Concentrated steady vorticities of the Euler equation on 2-d domains and their linear stability

We consider concentrated vorticities for the Euler equation on a smooth domain $\mathrm{\Omega }?{\mathbf{R}}^2$ in the form of

$\omega =\sum _{j=1}^N{\omega }_j{\chi }_{{\mathrm{\Omega }}_j},|{\mathrm{\Omega }}_j|=\pi r_j^2,\underset{{\mathrm{\Omega }}_j}{\int }{\omega }_{j}d\mu ={\mu }_j\ne 0,$

supported on well-separated vortical domains ${\mathrm{\Omega }}_j$, $j=1,\dots ,N$, of small diameters $O(r_j)$. A conformal mapping framework is set up to study this free boundary problem with ${\mathrm{\Omega }}_j$ being part of unknowns. For any given vorticities ${\mu }_1,\dots ,{\mu }_N$ and small $r_1,\dots ,r_N\in {\mathbf{R}}^{+}$, through a perturbation approach, we obtain such piecewise constant steady vortex patches as well as piecewise smooth Lipschitz steady vorticities, both concentrated near non-degenerate critical configurations of the Kirchhoff–Routh Hamiltonian function. When vortex patch evolution is considered as the boundary dynamics of $?{\mathrm{\Omega }}_j$, through an invariant subspace decomposition, it is also proved that the spectral/linear stability of such steady vortex patches is largely determined by that of the 2N-dimensional linearized point vortex dynamics, while the motion is highly oscillatory in the 2N-codim directions corresponding to the vortical domain shapes.     

Direct visualization of the nanoscopic three‐phase structure and stiffness of NBR/PVC blends by AFM nanomechanical mapping

The PeakForce Quantitative Nanomechanical Mapping based on atomic force microscope (AFM) is employed to first visualize and then quantify the elastic properties of a model nitrile rubber/poly(vinyl chloride) (NBR/PVC) blend at the nanoscale. This method allows us to consistently observe the changes in mechanical properties of each phase in polymer blends. Beyond measuring and discriminating elastic modulus and adhesion forces of each phase, we tune the AFM tips and the peak force parameters in order to reliably image samples. In view of viscoelastic difference in each phase, a three‐phase coexistence of an unmixed NBR phase, the mixed phase, and PVC microcrystallites is directly visualized in NBR/PVC blends. The nanomechanical investigation is also capable of recognizing the crosslinked rubber phase in cured rubber. The contribution of the mixed phase was quantified and it was found that the mechanical properties of blends are mainly determined by the homogeneity and stiffness of the mixed phase. This study furthers our understanding the structure–mechanical property relationship of thermoplastic elastomers, which is important for their potential design and applications. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 662–669     

Fluid‐structure coupling of linear elastic model with compressible flow models

Cavitation erosion is caused in solids exposed to strong pressure waves developing in an adjacent fluid field. The knowledge of the transient distribution of stresses in the solid is important to understand the cause of damaging by comparisons with breaking points of the material. The modeling of this problem requires the coupling of the models for the fluid and the solid. For this purpose, we use a strategy based on the solution of coupled Riemann problems that has been originally developed for the coupling of 2 fluids. This concept is exemplified for the coupling of a linear elastic structure with an ideal gas. The coupling procedure relies on the solution of a nonlinear equation. Existence and uniqueness of the solution is proven. The coupling conditions are validated by means of quasi‐1D problems for which an explicit solution can be determined. For a more realistic scenario, a 2D application is considered where in a compressible single fluid, a hot gas bubble at low pressure collapses in a cold gas at high pressure near an adjacent structure.     

Chemical versus Electrochemical Synthesis of Carbon Nano‐onion/Polypyrrole Composites for Supercapacitor Electrodes

The development of high‐surface‐area carbon electrodes with a defined pore size distribution and the incorporation of pseudo‐active materials to optimize the overall capacitance and conductivity without destroying the stability are at present important research areas. Composite electrodes of carbon nano‐onions (CNOs) and polypyrrole (Ppy) were fabricated to improve the specific capacitance of a supercapacitor. The carbon nanostructures were uniformly coated with Ppy by chemical polymerization or by electrochemical potentiostatic deposition to form homogenous composites or bilayers. The materials were characterized by transmission‐ and scanning electron microscopy, differential thermogravimetric analyses, FTIR spectroscopy, piezoelectric microgravimetry, and cyclic voltammetry. The composites show higher mechanical and electrochemical stabilities, with high specific capacitances of up to about 800 F g^?1 for the CNOs/SDS/Ppy composites (chemical synthesis) and about 1300 F g^?1 for the CNOs/Ppy bilayer (electrochemical deposition).     

Vinylic MIDA Boronates: New Building Blocks for the Synthesis of Aza‐Heterocycles

A two‐step synthesis of structurally diverse pyrrole‐containing bicyclic systems is reported. ortho‐Nitro‐haloarenes coupled with vinylic N‐methyliminodiacetic acid (MIDA) boronates generate ortho‐vinyl‐nitroarenes, which undergo a “metal‐free” nitrene insertion, resulting in a new pyrrole ring. This novel synthetic approach has a wide substrate tolerance and it is applicable in the preparation of more complex “drug‐like” molecules. Interestingly, an ortho‐nitro‐allylarene derivative furnished a cyclic β‐aminophosphonate motif.     

Full counting statistics of transport electrons through a two-level quantum dot with spin–orbit coupling

We study the full counting statistics of transport electrons through a semiconductor two-level quantum dot with Rashba spin–orbit (SO) coupling, which acts as a nonabelian gauge field and thus induces the electron transition between two levels along with the spin flip. By means of the quantum master equation approach, shot noise and skewness are obtained at finite temperature with two-body Coulomb interaction. We particularly demonstrate the crucial effect of SO coupling on the super-Poissonian fluctuation of transport electrons, in terms of which the SO coupling can be probed by the zero-frequency cumulants. While the charge currents are not sensitive to the SO coupling.     

Simultaneous determination of cinnamaldehyde and its metabolite in rat tissues by gas chromatography–mass spectrometry

Cinnamaldehyde (CA), an active ingredient isolated from the traditional Chinese medicine Cortex Cinnamomi, has a wide range of bioactivities. To clarify the distribution characteristics of CA, a selective and sensitive method utilizing gas chromatography–mass spetrometry was initially developed for simultaneously determining the concentration of CA and its metabolite cinnamyl alcohol in rat tissues. Selected ion masses of m/z 131, 105 and 92 were chosen, and separation of the analytes was performed on a DB‐5 ms (30 m × 0.25 mm, 0.25 µm, thickness) capillary column by gas chromatography–mass spectrometry. The calibration curves demonstrated good linearity and reproducibility over the range of 20–2000 and 20–4000 ng/mL for various tissue samples. Recoveries ranged from 86.8 to 107.5%, while intra‐ and interday relative standard deviations were all <11.3%. The analysis method was successfully applied in tissue distribution studies for CA and cinnamyl alcohol. As CA and cinnamyl alcohol may inter‐convert to one another, simultaneous determination of both analytes provides a comparative and accurate data for tissue study. The concentrations of CA and cinnamyl alcohol remaining in spleen were the highest among the main organs, including heart, liver, spleen, lung, kidney and brain. In addition, there was no long‐term accumulation of CA in rat tissues. Copyright © 2014 John Wiley & Sons, Ltd.