A static cosmological model in Einstein-Cartan theory

A static cosmological model in the Einstein-Cartan theory based on Lyra's modified Riemannian geometry is proposed. We assume that the spins of the individual particles composng the fluid are all aligned in the radial direction and observe the very interesting fact that if spin is there in this static Einstein universe, it should be constant and it can be given in terms of central density ₀ as . The geometry and properties of the model are discussed.     

Efficient Method for Demethylation of Aryl Methyl Ether Using Aliquat-336

A rapid method for selective cleavage of aryl methylethers can be achieved in the presence of a protic acid and a catalytic amount of phase-transfer catalyst (Aliquat-336). Aliquat-336 accelerates the rate of reaction and affords the corresponding phenols in excellent to good yields on a wide variety of substrates.

[Supplementary materials are available for this article. Go to the publisher's online edition of Synthetic Communications® for the following free supplemental resource(s): Full experimental and spectral details.]     

Studies on morphology of polyaniline films formed at liquid–liquid and solid–liquid interfaces at 25 and 5 °C,respectively, and effect of doping

It is well accepted that the morphology of the nanomaterials has great effect on the properties and hence their applications. Therefore, morphology of materials has become a focus of research in the scientific world. The present study shows that interfacial polymerization and subsequent self-assembly provides a control over the morphology, nanorod/nanosheet, of polyaniline (PANI) films synthesized by liquid–liquid interface reaction technique and solid–liquid interface reaction technique. The synthesized PANI films and its particulate structure are characterized by using various spectroscopic techniques such as UV–visible, ATR-IR, Raman and XPS. The study confirmed the formation, the structure, the size and shape of particles and morphology of PANI by using analytical techniques namely, SAED, SEM and TEM. An important observation is that doping with HCl significantly improves the nanorod formation at the interface. The doped PANI electrode exhibits a higher area with rectangular shape in CV cycle and better cycle stability when compared with the performance of undoped PANI films. We believe that the results of these studies can give valuable leads to manoeuvre formation of PANI films with desired morphology for various applications.

Overtone spectroscopy of some benzaldehyde derivatives

Overtone spectrum of o, m and p-nitrobenzaldehydes and p-chlorobenzaldehyde has been studied in 2000–12000 cm⁻¹ region. Vibrational frequencies and anharmonicity constants for aryl as well as alkyl CH stretch vibrations have been determined. We have also determined the internuclear distances for the aryl CH bond in the different molecules. The small variation observed in these distances is an indication of the substitution effect. It is observed that in the case of p-disubstituted benzens, the shift in aryl CH bond is proportional to sum of the Hammet σ of the substituents. However in the case of o-disubstituted benzenes it is only 80% of the para-substituted shift.     

Stereodivergent approach to Alzheimer's therapeutic agent (R)-(−) and (S)-(+)-arundic acid employing chiral 4-pentenol derivatives as building blocks

An efficient stereodivergent total synthesis of anti-Alzheimer agent (R)-(?) and (S)-(+)-arundic acid has been achieved from both chiral and nonchiral materials. This strategy features an efficient approach to separable diastereomeric C-2 chiral 4-pentenol intermediates employing proline catalysed asymmetric α-aminooxylation and [3,3] sigmatropic Claisen rearrangement are the highlights of present synthesis.     

Steady laminar flow past a heated horizontal plate embedded in a saturated porous medium

In this paper we study the boundary layer equations for steady laminar flow past a heated horizontal plate embedded in a saturated porous medium by adopting the formulation of Chandrasekhara [3], Kolar and Sastri [7]. The velocity distribution and temperature distribution are determined by using the implicit Crank-Nicolson-Predictor-Corrector method of finite difference scheme [7] and [1]. With the help of a compute the distributions are estimated at both (i+1/2)th and (i+1)th levels and they are presented in tabular form. The curves for these distributions are plotted. We calculate the shear stress and skin friction at the wall and observe that the skin-friction directly depends upon the dimensions of the plate and inversely depends upon the Reynolds numberRe. The heat flux and the Nusselt number are evaluated. Further we observe that the Nusselt number depends upon the length of the porous plate.

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Stetige laminare Strömung über eine in einem gesättigten porösen Medium eingebettete horizontale Platte

Zusammenfassung Diese Untersuchung befaßt sich mit den Grenzschichtgleichungen für eine stetige laminare Strömung über eine beheizte Platte, die in ein gesättigtes poröses Medium eingebettet ist, mittels des Formalismus von Chandrasekhara [3], Kolar und Sastri [7]. Die Geschwindigkeits- und Temperaturverteilung wurden unter Benutzung der impliziten Crank-Nicolson-Korrekturmethode des Finiten-Elemente-Schemas bestimmt. Die (i+1/2). und die (i+1). Ebene der Verteilungen wurden mit Computer-Hilfe berechnet und in Tabellenform dargestellt. Die Graphen der Temperatur- und Geschwindigkeitsverteilung wurden ausgeplottet. Die Schubspannungen und die Oberflächenreibung an der Wand wurden berechnet und es konnte festgestellt werden, daß die Oberflächenreibung direkt von der Größe der Platte abhängt und umgekehrt proportional der Reynolds-ZahlRe ist. Der Wärmestrom und die Nusselt-Zahl wurden bestimmt. Weiterhin konnte festgestellt werden, daß die Nusselt-Zahl von der Länge der porösen Platte abhängt.

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Nomenclature C _p specific heat of the convective fluid - D skin friction - k permeability of the porous medium - k _f thermal conductivity of the fluid - k _m the coefficient of thermal conductivity of the porous medium - k _s the conductivity of the solid matrix - N(x) Nusselt number - q(x) specific heat flux - Re local Reynolds number - T temperature - T ₀ temperature of the free stream - T _w temperature of the plate - u velocity in thex-direction - u ₀ velocity of the free stream - V velocity iny-direction - x coordinate axis along the plate - y coordinate axis normal to the plate Greek symbols thermal diffusivity - thickness of the velocity boundary layers in thex direction - thickness of the velocity boundary layer in they-direction - the porosity of the medium - dimensionless variable - kinematic viscosity of the fluid - density of the fluid - shear stress     

Rheology of polarizable non-piezoelectromagnetic material in relativity

Following the work of Carter on nonlinear perfectly elastic solid and perfect nonlinearly polarizable nonconducting solid, we have constructed models whose free gravitational field is of Petrov typeD: (i) in inertial reference frame (IRF), (ii) with pure expansion and (iii) with pure rotation with the assumption that the flow field is expressible in terms of two real null vectors of the Newman-Penrose (N-P) tetrad. By using the strain variation equation, the necessary and sufficient conditions on the dynamical variables are obtained in Newman-Penrose version. We observe that the initial pressure tensor depends on the polarizable and electromagnetic properties of the material. Further, we conclude that there does not exist such a material with pure expansion but there exists such a material moving rigidly with or without rotation. We obtain the Hawking energy conditions and invariants for this material in IRF.     

Extremes of nuclear structure

With the advent of medium and large gamma detector arrays, it is now possible to look at nuclear structure at high rotational forces. The role of pairing correlations and their eventual breakdown, along with the shell effects have showed us the interesting physics for nuclei at high spins — superdeformation, shape co-existence, yrast traps, alignments and their dramatic effects on nuclear structure and so on. Nuclear structure studies have recently become even more exciting, due to efforts and possibilities to reach nuclei far off from the stability valley. Coupling of gamma ray arrays with ‘filters’, like neutron wall, charged particle detector array, gamma ray total energy and multiplicity castles, conversion electron spectrometers etc gives a great handle to study nuclei produced online with ‘low’ cross-sections. Recently we studied, nuclei in mass region 80 using an array of 8 germanium detectors in conjunction with the recoil mass analyser, HIRA at the Nuclear Science Centre and, most unexpectedly came across the phenomenon of identical bands, with two quasi-particle difference. The discovery of magnetic rotation is another highlight. Our study of light In nucleus, 107In brought us face to face with the ‘dipole’ bands. I plan to discuss some of these aspects. There is also an immensely important development — that of the ‘radioactive ion beams’. The availability of RIB, will probably very dramatically influence our ‘conventional’ concept of nuclear structure. The exotic shapes of these exotic nuclei and some of their expected properties will also be touched upon.     

Velocity and temperature distributions on a semi-infinite flat plate embedded in a saturated porous medium

In this paper the velocity and temperature distributions on a semi-infinite flat plate embedded in a saturated porous medium are obtained for the governing equations (Kaviany [7]) following the technique adopted by Chandrashekara [2] which are concerned with the interesting situations of the existence of transverse, velocity and thermal boundary layers. Here the pressure gradient is just balanced by the first and second order solid matrix resistances for small permeability and observed that by increasing of the flow resistance the asymptotic value for the heat transfer rate increases. Further we concluded that the transverse boundary layers are thicker than that of axial boundary layers. Hence we evaluated the expressions for the boundary layer thickness, the shear stress at the semi-infinite plate and _T (the ratio of the thicknesses of the thermal boundary layer and momentum boundary layer). The variations of these quantities for different values of the porous parameterB and the flow resistanceF have been discussed in detail with the help of tables. The curves for velocity and temperature distributions have been plotted for different values ofB andF.Lastly we have evaluated the heat fluxq(x) and found that it depends entirely upon the Reynolds numberRe, Prandtl numberPr,B andF.