SOLUTIONS OF A SYSTEM OF FORCED BURGERS EQUATION IN TERMS OF GENERALIZED LAGUERRE POLYNOMIALS

In this article, we obtain explicit solutions of a linear PDE subject to a class of radial square integrable functions with a monotonically increasing weight function |x|(n-1)e(beta vertical bar x vertical bar 2)/2, beta >= 0, x is an element of R-n. This linear PDE is obtained from a system of forced Burgers equation via the Cole-Hopf transformation. For any spatial dimension n > 1, the solution is expressed in terms of a family of weighted generalized Laguerre polynomials. We also discuss the large time behaviour of the solution of the system of forced Burgers equation.

Ag nanoparticles-anchored reduced graphene oxide catalyst for oxygen electrode reaction in aqueous electrolytes and also a non-aqueous electrolyte for Li-O-2 cells

Silver nanoparticles-anchored reduced graphene oxide (Ag-RGO) is prepared by simultaneous reduction of graphene oxide and Ag+ ions in an aqueous medium by ethylene glycol as the reducing agent. Ag particles of average size of 4.7 nm were uniformly distributed on the RGO sheets. Oxygen reduction reaction (ORR) is studied on Ag-RGO catalyst in both aqueous and non-aqueous electrolytes by using cyclic voltammetry and rotating disk electrode techniques. As the interest in non-aqueous electrolyte is to study the catalytic performance of Ag-RGO for rechargeable Li-O-2 cells, these cells are assembled and characterized. Li-O-2 cells with Ag-RGO as the oxygen electrode catalyst are subjected to charge-discharge cycling at several current densities. A discharge capacity of 11 950 mA h g(-1) (11.29 mA h cm(-2)) is obtained initially at low current density. Although there is a decrease in the capacity on repeated discharge-charge cycling initially, a stable capacity is observed for about 30 cycles. The results indicate that Ag-RGO is a suitable catalyst for rechargeable Li-O-2 cells.

Symmetric supercapacitor based on partially exfoliated and reduced graphite oxide in neutral aqueous electrolyte

The partially exfoliated and reduced graphite oxide (PE-RGO) is prepared by low temperature thermal exfoliation of graphite oxide under air atmosphere. A symmetric carbon/carbon supercapacitor is studied in a Na2SO4 aqueous electrolyte. The discharge capacitance is 92 F g(-1), when symmetric cell is cycled between the potential ranges from 0 to 1.6 V. This system demonstrates a stable charge/discharge cycle behavior up to 3000 cycles when the cell is operated at a voltage window of 1.6 V. The utilization ratio of potential window is 90% for this system is attributed to the more negative value of electrodes potential when the cell voltage is set to 0 V. The low-temperature exfoliation approach is convenient for mass production of graphenes at low cost and it can be used as electrode material for energy storage applications. (C) 2014 Elsevier Ltd. All rights reserved.

Modal tailoring and closed-form solutions for rotating non-uniform Euler-Bernoulli beams

In this paper, the free vibration of a rotating Euler-Bernoulli beam is studied using an inverse problem approach. We assume a polynomial mode shape function for a particular mode, which satisfies all the four boundary conditions of a rotating beam, along with the internal nodes. Using this assumed mode shape function, we determine the linear mass and fifth order stiffness variations of the beam which are typical of helicopter blades. Thus, it is found that an infinite number of such beams exist whose fourth order governing differential equation possess a closed form solution for certain polynomial variations of the mass and stiffness, for both cantilever and pinned-free boundary conditions corresponding to hingeless and articulated rotors, respectively. A detailed study is conducted for the first, second and third modes of a rotating cantilever beam and the first and second elastic modes of a rotating pinned-free beam, and on how to pre-select the internal nodes such that the closed-form solutions exist for these cases. The derived results can be used as benchmark solutions for the validation of rotating beam numerical methods and may also guide nodal tailoring. (C) 2014 Elsevier Ltd. All rights reserved.

Comparative Studies on the Bioremediation of Hexavalent and Trivalent Chromium using Citrobacter freundii: Part I-Effect of parameters controlling Biosorption

The potential of Citrobacter freundii, a Gram negative bacteria for the remediation of hexavalent chromium (Cr(VI)) and trivalent chromium (Cr(III))) from aqueous solutions was investigated. Bioremediation of Cr(VI) involved both biosorption and bioreduction processes, as compared to only biosorption process observed with respect to Cr(III) bioremediation. In the case of Cr(VI) bioremediation studies, about 59 % biosorption was achieved at an equilibrium time of 2 h, initial Cr(VI) concentration of 4 mg/L, pH 1 and a biomass loading of 5x10(11) cells/mL. The remainder, 41 %, was found to be in the form of Cr(111) ions owing to bioreduction of Cr(VI) by the bacteria resulting in the absence of Cr(VI) ions in the residue, there by meeting the USEPA specifications. Similar studies were carried out using Cr(III) solution for an equilibrium time of 2 h, Cr(III) concentration of 4 mg/L, pH 3 and a biomass loading of 6.3x10(11) cells/mL., wherein a maximum biosorption of about 30 % was achieved.

High quality oxide-free metallic nanoparticles: a strategy for synthesis through laser ablation in aqueous medium

The paper explores the synthesis of oxide-free nanoparticles of Ag and Cu through laser ablation of pure targets under aqueous medium and tuning the quality and size through addition of Polyvinylpyrrolidone (PVP) in the medium. The size distribution of nanoparticles reduces from 37 +/- 30 nm and 13 +/- 5 nm to 32 +/- 12 nm and 4 +/- 1 nm for Ag and Cu with changes in PVP concentration from 0.00 to 0.02 M, respectively. Irregular shaped particles of Ag with Ag2O phase and a Cu-Cu2O core-shell particles form without the addition of PVP, while oxide layer is absent with 0.02 M of PVP. The recent understanding of the mechanism of particle formation during laser ablation under liquid medium allows us to rationalize our observation.

Selective and Sensitive Turn-on Chemosensor for Arsenite Ion at the ppb Level in Aqueous Media Applicable in Cell Staining

A newly designed and structurally characterized cell permeable diformyl-p-cresol based receptor (HL) selectively senses the AsO33- ion up to ca. 4.1 ppb in aqueous media over the other competitive ions at biological pH through an intermolecular H-bonding induced CHEF (chelationenhanced fluorescence) process, established by detailed experimental and theoretical studies. This biofriendly probe is highly competent in recognizing the existence of AsO33- ions in a living organism by developing an image under a fluorescence microscope and useful to estimate the amount of arsenite ions in various water samples.

Covalent assembly-disassembly of poly(ether imine) dendritic macromolecular monomers and megamers

Poly(ether imine) dendritic macromolecules were undertaken to study the reversible dendrimer monomer-megamer assembly-disassembly in aqueous solutions. Synthesis of thiol functionalized poly(ether imine) (PETIM) dendrimers and their covalent aggregation behavior in the aqueous solution of ethanol/water (2:1) is demonstrated. The dendritic megamers were characterized using microscopic techniques. Kinetics of the aggregation behavior was followed using turbidity measurements, light-scattering and atomic force microscopic techniques. Inherent luminescence behavior of PETIM dendrimer monomers was retained in the dendrimer megamers also, which allowed visualization of the megamers through confocal microscopy. Extent of thiol functionalities that remained after the megamer assembly was estimated through Ellman's assay. Subsequent to megamer assembly, disassembly of megamers to dendrimer monomers was conducted, using dithiothreitol reagent. Water-insoluble sudan I dye was encapsulated in dendrimer megamer and subsequent release profile was assessed during the disassembly in aqueous solutions. The studies were conducted using first, second and third generations, representing 4, 8 and 16 sulfhydryl groups at their peripheries of dendrimers, respectively. (C) 2014 Elsevier Ltd. All rights reserved.

Recent NMR Methodological Developments for Chiral Analysis in Isotropic Solutions

Chiral auxiliaries are used for NMR spectroscopic study of enantiomers. Often the presence of impurities, severe overlap of peaks, excessive line broadening and complex multiplicity pattern restricts the chiral analysis using 1D H-1 NMR spectrum. There are few approaches to resolve the overlapped peaks. One approach is to use suitable chiral auxiliary, which induces large chemical shift difference between the discriminated peaks (Delta delta(R,S)) and minimize the overlap. Another direction of approach is to design appropriate NMR experiments to circumvent some of these problems, viz, enhancing spectral resolution, unravelling the superimposed spectra of enantiomers, and reduction of spectral complexity. Large number of NMR techniques, such as two dimensional selective F-1 decoupling, RES-TOCSY, multiple quantum detection, frequency selective homodecoupling, band selective homodecoupling, broadband homodecoupling, etc. have been reported for such a purpose. Many of these techniques have aided in chiral analysis for molecules of diverse functionality in the presence of chiral auxiliaries. The present review summarizes the recently reported NMR experimental methodologies, with a special emphasis on the work carried out in authors' laboratory.

A bio-attuned ratiometric hydrogen sulfate ion selective receptor in aqueous solvent: structural proof of the H-bonded adduct

A new cell permeable quinazoline based receptor (1) selectively senses HSO4- ions of nanomolar region in 0.1 M HEPES buffer (ethanol-water: 1/5, v/v) at biological pH over other competitive ions through the proton transfer followed by hydrogen bond formation and subsequent anion coordination to yield the LHSO4]-LH+center dot 3H(2)O (2) ensemble, which has been crystallographically characterised to ensure the structure property relationship. This non-cytotoxic HSO4- ion selective biomarker has great potential to recognize the intercellular distribution of HSO4- ions in HeLa cells under fluorescence microscope.

Sensitivity of polarization fluctuations to the nature of protein-water interactions: Study of biological water in four different protein-water systems

Since the time of Kirkwood, observed deviations in magnitude of the dielectric constant of aqueous protein solution from that of neat water (similar to 80) and slower decay of polarization have been subjects of enormous interest, controversy, and debate. Most of the common proteins have large permanent dipole moments (often more than 100 D) that can influence structure and dynamics of even distant water molecules, thereby affecting collective polarization fluctuation of the solution, which in turn can significantly alter solution's dielectric constant. Therefore, distance dependence of polarization fluctuation can provide important insight into the nature of biological water. We explore these aspects by studying aqueous solutions of four different proteins of different characteristics and varying sizes, chicken villin headpiece subdomain (HP-36), immunoglobulin binding domain protein G (GB1), hen-egg white lysozyme (LYS), and Myoglobin (MYO). We simulate fairly large systems consisting of single protein molecule and 20000-30000 water molecules (varied according to the protein size), providing a concentration in the range of similar to 2-3 mM. We find that the calculated dielectric constant of the system shows a noticeable increment in all the cases compared to that of neat water. Total dipole moment auto time correlation function of water < dM(W) (0)delta M-W (t) > is found to be sensitive to the nature of the protein. Surprisingly, dipole moment of the protein and total dipole moment of the water molecules are found to be only weakly coupled. Shellwise decomposition of water molecules around protein reveals higher density of first layer compared to the succeeding ones. We also calculate heuristic effective dielectric constant of successive layers and find that the layer adjacent to protein has much lower value (similar to 50). However, progressive layers exhibit successive increment of dielectric constant, finally reaching a value close to that of bulk 4-5 layers away. We also calculate shellwise orientational correlation function and tetrahedral order parameter to understand the local dynamics and structural re-arrangement of water. Theoretical analysis providing simple method for calculation of shellwise local dielectric constant and implication of these findings are elaborately discussed in the present work. (C) 2014 AIP Publishing LLC.

Synergistic Effect of Mo plus Cu Codoping on the Photocatalytic Behavior of Metastable TiO2 Solid Solutions

Codoping with Cu and Mo is shown to have a synergistic effect on the photocatalytic activity of TiO2. The enhancement in activity is observed only if the synthesis route results in TiO2 in which (Cu, Mo) codopants are forced into the TiO2 lattice. Using X-ray photoelectron spectroscopy, Cu and Mo are shown to be present in the +2 and +6 oxidation states, respectively. A systematic study of the ternary system shows that TiO2 containing 6 mol % CuO and 1.5 mol % MoO3 is the most active ternary composition. Ab initio calculations show that codoping of TiO2 using (Mo, Cu) introduces levels above the valence band, and below the conduction band, resulting in a significant reduction in the band gap (similar to 0.8 eV). However, codoping also introduces deep defect states, which can have a deleterious impact on photoactivity. This helps rationalize the narrow compositional window over which the enhancement in photocatalytic activity is observed.

Simple chemical aqueous synthesis of dahlia nanoflower consisting of finger-like ZnO nanorods and observation of stable ultraviolet photoluminescence emission

In this work, we have reported the synthesis of dahlia flower-like ZnO nanostructures consisting of human finger-like nanorods by the hydrothermal method at 120 degrees C and without using any capping agent. Optical properties of the samples, including UV-vis absorption and photoluminescence (PL) emission characteristics are determined by dispersing the samples in water as well as in ethanol media. The quenching of PL emission intensity along-with the red shifting of the PL emission peak are observed when the samples are dispersed in water in comparison to those obtained after dispersing the samples in ethanol. It has been found that PL emission characteristic, particularly the spectral nature of PL emission, of the samples remains almost unaltered (except some improvement in UV PL emission) even after thermally annealing it for 2 h at the temperature of 300 degrees C. Also the synthesized powder samples, kept in a plastic container, showed a very stable PL emission even after 15 months of synthesis. Therefore, the synthesized samples might be useful for their applications in future optoelectronics devices. (C) 2014 Elsevier Ltd. All rights reserved.

Composition dependent non-ideality in aqueous binary mixtures as a signature of avoided spinodal decomposition

We explore the potential energy landscape of structure breaking binary mixtures (SBBM) where two constituents dislike each other, yet remain macroscopically homogeneous at intermediate to high temperatures. Interestingly, we find that the origin of strong composition dependent non-ideal behaviour lies in its phase separated inherent structure. The inherent structure (IS) of SBBM exhibits bi-continuous phase as is usually formed during spinodal decomposition. We draw analogy of this correlation between non-ideality and phase separation in IS to explain observation of non-ideality in real aqueous mixtures of small amphiphilic solutes, containing both hydrophilic and hydrophobic groups. Although we have not been able to obtain IS of these liquids, we find that even at room temperature these liquids sustain formation of fluctuating, transient bi-continuous phase, with limited lifetime (tau less than or similar to 20 ps). While in the model (A, B) binary mixture, the non-ideal composition dependence can be considered as a fluctuation from a phase separated state, a similar scenario is expected to be responsible for the unusually strong non-ideality in these aqueous binary mixtures.

Mode coupling theory analysis of electrolyte solutions: Time dependent diffusion, intermediate scattering function, and ion solvation dynamics

A self-consistent mode coupling theory (MCT) with microscopic inputs of equilibrium pair correlation functions is developed to analyze electrolyte dynamics. We apply the theory to calculate concentration dependence of (i) time dependent ion diffusion, (ii) intermediate scattering function of the constituent ions, and (iii) ion solvation dynamics in electrolyte solution. Brownian dynamics with implicit water molecules and molecular dynamics method with explicit water are used to check the theoretical predictions. The time dependence of ionic self-diffusion coefficient and the corresponding intermediate scattering function evaluated from our MCT approach show quantitative agreement with early experimental and present Brownian dynamic simulation results. With increasing concentration, the dispersion of electrolyte friction is found to occur at increasingly higher frequency, due to the faster relaxation of the ion atmosphere. The wave number dependence of intermediate scattering function, F(k, t), exhibits markedly different relaxation dynamics at different length scales. At small wave numbers, we find the emergence of a step-like relaxation, indicating the presence of both fast and slow time scales in the system. Such behavior allows an intriguing analogy with temperature dependent relaxation dynamics of supercooled liquids. We find that solvation dynamics of a tagged ion exhibits a power law decay at long times-the decay can also be fitted to a stretched exponential form. The emergence of the power law in solvation dynamics has been tested by carrying out long Brownian dynamics simulations with varying ionic concentrations. The solvation time correlation and ion-ion intermediate scattering function indeed exhibit highly interesting, non-trivial dynamical behavior at intermediate to longer times that require further experimental and theoretical studies. (c) 2015 AIP Publishing LLC.