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.

Structural model for the Cu-B site of dopamine beta-hydroxylase: Crystal structure of a copper(II) complex showing N3OS coordination with an axial sulfur ligation

A copper(II) complex containing a NSO-donor Schiff base and NN-donor 2,2'-bipyridine has been prepared and structurally characterized. The square pyramidal complex with an axial sulfur ligation is a structural model for the CUB site of dopamine-hydroxylase in its oxidized form. The copper(II) complex is catalytically active in the oxidation of ascorbic acid by dioxygen mediated by a copper(I) species which is proposed to have a four-coordinate structure with a N3S coordination geometry.

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.

Efficient visible light induced nuclease activity of a ternary mono-1,10-phenanthroline copper(II) complex containing 2-(methylthio)ethylsalicylaidimine

Ternary Schiff base copper(II) complex [CuL(phen)](ClO4), where HL is 2-(methylthio)ethylsalicylaldimine and phen is 1,10-phenanthroline, has been prepared and structurally characterized by X-ray crystallography. The complex shows a CuN3OS coordination in a square-pyramidal (4 + 1) geometry with the sulfur as an equatorial ligand. The complex is an avid binder to double-stranded DNA in the minor groove and exhibits both photonuclease and chemical nuclease activity. When exposed to UV light of 312 nm (96 W) or visible light of 532 nm (125 W) under aerobic conditions, the complex causes significant cleavage of supercoiled pUC19 DNA in the absence of any externally added reducing agent or H2O2.

Ternary copper(II) complexes of thiosemicarbazones and heterocyclic bases showing N3OS coordination as models for the type-2 centers of copper monooxygenases

Six ternary copper(II) complexes of general formulation [CuLB] (1-6), where L is dianionic ONS-donor thiosemicarbazones derived from the condensation of salicylaldehyde with thiosemicarbazides and B is NN-donor heterocyclic bases like 2,2'-bipyridine, 1,10-phenanthroline and 2,9-dimethyl-1,10-phenanthroline, are prepared from a reaction of copper(II) acetate hydrate with the heterocyclic base (B) and the thiosemicarbazone (H2L) in MeOH, and structurally characterized by X-ray diffraction technique. Crystal structures of the complexes display a distorted square-pyramidal (4 + 1) coordination geometry having the ONS-donor thiosemicarbazone bonded at the basal plane. The chelating heterocyclic bases exhibit axial-equatorial mode of bonding. The complexes are one-electron paramagnetic and they show axial X-band EPR spectra in DMF-toluene glass at 77 K giving g(parallel to)(A(parallel to)) and g(perpendicular to) values of similar to2.2 (175 x 10(-4) cm(-1)) and similar to2.0 indicating a {d(x2-y2)}(1) ground state. The complexes show a d-d band near 570 nm and a charge transfer band near 400 nm in DMF. The complexes are redox active and exhibit a quasireversible Cu(II)-Cu(I) couple in DMF-0.1 M tetrabutylammonium perchlorate near 0.1 V vs. SCE. They are catalytically active in the oxidation of ascorbic acid in presence of dioxygen. The complexes with a CuN3OS coordination model the ascorbate oxidation property of dopamine beta-hydroxylase and peptidylglycine a-hydroxylating monooxygeanase. (C) 2003 Elsevier Science B.V. All rights reserved.

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.

Dicopper(II) complexes showing DNA hydrolase activity and monomeric adduct formation with bis(4-nitrophenyl)phosphate

Ferromagnetic dicopper(II) complexes [Cu(2)(mu-O(2)CCH(3))(mu-OH)(L)(2)(mu-L(1))](PF(6))(2), where L = 1,10-phenanthroline (phen), L(1) = H(2)O in 1 and L = dipyrido[3,2-d:2',3'-f]quinoxaline (dpq), L(1) = CH(3)CN in 2, are prepared and structurally characterized. Crystals of 1 and 2 belong to the monoclinic space group of P2(1)/n and P2(1)/m, respectively. The copper(II) centers display distorted square-pyramidal geometry having a phenanthroline base and two oxygen atoms of the bridging hydroxo and acetate group in the basal plane. The fifth coordination site has weak axially bound bridging solvent molecule H(2)O in 1 and CH(3)CN in 2. The Cu center dot center dot center dot Cu distances are 3.034 and 3.046 angstrom in 1 and 2, respectively. The complexes show efficient hydrolytic cleavage of supercoiled pUC19 DNA as evidenced from the mechanistic studies that include T4 DNA ligase experiments. The binuclear complexes form monomeric copper(II) adducts [Cu(L)(2)(BNPP)](PF(6)) (L = phen, 3; dpq, 4) with bis(4-nitrophenyl)phosphate (BNPP) as a model phosphodiester. The crystal structures of 3 and 4 reveal distorted trigonal bipyramidal geometry in which BNPP binds through the oxygen atom of the phosphate. The kinetic data of the DNA cleavage reactions of the binuclear complexes under pseudo- and true-Michaelis-Menten conditions indicate remarkable enhancement in the DNA hydrolysis rate in comparison to the control data. (C) 2011 Elsevier B.V. All rights reserved.

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.