Wave theory of light leading to the generalized vectorial laws of reflection and refraction

This paper deals with the application of Huygens’ wave theory of light for the derivation of the generalized vectorial laws of reflection and refraction discovered by the author in 2005. The long-running literature falls short of such a theoretical proof of the generalized vectorial laws of reflection and refraction on the basis of wave theory. As such the present work is novel and original. At the same time it also enhances the theoretical foundation of the discovery of the generalized vectorial laws of reflection and refraction there by proving the efficiency and increasing the range of applicability of the wave theory of light as well.     

Analytical test functions for free vibration analysis of rotating non-homogeneous Timoshenko beams

In this paper, the governing equations for free vibration of a non-homogeneous rotating Timoshenko beam, having uniform cross-section, is studied using an inverse problem approach, for both cantilever and pinned-free boundary conditions. The bending displacement and the rotation due to bending are assumed to be simple polynomials which satisfy all four boundary conditions. It is found that for certain polynomial variations of the material mass density, elastic modulus and shear modulus, along the length of the beam, the assumed polynomials serve as simple closed form solutions to the coupled second order governing differential equations with variable coefficients. It is found that there are an infinite number of analytical polynomial functions possible for material mass density, shear modulus and elastic modulus distributions, which share the same frequency and mode shape for a particular mode. The derived results are intended to serve as benchmark solutions for testing approximate or numerical methods used for the vibration analysis of rotating non-homogeneous Timoshenko beams.     

Structural, dielectric relaxation and piezoelectric characterization of Sr substituted modified PMS-PZT ceramic

Pyrochlore phase free [Pb_0.94Sr_0.06] [(Mn_1/3Sb_2/3)_0.05(Zr_0.53Ti_0.47)_0.95] O₃ ceramics has been synthesized with pure Perovskite phase by semi-wet route using the columbite precursor method. The field dependences of the dielectric response and the conductivity have been measured in a frequency range from 50 Hz to 1 MHz and in a temperature range from 303 K to 773 K. An analysis of the real and imaginary parts of the dielectric permittivity with frequency has been performed, assuming a distribution of relaxation times. The scaling behavior of the dielectric loss spectra suggests that the distribution of the relaxation times is temperature independent. The SEM photographs of the sintered specimens present the homogenous structures and well-grown grains with a sharp grain boundary. The material exhibits tetragonal structure. When measured at frequency (100 Hz), the polarization shows a strong field dependence. Different piezoelectric figures of merit (k_p, d₃₃ and Q_m) of the material have also been measured obtaining their values as 0.53, 271 pC/N and 1115, respectively, which are even higher than those of pure PZT with morphotropic phase boundary (MPB) composition. Thus the present ceramics have the optimal overall performance and are promising candidates for the various high power piezoelectric applications.     

La(OTf)3-catalyzed one-pot synthesis of meso-substituted porphyrinic thiazolidinones

Abstract  

An improved synthetic procedure is developed for the regioselective nitration of a phenyl group of meso-tetraphenylporphyrin by using NaNO₂ in a mixture of trichloroacetic acid and AcOH. The meso-(4-nitrophenyl)porphyrins are successfully reduced to corresponding meso-(4-aminophenyl)porphyrins by SnCl₂ under acidic conditions. In addition, an efficient one-pot methodology for synthesizing a series of novel meso-substituted porphyrinic thiazolidinone conjugates is developed by reacting meso-(4-aminophenyl)porphyrins with various aromatic aldehydes and mercaptoacetic acid in refluxing toluene using La(OTf)₃ as a catalyst. The products obtained are characterized on the basis of their spectral data. Preliminary photophysical properties of the newly synthesized compounds are reported.     

Solid supported palladium(0) nano/microparticle: a ligand-free efficient recyclable heterogeneous catalyst for mono- and β,β-double-Heck reaction

Solid supported palladium nano/microparticles were found to be active catalysts to perform mono- and β,β-double-Heck reactions. Different β-unsubstituted and substituted alkenes including acrylate, methacrylate, crotonate, styrene, acrylonitrile, and acrylamide were investigated successfully for mono- and β,β-double-Heck reactions with aryl iodide under milder reaction condition. One-pot β,β-double-Heck reaction of aryl iodides with α,β-unsaturated ester, amide, nitrile, and styrene derivatives were also performed under standard reaction conditions. Wide functional group tolerance, easy catalyst recovery, and recyclability up to twelve times without significant loss of catalytic activity added extra importance to the present process.     

Vibration suppression of a string through cyclic application and removal of constraints

A new method for the control of string vibration is presented. The method relies on application and removal of a constraint at one point on the string close to one of its boundaries. Application of the constraint temporarily results in two vibrating strings, one of which is significantly shorter in length than the other. The vibration of the shorter length string decays rapidly due to high damping and results in reduction in the overall energy of the system. Removal of the constraint does not change the energy of the system but allows the constraint to be applied repeatedly for vibration suppression. A mathematical model of the cycle of constraint application and removal is presented and multiple cycles of constraint application and removal are simulated. Experiments were performed with a coiled extension spring which behaves like a lightly damped string. Simulation and experimental results match well with each other and demonstrate the efficacy of the simple control strategy.     

Singularity-free dark energy star

We propose a model for an anisotropic dark energy star where we assume that the radial pressure exerted on the system due to the presence of dark energy is proportional to the isotropic perfect fluid matter density. We discuss various physical features of our model and show that the model satisfies all the regularity conditions and is stable as well as singularity-free.     

Concentration‐dependent Raman study of noncoincidence effect in the NH2 bending and CO stretching modes of HCONH2 in the binary mixture (HCONH2 + CH3OH)

The isotropic and anisotropic parts of the Raman spectra of NH₂ bending and ν(CO) stretching modes of HCONH₂ in a hydrogen‐bonding solvent, methanol, at different concentrations have been analyzed carefully in order to study the noncoincidence effect (NCE). In neat HCONH₂, the experimentally measured values of noncoincidence Δν_nc are ∼11 and ∼18 cm⁻¹ for the NH₂ bending and ν(CO) stretching modes, which reduce to 0.45 and 1.14 cm⁻¹, respectively at the concentration of HCONH₂ in mole fraction, χ_m = 0.1. The experimental results have been explained on the basis of two models, namely, the microscopic prediction of Logan and the macroscopic model of Mirone and Fini. The relative success of the two models in explaining the experimental data for both the modes have been discussed. It has been observed that in case of the ν(CO) stretching vibrational mode the Logan model can reproduce the experimental data rather precisely, whereas in the case of the NH₂ bending mode, Mirone and Fini model yields more accurate results. Copyright © 2006 John Wiley & Sons, Ltd.     

Improper hydrogen bonding and motional narrowing in binary mixtures of 2‐ and 3‐bromopyridine in methanol probed by polarized Raman study and DFT calculations

A concentration‐dependent Raman study of the ν(C Br) stretching and trigonal bending modes of 2‐ and 3‐Br‐pyridine (2Br‐p and 3Br‐p) in CH₃OH was performed at different mole fractions of the reference molecule, 2Br‐p/3Br‐p, from 0.1 to 0.9 in order to understand the origin of blue/red wavenumber shifts of the vibrational modes due to hydrogen‐bond formation. The appearance of additional Raman bands in these binary systems at ∼617 cm⁻¹in the case of 2Br‐p and at ∼618 cm⁻¹ in the case of 3Br‐p compared to neat bromopyridine derivatives were attributed to specific hydrogen‐bonded complexes formed in the mixtures. The interpretation of experimental results is supported by density functional calculations on optimized geometries and vibrational wavenumbers of 2Br‐p and 3Br‐p and a series of hydrogen‐bonded complexes with methanol. The parameters obtained from these calculations were used for a qualitative explanation of the blue/red shifts. The wavenumber shifts and linewidth changes for the ν(C Br) stretching and trigonal bending modes as a function of concentration reveal that the caging effects leading to motional narrowing and diffusion‐causing line broadening are simultaneously operative, in addition to the blue shift caused due to hydrogen bonding. Copyright © 2007 John Wiley & Sons, Ltd.     

Tandem RAFT Polymerization and Click Chemistry: An Efficient Approach to Surface Modification

PS grafted silica nanoparticles have been prepared by a tandem process that simultaneously employs RAFT polymerization and click chemistry. In a single pot procedure, azide‐modified silica, an alkyne functionalized RAFT agent and styrene are combined to produce the desired product. As deduced by thermal gravimetric and elemental analysis, the grafting density of PS on the silica in the tandem process is intermediate between analogous “grafting to” and “grafting from” techniques for preparing PS brushes on silica. Relative rates of RAFT polymerization and click reaction can be altered to control grafting density.