Investigation of the effect of nonlocal scale on ultrasonic wave dispersion characteristics of a monolayer graphene

In this article, an ultrasonic wave propagation in graphene sheet is studied using nonlocal elasticity theory incorporating small scale effects. The graphene sheet is modeled as an isotropic plate of one-atom thick. For this model, the nonlocal governing differential equations of motion are derived from the minimization of the total potential energy of the entire system. An ultrasonic type of wave propagation model is also derived for the graphene sheet. The nonlocal scale parameter introduces certain band gap region in in-plane and flexural wave modes where no wave propagation occurs. This is manifested in the wavenumber plots as the region where the wavenumber tends to infinite or wave speed tends to zero. The frequency at which this phenomenon occurs is called the escape frequency. The explicit expressions for cutoff frequencies and escape frequencies are derived. The escape frequencies are mainly introduced because of the nonlocal elasticity. Obviously these frequencies are function of nonlocal scaling parameter. It has also been obtained that these frequencies are independent of y-directional wavenumber. It means that for any type of nanostructure, the escape frequencies are purely a function of nonlocal scaling parameter only. It is also independent of the geometry of the structure. It has been found that the cutoff frequencies are function of nonlocal scaling parameter (e(0)a) and the y-directional wavenumber (k(y)). For a given nanostructure, nonlocal small scale coefficient can be obtained by matching the results from molecular dynamics (MD) simulations and the nonlocal elasticity calculations. At that value of the nonlocal scale coefficient, the waves will propagate in the nanostructure at that cut-off frequency. In the present paper, different values of e(o)a are used. One can get the exact e(0)a for a given graphene sheet by matching the MD simulation results of graphene with the results presented in this paper. (C) 2010 Elsevier B.V. All rights reserved.

Intermolecular Chelate Linkage Isomerism of the Hydroxyimino Group in the Nickel(II), Copper(II), and Palladium(II) Complexes of Quadridentate Schiff-base Ligands

The C-nitrosation of bivalent quadridentate β-imino ketone complexes of nickel(II), copper(II), and palladium(II), with nitrosating reagents has been investigated. The chemical analysis and spectroscopic results reveal that one of the α-CH groups of the coordinated lignad undergoes selective nitrosation forming mono(hydroxyimino) derivative. The hydroxyimino group introduced coordinates through either N- or O- atom to metal(II) by dislodging the carbonyl group already coordinated. This gives rise to two linkage isomers, one with N-bonded and the other with O-bonded hydroxyimino group in the case of nickel(II) (except for 1d) and palladium(II), and a single isomer with O-bonded hydroxyimino group in copper(II) complexes. The isomers obtained from 1b and 1i have been separated by column chromatography. In chloroform each of the isomers of nickel(II) isomerizes to give an equilibrium mixture of two isomers, but not those of copper(II) and palladium(II).

Dispersion of resistivity anomalies in critical binary liquid systems

The critical resistivity in the binary liquid systems n-C7H16 + CH3OH and CS2 + CH3NO2 is measured from 10 Hz to 100 kHz. There is no noticeable effect of the frequency on the resistivity singularities. Thus any contribution from dielectric dispersion is not appreciable.

Enantioselective and Protecting Group-Free Synthesis of 1-Deoxythionojirimycin, 1-Deoxythiomannojirimycin, and 1-Deoxythiotalonojirimycin

1-Deoxythioglyconojirimycins were synthesized by using a protecting group-free strategy, starting from readily available carbohydrates, in good overall yield. Use of benzyl-triethylammonium tetrathiomolybdate, BnEt3N](2)MoS4, as a sulfur transfer reagent and borohydride exchange resin (BER) reduction of a lactone enabled the efficient synthesis of the title compounds.

Alkaloid synthesis: stereoselective approach towards fawcettimine-serratinine group of lycopodium alkaloids

The concept of carbocycle-heterocycle equivalency has been utilised to assemble the framework of fawcettimine-serratinine group of alkaloids from 1,5-cyclooctadiene through a common tricarbocyclic intermediate 3.

A multiplier theorem for the sublaplacian on the Heisenberg group

A multiplier theorem for the sublaplacian on the Heisenberg group is proved using Littlewood-Paley-Stein theory of g-functions.

Mixed Convection Induced in a Gas Flowing Past a Hot Horizontal Flat Plate

A boundary layer analysis of mixed convective motion over a hot horizontal flat plate is performed under the conditions of steady flow and low speed. Use of the Howarth-Dorodnytsyn transformation makes it possible to dispense with the usual Boussinesq approximation, and variable gas properties are accounted for via the assumption that dynamic viscosity and thermal conductivity are proportional to the absolute temperature. The formulation presented enables the entire mixed convection regime to be described by a single set of equations. Finite difference solutions when the Prandtl number is 0.72 are obtained over the entire range of the mixed convection parameter ξ from 0 (free convection) to 1 (forced convection) and heating parameter ▵ values from 2 to 12. The effects of both ξ and ▵on the velocity profiles, the temperature profiles, and the variation of skin friction and heat transfer functions are clearly illustrated in tables and graphs.

Modulus Spectroscopy and Dielectric Dispersion Studies in Alkali Metal Perchlorates

Alkali metal perchlorates (KClO4, RbClO4, and CsClO4) undergo a structural phase transition from the orthorhombic to the cubic phase at elevated temperatures. A detailed dielectric study of these crystals across the phase transition is carried out at different frequencies. The crystals are found to exhibit pronounced dielectric dispersion in the kHz frequency range. The results support the view that these transitions are of order–disorder type. The dielectric behaviour at temperatures above Tc is discussed in terms of modulus spectroscopy. An estimate of conductivity relaxation times above the phase transition temperatures made from modulus spectroscopy data gives values of 3.1, 12.2 and 17.7 μs for KClO4, RbClO4, and CsClO4, respectively.