Coefficient Inequalities for p-Valent Functions

In the present paper, the authors introduce a new subclass of p-valent analytic functions with complex order defined on the open unit disk U={z:z∈C and |z|1} and obtain coefficient inequalities for the functions in these class. Application of these results for the functions defined by the convolution are also obtained.     

Effect of buoyancy on the wakes of circular and square cylinders: a schlieren-interferometric study

Wakes behind heated cylinders, circular, and square have been experimentally investigated at low-Reynolds numbers. The electrically heated cylinder is mounted in a vertical airflow facility such that buoyancy aids the inertia of main flow. The operating parameters, i.e., Reynolds number and Richardson number are varied to examine flow behavior over a range of experimental conditions from forced to mixed convection regime. Laser schlieren-interferometry has been used for visualization and analysis of flow structures. Complete vortex shedding sequence has been recorded using a high-speed camera. The results on detailed dynamical characteristics of vortical structures, i.e., their size, shape and phase, Strouhal number, power spectra, convection velocity, phase shift, vortex inception length, and fluctuations are reported. On heating, alteration of organized (coherent) structures with respect to shape, size and their movement is readily perceived from instantaneous Schlieren images before they reduce to a steady plume. For both cylinders, Strouhal number shows a slow increase with an increase in Richardson number. At a critical value, there is complete disappearance of vortex shedding and a drop in Strouhal number to zero. The corresponding spectra evolve from being highly peaked at the vortex shedding frequency to a broadband appearance when vortex shedding is suppressed. The geometry of vortex structures transforms to a slender shape before shedding is suppressed. At this heating level, absence of multiple peaks in power spectra at cylinder centerline indicates absence of interaction between opposite shear layers. The convection velocity of vortices increases in stream wise direction to an asymptotic value and its variation is a function of Richardson number. The convection speed abruptly falls to zero at critical Richardson number. The phase difference of shed vortices between upstream and downstream location increases with an increase in Richardson number. Velocity profiles show an increase in fluid speed and beyond the critical point, buoyancy forces add enough momentum to cancel momentum deficit due to the cylinder. Overall, the combined effect of temperature gradient on the separating shear layer velocity profile in near field and vortical structures interaction in far field influences wake instability of a heated cylinder. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

PIV investigation of flow behind surface mounted permeable ribs

The flow behind surface mounted permeable rib geometries, i.e. solid, slit, split-slit and inclined split-slit ribs have been studied using flow visualization and PIV (2-C and 3-C) technique in streamwise and cross-stream measurement planes. The objective behind this study is to understand the flow structures responsible for heat transfer/mixing enhancement with simultaneous pressure penalty reduction by permeable rib geometries. The Reynolds number based on the rib height has been set equal to 5,538 and the open area ratio of permeable ribs is equal to 20%. The permeable rib geometries have shorter reattachment length in comparison to the solid rib. The maximum 41% reduction in reattachment length is observed for the inclined split-slit rib. The splitter mounted inside the slit leads to two corner vortices behind it. The corner vortices drag the flow from the primary recirculation bubble region towards the rib resulting in drop of the reattachment length. Two horseshoe vortices are present in the flow through the slit at both sides of the splitter due to the upstream flow separation. The slit inclination moves these horseshoe vortices closer to the bottom wall. A film like flow through the slit is present near the downstream corner of the inclined split-slit rib. The spanwise velocity gradient due to the splitter leads to vorticity and turbulence enhancement by vortex stretching. The inclination of the slit and the use of a splitter inside the slit are two important design parameters responsible in generation of near-wall longitudinal vortices. The flow field behind permeable ribs is dominated by vortical structures with definable critical flow patterns, i.e. node, saddle and foci. These predominant swirling flow motions contribute to the mixing enhancement behind permeable rib geometries. On leave from Mechanical Engineering Department, IIT Kanpur, U.P. 208016, India     

Interferometric study of buoyancy-driven convection in a differentially heated circular fluid layer

The present study is concerned with buoyancy-driven convection experiments in a circular horizontal differentially heated layer of air. The radius-to-height ratio of 14, and Rayleigh numbers of 5,861 and 12,124 have been considered. A Mach–Zehnder interferometer has been used to visualize the convection patterns in the fluid layer. The fluid layer has been imaged at view angles of 0, 45 and 90°. Results obtained show that fringe patterns appropriate for a cavity square in plan are seen in the fluid layer during the early stages of the experiments. After the passage of the initial transients, steady fringes have been observed in the fluid layer for a Rayleigh number of 5,861. At Ra=12,124, a dominant pattern was detectable combined with mild unsteadiness. The steady thermal field at Ra=5,861 displayed symmetry with respect to the viewing angle. A stronger three dimensionality was seen at the higher Rayleigh number. The average steady state Nusselt numbers were found to vary with view angle from 1.91 to 2.04 at Ra=5,861 and 2.28 to 2.43 at Ra = 12,124. The cavity-averaged Nusselt numbers are in good agreement with the available correlations.     

On “Comment on Supersymmetry, PT-symmetry and spectral bifurcation”

In “Comment on Supersymmetry, PT-symmetry and spectral bifurcation” [1], Bagchi and Quesne correctly show the presence of a class of states for the complex Scarf-II potential in the unbroken PT-symmetry regime, which were absent in [2]. However, in the spontaneously broken PT-symmetry case, their argument is incorrect since it fails to implement the condition for the potential to be PT-symmetric: C^PT[2(A − B) + α] = 0. It needs to be emphasized that in the models considered in [2], PT is spontaneously broken, implying that the potential is PT-symmetric, whereas the ground state is not. Furthermore, our supersymmetry (SUSY)-based ‘spectral bifurcation’ holds independent of the sl(2) symmetry consideration for a large class of PT-symmetric potentials.     

Complex solitary waves and soliton trains in KdV and mKdV equations

We demonstrate the existence of complex solitary wave and periodic solutions of theKorteweg-de Vries (KdV) and modified Korteweg-de Vries (mKdV) equations. The solutions ofthe KdV (mKdV) equation appear in complex-conjugate pairs and are even (odd) under thesimultaneous actions of parity (??) and time-reversal (??) operations. The corresponding localized solitons arehydrodynamic analogs of Bloch soliton in magnetic system, with asymptotically vanishingintensity. The ????-odd complex soliton solution is shown to beiso-spectrally connected to the fundamental sech² solution through supersymmetry. Physically, thesecomplex solutions are analogous to the experimentally observed grey solitons of non-liner Schödinger equation, governing the dynamics of shallow waterwaves and hence may also find physical verification.     

Reversal in solvatochromism in some novel styrylpyridinium dyes having a hydrophobic cleft

The influence of solvent polarity on the electronic transition of four different N-hexadecyl styrylpyridinium dyes has been investigated in 15 solvents. The E(T)(30) scale has been used to propose a quantitative approach towards the relative stability of the electronic ground and excited state species. The extents of contribution of dipolar aprotic solvents towards the solvation of the excited species have been determined to be 42-48% for some of the dyes. Instead of a steady solvatochromism, all the dyes suffer a reversal in solvatochromism. The transitions of the solvatochromism, referred to as solvatochromic switches, are found to be at E(T)(30) values of approximately 50 for methyl and N,N-dimethylamino substituted dyes while at 37.6 for hydroxyl substituted dye and approximately 45 for 4-(1-methyl-2-phenylethenyl) pyridinium dye. A reversal in the trend of solvent effect in the later dye corresponding to 4-(4-methyl styryl)pyridinium dye has been attributed to an analogy of series and parallel electron flow.     

A rapid room temperature chemical route for the synthesis of graphene: metal-mediated reduction of graphene oxide

A rapid and facile route for the synthesis of reduced graphene oxide sheets (rGOs) at room temperature by the chemical reduction of graphene oxide using Zn/acid in aqueous solution is demonstrated.     

Grain boundary defects induced room temperature ferromagnetism in V doped ZnO thin films

Vanadium (V) doped ZnO thin films (Zn_1‐xV_x O, where x = 0, 0.05, 0.10) have been grown on sapphire substrates by RF magnetron sputtering to realize room temperature ferromagnetism (RTFM). The grown films have been subjected to X‐ray diffraction (XRD), resonant Raman scattering, photoluminescence (PL) and vibrating sample magnetometer (VSM) measurements to investigate their structural, optical and magnetic properties, respectively. The full width at half maximum of XRD and Raman scattering peaks increases with V ion concentration indicates that the V ions have been substituted on Zn²⁺ ions in the ZnO matrix. The increase in oxygen vacancies with V concentration is evidenced by PL measurements. Rutherford backscattering spectrometry analysis confirms the presence of the V ions in the films. The room temperature VSM measurements reveal the signature of ferromagnetism in V doped ZnO thin films. It has been observed that the grain boundary defects, i.e., oxygen vacancies play a crucial role in inducing RTFM in V doped ZnO films. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Synthesis of nano ZnO thin film on Al foil by rf glow discharge plasma and its effect on E. coli and P. aeruginosa

Nano ZnO thin films were deposited on thin Al foils by a rf glow discharge plasma method in which sublimed zinc acetate vapor (precursor) reacted with oxygen plasma inside a low-pressure reactor. The films were microstructurally characterized using XRD, TEM, FESEM, optical reflectance and micro-Raman spectroscopy methods. In view of the good scope of ZnO coating in food packaging, the antibacterial activity in the ZnO thin films was studied by exposing the films to E. coli and P. aeruginosa for up to 8 h. Bacterial cell inhibition of up to 98–99 % was observed in the thin films.