A cell functional minimization scheme for domain decomposition method on non-orthogonal and non-matching meshes

We are interested in a robust and accurate domain decomposition algorithm with interface conditions of Robin type on non-matching multiblock grids using a cell functional minimization scheme, which has a good performance on non-orthogonal meshes. In order to treat the non-matching grids at the interface, we introduce the \(L^2\) projection operator to ensure weak continuity of the primary unknown and of the normal flux across the non-matching interface. Furthermore, we prove the wellposedness of local and global problems and obtain as well an error estimate of first order in a discrete \(H^{1}\) -norm only using the \(L^{2}\) projection operator on the non-matching interface, as done in the matching case. Numerical results are presented in confirmation of the theoretical results.     

Global existence and uniqueness of solution of the initial boundary value problem for a class of non-Newtonian fluids with vacuum

The aims of this paper are to discuss global existence and uniqueness of solution for a class of non-Newtonian fluids with vacuum in one-dimensional bounded interval. The important point in this paper is that we allow the initial vacuum. In particular, these results are used to prove similar results for more general non-Newtonian fluids, and applied to numerical computation. This work is partially supported by the 985 program of Jilin University, China Postdoctoral Sciences Foundation, and NSF Grant ([10571072]; [10601009]).     

Separation of isorhamnetin 3‐sulphate and astragalin from Flaveria bidentis (L.) Kuntze using macroporous resin and followed by high‐speed countercurrent chromatography

D4020 resin offered the best dynamic adsorption and desorption capacity for total flavonoids based on the research results from ten kinds of macroporous resin. A column packed with D4020 resin was used to optimize the separation of total flavonoids from Flaveria bidentis (L.) Kuntze extracts. The content of flavonoids in the product was increased from 4.3 to 30.1% with a recovery yield of 90%. After the treatment with gradient elution on D4020 resin, the contents of isorhamnetin 3‐sulfate and astragalin were increased from 0.49 to 8.70% with a recovery yield of 74.1% and 1.16 to 30.8%, with a recovery yield of 92.2%, respectively. Further purification was carried out by one‐run high‐speed countercurrent chromatography yielding 4.5 mg of isorhamnetin 3‐sulfate at a high purity of 96.48% and yielding 24.4 mg of astragalin at a high purity of over 98.46%.     

A cell functional minimization scheme for parabolic problem

We are interested in a robust and accurate finite volume scheme for 2-D parabolic problems derived from the cell functional minimization approach. The scheme has a local stencil, is locally conservative, treats discontinuity rigorously and leads to a symmetric positive definite linear system. Since the scheme has both cell centered unknowns and cell edge unknowns, the computational cost is an issue and a parallel algorithm is then suggested based on nonoverlapping domain decomposition approach. The interface condition is of the Dirichlet–Robin type and has a parameter λ. By choosing this parameter properly, the convergence of the iteration process could be sped up. Numerical results for linear and nonlinear problems demonstrate the good performance of the cell functional minimization scheme and its parallel version on distorted meshes.     

Exact projective solutions of generalized nonlinear Schrödinger system with variable parameters

A direct self-similarity mapping approach is successfully applied to a generalized nonlinear Schrödinger (NLS) system. Based on the known exact solutions of a self-similarity mapping equation, a few types of significant localized excitation with novel properties are obtained by selecting appropriate system parameters. The integrable constraint condition for the generalized NLS system derived naturally here is consistent with the known compatibility condition generated via the Painlev? analysis.     

Gold Nanoparticles as Dual Functional Sensor to Detect E.coliDH5α as a Model for Gram‐negative Bacteria

4‐aminothiophenol‐modified gold nanoparticles (PATP‐AuNPs) were used as colorimetric and Surface Enhanced Raman Scattering (SERS) probes for the sensitive detection of Escherichia coliDH5α, as a model for Gram‐negative bacteria. The nano‐probes were easy to prepare through Au‐S bonding. Under optimized conditions, the PATP‐AuNPs surface with positive charge can bind with negatively charged E.coliDH5α via electrostatic adhesion, resulting in a quick color change from red to blue, and also a dramatic SERS signal enhancement from thousands of AuNPs aggregated on the surface of bacteria, which was utilized for both colorimetric and SERS detection of E.coliDH5α. For colorimetric analysis, it is the first time that the classical partial least square (PLS) regression was utilized to deal with the relationship between adsorption and E.coliDH5α concentrations. Excellent linear relationship was observed from 1.1 x 10⁷ to 1.3 x 10⁸ cfu mL^‐1 with the average relative error (ARE) of 5.430, which was more accurate than the traditional extinction ration method. When coupled with confocal Raman microscope, this PATP‐AuNPs probes could be used to detection SERS signals produced from even one single bacterium. This bioassay is rapid, less expensive and convenient for bacteria detection and analysis. Therefore, PATP‐AuNPs system as a novel, versatile, on‐site and real‐time Gram‐negative bacteria sensor, would have a wide range of practical applications.     

回旋行波放大器输出端反射对其稳定性的影响

 基于回旋行波放大器的线性理论和反射边界条件，建立了渐变输出端存在反射时回旋行波放大器模型，分析了TE₀₁圆电模基波回旋行波放大器输出端反射对其增益、返波起振长度、返波起振电流和返波起振频率的影响。结果表明，随着反射增强，线性增益降低，返波起振长度和起振电流减小，返波起振频率的变化较小；反射增强将在一定程度内影响放大器的稳定性。     

Conformational stabilities and structural parameters of (CH3)(n)CH(3-n) CFO molecules

Variable temperature (-60 to -100 degrees C) studies of the infrared spectra (3500-400 cm(-1)) of propionyl fluoride (CH3CH2CFO) and 2-methylpropionyl fluoride ((CH3)2CHCFO), dissolved in liquid xenon have been recorded. From these data, the enthalpy difference has been determined to be 329 +/- 33 cm(-1) (3.94 +/- 0.39 kJ/mol) for propionyl fluoride with the trans conformer (methyl group eclipsing the oxygen atom) more stable than the gauche form. For 2-methylpropionyl fluoride, the enthalpy difference has been determined to be 297 +/- 30 cm(-1) (3.55 +/- 0.36 kJ/mol) with the gauche conformer (methyl group eclipsing the oxygen atom) more stable than the trans form. From these DeltaH values along with assigned torsional fundamentals for both conformers and accompanying "hot bands" the potential functions governing the conformational interchange have been calculated. Utilizing the infrared data from the xenon solution and ab initio frequency predictions from MP2/6-31G* calculations, a few reassignments of the fundamentals have been made. Ab initio calculations have been carried out with several different basis sets up to MP2/6-311 + G** from which structural parameters and conformational stabilities have been determined. Additionally, force constants, infrared intensities, Raman activities, depolarization ratios, and scaled vibrational frequencies have been determined from MP2/6-31G* calculations. Adjusted structural parameters have been obtained from combined ab initio predicted values and previously reported microwave data. These parameters are compared to those obtained from either the earlier microwave and/or electron diffraction studies. Similar ab initio calculations and structural parameter determinations have been carried out for acetyl fluoride (CH3CFO) and trimethylacetyl fluoride ((CH3)3CCFO) and compared to the corresponding experimental results when appropriate.     

Novel pseudo-morphotactic synthesis and characterization of tungsten nitride nanoplates

A novel pseudo-morphotactic transformation route was developed to synthesize polycrystalline β-W₂N nanoplates by thermally treating tungstate-based inorganic-organic hybrid nanobelts with a lamellar microstructure in an NH₃ flow. The tungstate-based hybrid nanobelts were formed in a water-in-oil-microemulsion-like “commercial H₂WO₄ powders/n-octylamine/heptane” reaction system. The as-obtained hybrid nanobelts were thermally treated in an NH₃ atmosphere at 650-800 °C for 2 h to form cubic β-W₂N nanoplates. XRD, SEM, TEM, FT-IR and TG-DTA were used to characterize the precursors and their final products. The polycrystalline β-W₂N nanoplates derived from hybrid nanobelts, with side lengths of several hundred nanometers, consist of small nanocrystals with an average grain size of 3.2 nm. The formation of β-W₂N nanoplates involved two steps: decomposing tungstate-based hybrid nanobelts into WO_y and W species and then nitridizing the active W-containing species to β-W₂N nanocrystals in an NH₃ flow. The platelike morphology of the β-W₂N nanocrystals was inherited from the precursor of tungstate-based inorganic-organic hybrid nanobelts.     

Analytic invariant curves for a planar mapping

This paper is concerned with the existence of analytic invariant curves for a planar mapping. By constructing a convergent power series solution of an auxiliary equation, analytic solutions of the original equation are obtained. In this paper, we discuss not only the general case, but also the critical cases as well, in particular, the case where β is a unit root is discussed.