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.     

一种基于FPGA的可变速率帧结构设计与实现

在简述V.35接口的基础上针对V.35接口速率可变的应用需求提出了一种速率可变的帧结构,该帧结构可支持N×64kb/s(3≤N≤32)速率,从而在V.35接口上实现了多种速率的低速业务传输.     

Caesium carbonate supported on hydroxyapatite‐encapsulated Ni0.5Zn0.5Fe2O4 nanocrystallites as a novel magnetically basic catalyst for the one‐pot synthesis of pyrazolo[1,2‐b]phthalazine‐5,10‐diones

A novel nanomagnetic basic catalyst of caesium carbonate supported on hydroxyapatite‐coated Ni_0.5Zn_0.5Fe₂O₄ magnetic nanoparticles (Ni_0.5Zn_0.5Fe₂O₄@HAP‐Cs₂CO₃) was prepared. This new catalyst was fully characterized using Fourier transform infrared spectroscopy, transmission and scanning electron microscopy, X‐ray diffraction and vibrating sample magnetometry techniques, and then the catalytic activity of this catalyst was investigated in the synthesis of 1H‐pyrazolo[1,2‐b]phthalazine‐5,10‐dione derivatives. Also, Ni_0.5Zn_0.5Fe₂O₄@HAP‐Cs₂CO₃ could be reused at least five times without significant loss of activity and could be recovered easily by applying an external magnet. Thus, the developed nanomagnetic catalyst is potentially useful for the green and economic production of organic compounds. Copyright © 2015 John Wiley & Sons, Ltd.     

A simple,rapid and sensitive method based on modified multiwalled carbon nanotube for preconcentration and determination of lead ions in aqueous media in natural pHs

In this study, multiwalled carbon nanotube (MWCNT) was modified by the pyridine group using a silane agent and characterized by infrared spectroscopy (IR), thermal analysis (TG/DTA), and elemental analysis (CHN) and scanning electron microscopy (SEM). The application of this sorbent was investigated in determination of lead ions in aqueous samples, using flame atomic absorption spectrometry (FAAS). Through this study, different parameters such as pH and sample flow rate on adsorption process and eluent concentration, volume and flow rate were optimized. The limit of detection (LOD), the relative standard deviation and the recovery of the method were 2 ng mL^?1, 1.3% and 99.7%, respectively. Two standard reference materials (NIST 1571 and NIST 1572) were used to verify accuracy of this method. Finally, the sorbent was successfully applied for extraction and determination of low levels of Pb(II) ions in aqueous samples.     

High-voltage and low specific on-resistance power UMOSFET using P and N type columns

For the first time, we present the unique features exhibited by power 4H–SiC UMOSFET in which N and P type columns (NPC) in the drift region are incorporated to improve the breakdown voltage, the specific on-resistance, and the total lateral cell pitch. The P-type column creates a potential barrier in the drift region of the proposed structure for increasing the breakdown voltage and the N-type column reduces the specific on-resistance. Also, the JFET effects reduce and so the total lateral cell pitch will decrease. In the NPC-UMOSFET, the electric field crowding reduces due to the created potential barrier by the NPC regions and causes more uniform electric field distribution in the structure. Using two dimensional simulations, the breakdown voltage and the specific on-resistance of the proposed structure are investigated for the columns parameters in comparison with a conventional UMOSFET (C-UMOSFET) and an accumulation layer UMOSFET (AL-UMOSFET) structures. For the NPC-UMOSFET with 10 µm drift region length the maximum breakdown voltage of 1274 V is obtained, while at the same drift region length, the maximum breakdown voltages of the C-UMOSFET and the AL-UMOSFET structures are 534 and 703 V, respectively. Moreover, the proposed structure exhibits a superior specific on-resistance (R_on,sp) of 2 mΩ cm², which shows that the on-resistance of the optimized NPC-UMOSFET are decreased by 56% and 58% in comparison with the C-UMOSFET and the AL-UMOSFET, respectively.