A superconvergent local discontinuous Galerkin method for nonlinear two-point boundary-value problems

In this paper, we present and analyze a superconvergent and high order accurate local discontinuous Galerkin (LDG) method for nonlinear two-point boundary-value problems (BVPs) of the form u ^″ = f (t, u), which arise in a wide variety of engineering applications. We prove the L ² stability of the LDG scheme and optimal L ² error estimates for the solution and for the auxiliary variable that approximates the first-order derivative. The order of convergence is proved to be p +?1, when piecewise polynomials of degree at most p are used. Our numerical experiments demonstrate optimal rates of convergence. Moreover, we show that the derivatives of the LDG solutions are superconvergent with order p +?1 toward the derivatives of Gausss-Radau projections of the exact solutions. Finally, we prove that the LDG solutions are superconvergent with order p +?3/2 toward Gauss-Radau projections of the exact solutions. Our computational results indicate that the observed numerical superconvergence rate is p +?2. Our proofs are valid for arbitrary regular meshes using piecewise polynomials of degree p ≥?1 and for the periodic, Dirichlet, and mixed boundary conditions. All proofs are valid under the hypotheses of the existence and uniqueness theorem for BVPs. Several numerical results are presented to validate the theoretical results.     

Structure and Mechanical Properties of 50/50 NR/SBR Blend/Pristine Clay Nanocomposites

A blend/clay nanocomposites of 50/50 (wt%) NR/SBR was prepared via mixing the latex of a 50/50 NR/SBR blend with an aqueous clay dispersion and co‐coagulating the mixture. The structure of the nanocomposite was characterized by transmission electron microscopy (TEM) and X-ray diffraction (XRD). Nanocomposites containing less than 10 phr clay showed a fully exfoliated structure. After increasing the clay content to 10 phr, both nonexfoliated (stacked layers) and exfoliated structures were observed in the nanocomposites. The results of mechanical tests showed that the nanocomposites presented better mechanical properties than clay‐free NR/SBR blend vulcanizate. Furthermore, tensile strength, tensile strain at break, and hardness (shore A) increased with increasing clay content, up to 6 phr, and then remained almost constant.     

Comparisons of mixed systems with decreasing failure rate component lifetimes using dispersive order

Because lifetimes of systems are not deterministic, partially, orders are used for comparison purposes which lead us to provide optimal system configurations. This paper deals with a signature‐based dispersive ordering of mixed systems. It is assumed that component lifetimes are independent and identically distributed, and the common distribution has a decreasing failure rate function. Some illustrative examples are also given.     

Influence of the pumping scheme in double-pass discrete Raman-fiber amplifiers

We demonstrate the effect of the pumping scheme in a double-pass discrete Raman-fiber amplifier. The copumping scheme outperforms the counterpumping scheme for small and medium signal power ranges. The performance discrepancy of about 0.3 dB is measured. However, the counterpumping scheme performs better than that of the copumping scheme for large signal powers. These effects are influenced by the pump distribution along the fiber-amplifying medium. The pump-depletion effect is found to be the main cause of the performance discrepancy between these two pumping schemes. These findings can be utilized as the guidelines in designing double-pass discrete Raman-fiber amplifiers.     

Fractality feature in incompressible three-dimensional magnetohydrodynamic turbulence

Direct Numerical Simulation (DNS) of decaying isotropic 3D magnetohydrodynamic (MHD) turbulence based on the 10243-modes in a periodic box is used to study the statistical properties of turbulence. In this paper, the presence of intermittency in MHD turbulence is investigated through the analysis of the Probability Distribution Function (PDF) for Elsässer fields and total energy fluctuations. We observe that the PDFs of the Elsässer fields fluctuations display a strong non-Gaussian behavior at small scale, which can be ascribed to multifractality feature, while the PDFs of the total energy fluctuations have the same shape over all observed scales and are monofractal. The PDFs have stretched exponential tail and satisfy the function P(|δX|) ～ exp(?A|δX| ^μ ). Numerically, we extract the exponent μ and find that it is constant for monofractal behavior as the length scale varies. To check the notion of self-similarity in the respective fluctuation, we apply the compensated structure functions.     

High-gain erbium-doped fiber amplifier incorporating a double-pass amplification technique as a preamplifier

We present a high-gain erbium-doped fiber amplifier to be utilized as a preamplifier. A double-pass amplification technique is used in the first-stage amplifier together with a tunable bandpass filter. The secondstage amplifier is a counter-pumped configuration and another tunable bandpass filter is utilized to filter out amplified spontaneous emission from the first-stage amplifier. This design is able to produce a high gain of 55.6 dB and a noise figure of 6.02 dB at 1530 nm with a signal power of ?45 dBm. The receiver sensitivity measurement shows that the proposed amplifier improves the minimum detectable power from ?33.7 to ?40.8 dBm for a bit-error rate of 10^?11 at 155 Mbps.

     

Phase Formation Studies of Lead(II) Copper(II) Oxotellurates: The Crystal Structures of Dimorphic PbCuTeO5, PbCuTe2O6, and [Pb2Cu2(Te4O11)](NO3)2

Two modifications of the oxotellurate(VI) PbCuTeO₅ were isolated as single crystals from product mixtures obtained from solid state reactions, whereas single crystals of the oxotellurates(IV) PbCuTe₂O₆ and [Pb₂Cu₂(Te₄O₁₁)](NO₃)₂ were grown under hydrothermal conditions. The crystal structures of all compounds comprise of characteristic coordination polyhedra, viz. nearly square [CuO₄] plaquettes for divalent copper, octahedral [TeO₆] units for hexavalent tellurium, trigonal‐pyramidal [TeO₃] and bisphenoidal [TeO₄] groups for tetravalent tellurium, and distorted [PbO_x] polyhedra for divalent lead. PbCuTeO₅ is dimorphic and crystallizes in a monoclinic and a triclinic modification, related by a translationengleiche group‐subgroup relation of index 2. PbCuTe₂O₆ represents the ideal composition of the rare mineral choloalite. The characteristic feature of the crystal structure of [Pb₂Cu₂(Te₄O₁₁)](NO₃)₂ is its layered set‐up, comprised of cationic [Pb₂Cu₂(Te₄O₁₁)]²⁺ ribbons (width approximately 6.7 Å) sandwiched between nitrate anions that are only weakly bound to the cationic layers.     

Hydrogen-bonded LC nanocomposites: characterisation of nanoparticle-LC interactions by solid-state NMR and FTIR spectroscopies

Although the molecular-level nanoparticle-liquid crystal (NP-LC) interactions are key for forming stable NP dispersions in LC, characterisation of these interactions is scarce in the literature. Recently, we have developed hydrogen-bonded LC nanocomposites based on mesogenic carboxylic acids and NPs functionalised with hydrogen-bond acceptor/donor groups. Here, we apply solid-state ¹H and ¹³C NMR and Fourier transform infrared spectroscopies to model systems consisting of mixtures of trans-4-n-butylcyclohexanecarboxylic acid (4-BCHA), 4-hexylbenzoic acid (6BA) and 4,4?-bipyridine. The binary mixture, 4-BCHA:6BA, was also studied. The results were compared to monolayer quantities of 6BA and 4-BCHA adsorbed on pyridine functionalised zirconia NPs (ZrO₂-n₃-pyridine) to understand the different effects of the functionalised NPs on the LC properties.