Stabilized Nonconforming Mixed Finite Element Method for Linear Elasticity on Rectangular or Cubic Meshes

Based on the primal mixed variational formulation, a stabilized nonconforming mixed finite element method is proposed for the linear elasticity on rectangular and cubic meshes. Two kinds of penalty terms are introduced in the stabilized mixed formulation, which are the jump penalty term for the displacement and the divergence penalty term for the stress. We use the classical nonconforming rectangular and cubic elements for the displacement and the discontinuous piecewise polynomial space for the stress, where the discrete space for stress are carefully chosen to guarantee the well-posedness of discrete formulation. The stabilized mixed method is locking-free. The optimal convergence order is derived in the $L^2$-norm for stress and in the broken $H^1$-norm and $L^2$-norm for displacement. A numerical test is carried out to verify the optimal convergence of the stabilized method.     

On the Brauer p-dimension of Henselian discrete valued fields of residual characteristic p > 0

Let $(K,v)$ be a Henselian discrete valued field with residue field $\stackrel{?}{K}$ of characteristic $p>0$, and ${\text{Brd}}_p(K)$ be the Brauer p-dimension of K. This paper shows that ${\text{Brd}}_p(K)\ge n$ if $[\stackrel{?}{K}:{\stackrel{?}{K}}^p]=p^n$, for some $n\in \mathbb{N}$. It proves that ${\text{Brd}}_p(K)=\infty$ if and only if $[\stackrel{?}{K}:{\stackrel{?}{K}}^p]=\infty$.     

Solution combustion synthesis,energy and environment: Best parameters for better materials

Solution combustion synthesis (SCS) is a worldwide used methodology for the preparation of inorganic ceramic and composite materials with controlled properties for a wide number of applications, from catalysis to photocatalysis and electrocatalysis, from heavy metal removal to sensoristics and electronics. The high versatility and efficiency of this technique have led to the introduction of many variants, which allowed important optimization to the prepared materials. Moreover, its ecofriendly nature encouraged further studies about the use of sustainable precursors for the preparation of nanomaterials for energy and environment, according to the concept of circular economy. On the other hand, the large variety of expressions to define SCS and the often-contradictory definitions of the SCS parameters witnessed a scarce consciousness of the potentiality of this methodology. In this review article, the most important findings about SCS and the selection criteria for its main parameters are critically reviewed, in order to give useful guidelines to those scientists who want to use this methodology for preparing materials with improved or new functional properties. This review aims as well (i) to bring more clarity in the SCS terminology (ii) to increase the awareness of the SCS as a convenient tool for the synthesis of materials and (iii) to propose a new perspective in the SCS, with special attention to the use of ecofriendly procedures. Part of the review is also dedicated to precautions and limitations of this powerful methodology.     

Unconditionally Superclose Analysis of a New Mixed Finite Element Method for Nonlinear Parabolic Equation

This paper develops a framework to deal with the unconditional superclose analysis of nonlinear parabolic equation. Taking the finite element pair $Q_{11}/Q_{01} × Q_{10}$ as an example, a new mixed finite element method (FEM) is established and the $τ$ -independent superclose results of the original variable $u$ in $H^1$-norm and the flux variable $\mathop{q} \limits ^{\rightarrow}= −a(u)∇u$ in $L^2$-norm are deduced ($τ$ is the temporal partition parameter). A key to our analysis is an error splitting technique, with which the time-discrete and the spatial-discrete systems are constructed, respectively. For the first system, the boundedness of the temporal errors is obtained. For the second system, the spatial superclose results are presented unconditionally, while the previous literature always only obtain the convergent estimates or require certain time step conditions. Finally, some numerical results are provided to confirm the theoretical analysis, and show the efficiency of the proposed method.     

基于图像处理的光学谐振腔自准直研究方法

针对我国氧碘化学激光器输出能量不断提高的情况下,主要限制光束质量的因素之一是出光过程中的光腔失调,提出了一种基于图像处理的光学谐振腔自准直研究方法。该研究方法利用氦氖穿腔光通过凹腔镜中心孔,并在凸腔镜后方放置工业相机,在屏幕上方形成一个干涉同心圆环。通过借助OpenCV库中二值化、霍夫圆检测等图像处理的方法,获得干涉同心圆环的圆心坐标,再通过以圆心为中心将图像分成上下左右四个部分,通过判断这四部分亮点像素的数量差值来预估干涉同心圆环的偏移状态,进而获得空腔条件下光学谐振腔发生变化的理论判据。实验结果表明,该方法可以获得相当精准的光学谐振腔失调判据,其失调判据选取左右亮点像素差值30000,上下亮点像素差值45000,为今后失调判据与步进电机自动调腔的结合做好充足的准备。     

The beneficial impacts of functional groups of CNT on structure and gas separation properties of PEBA mixed matrix membranes

Incompatibility between filler and polymer chains accompanied by particle agglomeration has a detrimental effect on the performance of mixed matrix membranes (MMMs). To obviate intermolecular forces of different additives, functional groups (-COOH, –NCO, and –NH₂) were grafted on the surface of multi-walled carbon nanotubes (MWCNTs) which were then incorporated as fillers in the poly(ether-block-amide) (PEBA) polymeric matrix in the range of 0.1–1 wt% loading. CO₂ permeability and ideal CO₂/N₂ and CO₂/CH₄ selectivity of MMMs was compared with the neat membrane, and the results revealed favorable enhancement and surpassed CO₂/N₂ Robeson's upper bound under 4–10 bar in the range of 15–55 °C. Mixed gas separation performance of MMMs, which is of vital importance in industrial applications, was also investigated. The results indicate that MWCNT-NCO created superior grafts with the polymer chains, and MMMs with this additive had a better gas separation performance with high mechanical and thermal stability.     

On the use of edge cracked short bend beam specimen for PMMA fracture toughness testing under mixed-mode I/II

In this paper an inclined edge cracked short beam specimen subjected to symmetric three-point bend loading was designed and examined for conducting mixed-mode I/II fracture toughness experiments. The aspect ratio (i.e. length to width ratio) and the loading span distance are considered much lower than the other conventional cracked bend beam samples. Crack tip parameters such as stress intensity factors and T-stress were computed numerically for this specimen by several finite element analyses and it was demonstrated that the specimen is able to produce full combinations of mode I and II including pure mode II. The practical capability of the short bend beam specimen was studied experimentally by conducting a set of mixed-mode fracture tests on PolymethylMethacrylate (PMMA) as a well-known model brittle material. The critical stress intensity factors, the direction of fracture kinking and the path of fracture trajectory were investigated both experimentally and theoretically using two stress and strain-based fracture criteria. The fracture toughness of tested PMMA was decreased by moving towards mode II case due to the effect of T-stress on the fracture mechanism of the short bend beam specimen.     

Hermitian adjacency matrix of the second kind for mixed graphs

This contribution gives an extensive study on spectra of mixed graphs via its Hermitian adjacency matrix of the second kind (N-matrix for short) introduced by Mohar [25]. This matrix is indexed by the vertices of the mixed graph, and the entry corresponding to an arc from u to v is equal to the sixth root of unity $\omega =\frac{1+\mathbf{i}\sqrt{3}}{2}$ (and its symmetric entry is $\overline{\omega }=\frac{1?\mathbf{i}\sqrt{3}}{2}$); the entry corresponding to an undirected edge is equal to 1, and 0 otherwise. The main results of this paper include the following: equivalent conditions for a mixed graph that shares the same spectrum of its N-matrix with its underlying graph are given. A sharp upper bound on the spectral radius is established and the corresponding extremal mixed graphs are identified. Operations which are called two-way and three-way switchings are discussed–they give rise to some cospectral mixed graphs. We extract all the mixed graphs whose rank of its N-matrix is 2 (resp. 3). Furthermore, we show that if $M_G$ is a connected mixed graph with rank 2, then $M_G$ is switching equivalent to each connected mixed graph to which it is cospectral. However, this does not hold for some connected mixed graphs with rank 3. We identify all mixed graphs whose eigenvalues of its N-matrix lie in the range $(?\alpha ,\alpha )$ for $\alpha \in \{\sqrt{2},\sqrt{3},2\}$.     

1D iron vanadate-reduced graphene oxide nanorod composite for efficient oxidative esterification of aldehydes

In this paper, we report a facile and one-pot hydrothermal synthesis of FeVO₄-rGO nanorod composite and its application as a heterogeneous catalyst in the oxidative esterification reaction of aldehydes using hydrogen peroxide oxidant. The nanomaterial is thoroughly characterized by different techniques, namely, XPS, FESEM, elemental mapping, XRD, Raman, HRTEM, etc. The as-prepared nanocatalyst shows good activity for the controlled base-free oxidative esterification of various aromatic aldehydes in alcohol solvents under refluxing conditions, achieving good yields of the desired esters. Furthermore, the substrate scope was explored over a wide array of substituted aromatic aldehydes with diverse electron-withdrawing and electron-donating groups in the phenyl ring. The presence of heterogeneous interfaces-induced properties in the nanorod composite results in synergistic effects to provide good catalytic performance. Thus, binary transition metal oxide-reduced graphene oxide-based nanocomposite as a nanocatalyst can open doors for efficient and sustainable esterification of aromatic aldehydes and aliphatic alcohols under oxidative conditions.