trimethylamine, phenethylamine, N ,α,α‐trimethylmethamphetamine, N‐acetylmethamphetamine, N‐formylmethamphetamine, and other chemicals were identified. A route‐specific impurity, N‐benzyl‐2‐methylaziridine, indicating a synthesis route based on ephedrine/pseudoephedrine was identified. Moreover, this is the first report on the detection of impurities such as phenethylamine, N ,α,α‐trimethylamine (a structurally related impurity), and clonitazene (as an adulterant) in an illicit methamphetamine sample.     

Sample plug induced peak splitting in capillary electrophoresis studied using dual backscattered interferometry and fluorescence detection

The appearance of unexpected peaks in capillary electrophoresis (CE) is common and can lengthen the time of method development as assay conditions and experimental parameters are varied to understand and mitigate the effects of the additional peaks. Additional peaks can arise when a single-analyte zone is split into multiple zones. Understanding the underlying mechanism of these phenomena, recognizing conditions that favor its presence, and knowing how to confirm and eliminate the effect are important for efficient method optimization. In this study, we examine how the overlap of analyte zones with the sample plug can lead to peak splitting. This is explored experimentally using dual detection CE, which enables both the sample plug and analyte zones to be independently and simultaneously measured from the same detection volume. Simulations performed via COMSOL Multiphysics confirm the origin of the splitting and help guide experiments to reduce and eliminate the effect. Our findings show that this peak splitting mechanism can arise in separations of both small and large molecules but is, especially, prevalent in separations of slowly migrating macromolecules. This effect is also more prevalent when using a short length-to-detector, as is commonly found in microfluidic applications. A simple diffusion-less model is introduced to develop strategies for reducing peak splitting that avoids modifying the apparatus, such as by lengthening the separation length, which can be difficult. Decreasing the sample plug length and slowing the electroosmotic flow can both reduce this effect, which is confirmed experimentally.     

几种常用激光解吸电离/质谱基质的基质簇峰行为研究

以常用于DNA分析的基质3-羟基吡啶甲酸(3-HPA),以及常用于高分子聚合物分析的基质2-(4-羟基苯基偶氮)苯甲酸(HABA)、反式-3-吲哚基丙烯酸(IAA)和1,8,9-三羟基蒽(Dithranol)为研究对象,考察了基质溶剂、浓度及激光强度对基质本身在激光解吸电离/质谱(LDI/MS)过程中产生基质簇峰的影响,对基质簇峰可能形成的过程进行了推测,并对各基质簇峰进行了归属,提出了基质簇离子峰m/z值遵循的计算公式。     

岩石结构面的表面形态特征研究

本文用理论分析和数值模拟方法对具有不同粗糙度和起伏度的岩石结构面的形态特征作了定量研究, 着重研究了结构面表面形态参数与基本形态特征参数的关系, 并研究了它们的采样效应。得到了一系列在建立表面形态参数与物理量相互关系时对合理选用表面形态参数有重要意义的结果, 并可为选取合理的采样间隔和最小采样长度提供依据。