Efficient linear solvers for incompressible flow simulations using Scott‐Vogelius finite elements

Recent research has shown that in some practically relevant situations like multiphysics flows (Galvin et al., Comput Methods Appl Mech Eng, to appear) divergence‐free mixed finite elements may have a significantly smaller discretization error than standard nondivergence‐free mixed finite elements. To judge the overall performance of divergence‐free mixed finite elements, we investigate linear solvers for the saddle point linear systems arising in ((P_k)^d,P _k‐1^disc) Scott‐Vogelius finite element implementations of the incompressible Navier–Stokes equations. We investigate both direct and iterative solver methods. Due to discontinuous pressure elements in the case of Scott‐Vogelius (SV) elements, considerably more solver strategies seem to deliver promising results than in the case of standard mixed finite elements such as Taylor‐Hood elements. For direct methods, we extend recent preliminary work using sparse banded solvers on the penalty method formulation to finer meshes and discuss extensions. For iterative methods, we test augmented Lagrangian and \begin{align*}\mathcal{H}\end{align*} ‐LU preconditioners with GMRES, on both full and statically condensed systems. Several numerical experiments are provided that show these classes of solvers are well suited for use with SV elements and could deliver an interesting overall performance in several applications.© 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

Benzo-bisimidazole based nanosheets having porphyrin like internal core with high second order nonlinear optical response: A theoretical perspective

The 2D network having porphyrin like internal core are well established in literature due to their remarkable molecular tunability, photophysical and optoelectronics properties. Therefore, in the quest to attain the high performance nonlinear optical (NLO) response we have designed single Benzo-bisimidazole (BIZ) unit which has porphyrin like motif and expanded it strategically in such a way that it forms cage and further it convert into 2D nanosheet. Density functional theory (DFT), sum-over-state models and time dependent-DFT (TD-DFT) simulation were performed for geometric and electronic properties calculation. Expanding the BIZ plays a pivotal role in enhancement of the first static hyperpolarizability (β_tot) from 205.65 to 13754.59 au. Further, alkali metals substitution leads to gigantic enhancement of β_tot value from 2200.17 to 636673.60 au which is enormously higher than that of recently reported porphyrin derivative (47950 au). Calculated results revealed that the gap between highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) become narrow down from 6.28 eV ( 1 ) to 1.70 eV ( 6 ). It is to note that the designed molecules exhibit red shift of absorption. Further, density of states (DOS), and transition density matrix (TDM) analysis have also performed to explore the charge transfer and structure property relationship.     

Interaction between isoamyl adenine and rice cytokinin oxidase

Cytokinin (CTK) dehydrogenase is responsible for regulating the endogenous CTK content by oxidative removal of the side chain. Herein, we have applied fluorescence method to study the interaction between CTK dehydrogenase and CTK in vitro and obtain some parameters of their interaction. We found that addition of isopentenyl adenine can quench the fluorescence of CTK dehydrogenase, and the quenching mechanism was to be a static quenching procedure. We have measured the number of binding sites n and the apparent binding constant K and have calculated the thermodynamics parameter ΔH, ΔG, and ΔS by fluorescence quenching method. Based on thermodynamics parameter’s results, we concluded that their binding reaction was both entropy driven and the enthalpy driven, and the Van der Waals force and hydrogen bond force played a major role in the interaction. Based on the synchronous fluorescence spectrometry results, we demonstrated that the binding site between isopentenyl adenine and CTK dehydrogenase is in the microenvironment of both tryptophan and tyrosine. The fluorescence signal of coenzyme, flavin adenine dinucleotide, decreases gradually with the addition of isopentenyl adenine. And this method can be used for isopentenyl adenine routine assay. Under optimized experimental parameters, the linear segment increases from 0.6 µM to 100 µM with a regression equation of ΔF = 0.04 + 0.15c_ip (r = 0.999, c_ip in µM) with the detection limit of 0.15 µM iP.     

Extending spin-symmetry projected coupled-cluster to large model spaces using an iterative null-space projection technique

Recently, we introduced an orbital-invariant approximate coupled-cluster (CC) method in the spin-projection manifold. The multi-determinantal property of spin-projection means that the parametrization in the spin-extended CC (ECC) ansatz is nonorthogonal and overcomplete. Therefore, the linear dependencies must be removed by an orthogonalization procedure to obtain meaningful solutions. Multi-reference methods often achieve this by diagonalizing a metric of the equation system, but this is not feasible with ECC because of the enormous size of the metric, a consequence of the incomplete active space of the spin-projected Hartree–Fock reference. As a result, the applicability of ECC has been limited to small benchmark systems, for which the ansatz was shown to be superior to the configuration interaction and linearized approximations. In this article, we provide a solution to this problem that completely avoids the metric diagonalization by iteratively projecting out its null-space from the working equations. As the additional computational cost required for this iterative projection is only marginal, it greatly expands the application range of ECC. We demonstrate the potential of approximate ECC by studying the complete basis set limit of F₂ and transition metal complexes such as NiO, Mn₂, and [Cu₂O₂]²⁺ , which have all been hindered by the prohibitively large metric size. We also identify the potential inadequacy of the molecular orbitals given by spin-projected Hartree–Fock in some cases, and propose possible solutions. © 2018 Wiley Periodicals, Inc.     

静动结合的化学腐蚀法制备近场光学探针的理论分析

理论上分析了静动结合的化学腐蚀法制备探针的具体机理及过程。在静态腐蚀的过程中, 利用流体力学Young-Laplace方程的一级近似解获得了光纤插入到HF酸中形成的新月形高度。在动态腐蚀过程中, 详细分析了当静态腐蚀时间和动态腐蚀时间分别取不同值时, 光纤移动速度对光纤探针结构的影响。利用此法可制备出尖端锐利、大锥角或多锥体等各种结构的光纤探针。这为实验上制备出性能优良的探针, 为拓宽扫描近场光学显微镜的应用范围奠定基础。将上述理论分析的结果与本文实验中所得初步结果进行了比较, 所得结果一致。     

含圆孔纳米薄膜在拉伸加载下变形机理的原子级模拟研究

采用分子静力学方法结合量子修正的 Sutton-Chen多体势研究了含圆孔的纳米薄膜在单向加载过程中的力学行为,并采用共近邻分析方法研究了薄膜的微结构演化过程.模拟结果表明：孔洞的引入显著地降低了纳米薄膜的杨氏模量和屈服应力;在拉伸过程中,孔洞的形状随着应变的增加逐渐由圆形变为椭圆形,最终孔洞闭合;纳米薄膜在进入塑性变形阶段后,薄膜内部出现原子的堆跺层错,这种层错结构的出现是肖克莱不全位错在薄膜内部沿着{111}面的［112］方向运动的结果. 关键词： 纳米薄膜 力学性质 位错 分子静力学     

A divergence-conforming hybridized discontinuous Galerkin method for the incompressible Reynolds-averaged Navier-Stokes equations

We present a hybridized discontinuous Galerkin (HDG) method for the incompressible Reynolds-averaged Navier-Stokes equations coupled with the Spalart-Allmaras one-equation turbulence model. The method extends upon an HDG method recently introduced by Rhebergen and Wells for the incompressible Navier-Stokes equations. With a special choice of velocity and pressure spaces for both element and trace degrees of freedom (DOFs), the method returns pointwise divergence-free mean velocity fields and properly balances momentum and energy. We further examine the use of different polynomial degrees and meshes to see how the order of the scalar eddy viscosity affects the convergence of the mean velocity and pressure fields, specifically for the method of manufactured solutions. As is standard with HDG methods, static condensation can be employed to remove the element DOFs and thus dramatically reduce the global number of DOFs. Numerical results illustrate the effectiveness of the proposed methodology.     

Efficient Synthesis of Five Types of Heterocyclic Compounds via Intramolecular Elimination Using Ultrasound‐Static Heating Technique

An experimental technique, ultrasound‐static heating, has been developed for the efficient synthesis of heterocyclic compounds. The technique involves ultrasonic irradiation and static heating processes. First, the ultrasonic irradiation process is performed to form an intermediate of the heterocyclic compound under mild conditions and the subsequent static heating process (heating the intermediate under solvent‐free conditions without stirring) produces the target heterocyclic compounds via intramolecular elimination.