A cost‐effective curvature calculation approach for interfacial flows on unstructured meshes

We present a simple and cost‐effective curvature calculation approach for simulations of interfacial flows on structured and unstructured grids. The interface is defined using volume fractions, and the interface curvature is obtained as a function of the gradients of volume fractions. The gradient computation is based on a recently proposed gradient recovery method that mimicks the least squares approach without the need to solve a system of equations and is quite easy to implement on arbitrary polygonal meshes. The resulting interface curvature is used in a continuum surface force formulation within the framework of a well‐balanced finite‐volume algorithm to simulate multiphase flows dominated by surface tension. We show that the proposed curvature calculation is at least as accurate as some of the existing approaches on unstructured meshes while being straightforward to implement on any mesh topology. Numerical investigations also show that spurious currents in stationary problems that are dependent on the curvature calculation methodology are also acceptably low using the proposed approach. Studies on capillary waves and rising bubbles in viscous flows lend credence to the ability of the proposed method as an inexpensive, robust, and reasonably accurate approach for curvature calculation and numerical simulation of multiphase flows.     

On the radius of spatial analyticity for the modified Kawahara equation on the line

First, by using linear and trilinear estimates in Bourgain type analytic and Gevrey spaces, the local well‐posedness of the Cauchy problem for the modified Kawahara equation on the line is established for analytic initial data that can be extended as holomorphic functions in a strip around the x‐axis. Next we use this local result and a Gevrey approximate conservation law to prove that global solutions exist. Furthermore, we obtain explicit lower bounds for the radius of spatial analyticity given by , where can be taken arbitrarily small and c is a positive constant.     

Contingent derivatives and regularization for noncoercive inverse problems

Abstract

We study the inverse problem of parameter identification in noncoercive variational problems that commonly appear in applied models. We examine the differentiability of the set-valued parameter-to-solution map using the first-order and the second-order contingent derivatives. We explore the inverse problem using the output least-squares and the modified output least-squares objectives. By regularizing the noncoercive variational problem, we obtain a single-valued regularized parameter-to-solution map and investigate its smoothness and boundedness. We also consider optimization problems using the output least-squares and the modified output least-squares objectives for the regularized variational problem. We give a complete convergence analysis showing that for the output least-squares and the modified output least-squares, the regularized minimization problems approximate the original optimization problems suitably. We also provide the first-order and the second-order adjoint method for the computation of the first-order and the second-order derivatives of the output least-squares objective. We provide discrete formulas for the gradient and the Hessian calculation and present numerical results.     

Biological activity of new amino phospha betaines with C10–C18 alkyl groups

New amino phospha betaines were obtained by quaternization of potassium salt of amino phosphonate and higher alkyl bromides. The structure of isopropyl (N-dodecyl-N,N- dimethylammoniomethyl)phosphonate was confirmed by single crystal X-ray diffraction. All synthesized compounds demonstrate high antibacterial and antifungal activities.     

Hyperpolarization of Amino Acids in Water Utilizing Parahydrogen on a Rhodium Nanocatalyst

NMR offers many possibilities in chemical analysis, structural investigations, and medical diagnostics. Although it is broadly used, one of NMR spectroscopies main drawbacks is low sensitivity. Hyperpolarization techniques enhance NMR signals by more than four orders of magnitude allowing the design of new contrast agents. Parahydrogen induced polarization that utilizes the para-hydrogen's singlet state to create enhanced signals is of particular interest since it allows to produce molecular imaging agents within seconds. Herein, we present a strategy for signal enhancement of the carbonyl ¹³C in amino acids by using parahydrogen, as demonstrated for glycine and alanine. Importantly, the hyperpolarization step is carried out in water and chemically unmodified canonical amino acids are obtained. Our approach thus offers a high degree of biocompatibility, which is crucial for further application. The rapid sample hyperpolarization (within seconds) may enable the continuous production of biologically useful probes, such as metabolic contrast agents or probes for structural biology.     

Green Synthesis of new Trizole Based Heterocyclic Amino Acids Ligands and their Transition Metal Complexes. Characterization,Kinetics, Antimicrobial and Docking Studies

Two novel amino acids imine ligands (H₂L₁ and H₂L₂) have been synthesized using green condensation reaction from 2‐[3‐Amino‐5‐(2‐hydroxy‐phenyl)‐5‐methyl‐1,5‐dihydro‐[1, 2, 4]triazol‐4‐yl]‐3‐(1H‐indol‐3‐yl)‐propionic acid with benzaldehyde/p‐flouro benzaldehyde (1:1 molar ratio) in the presence of lemon juice as a natural acidic catalyst in aqueous medium. Their transition metal complexes have been prepared in a molar ratio (1:1). Characterization of the ligands and complexes using elemental analysis, spectroscopic studies, ¹HNMR, ¹³CNMR, and thermal analysis has been reported. E*, ΔH*, ΔS* and ΔG* thermodynamic parameters, were calculated to throw more light on the nature of changes accompanying the thermal decomposition process of these complexes. The molar conductance measurement of metal complexes showed nonelectrolyte behavior. The metal complexes of the two ligands have tetrahedral geometry with a general molecular structure [M(H₂L)X_n], where [(M = Mn (II), Co (II), Cu (II) and Zn (II), X = Cl, n = 2]; M = VO (II), X = SO₄, n = 1] for H₂L₁. [M = Co (II), Cu (II), Zn (II)] for H₂L₂. Antibacterial activity of the complexes against (Bacillis subtilis, Micrococcus luteus, Escherichia coli), also antifungal activity against (Aspergillus niger, Candida Glabarta, Saccharomyces cerevisiae) have been screened. The results showed that all complexes have antimicrobial activity higher than free ligands. Molecular docking studies results showed that, all the synthesized compounds having minimum binding energy and have good affinity toward the active pocket, thus, they may be considered as good inhibitor of targeting PDB code: 1SC7 (Human DNA Topo‐isomerase I).     

A Runge-Kutta–based WENO reconstruction on moving mesh for compressible fluids

In this paper, we construct a high-order moving mesh method based on total variation diminishing Runge-Kutta and weighted essential nonoscillatory reconstruction for compressible fluid system. Beginning with the integral form of fluid system, we get the semidiscrete system with an arbitrary mesh velocity. We use weighted essential nonoscillatory reconstruction to get the space accuracy on moving meshes, and the time accuracy is obtained by modified Runge-Kutta method; the mesh velocity is determined by moving mesh method. One- and two-dimensional numerical examples are presented to demonstrate the efficient and accurate performance of the scheme.     

有耗介质层上多导体传输线的电磁耦合时域分析方法

目前,针对空间电磁场作用有耗介质层上传输线的电磁耦合,仍缺乏有效的数值分析方法.因此,本文提出一种高效的时域混合算法,很好地解决了有耗介质层上传输线电磁耦合建模难的问题.首先,对经典传输线方程进行改进,推导了适用于有耗介质层上多导体传输线电磁耦合分析的修正传输线方程.然后,结合时域有限差分方法和相应插值技术,求解修正传输线方程,获得多导线及其端接负载上的电压和电流响应,并实现空间电磁场辐射与多导线瞬态响应的同步计算.最后,通过相应计算实例的数值模拟,与CST软件的仿真结果进行对比,验证了时域混合算法的正确性和高效性.     

NMR studies on 4‐thio‐5‐furan‐modified and 4‐thio‐5‐thiophene‐modified nucleosides

Systematic NMR characterization of 4‐thio‐5‐furan‐pyrimidine nucleosides or 4‐thio‐5‐thiophene‐pyrimidine nucleosides (ribonucleosides and 2′‐deoxynucleosides) was performed. All proton and carbon signals of 4‐thio‐5‐thiophene‐ribouridine and related analogues were unambiguously assigned. The orientations of the base (4‐thiouridine or its deoxy analogue) relative to the ring (furan or thiophene) are explored by a NMR approach and further supported by X‐ray crystallographic studies. The procedures presented here would be applicable to other modified nucleosides and nucleotides. Copyright © 2016 John Wiley & Sons, Ltd.     

Orchestrating the Biosynthesis of an Unnatural Pyrrolysine Amino Acid for Its Direct Incorporation into Proteins Inside Living Cells

We here report the construction of an E. coli expression system able to manufacture an unnatural amino acid by artificial biosynthesis. This can be orchestrated with incorporation into protein by amber stop codon suppression inside a living cell. In our case an alkyne‐bearing pyrrolysine amino acid was biosynthesized and incorporated site‐specifically allowing orthogonal double protein labeling.