On Hr(curl,Ω) estimates for a Maxwell type system in convex domains

In bounded convex domains, the regularity of a vector field u with its $\mathrm{div}\mathbf{u}$, $\mathrm{curl}\mathbf{u}$ in $L^r$ space and the tangential component or the normal component of u over the boundary in $L^r$ space, is established for $1<r<\infty$. As an application, we derive an $H^r(\mathrm{curl},\mathrm{\Omega })$ estimate for solutions to a Maxwell type system with an inhomogeneous boundary condition in convex domains. In contrast to the well-posed region of r in the space $H^r(\mathrm{curl},\mathrm{\Omega })$ for the Maxwell type system in Lipschitz domains given by Kar and Sini (2016) [16], we extend the well-posed region to be optimal.     

Semiconvergence analysis of the randomized row iterative method and its extended variants

The row iterative method is popular in solving the large‐scale ill‐posed problems due to its simplicity and efficiency. In this work we consider the randomized row iterative (RRI) method to tackle this issue. First, we present the semiconvergence analysis of RRI method for the overdetermined and inconsistent system, and derive upper bounds for the noise error propagation in the iteration vectors. To achieve a least squares solution, we then propose an extended version of the RRI (ERRI) method, which in fact can converge in expectation to the solution of the overdetermined or underdetermined, consistent or inconsistent systems. Finally, some numerical examples are given to demonstrate the convergence behaviors of the RRI and ERRI methods for these types of linear system.     

基于NiCo2O4纳米片电极的非对称混合电容器

The looming global energy crisis and ever-increasing energy demands have catalyzed the development of renewable energy storage systems. In this regard, supercapacitors (SCs) have attracted widespread attention because of their advantageous attributes such as high power density, excellent cycle stability, and environmental friendliness. However, SCs exhibit low energy density and it is important to optimize electrode materials to improve the overall performance of these devices. Among the various electrode materials available, spinel nickel cobaltate (NiCo₂O₄) is particularly interesting because of its excellent theoretical capacitance. Based on the understanding that the performances of the electrode materials strongly depend on their morphologies and structures, in this study, we successfully synthesized NiCo₂O₄ nanosheets on Ni foam via a simple hydrothermal route followed by calcination. The structures and morphologies of the as-synthesized products were characterized by X-ray diffraction, scanning electron microscopy, and Brunauer-Emmett-Teller (BET) surface area analysis, and the results showed that they were uniformly distributed on the Ni foam support. The surface chemical states of the elements in the samples were identified by X-ray photoelectron spectroscopy. The as-synthesized NiCo₂O₄ products were then tested as cathode materials for supercapacitors in a traditional three-electrode system. The electrochemical performances of the NiCo₂O₄ electrode materials were studied and the area capacitance was found to be 1.26 C·cm^-2 at a current density of 1 mA·cm^-2. Furthermore, outstanding cycling stability with 97.6% retention of the initial discharge capacitance after 10000 cycles and excellent rate performance (67.5% capacitance retention with the current density from 1 to 14 mA·cm^-2) were achieved. It was found that the Ni foam supporting the NiCo₂O₄ nanosheets increased the conductivity of the electrode materials. However, it is worth noting that the contribution of nickel foam to the areal capacitance of the electrode materials was almost zero during the charge and discharge processes. To further investigate the practical application of the as-synthesized NiCo₂O₄ nanosheets-based electrode, a device was assembled with the as-prepared samples as the positive electrode and active carbon (AC) as the negative electrode. The assembled supercapacitor showed energy densities of 0.14 and 0.09 Wh·cm^-3 at 1.56 and 4.5 W·cm^-3, respectively. Furthermore, it was able to maintain 95% of its initial specific capacitance after 10000 cycles. The excellent electrochemical performance of the NiCo₂O₄ nanosheets could be ascribed to their unique spatial structure composed of interconnected ultrathin nanosheets, which facilitated electron transportation and ion penetration, suggesting their potential applications as electrode materials for high performance supercapacitors. The present synthetic route can be extended to other ternary transition metal oxides/sulfides for future energy storage devices and systems.     

Piezoelectric Actuator Placement Optimization and Active Vibration Control of a Membrane Structure

The placement optimization of piezoelectric actuators and active vibration control of a membrane structure are studied in this paper. The classical linear quadratic regulator controllers are designed to suppress the unwanted vibration. Simulation results indicate that the optimal locations of piezoelectric actuators are affected deeply by the additional mass and stiffness of actuators, the computational efficiency of particle swarm optimizer is higher than that of genetic algorithm for this particular problem, and the control performance of optimally placed actuators is better than that of non-optimally placed actuators.     

Surface Tension Effect on Harmonics of Rayleigh-Taylor Instability

Using the method of the parameter expansion up to the third order, explicitly investigates surface tension effect on harmonics at weakly nonlinear stage in Rayleigh-Taylor instability (RTI) for arbitrary Atwood numbers and compares the results with those of classical RTI within the framework of the third-order weakly nonlinear theory. It is found that surface tension strongly reduces the linear growth rate of time, resulting in mild growth of the amplitude of the fundamental mode, and changes amplitudes of the second and third harmonics, as is expressed as a tension factor coupling in amplitudes of the harmonics. On the one hand, surface tension can either decrease or increase the space amplitude; on the other hand, surface tension can also change their phases for some conditions which are explicitly determined.     

Ultrastretchable and conductive core/sheath hydrogel fibers with multifunctionality

Conductive hydrogels with ionic compounds possess great potential for the development of soft smart devices. A dielectric scarfskin is typically required for these devices to prevent short circuiting, leading to devices with lower stretchability than the hydrogel. Henceforth, commonly used dielectric materials, such as PDMS and Ecoflex, cannot be largely stretched. Hydrogel devices with ultrastretchability are required to accommodate hostile application environments. Herein, we propose a hydrogel fiber coated with a dielectric layer that can be stretched to over 2000% of its initial length. The fiber remains conductive when stretched to ~1300%. In addition, the core/sheath hydrogel fiber can be endowed with a variety of functional properties, such as electroluminescence (EL), photoluminescence (PL), and magnetic‐responsiveness, demonstrating scalability of the resultant fiber. The present work can pave the way for numerous next‐generation soft devices, such as smart textiles and wearable electronics. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 272–280     

Effects of substituents on bridging ligands on the single‐molecule magnet properties of Zn2Dy2 cluster complexes

Two new Zn₂Dy₂ complexes were constructed from Zn (II) salen‐type Schiff base complex fragment and 2,6‐pyridinedimethanol (H₂pdm) or its Br‐substituted analogue (4‐bromopyridine‐2,6‐diyl)dimethanol (H₂Brpdm); their molecular formulas are [Zn₂Dy₂(L)₂(pdm)₂(MeOH)₂](ClO₄)₂ [ 1 , H₂L = N, N′‐ bis(3‐methoxysalicylidene)‐1,3‐diaminopropane] and [Zn₂Dy₂(L)₂(Brpdm)₂(MeOH)₂](ClO₄)₂ [ 2 ], the Dy (III) ions of which have a NO₇ triangular dodecahedral coordination sphere. The two complexes show not only ferromagnetic interaction but also field‐induced single‐molecule magnet (SMM) behavior, which are rare Dy (III)‐containing cluster complexes with the NO₇ triangular dodecahedral coordination sphere that can show good magnetic relaxation. The energy barrier value of complex 2 is higher than those of complex 1 and the Dy (III) complexes with the DyNO₇ triangular dodecahedral coordination configuration reported in the literature.     

Rational Design of Two-Dimensional Magnetic Chromium Borides Based on First-Principles Calculation

Two-dimensional(2D) magnetic materials have been experimentally recognized recently,however,the Curie temperatures(TC) of known 2D systems are quite low.Generally,magnetic systems can be seen as constituent magnetic elements providing spins and the non-magnetic elements providing frameworks to host the magnetic elements.Short bond lengths between the magnetic and non-magnetic elements would be beneficial for strong magnetic interactions and thus high TC.Based on this,we propose to combine the magnetic element Cr and the non-magnetic element boron to design novel 2D magnetic systems.Using our self-developed software package IM2 ODE,we design a series of chromium-boride based 2D magnetic materials.Nine stable magnetic systems are identified.Among them,we find that CrB4-Ⅰ,CrB4-Ⅱ and CrBs-Ⅰ with common structural units [CrB8] are ferromagnetic metals with estimated TC of 270 K,120 K and 110 K,respectively.On the other hand,five CrB3 phases with structural units [Cr2B12] are antiferromagnetic metals.Additionally,we also find one antiferromagnetic semiconductor CrB2-Ⅰ.Our work may open new directions for identifying 2D magnetic systems with high TC.     

Tuning Emission Wavelength of Polymorphous Crystal via Controllable Alkyl Chain Stacking and Its Vapor- and Thermo-Responsive Fluorescence

Tuning fluorescence colour of solid-state materials has become a topic of increasing interest for both fundamental mechanism study and practical applications such as sensors, optical recording and security printing. In this work, a fluorescent colour tuneable molecule BA-C16 is rationally designed and facilely synthesized by attaching flexible long alkyl chains to 2-hydroxybenzophenone azine ( BA ), which shows both aggregation-induced emission (AIE) and excited-state intramolecular proton transfer (ESIPT) characteristics. Compared to BA , the simple introduction of long alkyl chains in BA-C16 leads to an emission wavelength redshift from 542 to 558 nm. This strategy of extending emission wavelength is rarely reported, and is ascribed to the enlarged through-space π-conjugation between interplanar molecules in the aggregate of BA-C16 . Three crystals of BA-C16 are obtained with green, yellowish green and yellow emission. According to characterization by X-ray crystallography, X-ray powder diffraction and differential scanning calorimetry, alkyl chains play an important role in inducing different stacking modes of the three crystals, which further leads to polymorph-dependent fluorescence colour. BA-C16 exhibits tuneable solid-state fluorescence upon vapor fumigation, or annealing based on a transition between a “near-monomer” crystalline state and a “dimer” crystalline state. BA-C16 is further applied for rewritable fluorescence printing tuned by vapor- and thermal-treatment.