Numerical solution of reaction–diffusion equations by compact operators and modified equation methods

A system of reaction–diffusion equations which governs the propagation of an ozone decomposition laminar flame in Lagrangian co-ordinates is analysed by means of compact operators and modified equation methods. It is shown that the use of fourth-order accurate compact operators yields very accurate solutions if sufficient numbers of grid points are located at the flame front, where very steep gradients of temperature and species concentrations exist. Modified equation methods are shown to impose a restriction on the time step under certain conditions. The solutions obtained by means of compact operators and modified equation methods are compared with solutions obtained by other methods; good agreement is obtained.     

Electric field gradient in nanostructured SnO2 studied by means of PAC spectroscopy using 111Cd or 181Ta as probe nuclei

Electric quadrupole interactions were studied in pure and Mn-doped powder samples and thin films of SnO₂ using perturbed γγ angular correlation spectroscopy (PAC). The powder samples were prepared by Sol gel method and the thin film were prepared on the Si (100) substrate by sputtering technique using Sn in the oxygen atmosphere. The samples were characterized by x-ray diffraction, energy dispersive spectroscopy and scanning electron microscopy. The thickness of the film was 100 nm. The average particle size of the SnO₂ powder samples was determined to be smaller than 60 nm. The radioactive ¹¹¹In and ¹⁸¹Hf tracers were introduced in the powder samples during the sol gel chemical process. Radioactive ¹¹¹In was implanted on the SnO₂ thin films using the University of Bonn ion implanter (BONIS). PAC measurements were carried out in a four BaF₂ detector spectrometer in the temperature range of 77–973 K for samples annealed at different temperatures. The PAC results for both nuclear probes show the presence of two electric quadrupole interactions. The major fractions in both cases correspond to the substitutional sites in the rutile phase of SnO₂. The results are compared with previous PAC measurements.     

An integrated experimental and theoretical investigation of the vibrational modes and molecular structure of a new Cu(II)–phosphocreatine complex

A new complex of Cu(II) of stoichiometry [Cu(PCr)(H₂O)] was prepared from aqueous solution at pH 6. Its synthesis, characterization, thermogravimetric, vibrational spectroscopy, and electron paramagnetic resonance analyses were described and suggest that phosphocreatine (PCr) in solid state is acting as a tridentate ligand (the nitrogen atom of the guanidine group and the oxygen atoms of the phosphate group and the carboxylate group being the donor atoms). The fourth position is occupied by a water molecule. These results were confirmed through computational calculations (DFT/B3LYP:6-311G theoretical procedure). The tetra coordination of Cu(II) arranged in a quadratic planar geometry was found to be more stable in the DFT calculations. The calculated vibrational spectrum agrees well with the FT-IR experimental spectrum.     

Recovering risk-neutral probability density functions from options prices using cubic splines and ensuring nonnegativity

We present a new approach to estimate the risk-neutral probability density function (pdf) of the future prices of an underlying asset from the prices of options written on the asset. The estimation is carried out in the space of cubic spline functions, yielding appropriate smoothness. The resulting optimization problem, used to invert the data and determine the corresponding density function, is a convex quadratic or semidefinite programming problem, depending on the formulation. Both of these problems can be efficiently solved by numerical optimization software.     

Factors affecting interaction of radiocesium with freshwater solids

The paper aims at the analysis of principal factors affecting the interaction of radiocesium with freshwater solids, important for the migration of radiocesium in rivers. Uptake of radiocesium by bottom sediments and suspended solids from small streams was studied as a function of pH and composition of aqueous phase, of the concentration of cesium in water and of the composition of freshwater solids, using laboratory model experiments. pH had negligible effect on the uptake in the pH range 5–9, the uptake decreased at pH values less than 3–5 depending on the nature and concentration of the solids. Addition of cations suppressed the uptake in the order K⁺>Na⁺>Ca²⁺, the suppression began at 0.001, 0.01 and 0.1 mol.dm^?3 concentration, respectively. Increase in cesium concentration in water caused a decrease of radiocesium uptake, but at very low concentrations of cesium combined with higher concentration of sediment (2g·dm^?3) the uptake was independent of cesium concentration. Removal of carbonates, oxidic coatings and organic matter from a sediment did not affect the sorption properties of the sediment. The nature of the effects found confirms that cesium is sorbed mainly by clay components of freshwater solids. Results obtained are compared with literature data and conclusions are drawn on the importance of the factors studied for modelling of radiocesium migration in rivers.     

Correlation between nanohole volume and mechanical properties of amine‐cured epoxy resin blended with poly(ethylene oxide)

A set of diglycidylether of bisphenol‐A (DGEBA)/4,4′‐diaminodiphenylmethane (DDM) epoxy matrix modified with poly(ethylene oxide) (PEO), pre‐cured at two different temperatures, was examined by positron annihilation lifetime spectroscopy (PALS). The aim was to investigate the correlation between local free volume and mechanical properties. A negative deviation from the linear additivity rule of the local free volume is observed at both cure schedules. Using together the local free volume and mechanical results allows to conclude that the cure temperature makes small contribution to the flexural strength and modulus of blends but is responsible for the composition‐dependent rise of the fracture toughness. It is proposed that this behavior is a consequence of the nearest‐neighbor intrachain contacts or self‐association of the epoxy‐OH groups during cure leading to a non‐uniform space distribution of the DGEBA–PEO contacts, which causes the deflection of the crack path. Copyright © 2008 John Wiley & Sons, Ltd.     

Effect of melt flow rate of polycarbonate and cobalt catalyst on properties of PET/PC (80/20 wt%) reactive blending

The influence of PC melt flow rate (MFR) on phase behavior, thermal and rheological properties of catalysed and non-catalysed poly(ethylene terephthalate)/polycarbonate (PET/PC) (80/20 wt%) reactive blending were investigated. Two types of PC named PC1 and PC2 with MFR 3.1 and 10.8 g/10 min, respectively, were used. Each PC and the catalyst showed significant influence on calorimetric properties, thermal stability and WAXS patterns of the blends. Regarding to TG/DTG, the blends degraded in two steps which were attributed to PET rich phase and PC one and permit to infer that a partially miscible blends were produced.