Lie-group method solution for two-dimensional viscous flow between slowly expanding or contracting walls with weak permeability

The non-linear equations of motion describing the laminar, isothermal and incompressible flow in a rectangular domain bounded by two weakly permeable, moving porous walls, which enable the fluid to enter or exit during successive expansions or contractions, are considered. We apply Lie-group method for determining symmetry reductions of partial differential equations. Lie-group method starts out with a general infinitesimal group of transformations under which given partial differential equations are invariant, then, the determining equations are derived. The determining equations are a set of linear differential equations, the solution of which gives the infinitesimals of the dependent and independent variables. After the group has been determined, a solution to the given partial differential equation may be found from the invariant surface condition such that its solution leads to similarity variables that reduce the number of independent variables in the system. Effect of the permeation Reynolds number R_e and the dimensionless wall dilation rate α on self-axial velocity have been studied both analytically and numerically and the results are plotted.     

Synthesis of 5-heteroarylazulenes: first selective electrophilic substitution at the 5-position of azulene

1,3-Di-tert-butylazulene reacted with highly electrophilic trifluoromethanesulfonate of N-containing heterocycles to give 5-(dihydroheteroaryl)azulene derivatives in good yield and treatment of the 5-(dihydroheteroaryl)azulene derivatives with KOH afforded 5-(heteroaryl)azulenes in excellent yield.     

Compatibility and Marginality

We present a way of introducing joint distibution function and its marginal distribution functions for non-compatible observables. Each such marginal distribution function has the property of commutativity. Models based on this approach can be used to better explain some classical phenomena in stochastic processes.     

Baeyer–Villiger oxidation of cyclohexanone to ε-caprolactone in airlift sonochemical reactor

Baeyer–Villiger oxidation of cyclohexanone to ε-caprolactone was studied in a new type reactor – the airlift loop sonochemical reactor. The reactor plays a synergistic effect of sonochemsity and higher oxygen transfer rate. The influences of ultrasound intensity, reaction temperature, the molar ratio of benzaldehyde to cyclohexanone and oxygen gas flow rate on the conversion and selectivity of cyclohexanone were investigated and discussed. Under ultrasound, the amount of benzaldehyde can be reduced from 75% to 67%. Ultrasound not only intensified the rates of reactions but also increased the yield of product. The optimized operation conditions are listed as follows: the reaction temperature is 30 °C, the molar ratio of cyclohexanone to benzaldehyde is 1:2, the oxygen gas flow rate is 1.15 cm s⁻¹, and ultrasonic irradiations 2 h at 40 kHz, 2.25 W cm⁻². Under the optimum operation conditions, the average molar yield of ε-caprolactone comes up to 87.7%.     

Critical point transitions of wurtzite indium nitride

The optical transmission, photoluminescence, and reflection spectra have been measured on a high-quality wurtzite indium nitride (InN) single crystal in the range of 0.5–20.0 eV. The fundamental bandgap of intrinsic InN has been extracted by taking into account the Burstein–Moss shift, bandgap renormalization and Urbach band tail effects, and found to be very close to the recent strongly re-established value of ∼1.2 eV. With the aid of Adachi's dielectric function model for the vacuum ultraviolet reflection spectra and the empirical pseudopotential method approach for the electron band-structure, we are able to identify up to nine electronic transitions, showing clear picture for the critical point transitions in InN. The temperature dependence of these interband transitions has also been revealed.     

Tracing of interference fringes using average gray value and simultaneous row and column scan

An algorithm for computer tracing of interference fringes is reported. The method uses the average gray-level value for thresholding, row and column scans for determining the type of the scan and simultaneous row and column scan for tracing. The proposed method yield good result even for low-contrast and high-noise images. The program for the interferogram tracing was written using MATLAB6.     

Double sine-Gordon model revisited

We reconsider the mass spectrum of double sine-Gordon theory where recent semiclassical results called into question the previously accepted picture. We use the truncated conformal space approach (TCSA) to investigate the claims. We demonstrate that the numerics supports the original results, and strongly disagrees with those obtained from semiclassical soliton form factor techniques. Besides the numerical analysis, we also discuss the underlying theoretical arguments.     

Magnetic properties of HITPERM-type alloys at high temperature

(Fe,Co)–Zr,Hf)–Cu–B (HITPERM-type) alloys with variable Hf, Zr and Co content were isothermally crystallised at 500–650 °C for 1 h, and the optimum nanocrystallisation temperature was selected on the basis of the minimum coercive field at room temperature. The quasistatic hysteresis loops were measured at temperature from 20 to 650 °C. Subsequently, the optimally annealed alloys were subjected to long-term annealing at 500, 550 and 600 °C. Working temperature of 600°C is too high for the investigated alloys to maintain stable magnetic properties. Temperature of 550 or 500 °C permits the material to be magnetically stable for a long period. The magnetic hysteresis loops recorded for the nanocrystalline alloys, where Fe:Co ratio is close to 1 and refractory metals content is 7 at.%, prove that coercive field increases slightly with temperature, but remains in the range of 20–40 A/m (depending on the alloy composition) from 20 to 550 °C. This proves that the investigated alloys, after optimisation of chemical composition, may be suitable for high temperature use.     

Quantitative methods for nanopowders characterization

The size, shape and surface topology have a strong influence on powders properties, such as: mechanical, optical, catalytic, etc. In addition, when particles have a nanometer size, the dispersion of these features plays an important role.There are a number of techniques, which could be used in order to characterize powders in terms of particle size and shape. However, due to the scale of analysis, well beyond the wavelength of visible light, most of them cannot be applied for investigations of nanopowders.In this paper, transmission electron microscopy (TEM) image analysis and X-ray methods are presented as promising and complementary techniques. An example of their application to ZrO₂ nanopowder is shown. The advantages and limitations of each method are described.