Asymptotic solutions of the flow of a Johnson-Segalman fluid through a slowly varying pipe using double perturbation strategy

A double perturbation strategy is presented to solve the asymptotic solutions of a Johnson-Segalman (J-S) fluid through a slowly varying pipe. First, a small parameter of the slowly varying angle is taken as the small perturbation parameter, and then the second-order asymptotic solution of the flow of a Newtonian fluid through a slowly varying pipe is obtained in the first perturbation strategy. Second, the viscoelastic parameter is selected as the small perturbation parameter in the second perturbation strategy to solve the asymptotic solution of the flow of a J-S fluid through a slowly varying pipe. Finally, the parameter effects, including the axial distance, the slowly varying angle, and the Reynolds number, on the velocity distributions are analyzed. The results show that the increases in both the axial distance and the slowly varying angle make the axial velocity slow down. However, the radial velocity increases with the slowly varying angle, and decreases with the axial distance. There are two special positions in the distribution curves of the axial velocity and the radial velocity with different Reynolds numbers, and there are different trends on both sides of the special positions. The double perturbation strategy is applicable to such problems with the flow of a non-Newtonian fluid through a slowly varying pipe.     

Recent advances in microfluidic cell sorting techniques based on both physical and biochemical principles

Microfluidic technologies for isolating cells of interest from a heterogeneous sample have attracted great attentions, due to the advantages of less sample consumption, simple operating procedure, and high separation accuracy. According to the working principles, the microfluidic cell sorting techniques can be categorized into biochemical (labeled) and physical (label‐free) methods. However, the inherent drawbacks of each type of method may somehow influence the popularization of these cell sorting techniques. Using the multiple complementary isolation principles is a promising strategy to overcome this problem, therefore there appears to be a continuing trend to integrate two or more sorting methods together. In this review, we focus on the recent advances in microfluidic cell sorting techniques relied on both physical and biochemical principles, with emphasis on the mechanisms of cell separation. The biochemical cell sorting techniques enhanced by physical principles and the physical cell sorting techniques enhanced by biochemical principles, are first introduced. Then, we highlight on‐chip magnetic‐activated cell sorting, on‐chip fluorescence‐activated cell sorting, multi‐step cell sorting and multi‐principle cell sorting techniques, which are based on both physical and biochemical separation mechanisms. Finally, the challenges and future perspectives of the integrated microfluidics for cell sorting are discussed.     

Tricolor Luminescence Switching by Thermal and Mechanical Stimuli in the Crystal Polymorphs of Pyridyl‐substituted Fluorene

Stimuli‐responsive organic luminescence‐switching materials have attracted much attention for a decade. Most of the reported examples display a reversible two‐color luminescence switching, and multicolor‐switching materials remain extremely rare. Herein, we report a simple organic molecule, 4,4′‐(9,9‐dimethyl‐9H‐fluorene‐2,7‐diyl)dipyridine ( MFDP ), which exhibits three different crystal polymorphs ( V‐MFDP , B‐MFDP and G‐MFDP ) with different luminescent colors. Furthermore, the three crystal polymorphs show a reversible tricolor fluorescent switching from violet to blue and to green upon physical stimuli. The single‐crystal structures of the three polymorphs were obtained, and the results indicate that the stimuli‐responsive properties of the three polymorphs come from the different stacking modes induced by intermolecular interactions. The competition between weak π–π stacking and weak hydrogen bonding is the main reason for the the phase transformations among the three crystal polymorphs.     

The effect of the coordination orientation of N atoms on polymeric structures: synthesis and characterization of one‐ and two‐dimensional CuII coordination polymers based on 4‐amino‐3‐(pyridin‐2‐yl)‐5‐[(pyridin‐3‐ylmethyl)sulfanyl]‐1,2,4‐triazole

Three new one‐ (1D) and two‐dimensional (2D) Cu^II coordination polymers, namely poly[[bis{μ₂‐4‐amino‐3‐(pyridin‐2‐yl)‐5‐[(pyridin‐3‐ylmethyl)sulfanyl]‐1,2,4‐triazole}copper(II)] bis(methanesulfonate) tetrahydrate], {[Cu(C₁₃H₁₂N₅S)₂](CH₃SO₃)₂·4H₂O}_n ( 1 ), catena‐poly[[copper(II)‐bis{μ₂‐4‐amino‐3‐(pyridin‐2‐yl)‐5‐[(pyridin‐4‐ylmethyl)sulfanyl]‐1,2,4‐triazole}] dinitrate methanol disolvate], {[Cu(C₁₃H₁₂N₅S)₂](NO₃)₂·2CH₃OH}_n ( 2 ), and catena‐poly[[copper(II)‐bis{μ₂‐4‐amino‐3‐(pyridin‐2‐yl)‐5‐[(pyridin‐4‐ylmethyl)sulfanyl]‐1,2,4‐triazole}] bis(perchlorate) monohydrate], {[Cu(C₁₃H₁₂N₅S)₂](ClO₄)₂·H₂O}_n ( 3 ), were obtained from 4‐amino‐3‐(pyridin‐2‐yl)‐5‐[(pyridin‐3‐ylmethyl)sulfanyl]‐1,2,4‐triazole with pyridin‐3‐yl terminal groups and from 4‐amino‐3‐(pyridin‐2‐yl)‐5‐[(pyridin‐4‐ylmethyl)sulfanyl]‐1,2,4‐triazole with pyridin‐4‐yl terminal groups. Compound 1 displays a 2D net‐like structure. The 2D layers are further linked through hydrogen bonds between methanesulfonate anions and amino groups on the framework and guest H₂O molecules in the lattice to form a three‐dimensional (3D) structure. Compound 2 and 3 exhibit 1D chain structures, in which the complicated hydrogen‐bonding interactions play an important role in the formation of the 3D network. These experimental results indicate that the coordination orientation of the heteroatoms on the ligands has a great influence on the polymeric structures. Moreover, the selection of different counter‐anions, together with the inclusion of different guest solvent molecules, would also have a great effect on the hydrogen‐bonding systems in the crystal structures.     

A Note on Exponential Decay in the Random Field Ising Model

For the two-dimensional random field Ising model (RFIM) with bimodal (i.e., two-valued) external field, we prove exponential decay of correlations either (i) when the temperature is larger than the critical temperature of the Ising model without external field and the magnetic field strength is small or (ii) at any temperature when the magnetic field strength is sufficiently large. Unlike previous work on exponential decay, our approach is not based on cluster expansions but rather on arguably simpler methods; these combine an analysis of the Kertész line and a coupling of Ising measures (and also their random cluster representations) with different boundary conditions. We also show similar but weaker results for the RFIM with a general field distribution and in any dimension.     

Design of weakly-coupled three-spatial-mode rectangular-ring core fiber for short-reach MDM networks in C + L band

We propose a novel weakly-coupled three-spatial-mode rectangular-ring core fiber for short-reach mode-division multiplexing (MDM) networks in C?+?L band. We investigate the influence of geometrical parameters on n_eff, min?n_eff, and A_eff with regions that meet the three-spatial-mode condition of the proposed fiber. Bending loss of each guided mode and DMD between adjacent spatial modes are also studied. Large effective refractive index difference between adjacent spatial modes is achieved with min?n_eff?~?0.004. Results imply that the designed fiber can simplify or eliminate MIMO-DSP for short-reach MDM networks such as optical interconnects, data centers, and optical access networks.     

The effect of low temperature AlN interlayers on the growth of GaN epilayer on Si (111) by MOCVD

Low temperature (LT) AlN interlayers were used to effectively reduce the tension stress and micro-cracks on the surface of the GaN epilayer grown on Si (111) substrate. Optical Microscopy (OM), Atomic Force Microscopy (AFM), Surface Electron Microscopy (SEM) and X-Ray Diffraction (XRD) were employed to characterize these samples grown by metal-organic chemical vapor deposition (MOCVD). In addition, wet etching method was used to evaluate the defect of the GaN epilayer. The results demonstrate that the morphology and crystalline properties of the GaN epilayer strongly depend on the thickness, interlayer number and growth temperature of the LT AlN interlayer. With the optimized LT AlN interlayer structures, high quality GaN epilayers with a low crack density can be obtained.     

Simulation of the electrical characteristics of a one-dimensional quantum dot array

A quantum dot array, consisting of Au dots, was prepared by the linear aggregation technique and assembled between two electrodes. We study the voltage–current characteristic of the quantum dot array, using a Non-Equilibrium Green’s Function (NEGF) model based on the Keldysh formalism. The results of our simulation and experimental data are compared. The simulated voltage–current curve is a reasonable fit with the measured data. It shows that the present model can be used to study quantum dot arrays. Furthermore, our results indicate that the electrical characteristics of an Au dot array are directly related to the coupling parameters.     

正则解析半群与正则Cosine函数

在本文中，我们的主要结果是：若Ａ是一个正则解析半群的生成元，则Ａ也一定是某正则Ｃｏｓｉｎｅ函数的生成元．