A new highly accurate discretization for three‐dimensional singularly perturbed nonlinear elliptic partial differential equations

We employ a new fourth‐order compact finite difference formula based on arithmetic average discretization to solve the three‐dimensional nonlinear singularly perturbed elliptic partial differential equation ε(u_xx + u_yy + u_zz) = f(x, y, z, u, u_x, u_y, u_z), 0 < x, y, z < 1, subject to appropriate Dirichlet boundary conditions prescribed on the boundary, where ε > 0 is a small parameter. We also describe new fourth‐order methods for the estimates of (?u/?x), (?u/?y), and (?u/?z), which are quite often of interest in many physical problems. In all cases, we require only a single computational cell with 19 grid points. The proposed methods are directly applicable to solve singular problems without any modification. We solve three test problems numerically to validate the proposed derived fourth‐order methods. We compare the advantages and implementation of the proposed methods with the standard central difference approximations in the context of basic iterative methods. Numerical examples are given to verify the fourth‐order convergence rate of the methods. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2006     

Grafting of vinyl monomers onto sisal fiber in aqueous solution

Graft copolymerization of acrylonitrile (AN) onto sisal fibers (chemically modified) was studied using the Mn(III)/EDTA redox system in aqueous solution. The effects of time, monomer (AN), metal ion [Mn(III)] substrate [ethylene diamine tetraacetic acid (EDTA)], temperature, and acid concentration on graft yield have been studied. The effects of thiourea on the graft yield has also been studied. A suitable mechanism is proposed.     

Working group report: Astroparticle and neutrino physics

The working group on astroparticle and neutrino physics at WHEPP-9 covered a wide range of topics. The main topics were neutrino physics at INO, neutrino astronomy and recent constraints on dark energy coming from cosmological observations of large scale structure and CMB anisotropy.     

Lateral shear interferometry with holo shear lens

A simple method for obtaining lateral shear using holo shear lenses (HSL) has been discussed. This simple device which produces lateral shears in the orthogonal directions has been used for lens testing. The holo shear lens is placed at or near the focus of the lens to be tested. It has also been shown that HSL can be used in speckle shear interferometry as it performs both the functions of shearing and imaging.     

A new approach for heavy ion fusion spin distribution

The method of optical model analysis of generalized elastic scattering angular distributions (GESA) has been applied to heavy ion scattering to derive fusion spin distributions. This method is used to reproduce the coupled channel fusion spin distributions. When applied to experimental data, particularly to the fissile systems like¹⁶O +²³²Th, the method gives large mean square spin values in agreement with “anomalous” values derived from experimental fission fragment anisotropies.     

Effect of Al on the electrochemical corrosion behaviour of Pb free Sn-8.5 Zn-0.5 Ag-XAl-0.5 Ga solder in 3.5% NaCl solution

The effect of Al on the electrochemical corrosion behaviour of Pb-free Sn-8.5 Zn-0.5 Ag-XAl-0.5 Ga solder in 3.5% NaCl solution was investigated by using potentiodynamic polarization techniques. The X content in the solder varied from 0.1 to 3 wt.%. Polarization studies revealed that an increase in Al content upto 1.5 wt.% decreased the corrosion current density (I_corr), corrosion rate of the solder and shifted the corrosion potential (E_corr) towards more noble values. However, higher content of Al, i.e. 3 (wt.%) in the five-element solder enhanced the corrosion rate and resulted in a significant increase in the E_corr towards more negative values. Passivation behaviour was noticed in all the solders having varying Al content, but the passive film formed at 1.5 wt.% Al was most stable due to its low passivation current density (i_p) and low critical current density (i_cc) value in comparison to the other solders. XPS and Auger depth profile results revealed that the passive film consisted of oxides/hydroxides of Al and Zn formed on the surface of the solder with Sn being formed in the subsequent layer. Considerable aluminium segregation occurred towards the surface principally as Al₂O₃/Al(OH)₃ with increase in Al content to 1.5 wt.% in the five element solder. The formation of Al₂O₃ seemed to prevent the oxidation of zinc on the surface of the solder.     

Astrophysical constraints on particle properties

I summarize some astrophysical phenomenon like gamma ray bursters, astrophysical proof of the existence of blackholes, Active galactic nuclei — as high energy neutrino sources, and some unsolved issues in supernova. I touch on the aspects where novel particle properties (like neutrino mass and magnetic moment) are invoked to understand the astronomical observations.     

Effects of admixtures of potassium bromide on the thermal decomposition of potassium bromate

The effects of admixtures of potassium bromide (2.5% and 5%) on the thermal decomposition of potassium bromate were studied within the temperature range 653–683 K. The fraction decomposed() vs. time (t) relations revealed (i) initial gas evolution, (ii) acceleratory and (iii) decay steps. The data were analysed on the basis of the first-order law with two rate constantsk ₁ andk ₂,k ₁ being the rate constant for the initial, slow first-order process (0.02, 0.26), andk ₂ being the rate constant for the subsequent faster process, holding within the range 0.21 to 0.98. Upon increase of the concentration of added potassium bromide to 5%, the range for the slow and faster processes became 0.01 to 0.16 and 0.1 to 0.98, respectively. At a given temperature,k ₁ increased with increasing bromide concentration, whereask ₂ almost identical for pure potassium bromate and its mixtures (2.5% and 5% bromide).

---

Zusammenfassung Im Temperaturbereich von 653–683 K wurde der Einfluß von Beimengen von Kaliumbromid (2,5% und 5%) auf die thermische Zersetzung von Kaliumbromat untersucht. Die Funktion der zersetzten Menge () in Abhängigkeit von der Zeit (t) weist eine anfängliche Gasentwicklung(i), eine beschleunigte(ii) und eine abklingende Stufe(iii) auf. Die Daten wurden auf der Grundlage einer Kinetik erster Ordnung mit den zwei Geschwindigkeitskonstantenk ₁ undk ₂ durchgeführt, wobeik ₁ die Geschwindigkeitskonstante für den einleitenden, langsameren Schritt erster Ordnung ist (0,02, 0,26) undk ₂ die Geschwindigkeitskonstante für den darauffolgenden schnelleren Vorgang mit Werten zwischen 0,21 und 0,98. Bei Erhöhung der Konzentration von Kaliumbromid auf 5% betrug der Bereich für den langsameren und den schnelleren Vorgang 0,01 bis 0,16 bzw. 0,10 bis 0,98. Bei gegebener Temperatur steigtk ₁ mit zunehmender Kaliumbromidkonzentration an, währendk ₂ für reines Kaliumbromat und seine Mischungen mit 2,5% und 5% Kaliumbromid fast identisch bleibt.

---

653–683 (2,5 5%) . , . k ₁ k ₂, ( 0,02 0,26), - 0,21–0,98. 5% k ₁ k ₂ , , 0,01–0,16 0,1–0,98. k ₁, , k ₂ , (2,5 5%) .

---

---

The work is dedicated to the memory of the late Prof. S. R. Mohanty.     

Sulfinimine-mediated asymmetric synthesis of 1,3-disubstituted tetrahydroisoquinolines: a stereoselective synthesis of cis- and trans-6,8-dimethoxy-1,3-dimethyl-1,2,3,4-tetrahydroisoquinoline

[reaction: see text] The highly diastereoselective addition of lateral lithiated o-tolunitriles to sulfinimines followed by treatment of the resulting sulfinamide with MeLi, hydrolysis, and reduction represents a concise new methodology for the asymmetric synthesis of 1,3-disubstituted tetrahydroisoquinolines.