A class of solvable coupled nonlinear oscillators with amplitude independent frequencies

Existence of amplitude independent frequencies of oscillation is an unusual property for a nonlinear oscillator. We find that a class of N coupled nonlinear Liénard type oscillators exhibit this interesting property. We show that a specific subset can be explicitly solved from which we demonstrate the existence of periodic and quasiperiodic solutions. Another set of N coupled nonlinear oscillators, possessing the amplitude independent nature of frequencies, is almost integrable in the sense that the system can be reduced to a single nonautonomous first order scalar differential equation which can be easily integrated numerically.     

The Intensities of f↔f Transitions and Bonding in Fluorinated Lanthanide β-Diketone Chelates

Abstract

Interest in the intensity of lanthanide f?f spectra have begun nearly forty years ago, but most of the work was done after the publication of the theory of lanthanide intensity by Judd¹ and Ofelt² independently in 1962. Since then a number of lanthanide complexes having O-, N- or mixed donor ligands have been studied for the one reason or the other. Various β-diketone chelates were studied^3–7 for the reason that they proved to be good lasing materials. The present communication extends this study further to fluorinated β-diketone chelates of Pr³⁺ and Nd³⁺ which gives useful information regarding interelectronic repulsion, spin-orbit interaction, nephelauxetic effect and bonding in these chelates.     

Quantification of β-Sitosterol in Hairy Root Cultures and Natural Plant Parts of Butterfly Pea (Clitoria ternatea L.)

JPC – Journal of Planar Chromatography – Modern TLC - A simple normal-phase high-performance thin-layer chromatography (HPTLC) method has been developed for the quantification of...     

Assessment of high-resolution methods for numerical simulations of compressible turbulence with shock waves

Flows in which shock waves and turbulence are present and interact dynamically occur in a wide range of applications, including inertial confinement fusion, supernovae explosion, and scramjet propulsion. Accurate simulations of such problems are challenging because of the contradictory requirements of numerical methods used to simulate turbulence, which must minimize any numerical dissipation that would otherwise overwhelm the small scales, and shock-capturing schemes, which introduce numerical dissipation to stabilize the solution. The objective of the present work is to evaluate the performance of several numerical methods capable of simultaneously handling turbulence and shock waves. A comprehensive range of high-resolution methods (WENO, hybrid WENO/central difference, artificial diffusivity, adaptive characteristic-based filter, and shock fitting) and suite of test cases (Taylor–Green vortex, Shu–Osher problem, shock-vorticity/entropy wave interaction, Noh problem, compressible isotropic turbulence) relevant to problems with shocks and turbulence are considered. The results indicate that the WENO methods provide sharp shock profiles, but overwhelm the physical dissipation. The hybrid method is minimally dissipative and leads to sharp shocks and well-resolved broadband turbulence, but relies on an appropriate shock sensor. Artificial diffusivity methods in which the artificial bulk viscosity is based on the magnitude of the strain-rate tensor resolve vortical structures well but damp dilatational modes in compressible turbulence; dilatation-based artificial bulk viscosity methods significantly improve this behavior. For well-defined shocks, the shock fitting approach yields good results.     

Effect of barium titanate nanoparticles of different particle sizes on electro-optic and dielectric properties of ferroelectric liquid crystal

A comparative study of two different particle sizes of ferroelectric barium titanate (BaTiO₃) nanoparticles as a dopant on the molecular structure, spontaneous polarization and dielectric behavior of a pure ferroelectric liquid crystal 6F₆T have been studied. It has been found that there is a remarkable decrease in isotropic temperature of both doped samples as compared to the pure 6F₆T sample. The spontaneous polarization also decreases for both the doped samples and the reduction is more pronounced in case of the dopant with large particle size. The dielectric spectroscopy confirms the presence of soft mode as well as Goldstone mode and also shows the decrease in the value of dielectric permittivity ?' as a function of frequency for both doped samples. The improvised properties of liquid crystal host doped with BaTiO₃ nanoparticles mainly depend upon the synthesis method of nanoparticles and also upon the particle size of dopant.     

TRANSITION METAL,NON-METAL CARBONYL CLUSTRS AS SUPPORTS FOR UNUSUAL ACETYLIDE REACTIVITY

Group 16 elements serve as useful bridging and stabilising single atom ligands in mixed-metal carbonyl complexes and impart unusual reactivity on coordinated acetylenic moieties. Reactions of [Fe ₃ (CO) ₉ (μ ₃ -E) ₂ ] (E = S, or Se) with mononuclear acetylide complexes, [CpM(CO)_3-x(CCR)] (M = Mo or W, x = 0, R = Ph; M = Fe, x = 1, R = Ph or ferrocenyl) under facile conditions yield complexes featuring acetylide coupling, acetylide-flip and formation of oxo and acetylide-bridged complexes. In presence of free acetylenes, unusual ligand systems arising from C─S bond formation are observed and under certain conditions, formation of quinones by coupling of acetylenes with carbon monoxide is facilitated.     

Reactivity of a Cyclopentadienyl Containing Heterobimetallic Alkoxide

The synthesis of the new heteroleptic heterotrimetallic cluster, [(C₅H₅)Sn(μ-OBu^t)₂Ge(OBu^t)Mo(CO)₅] (1) has been achieved by a thermally induced CO substitution of the transition metal derivative, Mo(CO)₆, by the basic germanium atom of the cyclopentadienyl heterobimetallic alkoxide, [(C₅H₅)Sn(μ-OBu^t)₂Ge(OBu^t)]. The microanalysis, molecular weight (monomer in benzene), IR and multinuclear NMR data and X-ray diffraction study is consistent with the formulation of 1. The Sn atom has a trigonal pyramidal coordination environment formed by a aysmmterically π-bonded terminal C₅H₅ ring and two symmetrically bridged tert-butoxy groups. The four-coordinate Ge atom lies at the centre of a distorted tetrahedron and is terminally attached to a tert-butoxy group and a Mo(CO)₅5^? fragment.