On pointwise decay rates of time‐periodic solutions to the Navier–Stokes equation

We study the existence of a time‐periodic solution with pointwise decay properties to the Navier–Stokes equation in the whole space. We show that if the time‐periodic external force is sufficiently small in an appropriate sense, then there exists a time‐periodic solution $\{u,p\}$ of the Navier–Stokes equation such that $|{?}^j{u(t,x)|=O(|x|}^{1?n?j})$ and $|{?}^j{p(t,x)|=O(|x|}^{?n?j})(j=0,1,\dots )$ uniformly in $t\in \mathbb{R}$ as $|x|\to \infty$. Our solution decays faster than the time‐periodic Stokes fundamental solution and the faster decay of its spatial derivatives of higher order is also described.     

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.     

Mass distribution and skewness for passive scalar transport in pipes with polygonal and smooth cross sections

We extend our previous results characterizing the loading properties of a diffusing passive scalar advected by a laminar shear flow in ducts and channels to more general cross‐sectional shapes, including regular polygons and smoothed corner ducts originating from deformations of ellipses. For the case of the triangle and localized, cross‐wise uniform initial distributions, short‐time skewness is calculated exactly to be positive, while long‐time asymptotics shows it to be negative. Monte Carlo simulations confirm these predictions, and document the timescale for sign change. The equilateral triangle appears to be the only regular polygon with this property—all others possess positive skewness at all times. Alternatively, closed‐form flow solutions can be constructed for smooth deformations of ellipses, and illustrate how both nonzero short‐time skewness and the possibility of multiple sign switching in time is unrelated to domain corners. Exact conditions relating the median and the skewness to the mean are developed which guarantee when the sign for the skewness implies front (more mass to the right of the mean) or back (more mass to the left of the mean) “loading” properties of the evolving tracer distribution along the pipe. Short‐ and long‐time asymptotics confirm this condition, and Monte Carlo simulations verify this at all times. The simulations are also used to examine the role of corners and boundaries on the distribution for short‐time evolution of point source , as opposed to cross‐wise uniform, initial data.     

Molecular structure,vibrational spectroscopic and chemical reactivity of nematogenic p-n-alkylbenzoic acids: A comparative computational analysis

Molecular structure and vibrational spectroscopic studies of higher homologous series nematogenic p-n-alkylbenzoic acids (nBAC) that have 6 (6BAC) and 7 (7BAC) carbon atoms in the alkyl chain have been investigated using the Density Functional Becke3-Lee-Yang-Parr (B3LYP) level with the basis set 6-31++G (d.p) and Hartree Fock (HF) with the same basis set. The observed vibrational spectra has been resolved and assigned in detail for comparision with both the molecules. These results indicate that DFT and HF values are slightly different at both the levels. A comparision of chemical reactivity such as HOMO (E_H), LUMO (E_L) energies, energy gap (E_g), ionization energy (I), electron affinity (A), electro negativity (χ), chemical hardness (η), electronic chemical potential (μ), electrophilicity index (ω), and softness (S) has been made. It has been observed that the decrement has occurred in the energy band gap value of isolated molecule with increment in alkyl chain length. This provides valuable information regarding enhancing the stability of liquid crystal materials by maintaining the conductivity.     

Hexagonal boron nitride quantum dots: Properties,preparation and applications

As a new type of quantum dots (QDs), hexagonal boron nitride quantum dots (BNQDs) exhibit promising potential in the applications of disease diagnosis, fluorescence imaging, biosensing, metal ion detection, and so on, because of their remarkable chemical stability, excellent biocompatibility, low cytotoxicity, and outstanding photoluminescence properties. However, the large-scale fabrication of homogeneous BNQDs still remains challenging. In this article, the properties and common fabrication methods of BNQDs are summarized based on the recent research progress. Then, the corresponding yields, morphologies, and fabrication mechanisms of these as-obtained BNQDs are discussed in detail. Moreover, the applications of these as-obtained BNQDs in different fields are also discussed. This article is expected to inspire new methods and improvements to achieve large-scale fabrication of homogeneous BNQDs, which will enable their practical applications in future.     

Direct Transformation of Arenols Based on C—O Activation

In the view of substrate availability, atomic efficiency and cost, directly using arenols as coupling partners in cross‐coupling, would be one of the most attractive goals. Up to date, many efforts have been made to activate the C—O bond of phenols with different strategies, for example, through in‐situ formed intermediates, through a catalytic reductive dearomatization‐condensation‐rearomatization sequence or catalytic deoxygenation. In this review, we summarized recent advances in cross‐couplings of arenols as the electrophiles via C—O activation.     

化学法改性煤沥青脱除苯并芘的研究

在管式反应器中采用苯甲酸、聚乙二醇、固体古马隆树脂（S）、液体古马隆树脂（L）为添加剂来降低煤沥青中有害物质苯并芘的含量，以期使得煤沥青可绿色化应用。采用紫外-可见分光光度计分析煤沥青中苯并芘含量。考察了反应温度、反应时间、添加剂添加量、催化剂等工艺条件对添加剂脱除煤沥青中苯并芘的影响。结果表明，不同工艺条件能降低煤沥青中苯并芘的含量。在优化条件下，不同添加剂对苯并芘脱除率由高到低依次为：液体古马隆树脂、聚乙二醇、苯甲酸和固体古马隆树脂。分析其反应机理，这与催化剂的酸性相关，发生亲电取代反应。结果表明，液体古马隆树脂（L）在催化剂存在下对煤沥青中苯并芘脱除率可达73.0%，显示了良好的应用前景。