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.

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.

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.

The velocity dispersion of giant molecular clouds. II - Mathematical and numerical refinements

The energy input to giant molecular clouds is recalculated, using the proper linearized equations of motion, including the Coriolis force and allowing for changes in the guiding center. Perturbation theory yields a result in the limit of distant encounters and small initial epicyclic amplitudes. Direct integration of the motion equations allows the strong encounter regime to be studied. The present perturbation theory result differs by a factor of order unity from that of Jog and Ostriker (1988). The result of present numerical integrations for the 2D (planar) velocity dispersion is presented. The accretion rate for a molecular cloud in the Galactic disk is calculated.

Non-Darcy mixed convection flow with thermal dispersion on a vertical cylinder in a saturated porous medium

The non-Darcy mixed convection flow on a vertical cylinder embedded in a saturated porous medium has been studied taking into account the effect of thermal dispersion. Both forced flow and buoyancy force dominated cases with constant wall temperature condition have been considered. The governing partial differential equations have been solved numerically using the Keller box method. The results are presented for the buoyancy parameter which cover the entire regime of mixed convection flow ranging from pure forced convection to pure free convection. The effect of thermal dispersion is found to be more pronounced on the heat transfer than on the skin friction and it enhances the heat transfer but reduces the skin friction.

Strong nonlocalization induced by small scale parameter on terahertz flexural wave dispersion characteristics of a monolayer graphene

This paper presents the strong nonlocal scale effect on the flexural wave propagation in a monolayer graphene sheet. The graphene is modeled as an isotropic plate of one atom thick. Nonlocal governing equation of motion is derived and wave propagation analysis is performed using spectral analysis. The present analysis shows that the flexural wave dispersion in graphene obtained by local and nonlocal elasticity theories is quite different. The nonlocal elasticity calculation shows that the wavenumber escapes to infinite at certain frequency and the corresponding wave velocity tends to zero at that frequency indicating localization and stationary behavior. This behavior is captured in the spectrum and dispersion curves. The cut-off frequency of flexural wave not only depend on the axial wavenumber but also on the nonlocal scaling parameter. The effect of axial wavenumber on the wave behavior in graphene is also discussed in the present manuscript. (C) 2010 Elsevier B.V. All rights reserved.

Microscopic Mechanism of 1/f Noise in Graphene: Role of Energy Band Dispersion

A distinctive feature of single-layer graphene is the linearly dispersive energy bands, which in the case of multilayer graphene become parabolic. A simple electrical transport-based probe to differentiate between these two band structures will be immensely valuable, particularly when quantum Hall measurements are difficult, such as in chemically synthesized graphene nanoribbons. Here we show that the flicker noise, or the 1/f noise, in electrical resistance is a sensitive and robust probe to the band structure of graphene. At low temperatures, the dependence of noise magnitude on the carrier density was found to be opposite for the linear and parabolic bands. We explain our data with a comprehensive theoretical model that clarifies several puzzling issues concerning the microscopic origin of flicker noise in graphene field-effect transistors (GraFET).

Linear electro‐optic dispersion in (‐)‐2‐(α‐methylbenzylamino)‐5‐nitropyridine single crystals

The variation of the linear electro-optic effect in (-)-2-(alpha-methylbenzylamino)-5-nitropyridine with the wavelength of the incident light at room temperature has been measured. The reduced half-wave voltages have been found to have the values 2.1, 2.8, and 6.0 kV at 488, 514.5, and 632.8 nm respectively and the corresponding values of the linear electro-optic coefficient have been evaluated.;The interpretation of the results in terms of the structures of the molecule and the crystal is discussed. The thermal variation of the birefringence has also been investigated and the coefficient for the temperature variation of the refractive index difference is found to have the value (d Delta n/dT)=9.3X10(-5) K-1.

Piezoelectrically stimulated dielectric dispersion in KAP single crystals

The frequency response of the dielectric constant (epsilon(r)), the loss tangent (tan delta) and impedance Z of potassium acid phthalate (KAP) single crystals, monitored along the polar axis, exhibit strong resonances in the frequency range 50-200 kHz, depending on the dimensions of the sample. The observed resonance effect, which is strongly dependent on the geometric shape and size of the sample, is attributed to its piezoelectric nature. The resonance peak positions have been monitored as a function of both temperature and uniaxial pressure. The stiffness coefficient (C), computed based on the resonance data, is found to decrease with increasing temperature and increase with increasing pressure. The electro-mechanical coupling coefficient (k), obtained by resonance-anti-resonance method, has also been found to increase with rise in temperature. The epsilon(r) behaviour along the polar axis, as a function of temperature is consistent with that of k. The preliminary results on the influence, of partial replacement of K+ ions in the KAP crystal by Cs+ and Li+ ions, on the observed piezoelectric resonance effects are also included.

A study on determining the theoretical dispersion curve for Rayleigh wave propagation

A method has been presented to establish the theoretical dispersion curve for performing the inverse analysis for the Rayleigh wave propagation. The proposed formulation is similar to the one available in literature, and is based on the finite difference formulation of the governing partial differential equations of motion. The method is framed in such a way that it ultimately leads to an Eigen value problem for which the solution can be obtained quite easily with respect to unknown frequency. The maximum absolute value of the vertical displacement at the ground surface is formed as the basis for deciding the governing mode of propagation. With the proposed technique, the numerical solutions were generated for a variety of problems, comprising of a number of different layers, associated with both ground and pavements. The results are found to be generally satisfactory. (C) 2011 Elsevier Ltd. All rights reserved.

Measurement of axial dispersion coefficient in a packed bed using X-ray

Dispersion of the liquid in a porous media is of great importance in many areas of engineering and has been studied by several researchers so far. A new experimental method has been developed to measure the dispersion coefficient. X-ray absorption technique provides a better understanding of dispersion that characterizes the mixing phenomenon in the packed beds. This is because the method is non-invasive and also it gives tracer concentration data at every point within the bed. The axial dispersion in a cylindrical bed of non-porous and non-wetting spherical particles has been measured for the flow of water. Aqueous barium chloride solution has been used a as tracer. X-ray images, recorded on a videocassette, have been analyzed using an image processing software to extract the local interstitial velocity and concentration data in the bed. Local dispersion coefficient has been determined with the help of aforementioned data. By using these data, the overall dispersion coefficient in a packed bed can also be estimated.