Structural dynamics of 1,2-diiodoethane in cyclohexane probed by picosecond X-ray liquidography

We investigate the structural dynamics of iodine elimination reaction of 1,2-diiodoethane (C(2)H(4)I(2)) in cyclohexane by applying time-resolved X-ray liquidography (TRXL). The TRXL technique combines structural sensitivity of X-ray diffraction and 100 ps time resolution of X-ray pulses from synchrotron and allows direct probing of transient structure of reacting molecules. From the analysis of time-dependent X-ray solution scattering patterns using global fitting based on DFT calculation and MD simulation, we elucidate the kinetics and structure of transient intermediates resulting from photodissociation of C(2)H(4)I(2). In particular, the effect of solvent on the reaction kinetics and pathways is examined by comparison with an earlier TRXL study on the same reaction in methanol. In cyclohexane, the C(2)H(4)I radical intermediate undergoes two branched reaction pathways, formation of C(2)H(4)I-I isomer and direct dissociation into C(2)H(4) and I, while only isomer formation occurs in methanol. Also, the C(2)H(4)I-I isomer has a shorter lifetime in cyclohexane by an order of magnitude than in methanol. The difference in the reaction dynamics in the two solvents is accounted for by the difference in solvent polarity. In addition, we determine that the C(2)H(4)I radical has a bridged structure, not a classical structure, in cyclohexane.     

Audience noise in concert halls during musical performances

Noise generated by the audience during musical performances is audible and sometimes disturbing. In this study, an attempt to estimate such audience noise was carried out. From the recordings of performances in five performance spaces (four concert halls and one opera house), probability density functions of the sound pressure levels were obtained in octave bands, which were fitted with three Gaussian distribution curves. The Gaussian distribution curve with the lowest mean value corresponds to a mixture of the technical background noise and audience generated noise, which is named the mixed background noise. Finally, the audience noise distribution is extracted by energy subtraction of the technical background noise levels measured in an empty condition from the mixed background noise levels. As a single index, L(90) of the audience noise distribution is named the audience noise level. Empirical prediction models were made using the four orchestra concert halls, revealing that the audience noise level is significantly correlated with the technical background noise level. It is therefore concluded that a relaxation of the current background noise recommendations for concert halls is not recommended.     

Effects of edge screens on the absorption of blocks of theatre chairs

This paper reports new measurement results investigating the use of screens around samples of theatre chairs to minimize edge effects when measuring theatre chair absorption in reverberation chambers. The absorption measurements included both full scale and scale model measurements in reverberation chambers and a model recital hall. The use of screens has been proposed to better approximate the sound absorption of the larger blocks of chairs in auditoria. The method of measuring the absorption of blocks of chairs with screens around their edges and located in the corner of a reverberation chamber did not give results indicative of the values obtained for larger areas in auditoria. The addition of screens around samples of chairs did not eliminate the variation of absorption coefficients with perimeter/area ratio. The results of extrapolations from measurements of blocks of screened chairs to infinite samples gave lower absorption coefficients than found for blocks of unscreened chairs. The absorption of chairs in large performance halls can best be predicted using the P/A method to extrapolate from reverberation chamber measurements of smaller samples of unscreened chairs, with a range of P/A values, to the larger samples and lower P/A ratios of blocks of chairs typical of performance spaces.     

On the use of homogeneous polynomials to develop anisotropic yield functions with applications to sheet forming

This paper investigates the capabilities of several non-quadratic polynomial yield functions to model the plastic anisotropy of orthotropic sheet metal (plane stress). Fourth, sixth and eighth-order homogeneous polynomials are considered. For the computation of the coefficients of the fourth-order polynomial an improved set of analytic formulas is proposed. For sixth and eighth-order polynomials the identification uses optimization. Simple constraints on the optimization process are shown to lead to real-valued convex functions. A general method to extend the above plane stress criteria to full 3D stress states is also suggested. Besides their simplicity in formulation, it is found that polynomial yield functions are capable to model a wide range of anisotropic plastic properties (e.g., the Numisheet’93 mild steel, AA2008-T4, AA2090-T3). The yield functions have then been implemented into a commercial finite element code as constitutive subroutines. The deep drawing of square (Numisheet’93) and cylindrical (AA2090-T3) cups have been simulated. In both cases excellent agreement with experimental data is obtained. In particular, it is shown that non-quadratic polynomial yield functions can simulate cylindrical cups with six or eight ears. We close with a discussion on earing and further examples.     

Quantum Systems Connected by a Time-Dependent Canonical Transformation

We study both classical and quantum relation between two Hamiltoniansystems which are mutually connected by time-dependent canonical transformation. One is ordinary conservative system and the other istime-dependent Hamiltonian system. The quantum unitary operatorrelevant to classical canonical transformation between the two systems are obtained through rigorous evaluation. With the aid of the unitary operator, we have derived quantum states of the time-dependent Hamiltonian system through transforming the quantum states of the conservative system. The invariant operators of the two systems are presented and the relation between them are addressed. We showed that there exist numerous Hamiltonians, which gives the same classical equation of motion. Though it is impossible to distinguish the systems described by these Hamiltonians within the realm of classical mechanics, they can be distinguishable quantum mechanically.     

A moving interface crack between two dissimilar functionally graded piezoelectric layers under electromechanical loading

The dynamic propagation of an interface crack between two dissimilar functionally graded piezoelectric material (FGPM) layers under anti-plane shear is analyzed using the integral transform method. The properties of the FGPM layers vary continuously along the thickness. The properties of the FGPM layers vary differently and the two layers are connected weak-discontinuously. A constant velocity Yoffe-type moving crack is considered. Fourier transform is used to reduce the problem to two sets of dual integral equations, which are then expressed to the Fredholm integral equations of the second kind. Numerical values on the dynamic energy release rate (DERR) are presented for the FGPM to show the effects on the electric loading, gradient of material properties, crack moving velocity, and thickness of layers. Followings are helpful to increase of the resistance of the interface crack propagation of FGPM: (a) certain direction and magnitude of the electric loading; (b) increase of the gradient of material properties; (c) increase of the material properties from the interface to the upper and lower free surface; (d) increase of the thickness of FGPM layer. The DERR increases or decreases with increase of the crack moving velocity.     

Effect of apex strake incidence-angle on the vortex development and interaction of a double-delta wing

The vortex flow characteristics of a sharp-edged delta wing with an apex strake was investigated through the visualization and particle image velocimetry (PIV) measurement of the wing-leeward flow region, and the wing-surface pressure measurement. The wing model was a flat-plate, and 65°-sweep cropped-delta wing with sharp leading edges. The apex strake was also a flat-plate wing with a cropped-delta shape of 65°/90° sweep, and it can change its incidence angle. The flow Reynolds number was 2.2 × 10⁵ for the flow visualization and 8.2 × 10⁵ for the PIV and wing-surface pressure measurements. The physics of the vortex flow in the wing-leeward flow region and the suction-pressure distribution on the wing upper-surface were interrelated and analyzed. The effect of a positive (negative) strake incidence-angle was the upward movement of the strake and wing vortices away from (downward movement of the strake and wing vortices toward) the wing-upper surface and the delayed (enhanced) coiling interaction between them. This change of vortex flow characteristics projected directly on the suction pressure distribution on the wing upper-surface.     

Determination of Easy Axis in a Chemical Ferromagnet, 4-(p-Chlorobenzylideneamino)–TEMPO (TEMPO=2,2,6,6-Tetramethylpiperidin-1-Oxyl)

The trapping sites for muon and muonium in ferromagnetic p-Cl–Ph–CH=N–TEMPO [(4-(p-chlorobenzylideneamino)–TEMPO (TEMPO = 2,6,6-tetramethyl-piperidin-1-yloxyl)] and the hyperfine interaction tensors for these sites are obtained using first-principles Unrestricted Hartree–Fock theory. The calculated hyperfine interactions are used to compare the calculated zero field muon spin rotation (μSR) frequencies for different choices for the easy axis and the observed frequency. It has been concluded that the two trapping centers that can best explain the observed μSR frequency are a trapped singlet muonium near the radical oxygen and a trapped muon site near the chlorine. The direction of the easy axis also is determined to be the b-axis of the monoclinic lattice. This direction for the easy axis is confirmed by determining the direction of the distributed magnetization in the molecular solid which leads to a minimum dipole–dipole interaction energy. The consequences of this agreement for the easy axis direction by two independent procedures are discussed. This revised version was published online in September 2006 with corrections to the Cover Date.     

Generalized Liouville property for Schrödinger operator on Riemannian manifolds

In this paper, we prove that the dimension of the space of positive (bounded, respectively) -harmonic functions on a complete Riemannian manifold with -regular ends is equal to the number of ends (-nonparabolic ends, respectively). This result is a solution of an open problem of Grigor'yan related to the Liouville property for the Schr?dinger operator . We also prove that if a given complete Riemannian manifold is roughly isometric to a complete Riemannian manifold satisfying the volume doubling condition, the Poincaré inequality and the finite covering condition on each end, then the dimension of the space of positive (bounded, respectively,) solutions for the Schr?dinger operator with a potential satisfying a certain decay rate on the manifold is equal to the number of ends (-nonparabolic ends, respectively). This is a partial answer of the question, suggested by Li, related to the regularity of ends of a complete Riemannian manifold. Especially, our results directly generalize various earlier results of Yau, of Li and Tam, of Grigor'yan, and of present authors, but with different techniques that the peculiarity of the Schr?dinger operator demands. Received: 4 April 2000; in final form: 19 September 2000 / Published online: 25 June 2001     

Synthesis and structure of ansa-cyclopentadienyl pyrrolyl titanium complexes: [(η-C5H4)CH2(2-C4H3N)]Ti(NMe2)2 and [1,3-{CH2(2-C4H3N)}2(η-C5H3)]Ti(NMe2)

Reaction of ansa-cyclopentadienyl pyrrolyl ligand (C₅H₅)CH₂(2-C₄H₃NH) (2) with Ti(NMe₂)₄ affords bis(dimethylamido)titanium complex [(η⁵-C₅H₄)CH₂(2-C₄H₃N)]Ti(NMe₂)₂ (3) via amine elimination. A cyclopentadiene ligand with two pendant pyrrolyl arms, a mixture of 1,3- and 1,4-{CH₂(2-C₄H₃NH)}₂C₅H₄ (4), undergoes an analogous reaction with Ti(NMe₂)₄ to give [1,3-{CH₂(2-C₄H₃N)}₂(η⁵-C₅H₃)]Ti(NMe₂) (5). Molecular structures of 3 and 5 have been determined by single crystal X-ray diffraction studies.