Solution of convex conservation laws in a strip

In this paper we consider scalar convex conservation laws in one space variable in a stripD =(x, t): 0 ≤x ≤1,t > 0 and obtain an explicit formula for the solution of the mixed initial boundary value problem, the boundary data being prescribed in the sense of Bardos-Leroux and Nedelec. We also get an explicit formula for the solution of weighted Burgers equation in a strip.     

Elastic properties and spectroscopic studies of lithium lead borate glasses

Elastic properties of xLi₂O — 20PbO — (80-x)B₂O₃ glasses have been measured at a frequency of 10 MHz using X-cut and Y-cut quartz transducers. The trends in the variation of elastic moduli, Poisson’s ratio and Debye temperature have been studied. The elastic moduli namely longitudinal and young’s modulus show strong linear dependence while bulk and shear modulus vary marginally as a function of Li₂O concentration. The Poisson’s ratio is found to be almost constant and Debye temperature increases with the increase of Li₂O concentration. IR, MAS-NMR and glass transition temperature studies have been also carried out. Glass transition temperature is found to increase with increase of Li₂O concentration. IR and MAS-NMR spectra show characteristic features of borate network and systematic change as a function of Li₂O concentration. The variation in the elastic properties and structural features of IR and MAS-NMR indicate that Pb²⁺ ions are likely to occupy network forming positions in this glass system. Paper presented at the 2nd International Conference on Ionic Devices, Anna University, Chennai, India, Nov. 28–30, 2003.     

Cyclic-deformation behavior of notched mild-steel plates in plane stress

Notched rectangular SAE 1015 mild-steel plates were subjected to controlled cyclic nominal stresses or strains in a closed-loop servo-controlled fatigue-testing machine. Resistance strain gages were used to measure strains at the notch roots. These strains showed that large mean strains and strain ranges prevailed at these notches, though nominal strains were fully reversed and small. Inelastic stress- and strain-concentration factors calculated at various cycles were used to check the accuracy of the Neuber relation between these concentration factors and elastic stress-concentration factor. Limitations of this relation and characteristic notch-strain behavior mentioned above are discussed with reference to the peculiarities of the stress-strain relationships of this material.     

An experimental investigation of separating flow on a convex surface

The mean and turbulent characteristics of an incompressible turbulent boundary layer developing on a convex surface under the influence of an adverse pressure gradient are presented in this paper.The turbulence quantities measured include all the components of Reynolds stresses, auto-correlation functions and power spectra of the three components of turbulence. The results indicate the comparative influence of the convex curvature and adverse pressure gradient which are simultaneously acting on the flow. The investigation provides extensive experimental information which is much needed for a better understanding of turbulent shear flows.Nomenclature a, b constants in equation for velocity defect profile (Fig. 6) - c _f skin-friction coefficient (= _w/F _1/2 U ₁ ² ) - E(k ₁) one-dimensional wave number spectra - f frequency in Hz - G Clauser's equilibrium parameter = (H–1)/H(c _f /2) - H shape parameter (= ₁/ ₂) - k ₁ wave number (=2f/U) - L _u, L _v, L _w length scales of u, v and w fluctuations - p _s static pressure on the measurement surface - p _w reference tunnel wall static pressure - q ² total turbulent kinetic energy - R radius of curvature of the convex surface - R() auto-correlation function - T _u, T _v, T _w time scales of u, v and w fluctuations - U local mean velocity - U ₁ local free stream velocity - U _* friction velocity - u, v, w velocity fluctuations in x, y and z directions respectively - X streamwise coordinate measured along the surface from A (Fig. 1b) - x streamwise coordinate measured along the surface reckoned from station 9 - y coordinate normal to the surface - z spanwise coordinate - ₁/ _w · dp/dx - - boundary layer thickness - ₁ displacement thickness - ₂ momentum thickness - ₃ energy thickness - kinematic viscosity - density - time delay - _w wall shear stress     

New numerical simulation for fractional Benney–Lin equation arising in falling film problems using two novel techniques

The pivotal aim of the present work is to find the numerical solution for fractional Benney–Lin equation by using two efficient methods, called q ‐homotopy analysis transform method and fractional natural decomposition method. The considered equation exemplifies the long waves on the liquid films. Projected methods are distinct with solution procedure and they are modified with different transform algorithms. To illustrate the reliability and applicability of the considered solution procedures we consider eight special cases with different initial conditions. The fractional operator is considered in Caputo sense. The achieved results are drowned through two and three‐dimensional plots for different Brownian motions and classical order. The numerical simulations are presented to ensure the efficiency of considered techniques. The behavior of the obtained results for distinct fractional order is captured in the present framework. The outcomes of the present investigation show that, the considered schemes are efficient and powerful to solve nonlinear differential equations arise in science and technology.     

Enantiotropic nematic phases of quaternary ammonium halide salts based on trioctadecylamine

The neat phases of a series of quaternary ammonium halides based on trioctadecylamine have been investigated by optical microscopy, differential scanning calorimetry, and H NMR spectroscopy. Phase behaviour depends primarily on the structure of the fourth substituent on nitrogen and the thermal history of the samples. For instance, the iodide salts with methyl, ethyl, or propyl as the fourth substituent form enantiotropic nematic phases, while those with a proton or a longer alkyl substituent exhibit complex phase behaviour that does not include a liquid crystalline phase. Possible reasons are advanced for the unprecedented formation of nematic phases.     

Kinetics and mechanism of oxidation of some aliphatic esters by sodium N-bromo-p-toluenesulfonamide

The kinetics of oxidation of methyl, ethyl, n-propyl, isopropyl, and n-butyl acetates to acetic acid and the corresponding aldehyde by the title oxidant in aqueous HCl medium at 40°C has been studied. The reaction shows first-order with respect to [oxidant] and fractional orders in [H⁺] and [ester]. An isokinetic relationship was observed with β = 374 K indicating enthalpy as the rate controlling factor. Attempts have been made to arrive at a linear free energy relationship through the Taft treatment. Electron releasing groups in the ester moiety increase the rate with ρ* = ?9.88. A two-pathway mechanism, consistent with the observed kinetic data, has been proposed. © 1993 John Wiley & Sons, Inc.     

Estimation of cyanide ion in metal salts and complexes by means of chloramine-T and dichloramine-T

A simple and accurate method for the estimation of cyanide in salts and complexes is based on oxidation with chloramine-T (in pH 4 buffer) or dichloramine-T (in presence of acetic anhydride). The oxidation involves a two-electron change. Halides interfere with the estimation of KCN, but the interference can be eliminated by precipitating and determining zinc cyanide. A method for estimating KCN and KCNS in mixtures is also described.