On the mechanism of the N,N‐dimethyl amination of Grignard reagents: a kinetic study

A direct kinetic study is reported for the electrophilic amination of substituted phenylmagnesium bromides with N,N‐dimethyl O‐(mesitylenesulfonyl)hydroxylamine in THF. Rate data, Hammett relationship, and activation entropy are consistent with a S_N2 displacement involving the attack of carbanions to sp³N in the amination reagent (AR). Copyright © 2007 John Wiley & Sons, Ltd.     

Time Dependence of Joint Entropy of Oscillating Quantum Systems

The time dependent entropy (or Leipnik’s entropy) of harmonic and damped harmonic oscillator systems is studied by using time dependent wave function obtained by the Feynman path integral method. The Leipnik entropy and its envelope change as a function of time, angular frequency and damping factor. Our results for simple harmonic oscillator are in agreement with the literature. However, the joint entropy of damped harmonic oscillator shows remarkable discontinuity with time for certain values of damping factor. The envelope of the joint entropy curve increases with time monotonically. These results show the general properties of the envelope of the joint entropy curve for quantum systems.     

Radiometry and Radiation Efficiency of Twisted Gaussian Schell-Model Sources

Wavefields endowed with the coherence-induced property of optical twist have recently attracted a good deal of theoretical and experimental attention. We present the generalized radiometric theory of fields generated by twisted Gaussian Schell-model sources. The effects introduced by the novel, rotationally symmetric, twist phenomenon in the radiant intensity, generalized radiance, radiant emittance (irradiance), and the radiation efficiency are assessed. The radiance becomes directionally skewed as a result of the twist, whereas the radiant intensity remains axially symmetric. The twist reduces the radiation efficiency and broadens the radiation distribution, in agreement with the notion that the twist decreases the effective coherence. Several special cases, such as quasihomogeneous sources, are analyzed in detail. The radiometric results, which are physically consistent with the superposition models of twisted sources, are demonstrated by illustrative examples.     

Characterization,slab-pair modeling and phase analysis of circular fishnet metamaterials

Planar metamaterials, which have incident to normal plane excitation unlike SRR-type structures and that are easily fabricated in multilayer form, have received great interest in recent years. In this paper, one-dimensional and polarization independent circular fishnet metamaterials and their equivalent discontinuous slab-pair modeling for tuning resonance frequencies are introduced. After the numerical and experimental demonstration of the inclusions, the standard retrieval characterization methods and the correspondent/related backward-wave propagation observation are realized in order to check the physical explanation mentioned in the paper. In addition, a detailed phase analysis is performed in order to demonstrate the application of the suggested structure as a phase compensator.     

High-energy gamma-rays accompanying the spontaneous fission of 252Cf

The γ-ray spectrum of ²⁵²Cf(sf) was measured in the Darmstadt-Heidelberg Crystal Ball spectrometer, with a double ionization chamber mounted inside to detect the fission fragments. The measurement was aimed at a better understanding of an unusual component found in the high-energy region between 3 and 8 MeV, with fragment mass splits near symmetry. This component was proved to be predominantly emitted by the heavier fragment, to reach its highest intensity at a fragment mass split of 132:120, and to have an almost isotropic angular distribution. Calculations with the statistical code CASCADE could reproduce the main features.     

Effects of inclined magnetic field on mixed convection in a nanofluid filled double lid-driven cavity with volumetric heat generation or absorption using finite element method

A computational analysis has been performed on mixed convection in a double sided lid-driven cavity in the presence of volumetric heat generation or absorption. Effects of inclined magnetic field are also studied. The governing parameters are solved via Galerkin weighted residual finite element method in space and the Crank–Nicolson in time. Governing parameters are nanoparticle volume fraction (0.0?≤???≤?0.04), Richardson number (0.01?≤?Ri?≤?10), internal heat generation or absorption parameter $(?10\le q\le 10),$ inclination angle of magnetic field (0°?≤?γ?≤?90°) and Hartmann number (0?≤?Ha?≤?100). It is observed that the highest heat transfer is obtained in case of the maximum value of heat absorption. As a further finding, heat transfer decreases with increasing of Hartmann number and increases with increasing of nanoparticle volume fraction.     

On geometric interpretations of split quaternions

Quaternions are an important tool that provides a convenient and effective mathematical method for representing reflections and rotations in three-dimensional space. A unit timelike split quaternion represents a rotation in the Lorentzian space. In this paper, we give some geometric interpretations of split quaternions for lines and planes in the Minkowski 3-space with the help of mutual pseudo orthogonal planes. We classified mutual planes with respect to the casual character of the normals of the plane as follows; if the normal is timelike, then the mutual plane is isomorphic to the complex plane; if the normal is spacelike, then the plane is isomorphic to the hyperbolic number plane (Lorentzian plane); if the normal is lightlike, then the plane is isomorphic to the dual number plane (Galilean plane).     

Strain rate change tests with the Split Hopkinson Bar method

In this paper, methods to produce rapid strain rate changes for strain rate sensitivity measurements in Split Hopkinson Bar arrangements are presented and discussed. Two different cases are considered: a strain rate change test within the high strain rate region in compression, and a tension test incorporating a large strain rate jump directly from the low strain rate region to high strain rates. The former method is based on the loading wave amplitude manipulation, while the latter method is based on the incorporation of a low strain rate loading device into a Tensile Split Hopkinson Bar apparatus.     

Lyotropic Liquid Crystal to Soft Mesocrystal Transformation in Hydrated Salt–Surfactant Mixtures

Hydrated CaCl₂, LiI, and MgCl₂ salts induce self‐assembly in nonionic surfactants (such as C₁₂H₂₅(OCH₂CH₂)₁₀OH) to form lyotropic liquid‐crystalline (LLC) mesophases that undergo a phase transition to a new type of soft mesocrystal (SMC) under ambient conditions. The SMC samples can be obtained by aging the LLC samples, which were prepared as thin films by spin‐coating, dip‐coating, or drop‐casting of a clear homogenized solution of water, salt, and surfactant over a substrate surface. The LLC mesophase exists up to a salt/surfactant mole ratio of 8, 10, and 4 (corresponding to 59, 68, and 40 wt % salt/surfactant) in the CaCl₂, LiI, and MgCl₂ mesophases, respectively. The SMC phase can transform back to a LLC mesophase at a higher relative humidity. The phase transformations have been monitored using powder X‐ray diffraction (PXRD), polarized optical microscopy (POM), and FTIR techniques. The LLC mesophases only diffract at small angles, but the SMCs diffract at both small and wide angles. The broad surfactant features in the FTIR spectra of the LLC mesophases become sharp and well resolved upon SMC formation. The unit cell of the mesophases expands upon SMC transformation, in which the expansion is largest in the MgCl₂ and smallest in the CaCl₂ systems. The POM images of the SMCs display birefringent textures with well‐defined edges, similar to crystals. However, the surface of the crystals is highly patterned, like buckling patterns, which indicates that these crystals are quite soft. This unusual phase behavior could be beneficial in designing new soft materials in the fields of phase‐changing materials and mesostructured materials, and it demonstrates the richness of the phase behavior in the salt–surfactant mesophases.