Boundary conditions at a rigid wall for rough granular gases

We derive boundary conditions at a rigid wall for a granular material comprising rough, inelastic particles. Our analysis is confined to the rapid flow, or granular gas, regime in which grains interact by impulsive collisions. We use the Chapman-Enskog expansion in the kinetic theory of dense gases, extended for inelastic and rough particles, to determine the relevant fluxes to the wall. As in previous studies, we assume that the particles are spheres, and that the wall is corrugated by hemispheres rigidly attached to it. Collisions between the particles and the wall hemispheres are characterized by coefficients of restitution and roughness. We derive boundary conditions for the two limiting cases of nearly smooth and nearly perfectly rough spheres, as a hydrodynamic description of granular gases comprising rough spheres is appropriate only in these limits. The results are illustrated by applying the equations of motion and boundary conditions to the problem of plane Couette flow.

Highly selective deprotection of tert-butyl esters using ytterbium triflate as a catalyst under mild conditions

Ytterbium triflate catalyses the deprotection of tert-butyl esters selectively in the presence of other esters under mild conditions in almost quantitative yields. The reactions are carried out in nitromethane (45degrees - 50degreesC) using 5 mole percent of the catalyst.

On the utility of an instrumented impact set-up to characterise the response of discontinuous buffer strips in carbon–epoxy systems in dry and wet conditions

The use of an instrumented impact test set-up to evaluate the influence of water ingress on the impact response of a carbon–epoxy (C–E) laminated composite system containing discontinuous buffer strips (BS) has been examined. The data on the BS-free C–E sample in dry conditions are used as reference to compare with the data derived from those immersed in water. The work demonstrated the utility of an instrumented impact test set-up in characterising the response, first owing to the architectural difference due to introduction of buffer strips and then due to the presence of an additional phase in the form of water ingressed into the sample. The presence of water was found to enhance the energy absorption characteristics of the C–E system with BS insertions. It was also noticed that with an increasing number of BS layer insertions, the load–time plots displayed characteristic changes. The ductility indices (DI) were found to display a lower value for the water immersed samples compared to the dry ones.

On the solution of the problem of scattering of surface water waves by a sharp discontinuity in the surface boundary conditions

Closed-form analytical expressions are derived for the reflection and transmission coefficients for the problem of scattering of surface water waves by a sharp discontinuity in the surface-boundary-conditions, for the case of deep water. The method involves the use of the Havelock-type expansion of the velocity potential along with an analysis to solve a Carleman-type singular integral equation over a semi-infinite range. This method of solution is an alternative to the Wiener-Hopf technique used previously.

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.

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.