Secondary flow of Rivlin-Ericksen fluids between two concentric spheres oscillating about a fixed diameter

Summary The paper deals with the study of the nature of secondary flow of aRivlin-Ericksen fluid, contained between two concentric spheres, which perform oscillations about a fixed diameter. The steady part of the secondary flow is discussed in detail in the following three cases (i) the outer sphere at rest, the inner oscillating, (ii) the two spheres oscillating with the same angular velocity in the same sense and (iii) the spheres oscillating with the same angular velocity in opposite sense. In a previous paper, a similar problem was discussed for theOldroyd fluids. We find that the secondary flow is strongly dependent on the common frequency of oscillation of the two spheres and on the rotational nature of the motion for the present investigation also. Certain contrasting features of interest between the secondary flow field of the two fluids are also noted.     

Synthesis,bulk growth,polarizability and nonlinear optical properties of γ‐glycine single crystals

The role of sodium acetate, sodium nitrate, sodium hydroxide and malonic acid as additives in assisting the nucleation of γ‐polymorph from solution has been investigated. For the first time large dimensional bulk single crystals of γ‐glycine have been grown at the optimized concentration of the additives by the top seeded slow cooling technique. The bulk growth of single crystals elucidates well the unidirectional growth characteristics and the existence of merohedral twinning in γ‐ glycine. Polarizability, plasmon energy and Fermi energy has been evaluated for the first time for γ‐glycine single crystals based on an analytical approach. Structural affirmation of the nucleated polymorph has been carried out by Powder x‐ray diffraction and the thermal characteristics of the nucleated polymorph are well revealed by Differential Scanning Calorimetry. The non linear optical characteristics of γ‐glycine studied by Kurtz and Perry technique revealed increased SHG efficiency with the highest of about 2.2 in the presence of malonic acid compared to the standard Potassium dihydrogen orthophosphate (KDP).     

Impact of malonic acid on the segregation of glycine polymorphs – Analytical assisted molecular approach

Proton dissociation assisted negative polarity of malonic acid molecules admist glycine zwitterions leads to orgination of γ nucleation in the solution. Alteration in the nucleation behaviour and segregation of glycine polymorphs in the presence of malonic acid over a wide range of concentrations has been investigated both by experimental and analytical approaches. Complete changeover in the nucleation behaviour from 100% α to 100% γ is observed at the critical concentration of the additive. Shifting in the overall charge environment of the system towards cationic in the presence of malonic acid favours the nucleation of γ through induced charge compensation in the solution. Tuning of merohedral twinning in γ nucleation by the additive concentration has been well revealed in the present work. CNT based analytical approach employed elucidates well the experimental observations through the estimated interfacial energy, volume excess free energy, critical radius, activation energy barrier and nucleation rates of α and γ polymorphs. Structural affirmation of the nucleated polymorphs was carried out by powder x‐ray diffraction.     

Rotational diffusion of coumarin laser dye studied by fluorescence depolarization technique

Solute-solvent interactions play a major role in determining the physiochemical properties of solutions. Yet our understanding of this subject is far from complete. Rotational diffusion studies of medium-sized molecules provide a useful means to probe these interactions. The rate of diffusion is sensitive to the shape of the molecule and interaction between the solute and solvent molecules. Because of continuous interactions with their neighbours, molecules rotating in liquid, experience friction. By modeling this friction using various continuum-based theories, we can get better insight into the nature of the solute-solvent interactions. In the present work steady-state and time-resolved fluorescence polarization studies have been carried out with coumarin 30. The rotational reorientation of this probe has been measured in butanol at higher values of viscosity over temperature. However, it was found that coumarin 30 rotates faster in butanol compared to n-octanenitrile.     

Subsets of ideal topological spaces

Properties of α-I-open sets, t-I-sets, strong β-I-open sets, S _βI-sets and S-I-sets in ideal topological spaces are discussed. Also, we define a new class of sets called semi-I-locally closed sets which contains the class of all I-locally closed sets and is contained in the class of all semilocally closed sets.     

Ionic liquid mediated 1,3-dipolar cycloaddition of azomethine ylides: a facile and green synthesis of novel dispiro heterocycles

A greener, facile and efficient one-pot, three-component procedure for the synthesis of novel dispiropyrrolidine-bisoxindole derivatives by cycloaddition trapping of azomethine ylides generated in situ, via decarboxylative condensation of isatin with sarcosine (α-amino acid), has been reported in [bmim]PF₆, an ionic liquid as a recyclable solvent in excellent yield without using any catalyst. This protocol provides mild reaction conditions, high yields of product in short reaction time, high regio- and stereoselectivity, operational simplicity and environmentally benign procedure.     

Characterization of α and γ polymorphs of glycine crystallized from water‐ammonia solution

Crystallization of metastable α and stable γ polymorphs of glycine was carried out from aqueous solution in the presence of ammonia. Pure aqueous solution and solution with lower concentration of ammonia yield α nucleation and solution with a critical concentration of ammonia yield γ nucleation. Variation in the solubility of glycine in double distilled water and pH of the resulting solution due to the ammonia incorporation was studied in a range of temperatures. The induction period for the α and γ nucleation in the solution was determined and its variation due to the ammonia incorporation was also studied. Single crystals of both the polymorphs were grown by slow evaporation method. Effect of ammonia concentration and the resultant pH of the solution on the nucleation, growth and morphology of the grown polymorphs were investigated. The unidirectional growth of the γ polymorph along the polar axis was revealed. X‐ray powder diffraction method was employed to distinguish both the polymorphs structurally. Their thermal stability above room temperature was studied by differential scanning calorimetry which revealed that the as‐grown γ polymorph transforms to α at 179.6 °C while the as‐grown α retains its phase until melting. The optical transmittance of the grown γ polymorph was studied in the UV‐Vis‐Near IR region. The second harmonic generation (SHG) efficiency of the grown γ polymorph was studied with a Nd:YAG laser source and is about 6.8% higher than that of the inorganic standard KDP. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A general treatment of two dimensional plane flows,for a micropolar fluid

Summary In this paper we have studied the flow of a micropolar fluid, whose constitutive equations were given byEringen, in two dimensional plane flow. In two notes, we have discussed the validity of the boundary conditionv=a and its effect on the entire flow field. We have restricted our study to the case whenStokes' approximation is valid, i. e.slow motion for it is difficult to uncouple the equations in the most general case.

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Zusammenfassung Gegenstand dieser Untersuchung ist die zweidimensionale ebene Strömung einer mikropolaren Flüssigkeit, deren rheologische Stoffgleichung vonEringen angegeben worden ist. In zwei Abschnitten werden die Gültigkeit der Randbedingungv=a und die daraus resultierenden Konsequenzen für das gesamte Strömungsfeld diskutiert. Wir haben unsere Untersuchung auf den Anwendungsbereich der Stokesschen Näherung (d. h. auf eine schleichende Strömung) beschränkt, da die Entkoppelung der Gleichungen im allgemeinsten Fall Schwierigkeiten bereitet.

     

Ion cyclotron instabilities in a mildly relativistic hydrogen-deuterium fusion plasma

A dispersion relation for the perpendicular propagation of the electromagnetic ion cyclotron wave around the second harmonic of the deuterium ion gyrofrequency in a mildly relativistic, anisotropic Maxwellian plasma with hydrogen as the majority species and deuterium as the minority component has been derived. The work has been carried out in the frame of reference of the majority hydrogen ions; to these ions the waves at 2Θ_D would be at its own gyrofrequency. Using a small quantityɛ to order all relevant parameters of the plasma, it was possible to derive the dispersion relations in a simple form. To the lowest order the relativistic factors do not enter the dispersion relation. The plasma can now support two modes—one above and the other below the hydrogen gyrofrequency in agreement with the assumptions. This was also verified numerically using a standard root solver thereby justifying the correctness of the ordering scheme. In the next higher order, the dispersion relation is a quartic equation and is sensitively dependent on the relativistic factors. The plasma can now support four modes, both above and below the hydrogen gyrofrequency and consistent with the ordering scheme used. However the modes can now coalesce resulting in complex conjugate roots to the dispersion relation thereby indicating an instability. The advantage of such a scheme is that two dispersion relations — one of which is independent of the relativistic factors and the other which is sensitively dependent on them can be separated out.