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.     

Structural Aspects of P2-Type Na0.67Mn0.6Ni0.2Li0.2O2 (MNL) Stabilization by Lithium Defects as a Cathode Material for Sodium-Ion Batteries

A known strategy for improving the properties of layered oxide electrodes in sodium-ion batteries is the partial substitution of transition metals by Li. Herein, the role of Li as a defect and its impact on sodium storage in P2-Na_0.67Mn_0.6Ni_0.2Li_0.2O₂ is discussed. In tandem with electrochemical studies, the electronic and atomic structure are studied using solid-state NMR, operando XRD, and density functional theory (DFT). For the as-synthesized material, Li is located in comparable amounts within the sodium and the transition metal oxide (TMO) layers. Desodiation leads to a redistribution of Li ions within the crystal lattice. During charging, Li ions from the Na layer first migrate to the TMO layer before reversing their course at low Na contents. There is little change in the lattice parameters during charging/discharging, indicating stabilization of the P2 structure. This leads to a solid-solution type storage mechanism (sloping voltage profile) and hence excellent cycle life with a capacity of 110 mAh g^-1 after 100 cycles. In contrast, the Li-free compositions Na_0.67Mn_0.6Ni_0.4O₂ and Na_0.67Mn_0.8Ni_0.2O₂ show phase transitions and a stair-case voltage profile. The capacity is found to originate from mainly Ni³⁺/Ni⁴⁺ and O^2-/O^2-δ redox processes by DFT, although a small contribution from Mn⁴⁺/Mn⁵⁺ to the capacity cannot be excluded.     

Off‐grid DoA estimation method of wideband signals

In this paper, an off‐grid direction of arrival (DoA) estimation method is proposed for wideband signals. This method is based on the sparse representation (SR) of the array covariance matrix. Similar to the time domain DoA estimation methods, the correlation function of the sources was assumed to be the same and known. A new measurement vector is obtained using the lower‐left triangular elements of the covariance matrix. The DoAs are estimated by quantizing the entire range of continuous angle space into discrete grid points. However, the exact DoAs may be located between two grid points; therefore, this estimation has errors. The accuracy of DoA estimation is improved by the minimization of the difference between the new measurement vector and its estimated values. Simulation results revealed that the proposed method can enhance the DoA estimation accuracy of wideband signals.     

Limitations of the Clausius‐Mossotti function used in dielectrophoresis and electrical impedance studies of biomacromolecules

Dielectrophoresis (DEP) studies have progressed from the microscopic scale of cells and bacteria, through the mesoscale of virions to the molecular scale of DNA and proteins. The Clausius‐Mossotti function, based on macroscopic electrostatics, is invariably employed in the analyses of all these studies. The limitations of this practice are explored, with the conclusion that it should be abandoned for the DEP study of proteins and modified for native DNA. For macromolecular samples in general, a DEP theory that incorporates molecular‐scale interactions and the influence of permanent dipoles is more appropriate. Experimental ways to test these conclusions are proposed.     

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).     

Nano palladium supported on high‐surface‐area metal–organic framework MIL‐101: an efficient catalyst for Sonogashira coupling of aryl and heteroaryl bromides with alkynes

Palladium nanoparticle‐incorporated metal–organic framework MIL‐101 (Pd/MIL‐101) was successfully synthesized and characterized using X‐ray diffraction, nitrogen physisorption, X‐ray photoelectron, UV–visible and infrared spectroscopies, and transmission electron microscopy. The characterization techniques confirmed high porosity and high surface area of MIL‐101 and high stability of nano‐size palladium particles. Pd/MIL‐101 nanocomposite was investigated for the Sonogashira cross‐coupling reaction of aryl and heteroaryl bromides with various alkynes under copper‐free conditions. The reusability of the catalyst was tested for up to four cycles without any significant loss in catalytic activity. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

Achieving Rich and Active Alkaline Hydrogen Evolution Heterostructures via Interface Engineering on 2D 1T‐MoS2 Quantum Sheets

Large‐scale production of hydrogen from water‐alkali electrolyzers is impeded by the sluggish kinetics of hydrogen evolution reaction (HER) electrocatalysts. The hybridization of an acid‐active HER catalyst with a cocatalyst at the nanoscale helps boost HER kinetics in alkaline media. Here, it is demonstrated that 1T–MoS₂ nanosheet edges (instead of basal planes) decorated by metal hydroxides form highly active ${\text{edge}}_{{\text{1T‐MoS}}_{\text{2}}}$/ ${\text{edge}}_{\text{Ni}{(\text{OH})}_{\text{2}}}$ heterostructures, which significantly enhance HER performance in alkaline media. Featured with rich ${\text{edge}}_{{\text{1T‐MoS}}_{\text{2}}}$/ ${\text{edge}}_{\text{Ni}{(\text{OH})}_{\text{2}}}$ sites, the fabricated 1T–MoS₂ QS/Ni(OH)₂ hybrid (quantum sized 1T–MoS₂ sheets decorated with Ni(OH)₂ via interface engineering) only requires overpotentials of 57 and 112 mV to drive HER current densities of 10 and 100 mA cm^?2, respectively, and has a low Tafel slope of 30 mV dec^?1 in 1 m KOH. So far, this is the best performance for MoS₂‐based electrocatalysts and the 1T–MoS₂ QS/Ni(OH)₂ hybrid is among the best‐performing non‐Pt alkaline HER electrocatalysts known. The HER process is durable for 100 h at current densities up to 500 mA cm^?2. This work not only provides an active, cost‐effective, and robust alkaline HER electrocatalyst, but also demonstrates a design strategy for preparing high‐performance catalysts based on edge‐rich 2D quantum sheets for other catalytic reactions.