Stability estimates for h-p spectral element methods for elliptic problems

In a series of papers of which this is the first we study how to solve elliptic problems on polygonal domains using spectral methods on parallel computers. To overcome the singularities that arise in a neighborhood of the corners we use a geometrical mesh. With this mesh we seek a solution which minimizes a weighted squared norm of the residuals in the partial differential equation and a fractional Sobolev norm of the residuals in the boundary conditions and enforce continuity by adding a term which measures the jump in the function and its derivatives at inter-element boundaries, in an appropriate fractional Sobolev norm, to the functional being minimized. Since the second derivatives of the actual solution are not square integrable in a neighborhood of the corners we have to multiply the residuals in the partial differential equation by an appropriate power of r_k, where r_k measures the distance between the pointP and the vertexA _k in a sectoral neighborhood of each of these vertices. In each of these sectoral neighborhoods we use a local coordinate system (τ_k, θ_k) where τ_k = lnr_k and (r_k, θ_k) are polar coordinates with origin at A_k, as first proposed by Kondratiev. We then derive differentiability estimates with respect to these new variables and a stability estimate for the functional we minimize. In [6] we will show that we can use the stability estimate to obtain parallel preconditioners and error estimates for the solution of the minimization problem which are nearly optimal as the condition number of the preconditioned system is polylogarithmic inN, the number of processors and the number of degrees of freedom in each variable on each element. Moreover if the data is analytic then the error is exponentially small inN.     

Spectrophotometric determination of thermal transition of polymeric systems using photochromic probes

Mercury-dithizone complex both free and bonded to a polymeric system has been synthesized and used to measure the thermal transition of polystyrene, poly(vinyl acetate), and some other polymers. The thermal relaxation rate of the activated complex in dark has been found to be dependent on the free volume of a polymer matrix. The rate goes through a maximum above T_g of a polymer. A very sensitive method, based on thermal recovery of activated photochromic probe chromophore has been devised to measure the thermal transition of both single and multicomponent polymer matrices. © 1995 John Wiley & Sons, Inc.     

Condensation of self-assembled lyotropic chromonic liquid crystal sunset yellow in aqueous solutions crowded with polyethylene glycol and doped with salt

We use optical and fluorescence microscopy, densitometry, cryo-transmission electron microscopy (cryo-TEM), spectroscopy, and synchrotron X-ray scattering to study the phase behavior of the reversible self-assembled chromonic aggregates of an anionic dye Sunset Yellow (SSY) in aqueous solutions crowded with an electrically neutral polymer polyethylene glycol (PEG) and doped with the salt NaCl. PEG causes the isotropic SSY solutions to condense into a liquid-crystalline region with a high concentration of SSY aggregates, coexisting with a PEG-rich isotropic (I) region. PEG added to the homogeneous nematic (N) phase causes separation into the coexisting N and I domains; the SSY concentration in the N domains is higher than the original concentration of PEG-free N phase. Finally, addition of PEG to the highly concentrated homogeneous N phase causes separation into the coexisting columnar hexagonal (C) phase and I phase. This behavior can be qualitatively explained by the depletion (excluded volume) effects that act at two different levels: at the level of aggregate assembly from monomers and short aggregates and at the level of interaggregate packing. We also show a strong effect of a monovalent salt NaCl on phase diagrams that is different for high and low concentrations of SSY. Upon the addition of salt, dilute I solutions of SSY show appearance of the condensed N domains, but the highly concentrated C phase transforms into a coexisting I and N domains. We suggest that the salt-induced screening of electric charges at the surface of chromonic aggregates leads to two different effects: (a) increase of the scission energy and the contour length of aggregates and (b) decrease of the persistence length of SSY aggregates.     

Direct observation of diffuse cone behavior in de Vries smectic-A and -C phases of organosiloxane mesogens

Simultaneous and direct x-ray measurements of the smectic layer spacing, molecular tilt, and orientational order in the de Vries smectic A (SmA) and C (SmC) phases of two organosiloxane mesogens reveal that (i) the SmC (tilt) order parameter exponent β=0.26±0.01 for 2nd order SmA-SmC transition--in excellent agreement with the tricritical behavior, (ii) the siloxane and hydrocarbon parts of the molecules are segregated and oriented parallel to the director with very different degree of orientational order, and (iii) thermal evolution of the effective molecular length is different in the two phases.     

Nanonails structured ferric oxide thick film as room temperature liquefied petroleum gas (LPG) sensor

In the present work, ferric oxide nanonails were prepared by screen printing method on borosilicate glass substrate and their electrical and LPG sensing properties were investigated. The structural and morphological characterizations of the material were analyzed by means of X-ray diffraction (XRD) and Scanning electron microscopy (SEM). XRD pattern revealed crystalline α-phase and rhombohedral crystal structure. SEM images show nanonails type of morphology throughout the surface. Optical characterization of the film was carried out by UV-visible spectrophotometer. By Tauc plot the estimated value of band gap of film was found 3.85 eV. The LPG sensing properties of the ferric oxide film were investigated at room temperature for different vol.% of LPG. The variations in electrical resistance of the film were measured with the exposure of LPG as a function of time. The maximum values of sensitivity and sensor response factors were found 51 and 50 respectively for 2 vol.% of LPG. The activation energy calculated from Arrhenius plot was found 0.95 eV. The response and recovery time of sensing film were found ∼120 s and 150 s respectively. These experimental results show that nanonails structured ferric oxide is a promising material as LPG sensor.     

X‐ray diffraction from the uniaxial and biaxial nematic phases of bent‐core mesogens

X‐ray diffraction patterns for the uniaxial and biaxial nematic phases exhibited by rigid bent‐core mesogens were calculated using a simple model for the molecular form factor and a modified Lorentzian structure factor. The X‐ray diffraction patterns depend strongly on the extent of the alignment of the molecular axes as well as the orientation of molecular planes. The X‐ray diffraction can be unequivocally used to identify the biaxial nematic phase, study the uniaxial–biaxial phase transition, and estimate the order parameters of the nematic phase.     

Anisotropic surface morphology of azopolymer films generated by polarized UV light irradiation

X-ray reflectivity measurements reveal anisotropy of the vertical surface roughness caused by exposure to linearly polarized UV (LPUV) light in the films of two azopolymers. The irradiated surface is found to have higher roughness in the direction parallel to the direction of polarization than in the orthogonal direction. The photo-modification of the surface morphology is caused by spatial changes induced in polymer films by LPUV irradiation. The important role of surface roughness anisotropy in determining the alignment of liquid crystals is discussed.     

1,4‐Bis((1H‐pyrrol‐2‐yl)methylene)thiosemicarbazide Complexes of Zn(II), Cd(II) and Hg(II): Single Source Precursor in Thermal Synthesis of Nanoparticle

Six complexes of Zn(II), Cd(II) and Hg(II) with sulphur containing Schiff base ligand, 1,4‐bis((1H‐pyrrol‐2‐yl)methylene)thiosemicarbazide in 1:1 and 1:2 ratio has been synthesized. Complexes were characterized by molar conductance measurement, elemental analyses, FT‐IR, ¹H‐NMR, and FAB/ESI‐Mass. The complexes were used as a single source precursor for the synthesis of ZnS/CdS/HgS nanoparticles by their thermal decomposition in the presence of different surfactants. The precursor: surfactant ratio and temperature plays important role in determining the size of the nanoparticles. The size and morphology of nanoparticles has been ascertained by UV‐Vis spectroscopy, XRD measurements and Transmission Electron Microscopy (TEM). Schiff base, complexes and nanoparticles were tested for antibacterial activity and MIC values against E. coli. The complexes were found more potent than the corresponding Schiff bases and nanoparticles.     

I2-DMSO-Mediated Cascade Cyclization of β-Ketosulfoxonium Ylides and β-Enaminones: Synthesis of Quaternary-Carbon-Centered 2-Hydroxy-pyrrol-3(2H)-ones

A novel I₂-DMSO-mediated cascade cyclization approach for synthesizing 2-hydroxy-pyrrol-3(2H)-one scaffold from readily accessible β-ketosulfoxonium ylides and β-enaminone derivatives has been developed. Under metal-free and mild conditions, this cascade transformation facilitates the formation of one C−C bond and one C−N bond in a single reaction vessel, exhibiting a wide range of functional group compatibility. In addition, this method added an active hydroxyl group to a quaternary carbon center.     

The effectiveness of manufacturer vs. retailer rebates within a newsvendor framework

This paper studies the impact of direct rebates to the end customer from the manufacturer and/or from the retailer upon the profitability and effectiveness of the policies of both channels. Effectiveness is measured by the ratio of the retailer’s to the manufacturer’s profits and by the sum of the profits for the two parties across scenarios wherein at least one of the parties offers a rebate. The main result is to prove analytically the conditions under which either all three scenarios are equally profitable or the retailer-only rebate policy is dominant. Another important result is to illustrate the likelihood that the manufacturer is able to coordinate the supply chain, by the appropriate choice of its pricing and rebate policies, thereby inducing the retailer to do likewise with its associated best pricing, ordering and rebate policies. Finally, numerical examples highlight the main features of the paper.