Exact N-wave solutions of generalized Burgers equations

Exact N-wave solutions for the generalized Burgers equation u(t) + u(n)u(x) + (j/2t + alpha) u + (beta + gamma/x) u(n+1) = delta/2u(xx),where j, alpha, beta, and gamma are nonnegative constants and n is a positive integer, are obtained. These solutions are asymptotic to the (linear) old-age solution for large time and extend the validity of the latter so as to cover the entire time regime starting where the originally sharp shock has become sufficiently thick and the viscous effects are felt in the entire N wave.

Transition from disc to rod-like shape of 16-3-16 dimeric micelles in aqueous solutions

Small-angle neutron scattering (SANS) measurements from bis-cationic C16H33N+(CH3)(2)-(CH2)(3)-N+ (CH3)(2)C16H33 2Br(-) dimeric surfactant, referred to as 16-3-16, at different concentrations and temperatures, are reported. It is seen that micelles are disc-like for concentrations C = 2.5 and 10 mM at temperature T = 30 degrees C. At low concentration C = 0.5 mM micelles are rod-like. Similarly, there is a disc to rod-like transition of micelles on increasing the temperature. For C = 2.5 mM, micelles are rod-like at T = 45 and 70 degrees C.

Rheology of particle-loaded semi-dilute polymer solutions

We present measurements of the rheology of suspensions of rigid spheres in a semi-dilute polymer solution from experiments of steady and oscillatory shear. For a given value of the shear rate gamma, addition of particles enhances the viscosity and the first normal stress difference but decreases the magnitude of the second normal stress difference. The viscosity eta exhibits a power law variation in gamma for a range of gamma that grows with phi. The first normal stress N-1 is positive and its value grows with phi; it exhibits a clear power law variation for the entire range of gamma that was studied. The second normal stress difference N-2 is negative for the pure polymer solution and much smaller in magnitude than N-1; on addition of particles, its magnitude further decreases, and it appears to change sign at large phi. The behavior of N-1 and N-2 is at odds with the findings of recent studies on particle-loaded dilute polymer solutions and polymer melts. The small-amplitude oscillatory shear experiments show the linear viscoelastic properties, G(') and G('), increasing with phi at a given value of the angular frequency omega. The dynamic viscosity of the suspension differs substantially from its steady shear viscosity, and the difference increases as gamma, omega -> 0.

Correlating The Features Of Topography To Friction By Sliding Experiments

Friction can influence the quality of the finished product to a large extent in certain manufacturing processes. Sheet metal forming is a particular case, where the friction between the hard-die and the relatively soft work-piece can be extremely important. Under such conditions, topography of the harder surface can influence the resistance to traction at the interface. This paper discusses about the correlation between certain features of the surface; topography and coefficient of friction based on experiments involving sliding of a few soft metal pins against a harder material. A brief description of the experimental procedure and the analysis are presented. A hybrid parameter which encapsulates both the amplitude features as well as the relative packing of peaks is shown to correlate well with the coefficient of friction.

Modeling of sonochemical decomposition of CCI4 in aqueous solutions

In the context of removal of organic pollutants from wastewater, sonolysis of CCl4 dissolved in water has been widely investigated. These investigations are either completely experimental or correlate data empirically. In this work, a quantitative model is developed to predict the rate of sonolysis of aqueous CCl4. The model considers the isothermal growth and partially adiabatic collapse of cavitation bubbles containing gas and vapor leading to conditions of high temperatures and pressures in them, attainment of thermodynamic equilibrium at the end of collapse, release of bubble contents into the liquid pool, and reactions in the well-mixed pool. The model successfully predicts the extent of degradation of dissolved CCl4, and the influence of various parameters such as initial concentration of CCl4, temperature, and nature of gas atmosphere above the liquid. in particular, it predicts the results of Hua and Hoffmann (Environ. Sci Technol, 1996, 30, 864-871), who found that degradation is first order with CCl4 and that Argon as well as Ar-O-3 atmospheres give the same results. The framework of the model is capable of quantitatively describing the degradation of many dissolved organics by considering all the involved species.

Analytical approximation solutions for 3-D optical waveguides: Review

The rectangular dielectric waveguide is the most commonly used structure in integrated optics, especially in semi-conductor diode lasers. Demands for new applications such as high-speed data backplanes in integrated electronics, waveguide filters, optical multiplexers and optical switches are driving technology toward better materials and processing techniques for planar waveguide structures. The infinite slab and circular waveguides that we know are not practical for use on a substrate because the slab waveguide has no lateral confinement and the circular fiber is not compatible with the planar processing technology being used to make planar structures. The rectangular waveguide is the natural structure. In this review, we have discussed several analytical methods for analyzing the mode structure of rectangular structures, beginning with a wave analysis based on the pioneering work of Marcatili. We study three basic techniques with examples to compare their performance levels. These are the analytical approach developed by Marcatili, the perturbation techniques, which improve on the analytical solutions and the effective index method with examples.

Inverse Sensitivity Analysis of Singular Solutions of FRF matrix in Structural System Identification

The problem of structural damage detection based on measured frequency response functions of the structure in its damaged and undamaged states is considered. A novel procedure that is based on inverse sensitivity of the singular solutions of the system FRF matrix is proposed. The treatment of possibly ill-conditioned set of equations via regularization scheme and questions on spatial incompleteness of measurements are considered. The application of the method in dealing with systems with repeated natural frequencies and (or) packets of closely spaced modes is demonstrated. The relationship between the proposed method and the methods based on inverse sensitivity of eigensolutions and frequency response functions is noted. The numerical examples on a 5-degree of freedom system, a one span free-free beam and a spatially periodic multi-span beam demonstrate the efficacy of the proposed method and its superior performance vis-a-vis methods based on inverse eigensensitivity.

Index properties of illite-bentonite mixtures in electrolyte solutions

Bentonite, commonly used for liner constructions in waste containment systems, possesses many limitations. Illite or illite containing bentonite has been proposed as an alternative material for liner construction. Their properties in different types of pore fluids are important to assess the long-term performance of the liner. Further, the illite-bentonite interaction occurs and changes their properties. The effect of these interactions is known when the pore fluid is only water. How their properties are modified in electrolyte solutions has been brought out in this paper. The index properties have been studied since they give an indication of their engineering properties. Due to reduction in the thickness of the diffused double layer and consequent particle aggregation in bentonite, the effect of clay-clay interaction reduces in electrolyte solutions. In electrolyte solutions, the liquid limit, the plasticity index, and free swell index of bentonite are lower than illite. The plasticity index of bentonite is further reduced in KCI solution. Clays with a higher plasticity index perform better to retain pollutants and reduce permeability. Hence, the presence of both illite and bentonite ensures better performance of the liner in different fluids.

Ion conductance in electrolyte solutions

We develop a new theoretical formulation to study ion conductance in electrolyte solutions, based on a mode coupling theory treatment of the electrolyte friction. The new theory provides expressions for both the ion atmosphere relaxation and electrophoretic contributions to the total electrolyte friction that acts on a moving ion. While the ion atmosphere relaxation term arises from the time-dependent microscopic interaction of the moving ion with the surrounding ions in the solution, the electrophoretic term originates from the coupling of the ion's velocity to the collective current mode of the ion atmosphere. Mode coupling theory, combined with time-dependent density functional theory of ion atmosphere fluctuations, leads to self-consistent expressions for these two terms which also include the effects of self-motion of the ion under consideration. These expressions have been solved for the concentration dependence of electrolyte friction and ion conductance. It is shown that in the limit of very low ion concentration, the present theory correctly reduces to the well-known Debye-Huckel-Onsager limiting law which predicts a linear dependence of conductance on the square root of ion concentration (c). At moderate and high concentrations, the present theory predicts a significant nonlinear and weaker dependence on root c which is in very good agreement with experimental results. The present theory is self-contained and does not involve any adjustable parameter.

Synergy between tribo-oxidation and strain rate response on governing the dry sliding wear behavior of titanium.

The present work provides an insight into the dry sliding wear behavior of titanium based on synergy between tribo-oxidation and strain rate response. Pin-on-disc tribometer was used to characterize the friction and wear behavior of titanium pin in sliding contact with polycrystalline alumina disk under ambient and vacuum condition. The sliding speed was varied from 0.01 to 1.4 ms(-1), normal load was varied from 15.3 to 76 N and with a sliding distance of 1500 m. It was seen that dry sliding wear behavior of titanium was governed by combination of tribo-oxidation and strain rate response in near surface region of titanium. Strain rate response of titanium was recorded by conducting uni-axial compression tests at constant true strain rate of 100 s(-1) in the temperature range from 298 to 873 K. Coefficient of friction and wear rate were reduced with increased sliding speed from 0.01 to 1.0 ms(-1). This is attributed to the formation of in situ self lubricating oxide film (TiO) and reduction in the intensity of adiabatic shear band cracking in the near surface region. This trend was confirmed by performing series of dry sliding tests under vacuum condition of 2 x 10(-4) Torr. Characterization tools such as optical microscopy, scanning electron microscopy, and X-ray diffractometer provided evidence of such processes. These experimental findings can be applied to enhance the dry sliding wear behavior of titanium with proper choice of operating conditions such as sliding speed, normal load, and environment.

Subsurface deformation in dry sliding of hypo-eutectic Al-Si alloys

The subsurface deformation during dry sliding of Al-Si alloys is studied by fragmentation of silicon particles. The size of the fragmented particles does not vary with load. The depth of deformation is found to increase with increase in normal load. This experimental observation agrees with load-deformation depth characteristics obtained by a slip line field model.

Approximate solutions of Fredholm integral equations of the second kind

This note is concerned with the problem of determining approximate solutions of Fredholm integral equations of the second kind. Approximating the solution of a given integral equation by means of a polynomial, an over-determined system of linear algebraic equations is obtained involving the unknown coefficients, which is finally solved by using the least-squares method. Several examples are examined in detail. (c) 2009 Elsevier Inc. All rights reserved.

Characterization of dry sliding wear of Al---Si alloys

Controversy exists in the published literature as to the effect of silicon content and pressure on the dry sliding wear of Al---Si alloys. The present paper attempts to clarify the question by reporting a statistical analysis of data obtained from factorially designed experiments conducted on a pinon-disc machine in the pressure range 0.105–1.733 MPa and speed range 0.19–0.94 m s−1. Under these conditions it was found that, in the range 4–24 wt.% Si, wear of binary unmodified alloys does not significantly differ between the alloys. However, it is significantly less than that corresponding to an alloy containing no silicon. The effect of pressure on wear rate was found to be linear and monotonie and, over the narrow range of speeds used, the wear rate was found to be unaffected by speed. The coefficient of friction was found to be insensitive to variations in silicon content, pressure and speed.

Light scattering studies on solutions of chlorinated rubber

Measurements have been made of the depolarisation factors \sigma u ,\sigma v ,\sigma h, and the intensity of scattering in the horizontal transverse direction, in the case of solutions of four different samples of chlorinated rubber in carbon tetrachloride. The size, shape and molecular weight of the micelles have been deduced by the application of the light scattering theories of Gans, Vrklajan and Katalinic and Debye. The extent to which the degradation of the rubber molecule occurs on chlorination has also been assessed.