Periodicity and chaos in a flexible crank-rocker mechanism

In this paper we introduce a crank-rocker mechanism at which the rocker is flexible. Using Hamilton’s principle we obtain the governing equations of motion for the elastic mode of the rocker. By applying the Bubnov–Galerkin global averaging method, we reduce the governing equations of motion to an ordinary differential equation which is Duffing’s oscillator with time varying coefficients. Through the application of Banach’s fixed-point theorem we predict the periodic solutions. Then we study the geometrical features of the motion near the 1 : 1, 1 : 2 and 2 : 1 commensurabilities. It is also shown that homoclinic and heteroclinic orbits can exist for the system.     

Sensitive determination of methadone in human serum and urine by dispersive liquid–liquid microextraction based on the solidification of a floating organic droplet followed by HPLC–UV

Dispersive liquid–liquid microextraction based on solidification of floating organic droplet was developed for the extraction of methadone and determination by high‐performance liquid chromatography with UV detection. In this method, no microsyringe or fiber is required to support the organic microdrop due to the usage of an organic solvent with a low density and appropriate melting point. Furthermore, the extractant droplet can be collected easily by solidifying it at low temperature. 1‐Undecanol and methanol were chosen as extraction and disperser solvents, respectively. Parameters that influence extraction efficiency, i.e. volumes of extracting and dispersing solvents, pH, and salt effect, were optimized by using response surface methodology. Under optimal conditions, enrichment factor for methadone was 134 and 160 in serum and urine samples, respectively. The limit of detection was 3.34 ng/mmL in serum and 1.67 ng/mL in urine samples. Compared with the traditional dispersive liquid–liquid microextraction, the proposed method obtained lower limit of detection. Moreover, the solidification of floating organic solvent facilitated the phase transfer. And most importantly, it avoided using high‐density and toxic solvents of traditional dispersive liquid–liquid microextraction method. The proposed method was successfully applied to the determination of methadone in serum and urine samples of an addicted individual under methadone therapy.     

Stability criteria for a class of fractional order systems

This paper deals with the stability problem in LTI fractional order systems having fractional orders between 1 and 1.5. Some sufficient algebraic conditions to guarantee the BIBO stability in such systems are obtained. The obtained conditions directly depend on the coefficients of the system equations, and consequently using them is easier than the use of conditions constructed based on solving the characteristic equation of the system. Some illustrations are presented to show the applicability of the obtained conditions. For example, it is shown that these conditions may be useful in stabilization of unstable fractional order systems or in taming fractional order chaotic systems.     

Synthesis,spectral and thermal studies of zinc(II) and mercury(II) complexes with bidentate Schiff-base ligand (234-MeO-Ba)<Subscript>2</Subscript>En: the crystal structure of Zn(234-MeO-Ba)<Subscript>2</Subscript>En)I<Subscript>2</Subscript>

New Symmetric bidentate Schiff-base ligands N,N′-bis(2,3,4-trimethoxybenzylidene)-1,2-di-aminoethane, (234-MeO-Ba)₂En, and its corresponding zinc(II) and mercury(II) complexes, Zn((234-MeO-Ba)₂En)I₂ (I), Hg((234-MeO-Ba)₂En)Cl₂ (II) have been synthesized and characterized by elemental analyses (CHN), FT-IR and 1H NMR spectroscopy. The thermal behaviors of complexes were study using thermogravimetry in order to evaluate their thermal stability and thermal decomposition pathways. The crystal structure of I was determined from single-crystal X-ray diffraction. The coordination polyhedron about the zinc(II) center in complex I is best described as a distorted tetrahedron.     

Nonlinear Oscillations of Viscoelastic Rectangular Plates

Nonlinear oscillations of viscoelastic simply supported rectangular plates are studied by assuming the Voigt–Kelvin constitutive model. Using Hamilton's principle in conjunction with the kinematics associated with Kirchhoff's plate model, the governing equations of motion including the effect of damping are represented in terms of the transversal deflection and a stress function. Utilizing the Bubnov–Galerkin method, the nonlinear partial differential equations are reduced to an ordinary differential equation which is studied geometrically by approximate construction of the Poincaré maps. Explicit expressions are given for periodic solutions.     

An efficient implicit unstructured finite volume solver for generalised Newtonian fluids

An implicit finite volume solver is developed for the steady-state solution of generalised Newtonian fluids on unstructured meshes in 2D. The pseudo-compressibility technique is employed to couple the continuity and momentum equations by transforming the governing equations into a hyperbolic system. A second-order accurate spatial discretisation is provided by performing a least-squares gradient reconstruction within each control volume of unstructured meshes. A central flux function is used for the convective terms and a solution jump term is added to the averaged component for the viscous terms. Global implicit time-stepping using successive evolution–relaxation is utilised to accelerate the convergence to steady-state solutions. The performance of our flow solver is examined for power-law and Carreau–Yasuda non-Newtonian fluids in different geometries. The effects of model parameters and Reynolds number are studied on the convergence rate and flow features. Our results verify second-order accuracy of the discretisation and also fast and efficient convergence to the steady-state solution for a wide range of flow variables.     

Reaction of peroxide radicals with methane on the titanium oxide surface: Effects of the composition of the initial mixture

The reaction of TiO₂-adsorbed methyl peroxide radicals with methane, accompanied by transfer of the products into the gas phase at ∼20°C, was studied by the kinetic methods and EPR spectroscopy. In a definite range of methane concentrations, the reaction was accompanied by an increase in the total concentration of free radicals; i.e., these active species became not only regenerated, but also multiplied. The increase in the number of peroxide radicals was explained by the chain consumption of methane initiated by the reaction being studied.     

Electrosynthesis of a new selective chelating agent for solid phase extraction of Ni(II) from water samples: characterisation and analytical applications

A new polymer as a selective chelating agent for separation and preconcentration of nickel ions from water samples was prepared by electropolymerisation of 4-nitrophenol. Electrosynthesis was carried out on the lead cathode in aqueous sodium acetate solution. The electrode-product is a dark-brown powder, insoluble in water but soluble in methanol, N,N-dimethylformamide (DMF) and tetrahydrofuran (THF). The electrode-product was characterised by differential scanning calorimetry (DSC), gel permeation chromatography (GPC), FT-IR, ¹H-NMR, cyclic voltammetry (CV) and UV-Vis spectrometry. A proper mechanism and structure of the prepared polymer was suggested. A few drops of methanolic solution of electrode-product formed a blue complex with nickel ions in an aqueous medium in the pH range of 6 to 10. This new chelating reagent was used as a coating material on activated charcoal and applied for solid phase extraction of trace amounts of nickel ions from natural and waste waters. The effect of different parameters such as type of eluent, elution conditions, sample volume and sample flow rate and mass of coating material were studied. In the presence of co-existing ions, no significant interferences were observed. Under the optimal conditions, limits of detection (LOD) and quantification (LOQ) were 0.32 and 1 µg L^?1 Ni(II), respectively. The proposed method was used for determination of Ni(II) in some lagoons south of the Caspian Sea and waste waters of factories. The validity of this method was confirmed by the comparison of the obtained results with the results of ICP-OES.