Long-Period Gratings in Planar Optical Waveguides

Our progress in the study of long-period gratings (LPGs) in planar optical waveguides is reviewed. In particular,experimental LPGs in glass and polymer waveguides are presented to demonstrate the potential of LPG-based waveguide devices.     

The stable set problem and the lift-and-project ranks of graphs

We study the lift-and-project procedures for solving combinatorial optimization problems, as described by Lovász and Schrijver, in the context of the stable set problem on graphs. We investigate how the procedures' performances change as we apply fundamental graph operations. We show that the odd subdivision of an edge and the subdivision of a star operations (as well as their common generalization, the stretching of a vertex operation) cannot decrease the N₀-, N-, or N₊-rank of the graph. We also provide graph classes (which contain the complete graphs) where these operations do not increase the N₀- or the N-rank. Hence we obtain the ranks for these graphs, and we also present some graph-minor like characterizations for them. Despite these properties we give examples showing that in general most of these operations can increase these ranks. Finally, we provide improved bounds for N₊-ranks of graphs in terms of the number of nodes in the graph and prove that the subdivision of an edge or cloning a vertex can increase the N₊-rank of a graph.Research of these authors was supported in part by a PREA from Ontario, Canada and research grants from NSERC.Mathematics Subject Classification (2000): 0C10, 90C22, 90C27, 47D20     

Epoxy/amine‐functionalized short‐length vapor‐grown carbon nanofiber composites

Short length vapor‐grown carbon nanofibers (VGCNFs) were functionalized with 4‐aminobenzoic acid in polyphosphoric acid/phosphorous phentoxide medium via “direct” Friedel‐Crafts acylation reaction to afford aminobenzoyl‐functionalized VGCNFs (AF‐VGCNFs). The AF‐VGCNFs as a cocuring agent were mixed with epoxy resin by simple mechanical stirring in methanol which was added to help efficient mixing. After evaporation of methanol, 4,4′‐methylenedianiline as a curing agent was added to the mixture, which was then cured at elevated temperatures. The resultant composites displayed uniform dispersion of AF‐VGCNFs into cured epoxy matrix. During curing process, the amine functionalities on AF‐VGCNF together with 4,4′‐methylenedianiline were expected to be involved in covalent attachment to the epoxy resin. As a result, both tensile modulus and strength of the composites were improved when compared with those of pure epoxy resin. Thus, the AF‐VGCNFs play a role as an outstanding functional additive, which could resolve both dispersion and interfacial adhesion issues at the same time by functionalization of VGCNFs and covalent bonding between the additive and matrix, respectively. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 7473–7482, 2008     

Polarization phase shifting shearography for optical metrological applications

We present here a different and modified configuration in order to obtain the curvature fringes by incorporating phase shifting and image processing techniques. Optical fibers are used for obtaining shear fringes in which we have used Wollaston prism as the shear element.     

Comparisons of TVD schemes for turbulent transonic projectile aerodynamics computations with a two-equation model of turbulence

The development of a computer program to solve the axisymmetric full Navier--Stokes equations with k-ε two-equation model of turbulence using various total variation diminishing (TVD) schemes is the primary interest of this study. The computations are performed for the turbulent, transonic, viscous flow over a projectile with/without supporting sting at zero angle of attack. The predicted results, as well as the convergence characteristics, by various TVD schemes are compared with each other. The results show that the TVD schemes of higher-order accuracy do have influence on the regions of high gradients such as shock, base corner and base flow. However, the schemes of third-order accuracy do not necessarily improve the agreement with measured data (which is not available on the base) than that of second-order accuracy, but surely generate apparent different result of base flow. The supporting sting on the projectile base will complicate the base flow and the existence of the sting will slightly shift the shock location and slightly change the flow field after the shock. More iteration steps are needed to get the converged results in the computation for the projectile with sting.     

High-resolution discrete absorption spectrum of alpha-methallyl free radical in the vapor phase

The alpha-methallyl free radical is formed in the flash photolysis of 3-methylbut-1-ene, and cis-pent-2-ene in the vapor phase, and then subsequent reactions have been investigated by kinetic spectroscopy and gas-liquid chromatography. The photolysis flash was of short duration and it was possible to follow the kinetics of the radicals' decay, which occurred predominantly by bimolecular recombination. The measured rate constant for the alpha-methallyl recombination was (3.5+/-0.3) x 10(10) mol(-1) ls(-1) at 295+/-2K. The absolute extinction coefficients of the alpha-methallyl radical are calculated from the optical densities of the absorption bands. Detailed analysis of related absorption bands and lifetime measurements in the original alpha-methallyl high-resolution discrete absorption spectrum image were also carried out by image processing techniques.     

Room-temperature ferromagnetism of Cu-doped ZnO films probed by soft X-ray magnetic circular dichroism

We report direct evidence of room-temperature ferromagnetic ordering in O-deficient ZnO:Cu films by using soft x-ray magnetic circular dichroism and x-ray absorption. Our measurements have revealed unambiguously two distinct features of Cu atoms associated with (i) magnetically ordered Cu ions present only in the oxygen-deficient samples and (ii) magnetically disordered regular Cu2+ ions present in all the samples. We find that a sufficient amount of both oxygen vacancies (V(O)) and Cu impurities is essential to the observed ferromagnetism, and a non-negligible portion of Cu impurities is uninvolved in the magnetic order. Based on first-principles calculations, we propose a microscopic "indirect double-exchange" model, in which alignments of localized large moments of Cu in the vicinity of the V(O) are mediated by the large-sized vacancy orbitals.     

Existence theorems and Hyers-Ulam stability for a class of Hybrid fractional differential equations with $p$-Laplacian operator

In this paper, we prove necessary conditions for existence and uniqueness of solution (EUS) as well Hyers-Ulam stability for a class of hybrid fractional differential equations (HFDEs) with $p$-Laplacian operator. For these aims, we take help from topological degree theory and Leray Schauder-type fixed point theorem. An example is provided to illustrate the results.     

Phase transformations and structural characteristics of AL–Cu–Co(–Si) decagonal phase

The phase transformations and structural characteristics of the Al-Cu-Co-Si alloy have been studied by neutron diffraction and high-resolution electron microscopy. The Al₆₅Cu_17.5Co_17.5 decagonal phase is stable in the temperature range between 973 K and 1350 K. At the low-temperature end, it relaxes to a microcrystalline approximant structure. At the high-temperature end, it melts directly into liquid. Two distinct orthorhombic phases are identified in the Al₆₃Cu_17.5Co_17.5Si₂ microcrystalline structure. They are composed of several structure units that can also construct the Penrose tiling. Because of lack of units, a single orthorhombic phase cannot undergo the transformation towards the high-temperature decagonal phase. An analysis of the orientation relationships between the CsCl and orthorhombic phases leads to the definition of Penrose tiling-like subnetworks inside the orthorhombic unit cells so that these orthorhombic phases can be regarded as the periodic patchworks of quasiperiodic subnetworks.     

Effect of Ethanol on the Partition Coefficient Of Cyclohexylacetate Between Bulk and Cetyltrjmethylammonium Bromide Micellar Pseudophases

Variation of the partition coefficient of cyclohexylacetate (CA) was studied by a differential absorption spectroscopic method as a function of ethanol and (CTAB) cetyltrimethylammoniumbromide concentrations. Approach used was based upon the pseudo-two phase model, including effect of ethanol concentrations on the critical micelle concentration (CMC) of CTAB. Ethanol enhanced micelle formation of CTAB at concentrations below 1% by volume, had a slight inhibitory effect at higher concentrations and totally inhibited at a concentration above 15% by volume.

Various amounts of ethanol were used with a purpose of changing the solubility of CA in water. The differential absorbance (AA), was almost zero at low concentrations of CTAB, however an increase in AA began at a certain concentration of CTAB which can accordingly be assumed to be consistent with CMC of CTAB in the presence of ethanol. As CTAB concentration increased above CMC, ΔA reached a plateau. In this plateau, ΔA can reasonably be interpreted as the saturation of CA in micellar phase.

Plateau values of ΔA decreased with increasing ethanol concentration. This showed that the fraction of CA in the micellar phase depended on the ethanol concentration in terms of changing the solubility. Partition coefficients, K_c, were obtained from the plots of 1/ΔA against 1/[C_CA] +[C³ _m], which were linear in high CTAB concentrations. It was also seen that as ΔA, K_c decreased when the ethanol percentage were increased. In other words, the lower the solubility of CA in the bulk, the higher the partition coefficient.