Multimode polarization degree of mixture optical states in integrated directional couplers

Mixture multimode optical field classical states propagating in N?×?N integrated directional couplers are analyzed by using the density matrix formalism in a N-dimensional optical space. These mutimode optical fields present a kind of generalized polarization and accordingly a definition of a multimode polarization degree is proposed. It is based on the distance measure between a mixture state and an unpolarized state in a N-dimensional optical space so that in the case N=2 the standard polarization degree is recovered. It is shown that directional couplers can reduce or increase remarkably the multimode polarization degree of a mixture state. Likewise a simple measurement technique, based on Y junctions, of this multimode polarization degree is proposed. Finally all the results can be formally extended to the special case of multimode single photon quantum states.     

Simultaneous measurement of normal force and electrical resistance during isothermal crystallization for carbon black filled high-density polyethylene

The kinetics of isothermal crystallization for high-density polyethylene (HDPE) containing different volume fraction (Φ) of carbon black (CB) have been evaluated by using differential scanning calorimetry (DSC) at 123, 124, and 125 °C where the rate of crystallization is moderate. Simultaneous measurement of normal force (F _N) and electrical resistance (R) has been performed to probe the process of isothermal crystallization at strain zero. Results reveal that, at the early stage of crystallization, F _N is almost independent of time (t) while relative resistance (R/R ₀) changes slightly with increasing time t. However, a significant increment in F _N and a remarkable change in R/R ₀ can be observed at the same critical time (t _c), and the value of t _c is dependent on the crystallization temperature and CB content, which is available for describing the isothermal crystallization as a characteristic parameter. It is found that t _c is greater than induction time of crystallization (t ₀) due to the less sensitivity of mechanical and electrical responses than enthalpy to the structural changes in the composites. It is suggested that mechanical and electrical simultaneous measurement endows us a novel approach to probing the formation of percolation network involving in crystallization of polymer matrix.     

Concurrent Cholesky factorization of positive definite banded Hermitian-matrices

First the Cholesky factorization is extended to cover uniformly partitioned banded positive definite matrices of rank n which may be real symmetric or Hermitian. Then two stratagems are given for the use of the algorithm in concurrent machines where the number of processing elements is less than required to factor the matrix in as few serial steps as possible, and where uniformly high efficiency is expected from all processing elements. Expressions are given for the efficiency factor e appearing in the speed-up expression g = eN, and these are specialized for the N node hypercube machine as a function of partition size s, the number N of processing elements of the hypercube machine, and the cost μ of interelement transmission relative to computation. It is shown that efficiency factor e is inversely proportional to μ/s, and that e is almost independent of N when N is large and μ/s = 0. The task is completed in n/s serial steps with no limit on n. The half bandwidth b of the matrix is 2Ns.     

Structure and photochromism of polyoxometalates nanoparticles in cross-linked polymer networks

Cross-linked polymer (P(VP-MB)) based on N-vinylpyrrolidone (VP) and N, N′-methylene-bis-acrylamide (MB) was used as polymer matrix to construct photochromic nanocomposite thin films with entrapping the Keggin-type polyoxometalates (POM). The microstructure, photochromic behavior, and mechanism of the films were studied with transmission electron microscopy (TEM), Fourier transform infrared spectroscopy (FT-IR), ultraviolet-visible spectra (UV-vis), and electron resonance spectra (ESR). The transparent films changed from colorless to blue under UV irradiation. The films showed good reversible photochromism and could recover the colorless state gradually in the air, where oxygen plays an important role during the bleaching process. The heteropolyanions dispersed in composite films uniformly and exhibited strong coulombic interaction with cross-linked polymer. Composite films contained molybdenum had higher photochromic efficiency and slower bleaching reaction than films contained tungsten. According to ESR, the photochromic mechanism was followed by charge-transfer happened between POM and cross-linked polymer.     

A fast solution method for three-dimensional many-particle problems of linear elasticity

A boundary element method for solving three-dimensional linear elasticity problems that involve a large number of particles embedded in a binder is introduced. The proposed method relies on an iterative solution strategy in which matrix–vector multiplication is performed with the fast multipole method. As a result the method is capable of solving problems with N unknowns using only 𝒪(N) memory and 𝒪(N) operations. Results are given for problems with hundreds of particles in which N=𝒪(10⁵). © 1998 John Wiley & Sons, Ltd.     

Evolution of an N-level system via automated vectorization of the Liouville equations and application to optically controlled polarization rotation

The Liouville equation governing the evolution of the density matrix for an atomic/molecular system is expressed in terms of a commutator between the density matrix and the Hamiltonian, along with terms that account for decay and redistribution. To find solutions of this equation, it is convenient first to reformulate the Liouville equation by defining a vector corresponding to the elements of the density operator, and determining the corresponding time-evolution matrix. For a system of N energy levels, the size of the evolution matrix is N^2?×^?N². When N is very large, evaluating the elements of these matrices becomes very cumbersome. We describe a novel algorithm that can produce the evolution matrix in an automated fashion for an arbitrary value of N. As a non-trivial example, we apply this algorithm to a 15-level atomic system used for producing optically controlled polarization rotation. We also point out how such a code can be extended for use in an atomic system with arbitrary number of energy levels.     

Synthesis, characterization and fluorescence property of CdS/P(N-iPAAm) nanocomposites

A novel nanocomposite in which CdS nanoparticles were embedded in poly(N-isopropylacrylamide) (P(N-iPAAm)) matrix have been fabricated. The particle size of CdS nanoparticles ranged from 10 nm to 40 nm could be adjusted with the varying of the inorganic contents. The nanocomposites have been characterized by X-ray diffraction (XRD), transmission electron microscope (TEM), thermo-gravimetric analysis (TGA), high resolution transmission electron microscope (HRTEM), UV-vis absorption and fluorescence spectra (FLS) measurements. The cell volume of CdS nanoparticles embedded in polymer matrix was smaller than the standard value and the nanocomposites with 12.0% inorganic content showed a good fluorescence property.     

n-Fold Polarization Measures and Associated Thermodynamic Entropy of N Partially Coherent Pencils of Radiation

An n-fold (n=2,…,N) measure of the degree of polarization associated with an N×N coherency matrix characterizing N pencils of radiation is discussed. The measure is cast in terms of the N possible scalar invariants of the coherency matrix and automatically takes into account possible rank deficiency. When N = 2, the single polarization measure reduces to the usual expression for polarization as the fraction of the intensity contained in the polarized component. The N = 3 case is discussed as an illustrative example, with special reference to the rank deficiency of a plane wave arbitrarily oriented with respect to the given coordinate system. Finally, these results are used to redevelop von Laue's theory of the thermodynamic entropy of partially coherent pencils of radiation.     

Solid-phase extractant with dipicolinic acid N,N’-diethyl-N,N’-di(p-tolyl)diamide for preconcentration and separation of actinides and lanthanides

The sorption ability of a solid-phase extractant with dipicolinic acid N,N’-diethyl-N,N’-di(p-tolyl) diamide groups on fibrous polyacrylonitrile (PAN) matrix was studied. The conditions for immobilization of the reagent on PAN disks were determined, and the possibility of sorption preconcentration and separation of U(VI), Pu(IV), Am(III), and Eu(III) from 2–6 M HNO₃ solutions was examined. The solid-phase extractant obtained exhibits good kinetic properties and can be used for separation of Am(III) + EU(III).     

Development and characterisation of SiAlON composites with TiB2, TiN, TiC and TiCN

30 vol% of TiB₂, TiCN, TiN or TiC was added to a sialon matrix with an X-phase sialon (Si₁₂Al₁₈O₃₉N₈) and an Al₂O₃–Si₃N₄ (77/23 wt%) starting powder composition and hot pressed at 1650°C in vacuum. The microstructures of the obtained composites were characterised by means of X-ray diffraction and electron microscopy, and the mechanical properties; E-modulus, hardness, bending strength and fracture toughness were measured and evaluated.Fully dense composites with an X-phase sialon or a polyphase Al₂O₃–-sialon–X-sialon matrix with 30 vol% of TiB₂, TiN and TiCN were obtained. TiC, added as a dispersed phase, however reacts with the nitrogen from the Si₃N₄ during liquid phase sintering, with the formation of TiC_1–x N _x , SiC and a changed sialon matrix composition. In the case of the X-phase sialon starting composition, a mullite matrix is obtained after sintering. The microstructural observations with respect to the sialon-TiC composites are found to be in agreement with the thermodynamic calculations.     

Preparation,characterization and photocatalytic properties of nanoplate Bi<Subscript>2</Subscript>MoO<Subscript>6</Subscript> catalysts

Bismuth molybdate (Bi₂MoO₆) nanoplates have been successfully synthesized by a simple hydrothermal process. The nanoplates were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), Raman spectroscopy, and IR spectroscopy. The effects of hydrothermal temperature and reaction time on the structures and morphologies of the nanoplates were investigated. On the basis of TEM observation of time series samples, a possible formation mechanism of the nanoplates was proposed. Optical absorption experiments revealed that Bi₂MoO₆ nanoplates had absorption in visible-light region, but a blue shift appeared compared with the corresponding bulk materials. Photocatalytic experiments showed that the nanoplates exhibited good photocatalytic activities for degradation of N,N,N′,N′-tetraethylated rhodamine (RhB) under visible-light irradiation (λ > 420 nm).     

Interfacial microstructure of Si3N4/Si3N4 brazing joint with Cu–Zn–Ti filler alloy

In this study, Si₃N₄ ceramic was jointed by a brazing technique with a Cu–Zn–Ti filler alloy. The interfacial microstructure between Si₃N₄ ceramic and filler alloy in the Si₃N₄/Si₃N₄ joint was observed and analyzed by using electron-probe microanalysis, X-ray diffraction and transmission electron microscopy. The results indicate that there are two reaction layers at the ceramic/filler interface in the joint, which was obtained by brazing at a temperature and holding time of 1223 K and 15 min, respectively. The layer nearby the Si₃N₄ ceramic is a TiN layer with an average grain size of 100 nm, and the layer nearby the filler alloy is a Ti₅Si₃N_x layer with an average grain size of 1–2 μm. Thickness of the TiN and Ti₅Si₃N_x layers is about 1 μm and 10 μm, respectively. The formation mechanism of the reaction layers was discussed. A model showing the microstructure from Si₃N₄ ceramic to filler alloy in the Si₃N₄/Si₃N₄ joint was provided as: Si₃N₄ ceramic/TiN reaction layer/Ti₅Si₃N_x reaction layer/Cu–Zn solution.     

Development of non-iterative self correcting solution (NONSS) method for the viscoplastic analysis with the Chaboche model

In a finite element program for the viscoplastic analysis with Chaboche model, the non-iterative and self-correcting solution (NONSS) method, proposed by Tanaka and Miller has been implemented. Towards this, the necessary Jocobian coefficients have been derived analytically for the sopisticated 23-parameter Chaboche viscoplastic model and finally the tangent modulus matrix D^* and the residual viscoplastic stress vector ξ^* have been obtained in order to determine the global tangent stiffness matrix as well as pseudo-load vector. The computational efficiency of this method is demonstrated by solving a variety of bench mark problems over a wide range of rate sensitivity domain under complex monotonic and cyclic loading histories relevant to fast breeder reactor applications. An improved Self-Adaptive Eulers Forward (SAEF) method is taken as the reference for comparision. © 1998 John Wiley & Sons, Ltd.     

A probabilistic theory for the strength of discontinuous fibre composites

The strength of discontinuous fibre-reinforced composites is often reduced due to local stress concentrations at large fibre-end-gaps. A theoretical prediction of the strength of unidirectional fibre composites is performed based upon a probabilistic model of the fibre configuration. This work further develops the concepts of Bader, Chou and Quigley, and Fukuda and Chou. A limiting case of the present analysis shows good agreement with the results of Smith. Emphases are placed on the effect of matrix stress transfer properties including matrix plasticity. For a matrix deforming elastically, the strength is reduced as the composite size (N) increases. As compared with the rule-of-mixtures prediction for continuous fibre composites with identical fibre volume fraction, the reduction is shown to be proportional to (In N)^–P , with the exponent P being between 0.5 and 1 for two-dimensional composites and between 0.25 and 0.5 for three-dimensional composites. For a matrix deforming plastically, the local stress concentrations are reduced. Based upon the analytical expression of the local load sharing rule for a plastically deformed matrix, the composite strength is shown to approach the modified rule-of-mixtures of Kelly and Tyson as the matrix yield stress decreases.This work was done on leave from Applied Mechanics Section, Central Research Laboratories, Sumitomo Metal Industries, Ltd., Nishinagasuhumdori, Amagasaki, Japan.     

Algorithms for direct-access gaussian solution of structural stiffness matrix equation

Based on direct-access programming, algorithms have been developed for the generation, and solution by Gaussian elimination of the structural stiffness matrix equation resulted from application of the finite element method in engineering analyses. A large disk storage is used to store the rows of the stiffness matrix as directly accessible records. The developed algorithm BAND2R requires only 2N_b in-core words in implementing the Gaussian elimination where N_b is the semi-band width of the stiffness matrix. Algorithms BANDSQ and BDSQMX are presented which require N²_b in-core words but minimize the number of retrieving and restoring the direct-access records during the Gaussian elimination. BANDSQ has the direct-access feature in both the elimination and backward-substitution steps whereas BDSQMX has the direct-access feature only in the backward-substitution step of the Gaussian elimination. Illustrative applications of the developed algorithms are given and the computer core and time requirements for BAND2R, BANDSQ and BDSQMX are compared to those for the conventional Gaussian elimination of using sequential, in-core storages. Methods for reducing the semi-band width N_b of the structural stiffness matrix are also discussed.     

A New Class of Supersaturated Designs

Supersaturated designs are useful in situations in which the number of active factors is very small compared to the total number of factors being considered. In this article, a new class of supersaturated designs is constructed using half fractions of Hadamard matrices. When a Hadamard matrix of order N is used, such a design can investigate up to N – 2 factors in N/2 runs. Results are given for N ≤ 60. Extension to larger N is straightforward. These designs are superior to other existing supersaturated designs and are easy to construct. An example with real data is used to illustrate the ideas.     

Carbon fibre-reinforced silicon nitride composite

The processing of silicon nitride reinforced with carbon fibre was studied. The problems of physical and chemical incompatibility between carbon fibre and the silicon nitride matrix were solved by addition of a small amount of zirconia to the matrix and by low-temperature hot-pressing. The composite material possesses a much higher toughness than hot-pressed silicon nitride. Its work of fracture increased from 19.3 J m^–2 for unreinforced Si₃N₄, to 4770 J m^–2; its fracture toughness,K _lc , increased from 3.7 MN m^–3/2 for unreinforced material, to 15.6 MN m^–3/2. The strength remains about the same as unreinforced Si₃N₄ and the thermal expansion coefficient is only 2.51×10^–6 ° C^–1 (RT to 1000° C). It is anticipated that this composite may be promising because of its mechanical and good thermal shock-resistance properties.     

Impedance spectroscopy measurements of charge carrier mobility in 4,4'-N,N'-dicarbazole-biphenyl thin films doped with tris(2-phenylpyridine) iridium

The charge carrier mobility of green phosphorescent emissive layers, tris(2-phenylpyridine) iridium [Ir(ppy)₃]-doped 4,4'-N,N'-dicarbazole-biphenyl (CBP) thin films, has been determined using impedance spectroscopy (IS) measurements. The theoretical basis of mobility measurement by IS rests on a theory for single-injection space-charge limited current. The hole mobilities of the Ir(ppy)₃-doped CBP thin films were measured to be 10^− 10–10^− 8 cm²V^− 1 s^− 1 in the 2–7 wt.% Ir(ppy)₃-doped CBP from the frequency dependence of both conductance and capacitance. These hole mobility values are much lower than those of the undoped CBP thin films (~ 10^− 3 cm²V^− 1 s^− 1) because the Ir(ppy)₃ molecules act as trapping centers in the CBP host matrix. These mobility measurements in the Ir(ppy)₃-doped CBP thin films provide insight into the hole injection process.     

Computational and electrochemical studies on the inhibition of corrosion of mild steel by <Emphasis Type="SmallCaps">l</Emphasis>-Cysteine and its derivatives

This article presents the investigation of l-Cysteine (CYS) and its derivatives including N-Acetyl-l-Cysteine (NACYS), N-Acetyl-S-Benzyl-l-Cysteine (NASBCYS), and N-Acetyl-S-Hexyl-l-Cysteine (NASHCYS) as green chemical corrosion inhibitors for mild steel in 1 M HCl solutions. Weight loss method and Tafel polarization measurement were performed to determine the corrosion parameters and inhibition efficiencies. Experimental results showed that these compounds suppressed both anodic and cathodic reactions, and the inhibition efficiency of the four inhibitors followed the order NASBCYS > NASHCYS > NACYS > CYS. In order to further study the corrosion mechanisms, quantum chemical calculation and molecular dynamics method were applied. The relationships between quantum chemical parameters and corrosion inhibition efficiency were discussed. Molecular dynamics method was used to simulate the adsorption behavior of each inhibitor in solvent. The results showed that these four inhibitors can adsorb on mild steel surface by donor acceptor interactions between lone-pair electrons of heteroatoms/π-electrons of aromatic ring and vacant d-orbital of iron.     

Synthesis of nanometric-size magnesium nitride by the nitriding of pre-activated magnesium powder

Magnesium nitride (Mg₃N₂) was synthesized by the reaction of magnesium in the highly reactive form (Mg^*) with nitrogen at 450°C under normal pressure. The effect of doping with nickel dichloride on the nitridation of Mg^* was investigated. Differential thermal analysis (DTA) of Mg^* systems and transmission electron microscopy (TEM) measurement of the product formed were carried out. TEM measurement showed that the particle size of the Mg₃N₂ synthesized was in the nanometric range. The dependence of nitridation of the NiCl₂-doped Mg^* on temperature was investigated at temperatures ranging from 300 to 500°C. The nitridation of NiCl₂-doped Mg^* could occur even at temperature as low as 300°C.