On the stability of some second order numerical methods for weak approximation of Itô SDEs

In this paper, we first investigate the stability of two weak second order methods introduced by Debrabant and Rößler (Appl Numer Math 59:582–594, 2009) and Platen (Math Comput Simulation 38:69–76, 1995). We then propose a new weak second order predictor-corrector method, with an improved stability properties, based on the Rößler’s method as the predictor and the implicit method of Platen as the corrector. The stability functions of these methods, applied to a scalar linear test equation with multiplicative noise, are determined and their regions of stability are then compared with the corresponding stability regions of the test equation. Furthermore, we also investigate mean square stability (MS-stability) of these methods applied to a linear Itô 2-dimensional stochastic differential test equation. Numerical examples will be presented to support the theoretical results.     

Ultrafast three-photon counting in a photomultiplier tube

We demonstrate experimentally ultrafast three-photon counting by three-photon absorption in a GaAsP photomultiplier tube at the wavelength range of 1800-1900?nm, and analyze its sensitivity and time response. Pulse energy of ～500?fJ is shown to be detectable for ultrafast 170?fs pulses. The presented three-photon counter may serve as a unique tool for ultrafast quantum state characterization as well as for ultrasensitive third-order temporal measurements.     

Porous electrolyte-supported tubular micro-SOFC design

Due to the poor redox cycling resistance of the second generation of μ-SOFCs, a new generation of SOFC has been recently developed using a porous electrolyte-supported structure to overcome this problem. In this research, the porous structure was successfully fabricated with slip casting using calcined YSZ (ZrO₂ + 8 mol% Y₂O₃) with or without graphite as a pore former. Calcination of YSZ powder at 1300-1500 °C prior to making the slip leads to growth of YSZ crystals and particle size which results in a decrease in surface area and powder sinterability. This was found to be an important criterion in developing the porous structure as, due to the high sinterability of non-calcined YSZ, even the addition of graphite is inadequate to generate sufficient open porosity. A dense YSZ electrolyte layer was immediately coated on the porous structure using YSZ calcined at 1300 °C with a sequential slip casting method. Sample thickness was found to be a function of both graphite content as well as YSZ calcination temperature. Physical properties of the porous YSZ supports and SEM analysis of the support and coated electrolyte are presented.     

Studies of fractal growth patterns in poly (ethylene oxide) and chitosan membranes

Polymer electrolyte membranes containing various weight percent of salt have been prepared in the authors’ laboratory for the study of their potential applications in solid state electrochemical devices; however, the polymer electrolyte membranes were found to become sort of media for fractal growth, months after they were prepared. Fractal growth patterns in polymer membranes of poly (ethylene oxide) and chitosan membranes have been analyzed, and their fractal dimensions were determined. A diffusion-limited aggregate model which is based on the Brownian motion theory is applied to simulate the experimentally obtained fractal patterns. The approach was extended by performing computer simulations with computing resources available. The fractal dimension values of the simulated and the experimentally obtained original fractal patterns were marginally close. This indicates that the simulation work has successfully produced fractal patterns that are in fairly acceptable conformity with the fractal patterns observed in the polymer membranes.     

Excitonic effects of bilayer graphene: A simple approach

The present work investigates the excitonic effects on the bilayer graphene with layers of different thickness under the influence of external electric field through a simple numerical approach. The band structure and energy gap have been calculated using a tight-binding model including parameters like the second-nearest-neighbor-hopping energies t′ (in-plane) and γ (intra-layer) and the on-site energy Δ, in details. The binding energy of exciton for bilayer graphene has been calculated by Wannier model and Hartree–Fock approximation through the Bethe–Salpeter equation. Finally the optical conductivity spectrum of bilayer graphene has been calculated by using the effective mass approximation in two band model.     

Theoretical study on the molecular tautomerism of the 3-hydroxy-pyridin-4-one system

3-hydroxy-pyridin-4-one is a parent molecule for the family of hydroxypyridinones that are known in coordination chemistry as efficient metal ions chelators. In this work, relative stabilities of some possible tautomers were investigated using several quantum chemical methods: CBS (complete basis set methods), Gn, DFT (density functional theory), Hartree–Fock and MP2. Performed calculations show that the system under consideration exists as a mixture of two tautomers with comparable energies. Among them, the hydroxypyridinone structure of the studied molecular system seems to be a bit more stable than the o-dihydroxypyridine one, by a few kJ/mol only. Aromaticity and intra-molecular hydrogen bonding are the main effects influencing the stability of the studied tautomeric structures. Consequently, aromatic effects were calculated using several indices of aromaticity: HOMA (harmonic oscillator model of aromaticity), NICS (nucleus independent chemical shift), H, PDI (para delocalisation index), MCI (multi-centre index) and ASE (aromatic stabilisation energy). The strength of possible intra-molecular hydrogen bonds (H-bonds) was determined by means of the AIM (atoms-in-molecules) method and by calculating enthalpies for theoretical reactions that do or do not involve H-bonds. The AIM method was employed to understand how variations in atomic energies influence the stability of different tautomeric structures.     

Entropy as a measure of diffusion

The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large times the entropy tends exponentially to a constant. For systems with no stationary density, at large times the entropy is logarithmic with a coefficient specifying the speed of the diffusion. As an example, the large-time behaviors of the entropy and the variance are compared for various types of fractional-derivative diffusions.     

Comparison of quasi-steady-state and unsteady-state formulations in a freeze dryer modeling

An unsteady-state model is developed for primary and secondary stages of freeze drying process of skim milk. The results are compared with those obtained from a quasi-steady-state (QSS) formulation. The QSS formulation is not valid where the applied heat load is high. The applied heat load affects on the drying time the most compared to other parameters like chamber pressure and the radiation surface temperature.     

Thermal and Mechanical Properties of Ultra High Molecular Weight Polyethylene Fiber Reinforced High-Density Polyethylene Homocomposites: Effect of Processing Condition and Nanoclay Addition

A new method to prepare single-polymer high-density (HDPE)-ultra high molecular weight polyethylene (UHMWPE) fiber (PE-PE homocomposites) composed and also PE-PE homocomposites containing HDPE organo montmorillonite clay (OMMT) nanocomposites as a matrix (PE nanohomocomposites) was used. Owing to the major importance of fiber impregnation by the matrix and its effect on the adhesion of matrix/fiber and, consequently, the mechanical properties of the composite, a combination of powder impregnation and film stacking methods, utilizing compression molding, were used for manufacturing the PE-PE homocomposites and PE nanohomocomposites. In addition, PE nanohomocomposites with the matrix containing different amounts of nanoclay were prepared to investigate the effect of the clay on the interfacial and mechanical properties of the PE-PE nanohomocomposites. Several different processing conditions were examined to determine the best conditions for manufacturing of the PE-PE homocomposite and PE nanohomocomposites and it was concluded that 40 bar and 10 min of compression molding resulted in the highest overall mechanical properties. The PE-PE homocomposites and PE-PE nanohomocomposites showed identical trends for the relationship between the effects of processing conditions and mechanical properties. Mechanical results demonstrated that clay platelets could increase the interfacial strength by improving physical entanglements between fiber and matrix through better cocrystallization.     

A novel four-component reaction for the synthesis of disubstituted 1,3,4-oxadiazole derivatives

The 1:1 imine intermediate generated by the addition of benzyl amine to cyclobutanone is trapped by (N-isocyanimino)triphenylphosphorane in the presence of an aromatic carboxylic acid leads to the formation of the corresponding iminophosphorane intermediate. Disubstituted 1,3,4-oxadiazole derivatives are formed via intramolecular aza-Wittig reaction of the iminophosphorane intermediate. The reactions were completed in neutral conditions at room temperature. The disubstituted 1,3,4-oxadiazole derivatives, were produced in excellent yields.