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.

A sufficient criterion for Rayleigh-Taylor instability of incompressible viscous three-layer flow

Using normal mode analysis Rayleigh-Taylor instability is investigated for three-layer viscous stratified incompressible steady flow, when the top 3rd and bottom 1st layers extend up to infinity, the middle layer has a small thickness δ. The wave Reynolds number in the middle layer is assumed to be sufficiently small. A dispersion relation (a seventh degree polynomial in wave frequency ω) valid up to the order of the maximal value of all possible Kj (j less-than-or-equals, slant 0, K is the wave number) in each coefficient of the polynomial is obtained. A sufficient condition for instability is found out for the first time, pursuing a medium wavelength analysis. It depends on ratios (α and β) of the coefficients of viscosity, the thickness of the middle layer δ, surface tension ratio T and wave number K. This is a new analytical criterion for Rayleigh-Taylor instability of three-layer fluids. It recovers the results of the corresponding problem for two-layer fluids. Among the results obtained, it is observed that taking the coefficients of viscosity of 2nd and 3rd layers same can inhibit the effect of surface tension completely. For large wave number K, the thickness of the middle layer should be correspondingly small to keep the domain of dependence of the threshold wave number Kc constant for fixed α, β and T.

Diffusion coefficients for selected binary liquid systems: cyclohexanes and n-alkyl alcohols

In the present work the integral diffusion coefficients are estimated by using the diaphragm cell technique. The diffusion coefficients are measured at various compositions for two sets binary systems: one of cyclohexane and n-paraffinic alcohols and the other of methylcyclohexane and n-paraffinic alcohols. The alcohols used are seven members of homologous series of n-paraffinic alcohols from ethanol to octanol. The maximum possible error in the experimental diffusion coefficient could be 8% for both the cyclohexane-n-alkyl alcohol system and methylcyclohexane-n-alkyl alcohol system. A correlation for each of the two sets of binary systems is given. The maximum deviation in the correlations was less than 6.5 and 3.5% for cyclohexane-n-alkyl alcohols and methylcyclohexane-n-alkyl alcohols, respectively.

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.

Mutual diffusion coefficients of some binary liquid systems: benzene-n-alkyl alcohol

The mutual diffusion coefficients for binary liquid systems of benzene-n-alkyl alcohol at various compositions have been determined by the diaphragm cell method at 28-degrees-C. The alcohols used were the members of n-paraffinic alcohols ranging from C1 to C8. The maximum possible experimental error is 14%. The data were fitted with a generalized correlation, giving the deviation from the experimental data to within 2.75%, on average.

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.

Improving the phenomenology of Kl3 form factors with analyticity and unitarity

The shape of the vector and scalar K-l3 form factors is investigated by exploiting analyticity and unitarity in a model-independent formalism. The method uses as input dispersion relations for certain correlators computed in perturbative QCD in the deep Euclidean region, soft-meson theorems, and experimental information on the phase and modulus of the form factors along the elastic part of the unitarity cut. We derive constraints on the coefficients of the parameterizations valid in the semileptonic range and on the truncation error. The method also predicts low-energy domains in the complex t plane where zeros of the form factors are excluded. The results are useful for K-l3 data analyses and provide theoretical underpinning for recent phenomenological dispersive representations for the form factors.

Stiffness Coefficients of Layered Soil Systems

One of the most important dynamic properties required in the design of machine foundations is the stiffness or spring constant of the supporting soil. For a layered soil system, the stiffness obtained from an idealization of soils underneath as springs in series gives the same value of stiffness regardless of the location and extent of individual soil layers with respect to the base of the foundation. This paper aims to develop the importance of the relative positioning of soil layers and their thickness beneath the foundation. A simple and approximate procedure called the weighted average method has been proposed to obtain the equivalent stiffness of a layered soil system knowing the individual values of the layers, their relative position with respect to foundation base, and their thicknesses. The theoretically estimated values from the weighted average method are compared with those obtained by conducting field vibration tests using a square footing over different two- and three-layered systems and are found to be very good. The tests were conducted over a range of static and dynamic loads using three different materials. The results are also compared with the existing methods available in the literature.

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.

Transformation formula for exponential sums involving fourier coefficients of modular forms

In 1984 Jutila [5] obtained a transformation formula for certain exponential sums involving the Fourier coefficients of a holomorphic cusp form for the full modular group SL(2, Z). With the help of the transformation formula he obtained good estimates for the distance between consecutive zeros on the critical line of the Dirichlet series associated with the cusp form and for the order of the Dirichlet series on the critical line, [7]. In this paper we follow Jutila to obtain a transformation formula for exponential sums involving the Fourier coefficients of either holomorphic cusp forms or certain Maass forms for congruence subgroups of SL(2, Z) and prove similar estimates for the corresponding Dirichlet series.

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.

Exact-Solutions Of Linear Partial-Differential Equations With Variable-Coefficients

Backlund transformations relating the solutions of linear PDE with variable coefficients to those of PDE with constant coefficients are found, generalizing the study of Varley and Seymour [2]. Auto-Backlund transformations are also determined. To facilitate the generation of new solutions via Backlund transformation, explicit solutions of both classes of the PDE just mentioned are found using invariance properties of these equations and other methods. Some of these solutions are new.