Two-Parameter Uniformly Elliptic Sturm–Liouville Problems With Eigenparameter-Dependent Boundary Conditions

We consider the two-parameter Sturm–Liouville system $$ -y_1''+q_1y_1=(\lambda r_{11}+\mu r_{12})y_1\quad\text{on }[0,1], $$ with the boundary conditions $$ \frac{y_1'(0)}{y_1(0)}=\cot\alpha_1\quad\text{and}\quad\frac{y_1'(1)}{y_1(1)}=\frac{a_1\lambda+b_1}{c_1\lambda+d_1}, $$ and $$ -y_2''+q_2y_2=(\lambda r_{21}+\mu r_{22})y_2\quad\text{on }[0,1], $$ with the boundary conditions $$ \frac{y_2'(0)}{y_2(0)} =\cot\alpha_2\quad\text{and}\quad\frac{y_2'(1)}{y_2(1)}=\frac{a_2\mu+b_2}{c_2\mu+d_2}, $$ subject to the uniform-left-definite and uniform-ellipticity conditions; where $q_{i}$ and $r_{ij}$ are continuous real valued functions on $[0,1]$, the angle $\alpha_{i}$ is in $[0,\pi)$ and $a_{i}$, $b_{i}$, $c_{i}$, $d_{i}$ are real numbers with $\delta_{i}=a_{i}d_{i}-b_{i}c_{i}>0$ and $c_{i}\neq0$ for $i,j=1,2$. Results are given on asymptotics, oscillation of eigenfunctions and location of eigenvalues.

Towards the concept of hydrodynamic cavitation control

A careful study of the existing literature available in the field of cavitation reveals the potential of ultrasonics as a tool for controlling and, if possible, eliminating certain types of hydrodynamic cavitation through the manipulation of nuclei size present in a flow. A glass venturi is taken to be an ideal device to study the cavitation phenomenon at its throat and its potential control. A piezoelectric transducer, driven at the crystal resonant frequency, is used to generate an acoustic pressure field and is termed an �ultrasonic nuclei manipulator (UNM)�. Electrolysis bubbles serve as artificial nuclei to produce travelling bubble cavitation at the venturi throat in the absence of a UNM but this cavitation is completely eliminated when a UNM is operative. This is made possible because the nuclei, which pass through the acoustic field first, cavitate, collapse violently and perhaps fragment and go into dissolution before reaching the venturi throat. Thus, the potential nuclei for travelling bubble cavitation at the venturi throat seem to be systematically destroyed through acoustic cavitation near the UNM. From the solution to the bubble dynamics equation, it has been shown that the potential energy of a bubble at its maximum radius due to an acoustic field is negligible compared to that for the hydrodynamic field. Hence, even though the control of hydrodynamic macro cavitation achieved in this way is at the expense of acoustic micro cavitation, it can still be considered to be a significant gain. These are some of the first results in this direction.

Right-Definite Multiparameter Sturm–Liouville Problems With Eigenparameter-Dependent Boundary Conditions

We study a system of ordinary differential equations linked by parameters and subject to boundary conditions depending on parameters. We assume certain definiteness conditions on the coefficient functions and on the boundary conditions that yield, in the corresponding abstract setting, a right-definite case. We give results on location of the eigenvalues and oscillation of the eigenfunctions.

Effects of phase inhomogeneity and boundary conditions on the dynamic response of SMA wire actuators

This paper reports the simulation results from the dynamic analysis of a Shape Memory Alloy (SMA) actuator. The emphasis is on understanding the dynamic behavior under various loading rates and boundary conditions, resulting in complex scenarios such as thermal and stress gradients. Also, due to the polycrystalline nature of SMA wires, presence of microstructural inhomogeneity is inevitable. Probing the effect of inhomogeneity on the dynamic behavior can facilitate the prediction of life and characteristics of SMA wire actuator under varieties of boundary and loading conditions. To study the effect of these factors, an initial boundary value problem of SMA wire is formulated. This is subsequently solved using finite element method. The dynamic response of the SMA wire actuator is analyzed under mechanical loading and results are reported. Effect of loading rate, micro-structural inhomogeneity and thermal boundary conditions on the dynamic response of SMA wire actuator is investigated and the simulation results are reported.

Iodine-Catalyzed Amination of Benzoxazoles: A Metal-Free Route to 2-Aminobenzoxazoles under Mild Conditions

A facile metal-free route of oxidative amination of benzoxazole by activation of C-H bonds with secondary or primary amines in the presence of catalytic iodine in aqueous tert-butyl hydroperoxide proceeds smoothly at ambient temperature under neat reaction condition to furnish the high yield of the aminated product. This user-friendly method to form C-N bonds produces tertiary butanol and water as the byproduct, which are environmentally benign. The application of the methodology is demonsrated by synthesizing therapeutically active benzoxazoles.

Highly efficient dialkylphosphate-mediated syntheses of hydantoins and a bicyclohydantoin under solvent-free conditions

Diversely substituted hydantoins have been synthesized by new strategy from cyanamide based precursor, that is, methyl N-cyano-N-alkyl/arylaminoacetate. Dialkylphosphates were employed as the mild reagent to hydrolyze and cyclize the substrate in one step to give quantitative yields of the desired products. Syntheses of multivalent hydantoins viz bis-hydantoin, bicyclohydantoin have potentially widened the scope and applicability of the present method. Solvent-free conditions and very easy work-up procedure make the reaction convenient and eco-friendly. Single crystal structures of some of the representative compounds are also reported. (C) 2011 Elsevier Ltd. All rights reserved.

Lipid composition in microalgal community under laboratory and outdoor conditions

Microalgae are the most sought after sources for biofuel production due to their capacity to utilize carbon and synthesize it into high density liquid. Current energy crisis have put microalgae under scanner for economical production of biodiesel. Modifications like physiological stress and genetic variation is done to increase the lipid yield of the microalgae. A study was conducted using a microalgal consortium for a period of 15 days to evaluate the feasibility of algal biomass from laboratory as well as outdoor culture conditions. Native algal strains were isolated from a tropical freshwater lake. Preliminary growth studies indicated the relationship between the nitrates and phosphates to the community structure through the days. The lipid profile done using Gas chromatography – Mass spectrometry, revealed the profile of the algal community. Resource competition led to isolation of algae, aided in the lipid profile of a single alga. However, further studies on the application of the mixed population are required to make this consortium approach economically viable for producing algae biofuels.

Tribology of ethylene-air diffusion flame soot under dry and lubricated contact conditions

Soot particles are generated in a flame caused by burning ethylene gas. The particles are collected thermophoretically at different locations of the flame. The particles are used to lubricate a steel/steel ball on flat reciprocating sliding contact, as a dry solid lubricant and also as suspended in hexadecane. Reciprocating contact is shown to establish a protective and low friction tribo-film. The friction correlates with the level of graphitic order of the soot, which is highest in the soot extracted from the mid-flame region and is low in the soot extracted from the flame root and flame tip regions. Micro-Raman spectroscopy of the tribo-film shows that the a priori graphitic order, the molecular carbon content of the soot and the graphitization of the film as brought about by tribology distinguish between the frictions of soot extracted from different regions of the flame, and differentiate the friction associated with dry tribology from that recorded under lubricated tribology.

Influence of Switching Conditions on the VETO Magnitudes in a GIS

Estimation of very fast transient overvoltage (VFTO) has been carried out using EMTP for various switching conditions in a 420 kV gas-insulated substation (GIS). The variation of the VFTO peak along the GIS bus nodes for disconnector and circuit breaker switching operations, as well as the variation of VFTO peak with different magnitudes of trapped charges, have been studied. The results indicate a distinct pattern of variation of VFTO peak along the nodes of the GIS bus in the case of disconnector switch operation as compared to that of circuit-breaker operation. It has also been noticed that the variation of VFTO peak levels are not in direct proportion to the trapped charge present on the HV bus.