ABSOLUTELY UNSTABLE WAVES IN INVISCID HYDROELASTIC SYSTEMS

The effect of inviscid plug flow on the stability of several hydroelastic systems is investigated by determining the absolute or convective nature of the instability from the linear dispersion relation. The fluid-structure systems consist of plates and membranes with bounded and unbounded flow. A method is proposed to derive systematically in parameter space the boundary between convective and absolute instability, based on the particular symmetries of the dispersion relation as originally noted by Crighton and Oswell. This method is then applied to the case of plates with superimposed tension, thick plates with rotary inertia and walls made of plates or membranes bounding channel flow, oscillating in a sinuous or varicose mode of deformation. A relation is drawn with solutions by previous authors for plates, for pipes and for the Kelvin-Helmholtz instability with surface tension. To illustrate these results some temporal evolutions are calculated by using an integration in the wavenumber space. Based on the large set of new cases solved in the paper some general trends are discussed as to the influence of flow velocity, confinement and structural stiffness on the existence of absolutely unstable waves in inviscid hydroelastic systems.     

Commutators with idempotent values on multilinear polynomials in prime rings

Let R be a prime ring of characteristic different from 2, C its extended centroid, d a nonzero derivation of R, f(x ₁, . . . , x _n ) a multilinear polynomial over C, ρ a nonzero right ideal of R and m > 1 a fixed integer such that

$$\qquad \left ([d(f(r_{1},\ldots ,r_{n})),f(r_{1},\ldots ,r_{n})]\right )^{m}=[d(f(r_{1},\ldots ,r_{n})),f(r_{1},\ldots ,r_{n})] $$

for all r ₁, . . . , r _n ∈ρ. Then either [f(x ₁,…,x _n ),x _n+1]x _n+2 is an identity for ρ or d(ρ)ρ = 0.

     

La0.789Yb0.20Ho0.001Tm0.01F3纳米立方体的溶剂热合成及白色上转换发光性质

采用溶剂热方法制备了La0.789Yb0.20Ho0.001Tm0.01F3纳米立方体,并利用粉末X射线衍射仪、透射电子显微镜和X射线能谱仪表征了其组成、结构和形貌,用荧光分光光度计测量了样品的室温上转换发射光谱,结果表明,样品具有红、绿和蓝色3个发射带,其辐射跃迁分别归属于Tm3+的1G4→3H6(蓝色)和1G4→3...     

High-resolution FTIR spectrum of vinyl chloride: rovibrational analysis of the v 10 and v 11 fundamental bands

The Fourier transform gas-phase infrared spectra of the v ₁₀ and v ₁₁ bands of natural CH₂=CHCl have been measured with a resolution of 0.005 cm^?1 in the frequency range 820–1010 cm^?1. These vibrations of symmetry species A″ give rise to c-type bands and the transitions observed are characterized by δK _a = ±1 and δK _c = 0, ±2. Both J and K structures have been resolved in different subbranches and about 1800 (J ≤ 64, K _a ≤ 13) and 2800 (J ≤ 72, K _a ≤ 14) transitions for the v ₁₀ and v ₁₁ fundamentals, respectively, have been identified for the ³⁵Cl isotopomer. Combined analysis of the assigned data with the available ground state constants allowed the determination of the band origins, rotational and centrifugal distortion parameters for the v ₁₀ = 1 and v ₁₁ = 1 excited states of CH₂=CH³⁵Cl isotopic species. The molecular constants obtained account for slight perturbations in the v ₁₀ vibrational level.     

Direct correlation functions and bridge functions in additive hard-sphere mixtures

A method to obtain (approximate) analytical expressions for the radial distribution functions in a multicomponent mixture of additive hard spheres that was recently introduced is used to obtain the direct correlation functions and bridge functions in these systems. This method, which yields results practically equivalent to the generalized mean spherical approximation and includes thermodynamic consistency, is an alternative to the usual integral equation approaches and requires as input only the contact values of the radial distribution functions and the isothermal compressibility. Calculations of the bridge functions for a binary mixture using the Boublik-Mansoori-Carnahan-Starling-Leland equation of state are compared to parallel results obtained from the solution of the Percus-Yevick equation. We find that the conjecture recently proposed by Guzman and del Rio (1998, 98, Molec. Phys., 95, 645), stating that the zeros of the bridge functions occur approximately at the same value of the shifted distance for all pairs of interactions, is at odds with our results. Moreover, in the case of disparate sizes, even the Percus-Yevick bridge functions do not have this property. It is also found that the bridge functions are not necessarily non-positive.     

Exploring the MRCI method for calculating interaction energies: application to the HeNe potential curve

A multi-reference configuration interaction (MRCI) method is described, which is devised for the calculation of interaction energies of van der Waals complexes and applied to calculating the HeNe potential energy curve. The MRCI calculations make use of a generalized Pople-correction in order to account for the lack of size consistency. The orbital space is partitioned into three subspaces: the first active space (AS1), which contains the strongly occupied orbitals; the second active space (AS2), which contains the main intra-correlating orbitals; and the external space (ES). It is shown that, to keep the error below ± 0.2 K in the excitation scheme and the active orbital space it is sufficient to include only σ-orbitals in AS2 and to use an excitation scheme (labelled Qq-MRCI) that encompasses only up to quadruply excited configurations. The final active orbital space (AS2) turned out to be 2s(He), 2pσ(He), 3s(Ne), 3σ(Ne) and 3dσ(Ne). Other MRCI variants, in which most or all quadruply excited configurations were deleted from the CI expansion (Qt- and Tt-MRCI), were found to be inadequate. Using the Qq-MRCI scheme together with a 197-orbital ‘interaction optimized’ basis set (IO197), the MRCI interaction energy at R = 5.7 _a0 was calculated to be -21.12K. The corresponding values at the MP4 and CCSD(T) levels of theory are -20.06 K and -20.99 K, respectively, indicating that the MP4 method is inappropriate for highly accurate calculations on this system. Fitting the calculated data using a generalized Morse function, including an additional C₆/R⁶ term to account for a correct long-range behaviour of the potential, the MRCI well depth was calculated to be -21.16K at R_eq = 5.73a ₀. The MRCI and CCSD(T) potentials have the same quality and are found to be in good agreement with the Hartree-Fock dispersion (HFD-B) potential of Keil, M., Danielson, L. J., and Dunlop, P. J., 1991, J. Chem. Phys., 94, 296. It is concluded that, for basis IO197, the CCSD(T) method is sufficiently accurate for calculating the HeNe interaction. To recover the small, missing contributions (a few tenths of a Kelvin), MRCI should be used.     

Dynamics on reactive potential energy surfaces: hyperspherical view and signatures of ‘quantum chaos’

Adiabatic energy levels for two prototypical reactions, F + H₂ → HF + H and He + H⁺ ₂ → HeH⁺ + H, are analysed by means of statistical tests. These levels result from quantum mechanical calculations of dynamics based on the hyperspherical approach, and are given as a function of the total inertia of the system measured by the hyperradius ρ The nearest neighbour level spacing distributions of Brody and of Berry and Robnik, the spectral rigidity δ₃ of Dyson and Mehta and the correlation coefficient are reported, together with other properties, such as variance, skewness and kurtosis of the distributions. Trends are studied as a function of ρ, proposed as a natural control variable. For low ρ, which correspond to the transition state, evidence is found of Wigner-like behaviour, which is interpreted as the signature of quantum chaos. On the passage of the systems through intermediate ρ a mixture of Wigner- and Poisson-like behaviour emerges. The situation for high ρ where reactants and products of the reactions are well separated, is characterized by a tendency towards regular Poisson-like behaviour. A comparison between the two investigated systems shows that the chaotic regime in the transition state region is more pronounced for the He reaction, which proceeds through a deep well and whose dynamics are characterized by a rich resonance pattern.     

Density functional theory calculations of nuclear quadrupole coupling constants with calibrated 14N quadrupole moments

Density functional calculations of the electric field gradient tensor at the nitrogen nucleus in 13 test molecules, containing 14 nitrogen sites, have been performed using the linear combination of Gaussian-type orbital Kohn-Sham density functional theory (LCGTO-KSDFT) approach. Local and gradient corrected functionals were used for all-electron calculations. All the molecular structures were optimized at their respective levels of theory with extended basis sets. Calibrated ¹⁴N nuclear quadrupole moments were obtained through a fitting procedure between calculated electric field gradients and experimental nuclear quadrupole coupling constants of the test set of molecules for each basis set and functional considered. With these calibrated ¹⁴N nuclear quadrupole moments, the nuclear quadrupole coupling constants of the following selected systems were determined: fluoromethylisonitrile, pyridine, pyrrole, imadazole, pyrazole, 1,8-bis(dimethyl-amino)naphthalene, cyclotetramethylenetetranitramine, cocaine and heroin.     

Nanoscale imaging of buried structures with elemental specificity using resonant x-ray diffraction microscopy

We report the first demonstration of resonant x-ray diffraction microscopy for element specific imaging of buried structures with a pixel resolution of approximately 15 nm by exploiting the abrupt change in the scattering cross section near electronic resonances. We performed nondestructive and quantitative imaging of buried Bi structures inside a Si crystal by directly phasing coherent x-ray diffraction patterns acquired below and above the Bi M5 edge. We anticipate that resonant x-ray diffraction microscopy will be applied to element and chemical state specific imaging of a broad range of systems including magnetic materials, semiconductors, organic materials, biominerals, and biological specimens.