Approximate solutions for drag coefficient of bubbles moving in shear-thinning elastic fluids

The drag coefficient for bubbles with mobile or immobile interface rising in shear-thinning elastic fluids described by an Ellis or a Carreau model is discussed. Approximate solutions based on linearization of the equations of motion are presented for the highly elastic region of flow. These solutions are in reasonably good agreement with the theoretical predictions based on variational principles and with published experimental data. C _D Drag coefficient - E ^* Differential operator [E ^{* 2} = ²/² + (sin/ ²)/(1/sin /)] - El Ellis number - F _D Drag force - K Consistency index in the power-law model for non-Newtonian fluid - n Flow behaviour index in the Carreau and power-law models - P Dimensionless pressure [=(p – p ₀)/₀ (U /R)] - p Pressure - R Bubble radius - Re ₀ Reynolds number [= 2R U /₀] - Re Reynolds number defined for the power-law fluid [= (2R) ⁿ U ^2–n /K] - r Spherical coordinate - t Time - U Terminal velocity of a bubble - u Velocity - Wi Weissenberg number - Ellis model parameter - Rate of deformation - Apparent viscosity - ₀ Zero shear rate viscosity - Infinite shear rate viscosity - Spherical coordinate - Parameter in the Carreau model - ^* Dimensionless time [=/(U /R)] - Dimensionless length [=r/R] - Second invariant of rate of deformation tensors - ^* Dimensionless second invariant of rate of deformation tensors [=/(U /R)²] - Second invariant of stress tensors - ^* Dimensionless second invariant of second invariant of stress tensor [= / ₀ ² (U /R)²] - Fluid density - Shear stress - ^* Dimensionless shear stress [=/ ₀ (U /R)] - _1/2 Ellis model parameter - ₁ ^2/* Dimensionless Ellis model parameter [= _1/2/ ₀(U /R)] - Stream function - ^* Dimensionless stream function [=/U R ²]     

非线性弹性杆波动方程的显式精确解北大核心CSCD

应用sine-cosine方法对非线性弹性杆波动方程进行了求解,得到了该方程的一些新的周期波解和孤波解(材料常数n为不等于1的常数).对部分结果通过数学软件得到了解的图像,获得的结果有助于非线性弹性杆中孤波存在性问题的进一步研究.     

Second‐order elastic constants of hexagonal hydroxylapatite (P63) from ab initio quantum mechanics: Comparison between DFT functionals and basis sets

Three very popular Hamiltonians in the density functional theory framework, PBE, PBEsol, and B3LYP, and different basis sets (Gaussian‐type orbitals and plane waves) were employed to simulate the hydroxylapatite unit cell and its second‐order elastic constants. Dispersive interactions were included in the quantum‐mechanical treatment via the DFT‐D2 and Tkatchenko‐Scheffler schemes. The calculated bulk, shear, and Young's moduli were in the range of 82‐117 GPa, 42‐51 GPa, and 107‐134 GPa, respectively. The axial moduli, K_a and K_b, were instead in the range of 277‐322 GPa and 506‐509 GPa. The theoretical data, especially those from plan waves simulations, are in good agreement with available results in literature and further extend the knowledge of the mechanical and vibrational properties of hydroxylapatite.     

New analogs of temporin-LK1 as inhibitors of multidrug-resistant (MDR) bacterial pathogens

The peptide temporin-LK1 (1) was obtained from the skin secretion of frog Limnonectes kuhlii (Ranidae). It is a unique antimicrobial peptide with 17 residues, including four L-phenylalanines and single glycine. Mass spectrometry and Edmand degradation were used for the determination of sequence of amino acids in temporin-LK 1 (1), and confirmed by cDNA cloning. We report here the synthesis and structural studies of temporin-LK1 (1) and its analogs 2–4. Peptides 2–4 were prepared by substitution of achiral glycine residue of temporin-LK1 (1) with D-alanine, L-phenylglycine, and L-naphthylalanine, respectively. Peptides 1–4 were evaluated against multidrug-resistant (MDR) strains of Staphylococcus aureus and Pseudomonas aeruginosa. Analog 2 was found active against all MDR strains of S. aureus and P. aeruginosa at a much lower dose than the clinically used antibiotics.     

Misfit dislocations in limited inhomogeneous media: A review

Elastic fields of translation and misfit dislocations (resp. TD's and MD's) are investigated for two types of inhomogeneous materials.First, a multilayer formed by parallel heterointerfaces or free surfaces and containing one periodic array of interfacial MD's. In the more simple case of a thin layer on a substrate, analytic solutions can be found for the displacement field u relative to a single or a hexagonal periodic array of MD's. In the less simple case of a thin bicrystal and a layer sandwiched between two semi-infinite media, explicit solutions can still be extracted. For the general case of a multilayer material which involves a number N>2 heterointerfaces, analytic expressions become intractable. Solutions can nevertheless be obtained from the numerical inversion of linear equations which express the limiting boundary conditions along the heterointerfaces.Second, a thin bicrystal containing an heterointerface perpendicular to the two free surfaces of a foil. Starting from the elastic field of an edge TD parallel to the free surfaces, it is shown how to derive that of (i) a coherent heterointerface, (ii) a semicoherent heterointerface containing a single MD, and (iii) two close and parallel coherent heterointerfaces. Numerical calculations and graphs illustrate the solutions for metals (Al, Al₂Cu), semiconductor materials (CoSi₂, Si, GaAs), thin foils of the GaAs/Si type and a / superalloy.     

Investigation of radical pairs produced upon pulse action of elastic waves on the 3,6-di-tert-butylcatechol-3,6-di-tert-butyl-o-benzoquinone-sulfur system

The pulse action of elastic waves on polycrystalline mixtures of 3,6-di-tert-butylcatechol and 3,6-di-tert-butyl-o-benzoquinone produces radical pairs stable at room temperature, and the addition of polycrystalline sulfur considerably increases their yield. The dependences of formation and decay rates of paramagnetic centers on the composition of the mixture were studied. The threshold character of formation of paramagnetic centers at various powers of elastic wave pulse was established.Translated fromIzvestiya Akademii Nauk. Seriva Khimicheskaya, No. 4, pp. 864–868, April, 1996.     

Evaluation of elastic‐scattering cross sections for electrons and positrons over a wide energy range

Quantification of surface‐ and bulk‐analytical methods, e.g. Auger‐electron spectroscopy (AES), X‐ray photoelectron spectroscopy (XPS), electron‐probe microanalysis (EPMA), and analytical electron microscopy (AEM), requires knowledge of reliable elastic‐scattering cross sections for describing electron transport in solids. Cross sections for elastic scattering of electrons and positrons by atoms, ions, and molecules can be calculated with the recently developed code ELSEPA (Elastic Scattering of Electrons and Positrons by Atoms) for kinetic energies of the projectile from 10 eV to 50 eV. These calculations can be made after appropriate selection of the basic input parameters: electron‐density distribution, a model for the nuclear‐charge distribution, and a model for the electron‐exchange potential (the latter option applies only to scattering of electrons). Additionally, the correlation‐polarization potential and an imaginary absorption potential can be considered in the calculations. We report comparisons of calculated differential elastic‐scattering cross sections (DCSs) for silicon and gold at selected energies (500 eV, 5 keV, 30 keV) relevant to AES, XPS, EPMA, and AEM, and at 100 MeV as a limiting case. The DCSs for electrons and positrons differ considerably, particularly for medium‐ and high‐atomic‐number elements and for kinetic energies below about 5 keV. The DCSs for positrons are always monotonically decreasing functions of the scattering angle, while the DCSs for electrons have a diffraction‐like structure with several minima and maxima. A significant influence of the electron‐exchange correction is observed at 500 eV. The correlation‐polarization correction is significant for small scattering angles at 500 eV, while the absorption correction is important at energies below about 10 keV. Copyright © 2005 John Wiley & Sons, Ltd.     

Torsional potential and strain energy distribution in an extended chain under stress

Torsional potentialV() for the single bond transformation in an extended hexadecane, subjected to elongation, has been determined by molecular mechanics calculations. The stored elastic energy significantly modifies the potentialV(), the conformational energies and the barriers of transition. Apart from the soft torsional coordinate, elastic energy is also dissipated considerably by bond stretching and angle bending. Maximal variations of the valence coordinates occur in the vicinity of the torsional defect and dampen along the chain. At higher elongation, the gauche minimum on the potentialV() disappears and the calculations predict the abrupt gauche to trans transition. The energetics of torsion of a deformed chain are compared with the experimental data on the hydrodynamic extension of polymers in dilute solution by elongational flow. The calculations also provide details of a single bond transformation mechanism at conformational interconversions in a long chain, proposed by Helfand.     

气相色谱法测定托吡酯中有机溶剂残留量

用填充柱FID-GC外标法在线检测托毗酯中4种有机溶剂残留量，通过线性、准确度、精密度、专属性、最低检测限等试验，证明此方法分离度高、灵敏、准确、简便，能满足检测要求．     

Inequalities for a distribution with monotone hazard rate

Summary LetX be a positive random variable with the survival function and the densityf. LetX have the moments μ=E(X) and μ₂=E(X ²) and put ε=|1-μ₂/2μ²|. Put and . It is proved that the following inequalities hold: , for allx>0, ifq(x) is monotone and that , ifq ₁ (x) is monotone. It is also shown that Brown's inequality which holds wheneverq ₁ (x) is increasing is not valid in general whenq ₁ is decreasing. The Institute of Statistical Mathematics